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Wind Turbine Technology
Wind Turbine Technology
A.R. Jha, Ph.D.
CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4398-1507-6 (Ebook-PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright. com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
.This book is dedicated to my beloved parents who always encouraged me to pursue advanced research and development activities in the fields of science and technology for the benefit of mankind.
.............8 1..........................................4...4......4 1.................................................3 China ...............2 Pay-Off Periods for Utility-Scale Wind Turbines and Wind Farms ...........3.....................6.........................................................................6.........4 1.............................6 1.................13 1.........................................................4 Worldwide Utilization of Wind Turbines .............................10 1...................................3............................8 1..............................................................1 1..........10 1...................1 Denmark .....9 1...11 1...................4 United States ..............................................................4................4...........1 Critical Elements of Wind Turbine Systems and Their Principal Functions..................................................................4..........................................7 United Kingdom ..............................2 Germany ........4................................................1 Benefits ....................................1 Utility-Scale Wind Turbine Sources ..................14 1...........................2 Major Benefits and Problems Associated with Alternate Energy Sources ..6 Wind Turbine Classifications ..........................................7 1.16 1..............4...........4...................................8 France ....10 Italy ...................6 Belgium and the Netherlands ................................4...Contents Foreword ......................5...3 Benefits and Disadvantages of Wind Turbine Technology ............................................6 1.................................................................2 Disadvantages .......................xix 1 Chronological History of Wind Turbine Technology ............11 1.......................9 1......................................................16 1...........1 1..................10 1.........................11 Early Wind Turbine Development: Summary .....................................7 1...3...............4 Repowering to Increase Output by Existing Turbines..........................xvii Preface ....................1 Introduction ...........................17 vii ..................4.........3.........5 1.........11 1.......................5 Canada ....5 Operating Principles of Wind Turbines .......................4.........................................................................3 Unique Installation Requirements ..3 1...................................9 Russia ........................................
......9 Next Generation Wind Turbines with Unique Features ...................1 Windmills .....21 1.28 References .................25 1................................8.........................37 2....................6............2 Residential Design Configurations with Grid-Tied and Back-Up Capabilities ...........21 1............3 Residential Design Configurations with Grid-Tied and No-Battery Operation ..2.......................11 Summary .2 Vertical Axis Wind Turbine (VAWT)..35 2........3.............3.3..32 2..................................3 Wind Turbine Design Based on Jet Engine ............. 34 2..............................3 Modern Wind Turbines ........21 1.4 2 Design Aspects and Performance Requirements ..19 1.......................9...............................8.........................................................2 Types of Wind Turbines ...3......23 1...6 Wind Turbine and Tower Installers ...............3 VAWT Operating Requirements ......7 Potential Applications of Small Wind Turbines ..............23 1..................................10 Typical Wind Power Estimates for United States ........................................22 1................20 1....28 1.6......................31 2......7...................26 1....1 Wind Farm Dealers ................................6..................................1 Residential Design Configurations with Off-Grid Capabilities ......26 1...................39 ...........5 Total Installed Cost for 5-kW Wind Turbine in 2009 .............1 Introduction ......19 1.................23 1...................6.....38 2.......8.........5 Compact Wind Turbine and Energy Systems for Dual Applications ..................................9.........3 1......7 Wind Farm Developers...........3.....2 Wind Turbines Operating from Ocean Surfaces...........4 Hybrid Solar-Wind Turbine System Configurations .....................25 1......27 1........................................................5 Floating Offshore Wind Turbines ....................26 1..........6 Critical Electrical Components.....................35 2........22 1.....8 Design Configurations ................................................................31 2...36 2...................4 Vertical Axis Wind Turbines ..24 1................................................1 Horizontal Axis Wind Turbine (HAWT) ..............................7...........................9......4 Advantages and Disadvantages of VAWTs ..........................................8........8...............26 1..........6.............................................................................2 Renewable Energy Professionals ...............8................................1 Helix Wind Turbines .........................................27 1..........................................................................2.........................6.................8 Intermediate-Scale Wind Turbines ..viii ◾ Contents Small-Scale Wind Turbines ......................................................2 Farm Type and Dutch Type Wind Turbines ............................................................18 Component Cost Estimates for Small Wind Turbine Systems ....................9.........38 2............29 1.5 Operational Difficulties of VAWTs...9................22 1............................
5..6.....51 2..6.................63 Estimating Annual Hours of Capturing Wind Energy ....51 2.....................4 Fundamental Properties of Wind Energy ...2 Impacts of Variations in Design and Operating Parameters .5.....4 2....3..............43 2..60 2......... 40 2........................5...........41 2........7 Computations of Power Coefficients ...............................................................3 Impacts of Wind Speed and Installation Height on Performance.....6......7....... 64 2.....................................4..... 64 2.....3.41 2............................................4....5...41 2..........................60 2...........47 2.......67 2.................................4.....................39 2......1 Requirements for Long-Term Capture of Wind Energy .........48 2.....4...............6....5................5.....Contents ◾ ix 2.......45 2................4..............................................57 Annual Energy Acquisition from Specified Wind Turbine Site .5..8 Early European Wind Turbines ...........1 Wind Parameters over Ridges and Hills .....................62 2...5....55 2............3.5...........................................4 Performance Enhancement Schemes .........7 Simplified Procedure for Predicting Darrieus Wind Turbine Performance ........ 40 Off-Design Performance ..1 Annual Hours Estimation Using Empirical Method .......5 2...............2 Variations in Wind Speed and Direction .6 Maximum Power Coefficient as Function of Exit Pressure Coefficient and Interference Factor (a) ...............2 Impact of Wind Speed on Wind Energy Density.......................5 Global Wind Power Capacity Using High-Power Turbines ...............................50 2.................47 2.......6 ........................3........3 Impact of Drag and Lift Coefficients on Maximum Power Coefficient....2 Annual Energy Production Estimate Using Blade Element Momentum Method ................2 Power Generated from Wind Energy .............59 2.......................61 2................5 Use of Vortices for Creating Regions of High Wind Velocity..........50 2.4 Energy Integrals for Savonius Rotor in VAWT ..1 Techniques for Enhancing Power Output and Power Coefficient ..................1 Critical Design Aspects ........6......62 2......................58 2..59 2..5......6...........4.... 42 Techniques for Capturing Large Amounts of Wind Energy ............1 Available Wind Power.............................................................1 Impacts of Blade and Angle Parameters on Performance Capabilities ..7......................2 Techniques for Achieving High Power Coefficients ...........4.............................................6...................7............3 Installation Site Requirements for Optimum Performance ................3 Annual and Hourly Extraction of Wind Energy by Wind Turbine .......6 2....6..3.......7 Understanding Flow Phenomena of VAWTs...............39 2............
........................3 3 Design Aspects and Performance Capabilities of Wind Turbine Rotors ...101 3.................1 Properties of Airfoils ....3 Impacts of Airfoil Characteristics on Rotor Performance ..1 Impact of Wind Characteristics on Power Coefficient ........................107 3...................102 3..................105 3................................5.......2 Coriolis and Centrifugal Forces ..................79 3....80 3.....................................................................................................1 Airfoil Configuration for Two-Dimensional Aerodynamic Model ....................................................................5 Effects of Rotation ...........2 Two-Dimensional Flow Analysis over Cylinder ........1 Rotor Blades ..............................................6........3.........................................78 2....................................2 One-Dimensional Momentum Theory Using Alternate Control Volume ........2...........80 3......................8 Summary .....................3 Power Coefficient for Ideal One-Dimensional Wind Turbine ...1..........................................................97 3......2 Material Requirements for Rotor Blades .................2 One-Dimensional Theory for Ideal Rotor ......2........1 Rotor Performance ..............5..................3 Power Generated by Windstream ................1 Introduction ..........102 3......71 2..............75 2.......1 Rotor Types and Their Performance Capabilities ........................104 3...3 Two-Dimensional Aerodynamic Model .....................99 3...................................104 3.........100 3.4.....................6............4 Combined Impact of Rotor Tip Speed Ratio and Dragto-Lift Ratio on Power Coefficient .5.......................................7 Summary ................5 Rotor Design Requirements for Wind Farm Applications .........................................................................7....................86 3..............107 References .............. 84 3............1 Two-Dimensional Flow Analysis over Sphere .......................................86 3..............................6 Hydrodynamic Analysis of Flow over Rotor ...............97 3.................................6..109 ....................94 3....................x ◾ Contents Parameters Affecting Performance ........................................4.......6..................................7..........98 3.......1..........................104 3......79 3....103 3..2.........................................1.4.....................92 3...........2..........82 3. 77 References ...................................................2........................3 Vortex System behind Modern Wind Turbine ....80 3......4 Thrust Coefficient for Ideal One-Dimensional Wind Turbine ...............................71 2........................2........7.......................3......6 Tip Speed Ratio of Rotor ...2.............................................. 90 3.......................................................1 Parameters Affected by Streamlines Flowing over Wing ..............1 Axial Momentum Equation in Integral Format ................4 Three-Dimensional Aerodynamic Model for Wing of Finite Length ........................................
.........................1 Power Coefficient....................................3.............................144 5........................................... 111 4...............................131 4....................................112 4.............3 Torque Grading Coefficient ... 141 5............................ 114 4..............120 4.....................3.......4 Blade Loading Coefficient ................3.112 4....9 Mechanical Integrity ..1 Pitch Regulation Control........134 Sensors and Control Devices Required for Dynamic Stability and Improved Performance under Variable Wind Environments ...........3 Conditions for Maximum Power Output ............3...........................................130 4...8 Forces Acting on Blades ...2....125 4.........1 Aerodynamic Performance Analysis of Blade Elements...............143 5.........................3...........................................130 4.....................................................6 Impact of Tip Speed Ratio and Drag-to-Lift Coefficient on Wind Turbine Power Coefficient .........124 4.....................133 References ......................3............... 111 4.........Contents ◾ xi 4 Wind Turbine Blade Design Requirements ...........................................................4 Application of Beam Theory to Various Turbine Blade Configurations ...3 Blade Performance .................1 Introduction ................................3.2..........................2 Rotor Configurations for Induction Generators ....3......6...........9...1 Impacts of Bending Moments and Blade Instability on Performance .............2....2..........143 5..........................................142 5........................................125 4..140 5................ 117 4......121 4............137 5.............................5 Material Requirements for Blades .........................3............... 115 4..........................................................................122 4........................................ 116 4..............3 Yaw Control System.....................9...............2 Role of Wind Triangle ...........................2 Thrust and Power on Annular Area of Blade ........5...................2 Analysis of Performance of Propeller Blades ...5........7 Summary .......2.........................131 4.137 5........................................2 Shearing Forces and Bending Moments in Presence of External Forces...........6 Critical Features of Blade Section ..... 145 5 .7 Variations in Pitch Angle as Functions of Radius ...128 4...................................5 Electrical Generators .........................................3.......4 Transmission Systems ......3 Sensors for Monitoring Wind Parameters ....................................................3.........5 Variations of Flow Angle as Function of Tangential Speed Ratio and Flow Angle ......................................................2 Axial Interference Factor .......144 5........................... 118 4...................................................1 Structural Parameters and Stresses...........2 Regulation Control Systems .................................130 4...2...........2 Description of Pitch Regulation Control System ............................................ 116 4.....................................1 Induction Generators .6...........................139 5....1 Introduction ....... 116 4.
...1 Impact of Gravitational Loading .............4 Stall Regulated Rotors ........................1 Bearing Reliability .......167 6........169 6...................160 References ...................7........................149 5..5 Power Generating Capacity ...7......................2 Historical Background: Use at Remote Sites .............7........171 .....................................10 Critical Design Aspects of HAWT and VAWT Rotors..... 151 5...............3 Blade Twist Angle Adjustments ........................................... 157 5....................................................................... 152 5...........................4 Micro Wind Turbines for Rural Electrification.......................................... Dynamic Stability....................170 6........ 152 5................................ 161 5...................5 Factors Affecting Wind Energy Capture and Turbine Performance ..................10..................................................170 6............1 Rotor Design Classifications .....156 5.....10.......................3.3......7...........................163 6....................163 6...3.............................154 5........9 Automatic Shut-Down Capability ................................................1 Vortex System behind High-Capacity Turbine ...........7 Critical Rotor Performance Parameters....13 Summary ....................................2 Dynamic Stability and Structural Integrity ......156 5.2 Sensors for Ensuring Efficiency..3... 145 5...................149 5.3 Configurations of Stand-Alone Systems..........7.......................................xii ◾ Contents Performance Capabilities and Limitations of Synchronous Generators ..............................................170 6...............................3.......................................3............................168 6.............................12 Impacts of Loadings on Structural Integrity of Wind Turbine .........12....10 Techniques for Reducing Energy Consumption ......................................7 Cost Reduction Techniques .........149 5..............3...........6 6 Stand-Alone Wind Turbine Systems .8 Reducing Power Demands ...........9 Typical Energy Consumption by Electrical Appliances ....12.........................................156 5...8..........169 6.....147 5................6 Telecommunications Applications in Remote Areas ......................165 6..3 Monitoring of Stress Parameters ...3..............12....11............... 157 5.............166 6................11 Low Harmonic Content Electrical Generators for Improving Efficiency .1 Techniques for Improving Turbine Reliability and Performance ................................10.......1 Introduction ..2 Impact of Inertial Loading ..1 Hybrid System with Back-Up Capability ..146 5.............2 Micro Wind Turbines ........167 6............ and Structural Integrity .......... 153 5....................................................................................3 Applications of Micro Wind Turbines .....3..... 153 5.. 159 5.. 157 5....................................3...............147 5...............................................................................8 Impacts of Airfoil Characteristics on Blade and Turbine Performance .........166 6....................................................................3 Impact of Aerodynamic Loading ....
.................2 Concentrator Configuration Requirements ..........4 Hybrid Wind Turbines for Economic Electrification ...1 Wind Power Density and AEO Computations .............196 7....................................................2 Design Requirements for Irrigation .................................9 Multitasking Wind Turbines ......196 7....190 6..........7 Stand-Alone Wind Turbine–Based Systems for Various Applications.............................................4 Capabilities of Various Concentrator Schemes: Summary ......................197 7..............194 6...............182 6......... 191 6........173 6...........3 Sizing and Performance Parameters of Batteries ................5 Sizing of System Components .............................. 176 6........8..................................183 6......184 6................2...............190 6......5............................179 6..........Contents ◾ xiii Stand-Alone Systems for Remote Sites ...1 Refrigeration Appliances........................3 Close-to-a-Building Configuration ...3 Annual Energy Outputs of Wind Turbines........7...............9.1 Sphere-Like Configuration ..175 6.......8..............6.............2 Performance Capabilities of HR 3 Hybrid ........................3 Cost Estimate for Extending Line from Existing Utility .............................................................192 References ..5....3......4 7 Wind Energy Conversion Techniques in Built Environments ...........188 6...................171 6.......6 Stand-Alone Systems with Utility Power Back-Up .......175 6.5........................3 Selection of AC or DC Operation....................................................................186 6.....4.....7.....................3 Fuel Savings from Use of Hybrid Systems...188 6.............7......................................183 6..........................4 Sizing and Performance Parameters of Solar Panels ...............2 Air Conditioning Units ..........................................1 Introduction ............187 6............................................................. 176 6.........2.182 6..6..10 Summary ...... 181 6.....................................6.....8 Hybrid Systems for Village Electrification ...........189 6................................1 Telecommunications.185 6.............2 Sizing and Performance Capabilities of Inverters .............195 7.................. 174 6.....3 Estimating Pumping Capacity of Farm Windmill ..4...............................197 ..173 6......1 Low-Power Turbine Applications .........185 6.....195 7..........8..............179 6....................2 Cost Analysis for Stand-Alone Hybrid System .8......1 Successful Examples .4.................................2 In-Ducts-through-Buildings Configuration..................................9.....................4 Parameters of Generating System........................................1 Sizing and Performance Capabilities of Solar Arrays..1 Economic Aspects of Remote Systems ...2....2 Application of Village Electrification for Water Pumping ...................178 6.....9...........2........................196 7.9..................................4..................5........... 181 6.................................................................................
.5........................................................ 215 7..5...................... 220 7.........197 7..................2 Impact of Pressure Coefficient on Free Stream Quantities...........5..... 218 7.5........1 Building Characterization ....221 7.........4.......5..1 Atmospheric Boundary Layers ..202 7.............2 Impact of Atmospheric Boundary Layer on Wind Speed and Variations ...........................4.........207 7...................... 208 7.........5...8................203 Local Wind Characteristics in Built Environments .......... 226 7....3.3 Noise Arising from Nearby Wind Turbines .................. 200 7........1 Rotor Design Configurations for BAWT Systems .5.5 Power Absorbed by Actuator ...3.......4 Air Flow Properties .....2.......223 7......2 Streamlines around Buildings with Sharp Edges ............202 7...............8 Yawed Flow Requirements in Built Environment ..203 7..............210 7...........................4....................................................... 215 7.....3.........2 Impact of Roughness Length on Wind Speed Parameters .................221 7......5 Energy Design Buildings ........3 Vertical Wind Speed Gradient ..............7 Comparison of Wind Turbines in Built Environments .......1 Aerodynamic Noise Levels.......4 Deceleration of Air by Rotor..............8...197 7.............................8.............................199 7............4..........224 7.........3..................xiv ◾ Contents 7....3.....................................................................5..8...............3.5.1 Estimating Wind Speed in City Environment..4.................8.................................................3 Theoretical Aspects of Reynolds and Strouhal Numbers ..225 7...............................8.............216 7...8.................5..............................5............. 215 7....5.................................3........ 211 7..1 Requirements for Built Environments .......................3 Wind Potential in Built Environments .....4.......4 Probability Function of Wind Speed for BAWT Installations.3 Drag Force Components.................................................................212 7...... 214 Impact of Built Environment on BAWT Performance...3..... 218 7............................2 Drag-Driven Wind Turbine ....5..........5 Shadow Flicker from Blades.4.................4..4 Induced Vibrations from Turbine Blades .207 7...3 7............................................................5..... 226 ..3 Lift-Driven Wind Turbine ..4....3...........221 7.4.........209 7... 219 7.....5.............7 Impact of Stream Tube Length on Wind Energy Extraction ...1 Hydrodynamic Analysis of Flow over Sphere ..........................2 Computation of Total Aerodynamic Noise at Installation Site.. 208 7..3..................6 Hybrid-Driven Wind Turbines ..4 7...........................3....4.....6 Turbulent Structures.......
........................................7 Output Torque Performance ....4 Per-Kilowatt Electrical Energy Cost from Wind Turbine .................8.5....4....... High-Capacity Wind Turbine .......245 8...6 Summary ..........4...............................................Contents ◾ xv Boundary Conditions for Wind Turbines in Built Environments .......................................2...235 8.........1 Choice of Installation Site..8 Power Generated by Windstream as Function of Windstream Diameter .........230 8.....................248 8........227 7.....................................229 8........1 Higher Noise Levels ..................................................3 Per-Kilowatt Electrical Energy Cost .........2..................5 Maximum Extractable Power .241 8............3................2...........................3 Television and Radio Interference .............................................................5...1 Estimation of Noise Generated by Single.....2 Environmental Factors and Other Critical Issues .4 Estimating Critical Performance Parameters Using Classical BEM Theory ........2 Impact of Blade Design Parameters on Performance Level ............................................................................................238 8......2 Estimating Procurement Costs .242 8..................1 Continuous Availability of Electrical Energy ...............3.........3..................3....................1 Mechanical Shaft Power ..232 8...................1 Introduction .................5.....................249 8.......230 8..5........5...........................................4 Impact of Volumetric Flow Rate on Performance ................. 234 8...........2 Ambient Noise from Installation Site ....3 Problems Arising from Large Windstream Diameters ............................................1 Empirical Method for Computing Annual Energy Output of Wind Turbine .......... 228 7........251 ..........241 8...........3 Terrain Modifications to Augment Wind Speeds for Improved Performance ....8 8 Environmental Issues and Economic Factors Affecting Wind Turbine Installation ....................247 8...........................................5......238 8........................................................250 8.....227 References .........2.3..2.......................................3......................5 Justification of Wind Turbine Installation Based on Economics ....................................................................231 8.....2........250 8..239 8...........................................1 Estimating Noise Levels from Wind Turbines .233 8............242 8.............3......................................2 Wind Features and Their Effects........... 234 8....6 Power Coefficient........229 8.................................................................................................2................247 8....2........2..................248 8.....4......4.........251 8...................4 Quantitative Description of Wind Turbine Noise..........2.......2 Community Reaction to Wind Turbine Noise ..................242 8..
........257 8..............2 ...255 8...................255 8.....................................259 References .....4...............................................254 8............7...............................4 Sample Calculation for Estimating Cost of Electricity Generated by Wind Turbines.......7......................................6...261 8....258 8....................................2 Typical Design and Performance Characteristics of 2-MW Wind Turbine ..2 Mechanical Strength Requirements ...............4......258 8.6 Estimated Costs of Critical Components and Subsystems ..........................................................................1 Cost Estimates for Critical Components ..... 260 Index .......xvi ◾ Contents Cost of Electricity as Function of Turbine Cost and Life .....6..7 Wind Turbine Towers .3 More Elaborate Method of Computing Cost of Energy Generated by Wind Turbine ...............1 Tower Height Requirements ....................................253 8...............5.............3 Tower Classifications .........5....................7..................................258 8................................................5.............8 Summary ....257 8.................................................................................4.252 8.................
the earliest use entailed propelling boats. Furthermore. It is important to mention that fossil fuels are most economical and therefore they are most widely used. wind turbines are capable of generating large amounts of electricity at lower costs without generating harmful gases. Historically. Other energy sources that are currently in use include nuclear power. Larger and more efficient wind turbines were built in the United States during the first half of the 20th century. Federal Wind Energy Program. interest in the development of wind turbines was renewed with the help of the U. However.Foreword This book appears at a time when the future well-being and industrial development of nations involved in the 21st century's global economical progress are strictly dependent on the availability of oil and gas at reasonable prices to generate electricity. after the oil embargo of 1973. they have been the major contributors to environmental deterioration and global climate change. The worldwide increases in the demand for and consumption of energy since the latter part of the 20th century may be attributed to the rise of world population and the rapid pace of industrial development in emerging nations such as China. Solar energy-based power generation is an attractive source that offers unlimited output. but eliminates the dependence on foreign oil. Deployment of wind turbine technology offers not only a reliable and costeffective approach. solar energy. By 200 BCE. the Chinese utilized wind machines for pumping water and the Persians were grinding grains with wind devices. India. The level of activity for developing alternate energy sources has been dependent on the cost of fossil fuels. and wind. but it suffers from high initial investment cost and dangerous radiation effects. The development of windmill technology in Europe started in the early part of the 12th century. hydroelectric power. Nuclear power generation offers an attractive alternative energy source. However. Note that fossil fuels are not in abundant supply.S. The Sinhalese in Sri Lanka used monsoon winds to power furnaces in 300 BCE. and Brazil. but it is not xvii . The first windmill to generate electricity was built in Scotland in 1887. wind energy has been used since 5000 BCE. the interest in wind turbines declined with the fall of fossil fuel prices after World War II. followed by the development of large windmill turbines in 1890 in Holland.
Cambridge. government policy encourages rapid development of renewal energy sources in the United States. I strongly recommend this book to a broad audience including students. In summary. The book is well organized and emphasizes both theoretical and practical aspects of wind machines. Wind turbines use the kinetic energy of nature to generate electricity for distribution. A. each dedicated to a specific design aspect of wind turbine technology. environmental scientists. Murray Hill. presents a comprehensive guide to wind turbine technology and the technical considerations for designing wind turbines for various applications. This book contains eight chapters. Regardless of classification. Mathematical equations are provided for important turbine design parameters. variable pitch blade capability. Wind turbine technology offers the most attractive renewable energy source because it generates large amounts of electrical energy at lower cost based on unlimited wind energy and inflicts no adverse environmental impacts. Appropriate tapering of the rotor blades is selected to maximize the kinetic energy from the wind. and irrigation water pumping applications. New Jersey and Fellow and Laboratory Director (Retired) Polaroid Corporation. a wind turbine converts the kinetic energy of the wind into mechanical power that drives an electrical generator.xviii ◾ Foreword available during nights or in heavily clouded environments. and tall tower base structure to capture large amounts of wind energy. project managers. and renewal energy source planners. It is of great interest to mention that Denmark fills 40% of its electrical energy needs from wind turbine installations and plans installation of wind turbines capable of delivering more than 4200 MW of electrical power. research scientists. improved efficiency. wind energy sources are bound to play an important role in 21st century economic development. Utility-scale wind turbines with power ratings ranging from 100 kW to 5 MW have proven sufficient to power 100 to 500 homes simultaneously. Massachusetts . Single small wind turbines with electrical output levels below 25 kW are best suited for remotely located residential homes. The author of this book. PhD Distinguished Member of Technical Staff (Retired) Bell Laboratories. telecommunications dishes. Many utility company wind farms capable of generating electricity at low generating cost and under maintenance-free conditions have sprung up in rural and onshore regions in recent years. Optimum wind turbine performance is possible when a turbine is mounted on a tower of appropriate height in an onshore or offshore region. R. Dr. Shobha Singh. Jha. A small scale or 50 W generator is sufficient for boat applications. The advantages of a HAWT include high generating capacity. design engineers. Wind turbines can be classified as two major types: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs). The wind turbines come in different sizes based on their power generating capabilities.
and nuclear reactors to achieve lower cost of electricity generation. Rapid design and development activities must be undertaken in the fields of low-cost and efficient micro-hydro turbines and high-capacity wind turbines. microwave ovens. shopping centers. This book is well organized and covers critical cutting-edge xix . water coolers. computers. wind turbines. geothermal technology. Rapid development of low-cost energy sources is not only urgent to reduce the cost per watt of the electricity. particularly the United States and European countries. air conditioners.Preface Considerable interest in renewable energy sources and significant increases in cost of foreign oil have compelled various countries to search for low-cost energy sources and technologies such as solar cells. tidal wave turbines. Some European and third world countries are constructing wind farms to reduce their electric costs and eliminate dependency on foreign oil. Studies performed by the author on small. International energy experts predict that wholesale electricity prices will rise 35% to 65% by the year 2015. The future and welfare of Western industrial nations in the 21st century's global economy increasingly depend on the quality and depth of technological innovations that may be commercialized at a rapid pace. Under these circumstances. Mathematical expressions and the derivations highlighting their importance are provided for the benefit of students who intend to pursue further studies in wind turbine technology.and medium-capacity wind turbines at appropriate installation sites. fans. This book presents a balanced mixture of theory and practical applications. It is important to mention that several countries now deploy wind turbine technology to meet their electrical energy requirements at a lower cost per kilowatt hour. fax machines.and medium-capacity wind turbines indicate that these wind sources are best suited for land-based defense installations. The studies also demonstrate that micro wind turbines may meet the electricity needs of individuals for lights. residential uses. schools. but also to eliminate the dependency on and blackmail by oil-producing countries that are hostile toward Western nations. biofuel sources. several countries are focusing on deployment of alternate electrical energy sources involving micro. and other electrical devices and accessories. and large commercial buildings.
Wind machines offer lower costs compared to coal-fired thermal plants and nuclear reactor-based power sources. telecommunication systems. China has installed several hundred utilityscale turbines in the Gobi desert where average wind speed is consistently greater than 30 mph. Utility-scale wind turbines have power output ratings ranging from 100 kW to 2. and performance capabilities. Denmark meets at least 40% of its electrical energy needs from wind turbines installed in coastal regions where average annual wind velocity exceeds 15 mph. The bibliographies include significant reference materials. When several turbines are installed in wind farms. It is interesting that a wind turbine works as the reverse of an electrical fan: it converts the kinetic energy of the wind into electrical energy. This book was written specifically for engineers. Several developed and developing countries are leaning toward deployment of micro turbines because these wind power sources are most cost-effective for small business owners in isolated or less densely inhabited regions. remote operating sites. and program managers deeply engaged in the design. Wind turbines come in different forms and sizes. Chapter 2 deals with various types of wind turbines with major emphasis on design aspects. The author has made every attempt to provide wellorganized material using conventional nomenclature and consistent sets of symbols and units for rapid comprehension by readers with minimal knowledge of wind turbine technology. and irrigation applications. A wind turbine drives an electrical generator whose output can be stored in batteries or linked to commercial utility power grids. These turbines can be used . The latest performance parameters and experimental data on operational wind turbines provided throughout this book have been taken from various references with due credit given to authors and sources. project engineers. and tube wells. It is written in language appropriate for undergraduate and graduate students who hope to expand their horizons in this innovative field. research scientists. professors.xx ◾ Preface design aspects of this technology. educators. a wind turbine offers a cost-effective alternative renewable energy source. irrigation projects. It should be most useful to those who wish to add to their knowledge of renewable alternate energy sources. electricity generation costs approach those realized by coal-fired and nuclear reactor-based power sources. Medium-capacity machines are typically rated between 10 and 100 kW. Chapter 1 describes the chronological development of wind turbine technology and its generation of electrical energy at lower cost and without greenhouse effects. Coastal European countries have installed several medium-capacity wind turbines to operate machine shops. development. In brief. Each of the eight chapters is dedicated to a specific topic relevant to both residential and commercial applications. installation costs. It is interesting to mention that the energy produced by a wind turbine is useful in a thermodynamic sense. Small or micro wind turbines are typically rated below 10 kW and are best suited for individual homes.5 MW and are best suited for supplying electricity to local utility companies. and research related to wind systems for various applications.
Because of poor rotor efficiency. The maximum efficiency of 33% is achieved at a TSR of 6. The efficiency of a Darrieus rotor is generally poor and varies from 28% to 32% over a TSR ranging from 5 to 7. respectively. Critical circular control flow parameters and their effects on axial velocity components will be described.1. Efficiency improves when a TSR exceeds 3. Various types of rotors widely used by modern wind turbines and aspects of output performance and design simplicity are described. Regardless of the category. and just behind a rotor. two-dimensional (2-D). Chapter 3 is dedicated to design aspects and performance capabilities of wind turbine rotors. The expression for the rotational speed of the rotor will be developed as a function of axial induction factor and axial wind velocity. More than one million wind wheels have been used for water pumping in different parts of the world. and improved dynamic stability under strong wind conditions. The efficiency of the Savonius rotor is generally poor over a TSR of 1 to 2. Wind turbines are classified as two types: the horizontal axis wind turbine (HAWT) and the vertical axis wind turbine (VAWT) as illustrated in Figures 2. the kinetic energy generated by a wind turbine can be converted into electrical. or thermal energy or potential. TSRs for optimum rotor performance are indentified. One-dimensional (1-D). higher structural integrity. . respectively. The axial momentum equation will be derived using certain assumptions. Upwind and downwind rotors are widely used by high-capacity HAWTs while the Savonius and Darrieus rotors are best suited for VAWTs. Most high-capacity modern wind turbines belong to the HAWT category based on their straightforward design configuration. The chapter commences with a discussion of rotor classification. and power output. dynamic stability under violent wind conditions. The windmill has played a key role in water pumping applications. several types of high-capacity wind turbines have been manufactured by large companies such as General Electric in the United States and Mitsubishi in Japan. In addition. then moves to critical design requirements and performance capabilities of rotors with emphasis on reliability and dynamic control aspects. in front of. power coefficient.3. Since the early 1950s. Note that axial velocity components play key roles in the overall performance and dynamic stability of rotors that operate in various wind environments. and threedimensional (3-D) aerodynamic analyses of potential wind turbine rotors along with power and thrust coefficient aspects are discussed. high tip speed ratios (TSRs) ranging from 2 to 8 are required to achieve optimum performance in terms of reliability.2 and 2. particularly in remote locations. chemical. Various types of wind turbines ranging from the earliest versions to modern turbines are shown in Figure 2.5. The efficiency further improves to 53% and 57% as a TSR approaches 3 and 4.Preface ◾ xxi to produce clean fuels composed of hydrogen and oxygen or to develop fuel cells for other applications. It is important to note that a wind turbine installed in the right location offers high efficiency and year-round reliable operation with minimum operation and maintenance costs. Use of the Bernoulli equation is recommended for calculations of performance far upstream.
As mentioned earlier. and enhanced turbine performance are emphasized.2% at a TSR of 2 to 57. drag-to-lift coefficient. safety. Potential models using actual flow conditions to determine the characteristics of airfoils will. generator. Control mechanisms using microelectrical mechanical systems (MEMS) and nanotechnology-based sensors will be given serious consideration due to their fast response and higher accuracy for monitoring vital turbine operational parameters. Chapter 5 describes the sensors and devices required to maintain the dynamic stability and improved performance of rotors under variable wind conditions.3% at a TSR of 4 and 58. Critical associated components such as the rotor. therefore. The blade theory states that the outer contour of the blade must be based on aerodynamic considerations and the materials used in its fabrication must be fully capable of providing the required structural strength and stiffness. The aerodynamic considerations of the blade area can be modified to ensure greater structural integrity under severe wind environments. and aerodynamic loading on the mechanical integrity of blades will be identified with emphasis on tensile stress. and deflections at the loading and trailing edges of blades. and other elements responsible for the system reliability. Teetering of the hub design reduces the loads on the turbine. A gear box is required to reduce the rotational speed of the rotor needed to maintain the dynamic stability of the turbine under higher tip speeds. are widely used by high-capacity HAWTs. SAWTs are best suited for powering remote sites. The principal objectives of Chapter 4 are to apply the basic parameters of the blade theorem and then specify the blade design requirements for given wind turbine systems. most monitoring sensors and safety devices are located at the tops of towers.xxii ◾ Preface deployment of the Darrieus rotor is restricted to low-capacity wind turbines. They can deploy small or moderate capacity wind turbines and banks of batteries to carry electric power for household consumption during . Stall regulation. Chapter 6 discusses the performance capabilities and limitations of stand-alone wind turbine (SAWT) systems. The aerodynamic studies of rotor configurations performed by the author indicate that the upwind and downwind rotors demonstrated higher efficiencies and. compressive stress. and dynamic stability will be discussed in great detail. safe operation. inertial loading. The connection between the rotor blades and hub must be extremely rigid to maintain safe operation under variable wind conditions. The ideal efficiencies for such rotors range from 51. transmission system. Equations for the deflections and bending moments at specific points along the lengths of blades are provided. and yaw control mechanisms are described and reliability. Expressions for the torque and power coefficients as functions of TSR. Critical performance parameters for various rotor blades will be discussed.3% at a TSR of 6. The performance of a wind turbine is strictly dependent on the number of blades assigned to the rotor. Effects of loadings on the turbine rotor caused by the earth's gravitational field. thereby yielding higher dynamic stability of a turbine. regardless of electrical load. Structural aspects play a key role in determining SAWT performance capabilities and limitations. and blade radius will be derived. pitch control. be investigated.
Chapter 7 proposes three basic principles that allow concentration of wind energy at various locations on buildings. design. adverse effects on electronic radio and television signals. people in remote areas who cannot access commercial utility power are accepting the SAWT concept. Implementation of solar cell technology in a stand-alone wind turbine system offers a cost-effective and practical choice for the customers in remote and inaccessible areas where commercial utility power lines do not exist. sustainability. The building design determines the optimum locations of wind energy concentrators of four types: ◾ ◾ ◾ ◾ Wind turbines installed in wind ducts through adjacent buildings Wind turbines installed at the tops of the buildings Wind turbines installed at the sides of the buildings Wind turbines installed between two airfoil-shaped buildings The aerodynamic aspects of the four distinct concentrators and those of the wind turbines must be properly integrated to produce maximum energy yield. Various configurations for SAWT power sources must be investigated in terms of installation cost. Real-time measured data can be obtained in an open jet wind tunnel. as a result. transportation. assembly test. Any technique for converting wind energy into electrical energy in built environments must be cost-effective and incur minimum maintenance and operating costs. noise levels. maintenance and operational costs. and impacts on bird populations must be seriously considered prior to selection of a turbine installation site. It is important to mention that the installation of wind turbines in built environments presents complex problems that rarely surface in open environments. fabrication. disturbance of local ecology. and need for frequent maintenance are the principal drawbacks of SAWT power. and reliable performance. Environmental issues such as physical restrictions. tower design constraints.Preface ◾ xxiii winter and summer periods. However. Computer simulation can be performed via a computational fluid dynamic (CFD) code. relatively low power generating capability. new SAWT technology has solved some of these problems and. Economic factors include the initial cost for analysis. Chapter 7 deals with wind energy conversion techniques for wind turbine power sources operating in built environments. The selected energy conversion technique must deal with the judicious integration of wind turbine and building aspects in such a way that the building structure concentrates the wind energy exclusively on the turbines. Studies performed by the author indicate that initial installation cost. Mathematical models will be used to simulate air flow and verify parameters obtained through computer analysis. Chapter 8 focuses on environmental issues and economic factors affecting wind turbine installation. final . Data compiled by the Pacific Gas and Electric Company indicate that the number of SAWT power systems mushrooms at a rate of 29% annually and that the market for SAWT systems will continue to expand in areas not served currently by commercial utility companies.
Economic feasibility is determined strictly on the basis of costs and the value of the electrical energy generated based on preliminary cost estimates. but not least. and maintenance and operation. Ashok Sinha (retired senior vice president. Jha . for his critical review and also for accommodating last-minute additions and changes to retain consistency of the text. R. installation of turbine and tower. Finally the cost of generation of a kilowatt of electricity must be evaluated prior to the installation of a wind turbine.. I wish to thank my wife Urmila Jha. Inc. Sanjay Jha. I wish to thank Dr. I am very grateful to my wife who was very patient and supportive throughout the preparation of this book. my daughters Sarita and Vineeta.xxiv ◾ Preface checkout testing. California). Finally. His suggestions helped the author prepare a manuscript with remarkable coherency. and my son Lt. Applied Materials. Last. who inspired me to complete the book on time under a tight schedule. my son-in-law Anu. A. Santa Clara.
biofuel. telecommunications dishes. geothermal-.Chapter 1 Chronological History of Wind Turbine Technology 1. tidal wave turbines. A wind turbine advertisement states that 1 . wind turbine installation and electricity generating costs are lower compared to other electrical energy generation schemes involving coal fired steam turbo-alternators. tidal wave. Additionally.1 Introduction This chapter describes the history of wind turbine technology development and its potential applications. a wind turbine converts the kinetic energy of the wind into electrical energy. a fan uses electricity to generate wind. Wind turbine technology offers a cost-effective alternate renewal energy source. Wind turbines come in different sizes and types. biodiesel. biofuel-. Small wind turbines with output capacities below 10 kW are used primarily for residences. and biodiesel-based electrical energy sources and nuclear reactor-based generators. Furthermore. hydrogen. In more sophisticated terminology. It is important to mention that a wind turbine is capable of generating greater amounts of electrical energy with zero greenhouse effects compared to other energy generating schemes including solar cell. hydrothermal-. A wind turbine uses wind energy to generate the electricity. and biomass technologies. depending on power generating capacity and the rotor design deployed. this technology provides electrical energy without greenhouse effects or deadly pollution releases. A wind turbine is the reverse of an electrical fan. Wind turbine technology offers cost-effective solutions to eliminate the dependence on costly foreign oil and gas now used to generate electricity. and irrigation water pumping applications.
General Electric Company pioneered the development of wind turbine technology by exploiting its unique capabilities such as improved performance under variable wind environments. Wind blowing over the propeller blades causes the blades to "lift" and rotate at low speeds. a yaw motor drive assembly. More than 5. thereby realizing significant reductions in electricity generation costs. Optimum wind turbine performance is strictly dependent on blade taper angle and the installation height of the turbine on the tower. Furthermore. Denmark developed wind turbine technology as early as 1970 and expects to have wind turbine capacity exceeding 4500 MW by the end of 2010. a pitch motor drive assembly. The tapering of rotor blades is selected to maximize the kinetic energy from the wind. Winds are generally caused by uneven heating of the atmosphere by the sun. The major components of a wind turbine include a low-speed rotor consisting of two or three light-weight blades with optimum airfoil shapes operating at 30 to 60 RPM. and surrounding vegetation. and other accessories necessary to provide mechanical integrity under heavy wind gusts. Modern wind turbines are classified into two configurations: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs). a wind turbine converts the kinetic energy of the wind into mechanical power that drives an alternating current (AC) induction generator to produce electricity. and cost-effective electronics for local grids. Wind turbines using three blades are operated "upwind" with rotor blades facing into the wind. HAWTs with two or three blades are the most common. an anemometer. depending on rotor operating principles.5 MW are in use worldwide because of their high reliability and efficiency. they present much lower generating costs and zero maintenance and operating costs. a high-speed shaft mechanically coupled to low-speed via a gear box assembly and operating between 100 and 200 RPM. Denmark now obtains at least 40% of its electrical energy from wind turbine installations.000 General Electric wind turbines generating 1. a speed controller unit. and the rotation of the earth. and atmospheric pollution. a tower structure. using inexpensive off-the shelf components and excluding labor costs. variable speed control under reduced load conditions. a nacelle. Utility-scale wind turbines have high power ratings ranging from 100 kW to 5 MW—sufficient to power 10 to 500 homes. bodies of water. Regardless of classification.2 ◾ Wind Turbine Technology a prototype 5-kW system can be built for $200. wind flow patterns are modified by the earth's terrain features. or driving an AC induction motor to produce electricity that can be fed into a utility grid system. greenhouse gas emissions. However. The power generated by a wind turbine can be used to perform specific tasks such as grinding grain. In . pumping water. an AC induction generator operating at high speed. Current wind farms with large capacity wind turbine installations have sprung up in rural areas and offshore regions and are capable of generating electricity in excess of 500M MW for utility companies. The VAWT configuration is similar to an eggbeater design and employs the Darrieus model named for the famous French inventor. the irregularities of the earth's surface. a wind vane indicator.
2. electricity generated by wind turbines is cost-competitive with electricity from conventional energy sources such as coal fired power plants. gets about 38. 23. conventional diesel generators. tidal wave turbines.1% from nuclear plants. and 0. As stated earlier.Chronological History of Wind Turbine Technology ◾ 3 addition to the economic and environmental benefits provided by wind turbines. 1. Renewable energy sources present many benefits.7% from propane. geothermal and hydrothermal energy sources.1% of its energy from petroleum. Biodiesel power sources require large supplies of raw materials. They offer clean. hydraulic turbines.9% from biomass. Any energy generating source or scheme requires correct installation and specific operating conditions to ensure cost-effective operation. Nuclear power plants require heavy initial investment and present radiation dangers. biofuel. several countries are considering installations of wind turbines because of the high costs of fossil fuels and unpredictable petroleum supplies from OPEC countries. and tidal wave turbines require ocean waves with specific characteristics available primarily in Portuguese coastal regions.2 Major Benefits and Problems Associated with Alternate Energy Sources The United States is the world's greatest consumer of electricity. uninterrupted. such locations are known to exist only in Iceland.and high-temperature underground regions to harness energy sources. Based on the published data. the technology eliminates the dependence on costly foreign oil and neutralizes the political blackmail tactics used by hostile oil producing countries. every energy source (coal-fired generation.1% from solar cells. .3% from geothermal sources. Coal-fired power generating sources produce harmful polluting gases and aerosols. However.2% from coal. Wind turbines are effective for desalination of water in coastal areas that lack fresh water. Some sources require large initial investments during the installation phase. 0. The studies further indicate that wind turbine technology is best suited for desalinating seawater. As far as the cost of electricity generation (cents per kilowatt hour) is concerned.S. Hydro-turbine installations require water reservoirs to ensure constant water pressure. environmental impact-free electrical energy at reasonable cost. the U. 22. nuclear power.15% from wind turbines.7% from hydroelectric sources. Geothermal and hydrothermal energy sources require low. According to published data on energy sources. and food production in coastal regions. while others require unique operating environments available only in a specific geographic location or terrain. 0. Studies performed by the author indicate that wind and solar sources offer the cleanest and most cost-effective renewable energy. 1. and wind turbines) suffers from certain drawbacks. 2. 8. the worldwide electricity generation is roughly 1% from wind turbines.9% from natural gas. crop irrigation.
for example. It is important to mention that despite manageable shortcomings or problems. These two plates face each other but move in opposite directions. Iceland expects to capture as much as ten times the current geothermal power in near future. during strong winds. Note that water stored in a reservoir can be used to drive a water turbine when the operation of a wind turbine is not feasible. solar and wind turbine energy sources offer electrical energy with lower installation costs. Preliminary studies performed by the author predict that wind turbine technology will able to meet 10% of the world's electricity requirements by 2020. To accelerate the development of Iceland's geothermal and hydrothermal energy sources. the project focuses on well depths that will reach into hydrothermal vents most ideal for heating. Currently. and cost-effective operation. These two alternate energy sources provide clean energy free of environmental effects along with minimum cost and complexity compared to other energy sources mentioned above.3. The action generates enormous churning actions that produce high-temperature regions underneath the ground.3 Benefits and Disadvantages of Wind Turbine Technology 1. A combination of wind turbine technology with a hydroelectric power generating source would be attractive and practical because it takes very little time and effort to open or close a valve to a water turbine. higher reliability.1 Benefits Compared to other energy sources wind turbine technology offers affordability. It has allocated limited sources to develop wind turbine farms to generate electricity. The geothermal and hydrothermal sources of Iceland arise from the presence of two tectonic plates of the Mid-Atlantic Ridge System. pollution-free and maintenance-free operation. Energy experts in Iceland predict that by 2025 more than 80% of its electric energy requirements will be satisfied by clean energy from geothermal and hydrothermal sources.4 ◾ Wind Turbine Technology Note that Iceland meets 70% of its heating and electricity needs utilizing geothermal and hydrothermal energy sources in areas of low and high temperatures. This high-temperature water can be used for heating buildings or producing superheated steam to drive large turboalternators to generate 2000 to 4000 MW of electricity. a deep drilling project established in 2008 is capable of drilling 5 km deep to bring bore holes into contact with water at temperatures ranging from 400 to 600°C. Major benefits of wind turbine technology can be briefly summarized as follows: . 1. Hybrid power generating schemes are occasionally found most reliable and costeffective.
◾ Installation does not jeopardize the value of a home. and commercial buildings. Turbine installation and maintenance require intelligence. A typical 1. It is important to understand that wind turbines are generally loud and the turbine blades represent a danger to birds flying less than 350 ft above the ground. ◾ It delivers environmentally friendly and efficient electrical energy at lower cost. and power output. For example. Despite these benefits. The installation can be easily undone and leaves no adverse visible effects at installation sites. schools. users face no power shortages or failures as experienced by customers who depend on electrical utility grids. Most current wind turbine blades vary in length from 50 to 150 ft and the heights vary from100 to 300 ft. particularly if a component must be replaced on a tower typically ranging from 50 to 70 m in height. the cost of producing wind power has dropped four-fold since 1980. ◾ The turbine does not require frequent or intermittent maintenance or employment of operations personnel. an ordinary maintenance or erection technician is not qualified to perform the required tasks. in areas where electrical grids are not available. ◾ The technology essentially offers home-made electrical energy and off-grid living. where three 130-ft blades are connected to the tower head. However. local terrain features. 1. number of turbines on wind farm. rotor blade size. a constant high wind noise problem may be overcome by selecting installation sites away from residential areas.5 million including parts. Older turbines built 15 to 25 years ago are not only louder. wind turbine technology has a few shortcomings. for example in remote locations with difficult terrain features.3. Although maintenance is rarely required after careful installation. tower height.5-MW General Electric wind turbine costs around $2. depending on ground surface roughness. but also less cost-effective.Chronological History of Wind Turbine Technology ◾ 5 ◾ It saves substantial money on utility bills. Turbine noise increases with operating height.2 Disadvantages It would be unfair not to identify the potential disadvantages or the imminent dangers. A wind turbine normally sits about 30 stories above the ground at the hub. quick thinking. no maintenance or operational costs are incurred. installation. and electrical power generating requirements. based on Electric Power Research Institute estimates. vertical distribution of wind speeds. Other costly factors are site selection and tower structure. Damage to its tower structure or housing caused by strong winds may necessitate costly repairs or maintenance. and site selection. . office building. which is not readily possible with other technologies. This cost will be much higher for wind turbines with higher output ratings. or commercial building. Wind turbine installation cost depends on site selection. and output power rating. unlike steam and gas turbine-based alternator systems. split-second decision making. Consistent noise is the most annoying factor. particularly.
A repowering scheme is intended to harness more electrical energy by replacing existing wind turbines with higher capacity units.6 ◾ Wind Turbine Technology stamina. strong knees. Based on height restrictions. wind turbine technicians face inherent dangers while working alone almost 300 ft in the air with little support.4 Repowering to Increase Output by Existing Turbines Higher hub heights and re-powering schemes are highly desirable. It is extremely difficult for an ordinary technician to perform tasks in such a narrow environment. an agile and experienced technician will be able to reach the tower top in 10 minutes or less several times a day. Performance data from the Denmark Wind Turbine program indicate that wind farms with double the electrical power generating capacity of the original farms can deliver as much as four times more electrical energy with no changes in turbine design parameters. However. It is important to mention that higher hubs place the wind turbines in stronger and more consistent winds. They must select optimum parameters for rotor blades. Hub heights generally "maxed out" at 70 m in the 1990s. crack wind turbine technicians earn annual salaries in six figures. A wind turbine farm must achieve its full potential to meet the cost-effective design criteria. Under working conditions. 1. A turbine tower contains no elevator. The new turbine rotors developed in Germany ride even higher. and maintenance. In other words. These strict installation requirements must not be characterized as major disadvantages. 1. thereby increasing the number of operational hours per year that a wind turbine will operate most efficiently. and the ability to function at dizzying heights. and other conditions that will yield reliable. However. spacing between turbine units. a technician must be hypervigilant while working in tight spaces at heights exceeding 235 ft. For example. Wind turbine technicians require 8 weeks of rigorous training and classroom instruction covering installation. The German government is planning to approve a wind-farm repowering scheme that will produce more electricity by replacing several small wind turbines . if optimum turbine performance and maximum profit are the principal requirements.3 Unique Installation Requirements Wind turbines require unique installation specifications to operate with optimum efficiency. wind turbine installers and designers carefully consider turbine sites and wind farm conditions. They are installed on towers as high as 100 m or 328 ft. height of the turbine and tower structures. a repowering wind turbine site can generate 50% more electrical energy. operation. and efficient operation with minimum maintenance and operation costs.3. safe. in the presence of high-voltage electrical cables and spinning metal components. Access to the top is only possible by climbing rung by rung on a narrow-steel ladder inside the tower. The visual impact of a wind turbine is viewed as a negative factor because of the large blade spans—about 25 m in the 1980s and as large as 125 m today.3.
commercial. Denmark plans to generate more than 4500 MW of electrical energy by the year 2020 using wind turbine technology. Rising costs for foreign oil and gas have ruined the economies of several countries. Installations widely known as wind farms were built in large numbers to generate large amounts of electrical energy.4.4 Worldwide Utilization of Wind Turbines Several countries are looking into alternate methods of producing clean energy that will eliminate dependence on costly foreign oil and gas. Each large capacity turbine will be able to generate four times more compared to existing 2. Today's electricity generation windmills can reach heights close to that of the Washington Monument. which will be able to meet energy requirements for hundreds of homes. a 50-kW wind turbine facility went into operation as early as 1941 and a 100-kW operation went online in 1957 in Denmark. 1. The legislation will also authorize the operators . Current wind turbines are rated up to 5 MW generating capacity. The country is so bullish that it has plans to convert a 77-wind turbine facility into a 13-turbine facility using devices with larger capacities. According to the Historical Wind Turbine Development (HWTD) survey.1 Denmark Denmark pioneered wind energy technology as early as 1970. Wind turbine operation activities and installations in various countries will be described. 1. with blade lengths exceeding 100 m or 328 ft. four-wind turbine farm. Wind turbine technology mature. The technology is fully matured and turbines with various output capacities are available to meet residential. In April 2008.Chronological History of Wind Turbine Technology ◾ 7 with a few large units [1]. a small town in Missouri with a population close to 1500 became the first city in the United States to obtain all its electricity from wind power provided by a 5-MW. Several current wind farms will be replaced with farms of larger turbine units that will significantly increase the electrical energy produced by the farms. with particular attention paid to unit output capacity and unique performance parameters.5-MW capacity turbines. This trend is spreading in other countries because it achieves significant reduction in the cost of generating electricity with wind turbine technology. Since wind turbines are capable of generating large amounts of clean electrical energy ranging from 50 to 500 MW with minimum initial investment. the wind turbine technology is commanding great attention. the machines are reliable and operate continuously when constant wind is available. Wind turbines with higher megawatt capacities were installed between 1980 and 1990 in coastal regions. and industrial requirements. Its parliament is planning to introduce legislation in 2009 that will require wind park operators to compensate residents if installations of wind turbines reduce their property values.
4. the German government plans to approve a large wind farm scheme that will produce more electricity with many small-capacity wind turbines [1].000 MW by the 2012. German engineers installed a 10-kW wind turbine facility as early as 1936 and a 30-kW facility in 1958 and added more high-capacity wind turbine installations between 1980 and 2000. The availability of large quantities of electricity at minimum cost is critical because of China's huge population.4. 1. All these activities indicate that the country is about to expand the deployment of wind turbine technology to meet the needs of its citizens. available wind energy is unlimited. According the latest news on wind turbine-based energy generation sources.8 ◾ Wind Turbine Technology to dismantle the old and inefficient wind turbines and sell or ship them to Eastern European countries. Chinese energy experts predict that plans to install more high-capacity wind turbines in the Gobi region will boost the current power generation capability to exceed 10. Deployment of wind turbine technology offers clean and economical electricity. Vast open lands at high altitudes in Tibet and open areas in the Gobi desert are ideal sites for generating large amounts of electricity with simple machinery at minimum cost.3 billion people. According to the HWTD survey. The Gobi Desert is the most ideal location for wind turbine installations and most wind turbine facilities have been installed in that region. the country plans to add at least 15. China installed hundreds of 100-MW wind turbines in the Gobi Desert area and plans to install more wind turbines in some regions of Tibet. 1. electricity generated by wind farms will be more affordable than electrical energy produced by coal-fired steam turboalternators or nuclear power reactors. . Most of these wind turbine generators are connected to utility power grid systems to ensure continuous supplies of electrical energy at minimum cost to consumers.3 China The Peoples' Republic of China has large tracts of open lands in the Gobi Desert region. Between 2000 and 2008. Since China's population is approaching 1. where open land with yearround high winds is readily available.000 MW of new wind-power capacity by 2020. The association selected new turbine sites in hilly locations and coastal regions where optimum wind energy levels are constant throughout the year. According to the Wind Energy Industry Association of Germany. Several wind turbine installations with kilowatt ratings started to operate in the early 1980s in coastal regions where wind gusts were frequent.2 Germany Scientists and engineers in Germany developed wind turbine technology to generate electricity early but delayed the implementation of the technology to generate large amounts of electrical energy for consumers. where high wind speeds are prevalent throughout the year.
Chronological History of Wind Turbine Technology ◾ 9 1.5 Canada Both the eastern and western coastal regions of Canada are well suited for wind turbine installation because of high winds and a few selected areas in the Northern Canada are equally attractive for wind turbine installation. Appalachian Mountain states. utility-scale wind turbines (1 to 5 MW). Maine. Montana. with more than 25. wind turbines with power generating capacity ranging from 50 to 500 MW were installed between 2000 and 2008. and Washington) and in eastern coastal states (Massachusetts. In addition.S. and large turbines for wind farms (50 to 500 MW). energy requirements.4. manufacturers. and Iowa are considered the most attractive sites for wind farms capable of generating large amounts of electricity that could be fed into utility power grids. California. Texas. companies to meet the wind energy demands of citizens. Montana. up from the current 10% electrical energy generation from wind turbine technology. and Florida combined—would be needed. New York. California. access to .000 square miles—roughly equal to the size of Texas.5% of the total energy generated. Large flat lands in Montana. highly reliable wind turbine plants with capacities ranging from 100 kW to 5 MW presently operate at minimum cost. Renewable energy experts note that U.000 MW at the end of 2005 and surpassed Germany as the top wind power produce.000-acre wind farm is proposed for the Texas panhandle by the oilman T. dealers. wind turbine generating capacity exceeded 18.S. represents less than 0.S. Although wind energy consumption in the U. Boone Pickens.S. However. Wind turbines for residential applications operate in North Carolina. A 4000-MW. Wind accounted for nearly a third of all new power-producing capacity added in 2008. and similar regions are considered ideal for wind turbine installations. Vermont. Kansas. Energy experts predict that to meet total U. Connecticut. and other areas where high wind speeds are prevalent.4. U. Several wind farms with capacities ranging from 10 KW to 5 MW were installed between 1995 and 2000. Several U. Deployment of several large windmills is needed to generate electrical energy exceeding 1000 MW and more large-scale wind turbine projects are in the planning stage.000 MW in place at the end of 2008—enough to provide electricity to 5 million average households. Alaska coastal regions are also considered appropriate for wind turbine installations because of strong wind conditions throughout the year. Most of these installations are located in the western coastal regions (California. energy planners predict that wind energy sources could supply 20% of the country's electricity needs by 2030. 400.S. and Maine).S.4 United States The United States put its first 500-kW wind turbine into operation as early as 1987. 1. various types of wind turbines manufactured by several U. and installers specialize in small-scale wind turbines (10 to 100 kW). wind farms covering approximately 750. Oregon.
A few years ago. The British government put into operation a wind turbine with output capability exceeding 250 kW around 1983. Despite the variety of ideal locations for wind turbine installations.4.4. Wales. a few low-capacity utilityscale wind turbines with outputs ranging from 5 to 10 MW were installed on eastern coastal areas. England's western coastal regions. France implemented its first low-power-rating wind turbine (15 kW output) as early .8 France France's eastern and northern coastal regions are best suited for wind turbines. no capacity wind turbine was installed in Canada until 1987. The first utility-scale three-blade wind turbine with an output capacity exceeding 300 kW was installed in 1987. These smallscale installations are largely visible near dairy farms and open lands. and English Channel locations are considered most ideal for installation of wind turbines due to high winds. 1.1% of Canada's electricity is generated by wind turbine technology. 1. Since then. 1. According to the electric energy consumption survey. Some Small-scale wind turbines with outputs ranging from 10 to 100 kW for residential applications were installed from 2005 to 2008 to provide electricity for lighting and pumping. British energy planners in 2008 recommended a project involving 65 wind turbines on nearly 5. According to the international energy survey.000 acres of hillside near Llanbrynmair in Powys.4.7 United Kingdom Coastal regions of Scotland. Hundreds of wind turbine installations ranging from small-scale (10 to 100 kW) to utility-scale (2 to 5 MW) were installed between 1950 and 2008 to meet electrical energy requirements. the United Kingdom announced plans to build the tallest wind turbines to generate large amounts of electrical energy. A second unit with the same rating went into operation in 1957 and was immediately followed by a wind turbine capable of generating electrical energy in excess of 130 kW. particularly during the flood seasons common to the Netherlands. The first British wind turbine with a 100-kW power rating was installed in 1955. The project is expected to generate about 400 MW due to deployment of the newest high-efficiency wind turbines. mostly in the coastal regions where high winds are prevalent. several installations with higher power ratings have been commissioned in various parts of the country. several hundred small-scale facilities with capacities ranging from 10 to 50 kW were installed between 1990 and 2005 for residential and pumping applications. Wind turbine installations received great attention in England after 1950. barely 0.10 ◾ Wind Turbine Technology these regions is extremely difficult due to harsh climatic environments. In the early 1990s.6 Belgium and the Netherlands Belgium's coastal regions offer high winds throughout the year.
4. No reliable information on the number of wind turbine installations and wind farms in regular operation is available. when oil producing nations of the Middle East severely cut oil production and increased barrel prices ten times over a very short period. .11 Early Wind Turbine Development: Summary The author wishes to present a chronological development summary of wind turbines commencing from 1800. According to various European energy publications.9 Russia The first wind turbine with power output capability of 100 kW was installed in what was known as the Soviet Union as early as 1931. Deployment of wind turbine technology was not pursued more aggressively because of the availability of abundant oil at minimum cost in the southern states. The maximum capacity wind turbines became operational between 1973 and 1977. Published data on wind turbine installations in Italy indicate that several wind turbines rated at 200 and 225 kW were put into operation after oil prices suddenly increased ten-fold in 1973. Denmark plans to add more wind turbine installations to meet 40% of its energy requirements by 2020.4. Table 1. The French energy agency installed a 1000-kW (1 MW) wind turbine in 1963 to demonstrate the design and development capabilities of wind turbines with higher power output levels. wind turbines with capacities ranging from 100 kW to 5 MW operate in the northern and southern regions. Because unlimited cheap and highquality oil was available from Libya. That was followed by a wind turbine energy system with a power rating of 800 kW in 1958. 1. France is slowly but consistently adding more wind turbine installations in areas where high winds are prevalent.1 summarizes data on wind turbine installations in various countries prior to 1990. the Italian government was not interested in installing larger numbers of wind turbines. 1. Energy experts still believe Italy will not able to install large wind farms because of large populations concentrated in coastal regions that are most suitable for wind energy installations. a few wind turbines with outputs ranging from 200 to 500 kW went into operation in Italy between 1975 and 1990. According to published reports.Chronological History of Wind Turbine Technology ◾ 11 as 1929.4. Russia continues to use oil-fired power plants to generate large amounts of electricity. Published literature on renewal energy sources reveals that Denmark was the first country to install a 20-kW wind turbine as early as 1891 and it added four more wind turbines between 1941 and 1957. 1.10 Italy Italy is blessed with several coastal regions that are well suited for wind turbine installations and wind farm development. From 1960 to 2008. several wind turbines with power ratings ranging from 1 to 5 MW went into operation to minimize dependence on costly foreign oil.
. tower height. wind velocity. Power generated depends on blade diameter. wind direction. blade angle.12 ◾ Wind Turbine Technology Table 1.1 Operating Details of Wind Turbines Installed before 1990 Country Denmark Denmark Denmark Denmark Denmark France France France Germany Germany Germany Italy Italy Soviet Union Netherlands United Kingdom United Kingdom United Kingdom United Kingdom United States Installation Year 1891 1941 1942 1943 1957 1929 1958 1963 1926 1956 1958 1981 1976 1931 1987 1955 1957 1965 1983 1987 Rated Power (kW) 18 50 70 30 200 15 800 1000 30 200 100 225 200 100 300 100 100 130 250 500 Diameter (m) 23 17 24 18 24 20 30 35 20 33 34 32 33 30 30 15 24 25 20 34 Swept Area (m2) 408 237 452 254 452 314 716 962 314 855 908 804 855 707 707 177 468 491 314 955 Note: Data indicate blade diameters and swept area requirements as functions of electrical energy generated. and terrain features.
Rotor blade design parameters such as chord.1. twist angle. The operation is based on the scientific theory of fluid mechanics and some elements of aerodynamics.Chronological History of Wind Turbine Technology ◾ 13 1. and length are selected to achieve optimum aerodynamic performance and acceleration (a) Utility-scale wind turbine configuration (b) Small-scale wind turbine configuration Figure 1. Air currents that blow over flat terrains or over-the-hill regions have wind velocities ranging from 10 to 65 miles per hour and are sufficient to turn large blades attached to a high-speed shaft coupled to a generator [2]. Wind moves the propellers mounted on a rotor and the movement turns a high-speed shaft coupled to an electric or induction generator.1 Wind turbine configuration (a) utility-scale and (b) small-scale.5 Operating Principles of Wind Turbines It is helpful for readers to understand the basic operating principles of a wind turbine. Design configurations for a utility-scale wind turbine and small-scale wind turbine (for residential use) are depicted in Figure 1. Modern wind turbines catch the wind by turning into or away from air flows. .
low-speed shaft. controller. high-speed shaft. anemometer.1 Critical Elements of Wind Turbine Systems and Their Principal Functions As stated earlier.5. 1. electrical generator. yaw bearing. The critical components of a wind turbine are the tower. yaw motor. main enclosure. effects under various wind conditions at different tower height levels as indicated in Figure 1.2.14 ◾ Wind Turbine Technology VG With III turbines No turbines V (a) Effects of installation surroundings on wind velocity (b) Acceleration effects in the wind over the hills Figure 1. gear box. and nacelle and lowloss cables to carry the electrical energy down the tower. A step-up transformer at the base of the tower allows transfer of the wind-generated electricity to the utility . yaw drive. brake mechanism.2 Effects on wind turbine performance from (a) installation groundbased surroundings and (b) acceleration effects over the hills. pitch indicator. rotor blades. It is appropriate to identify the critical elements of a wind turbine and the operating functions provided by the critical components. wind turbine technology offers an attractive approach for an alternate source for producing large amounts of electrical energy at minimum cost. wind indicator.
The high-speed shaft is connected to a generator capable of producing electrical energy.Chronological History of Wind Turbine Technology ◾ 15 Rotor blades (each 125 feet) Enclosure generator location Rotating housing for the moving accessories Cables to carry the electricity down the tower Height = 230 feet Tower Storage area Step-transformer at tower base Ground level Figure 1. The wind moves the propeller that turns the low-speed and high-speed shafts. The enclosure depicted in the figure rotates to enable the rotor blades to face into or away from the wind.3 Wind turbine components. depending on wind direction. The gear box. All elements except the step-up transformer are located at the top of the tower as shown in Figure 1. The controller essentially directs the yaw motor to turn the rotor to face toward or away from the wind. The anemometer is a critical element of a wind turbine. Just behind the hub is the housing (see Figure 1. This essentially is the operating principle of a wind turbine.3. power grid. . In brief. the high-speed shaft drives a generator that converts mechanical energy into electrical energy.3) for the gear box and other components. converts the slow rotation (revolutions per minute or RPM) of the low-speed rotor shaft to higher RPM of the high-speed shaft which is mechanically coupled to a generator that produces the electricity. the heaviest element of the system. It gauges wind speed and direction and sends the information to the controller that in turn provides necessary data to critical elements of the system.
3-MW wind turbines in Texas to provide output sufficient to meet the electricity needs of more than 50. China.16 ◾ Wind Turbine Technology 1. The utility-scale turbines manufactured by GE are more reliable and safer according to the company's program manager.0 to 2. In brief. According to the program manager. India. The turbine nacelles are manufactured in Brande. Wind turbines are manufactured in various countries including the United States. Denmark.8 MW.000 households—about 310 households per megawatt of electricity generated by these turbines. It has manufacturing facilities in Germany and Denmark. and thunder. The 1. and improved performance are given serious consideration during the design and development phases. Vestas. Nordex Corporation. the dynamic stability of a wind turbine depends totally on the performance capability of the yaw mechanism.6. Switzerland. France.5 million excluding costs for installation and accessories needed to provide additional mechanical integrity for operation in harsh environments. . Mitsubishi wind turbines operate worldwide and no accidents have been reported to date. turbine blades are manufactured in a coastal town in Denmark. safety. Suzion Power Company. It is important to mention that yaw components (motor and controller) play a critical role in turbine performance under uncontrollable and unpredictable wind environments.6 MW. Turbine cost is based on power generating capacity. Germany. and 3.5. Reliability.1 Utility-Scale Wind Turbine Sources These types of wind turbines are available from various manufacturers and dealers such as General Electric (GE) Wind Energy Source. Mitsubishi Power Systems.5-MW GE wind turbine costs around $2. Denmark. Clipper Wind Power.5. and other technologically advanced countries.3-MW wind turbine now used worldwide. Siemens recently installed seventy 2.MW wind turbine is the most cost-effective and occupies minimum space. The latest 2. United Kingdom. and others. Siemens Corporation. Power ratings of its wind turbines range from 2. small-scale. Siemens Corporation has been a front player in the design and development of wind turbines in European countries.5. Mitsubishi Power Systems is another major supplier. Its latest and most popular model is the 2. and exhibits enormous resistance to wind storms. Procurement and installation costs are available from authorized Mitsubishi suppliers.4-MW wind turbine with a 92-m rotor is called the system with "smart yaw" capability because it can be assembled by small cranes at a desired site. 1. can operate with reverse configuration during high winds and under rapidly variable wind directions. the 2.6 Wind Turbine Classifications The three major categories based on energy generating capacity are utility-scale. lightning. its turbines are rated at 1. 2. and intermediate-scale wind turbines and all are commercially available from various sources. The corporate technical department is located in Germany. Procurement and installation costs can be obtained from Siemens dealers. Italy.
5 million and will be adequate to meet electricity needs for approximately 2500 homes based on the ability of a 1.2 Pay-Off Periods for Utility-Scale Wind Turbines and Wind Farms Pay-off period is the most important issue in a customer's mind before he signs a contract for installation of a wind turbine.5-MW wind turbine cost around $ 2.5-MW wind turbine to pay for itself.4 Large wind farm containing hundreds of turbines. as illustrated in Figure 1. assuming a $500 per year residential electricity bill (equivalent to about $42 per month).5 million as of January 2008. it would take 10 to 12 years for a 1. However.5-MW turbines indicate that a wind farm will cost around $12.6. a 1.5-MW unit to meet electricity requirements of 500 homes.4. and final operation check-out. including the turbine delivery and installation at the site. Figure 1. the pay-off periods for wind farms containing hundreds of utility-scale turbines will be much longer because of the large number of towers and generating units required. However. delivery costs.Chronological History of Wind Turbine Technology ◾ 17 1. . The customer deserves a clear and reliable response from a dealer and an installer. Linear interpolation indicates that a $1000 annual electricity bill will reduce the pay-off period to around 5 years. According to the best GE estimates. tower installation. tower procurement and installation costs are not included. It is important to note that pay-off periods for wind turbines are expected to be less than 50% of the pay-off periods for solar panel installations. Preliminary estimates on a wind farm installation composed of five 1. The pay-off period is strictly a function of the costs of turbine procurement. Based on procurement data from GE. tower procurement.
remote. Furthermore. and China maintain manufacturing facilities for small-scale wind turbines. about $5449. Small-scale wind turbines manufactured by Southwest Wind power are compact.3 Small-Scale Wind Turbines Several companies in the United States. The procurement and installation costs for high-capacity wind turbines cannot be justified for users whose electricity needs are less than 20 kW. and highly reliable. They are best suited for residential. All Small Wind Turbines.000 wind turbine generators in the past 20 years. and water pumping applications.18 ◾ Wind Turbine Technology 1. Japan. particularly at low wind speeds. and smoothly running system. efficiency. Wind turbines made by Aerostar deploy induction generators that allow simple direct utility interconnection without need for an inverter. technologies. and pay-back periods of these small wind turbines. Suzion. and Appalachian Wind Systems. Aerostar systems are available with a color touch screen displays. In the U. about $8104. A 1-kW unit costs about $1561. Lake Michigan Wind and Sun. Southwest has produced more than 90..298.2 summarizes details of small-scale wind turbines manufactured by U. about $24. Suzion turbines operate in Europe.S. Bornay. Other features are aerodynamic rotor control to ensure safe operation and acoustic isolation of moving parts to suppress noise.S. about $2753. a 3-kW unit. Europe. a Swiss company. Small-scale wind turbine customers are impressed with the performance. India. resulting in a low-cost. and a 20-kW unit. Table 1. is the major supplier of small-scale wind turbines and has successfully installed small wind turbines in several developing countries that are very pleased with the efficient performance and low procurement costs. dealers include Aerostar Wind Turbines. efficient. Scoraig Wind Electric. South Africa. aerodynamic design. They can be purchased directly from manufacturers or authorized dealers in the United States and European countries. Wind Turbine Industries. a 10-kW unit. Southwest Wind Power. sailboat. Bergey Wind Power. and Ethernet interfaces for continuous monitoring of performance from anywhere in the world. inexpensive. companies. a 2-kW unit. a 5-kW unit. reliability. quiet. data logging of wind speeds and turbine output levels.6. This eliminates reliability problems and decreases system cost. affordability. offshore platform. Singapore. Newer versions of wind turbines incorporate advanced materials. and design concepts such as variable generator excitation control techniques that substantially improve energy capture. . and other countries. about $13.410 (prices exclude installation and shipping costs). The company manufactures small turbines with power ratings ranging from 1 kW to 20 kW. Aerostar wind turbines use the two-blade teetering rotor design that substantially reduces loads on the turbine and tower structure. telecommunications transmitter.
4 Component Cost Estimates for Small Wind Turbine Systems Exact cost estimates for wind turbine major components are not readily available. delivery. turbine.2 Technical Data for Small-Scale Wind Turbines Manufactured in United States Manufacturer Abundant Renewable Energy Aerostar AeroVironment Bergey Windpower Gala-Wind Ltd. . some dealers quote tower cost without installation and delivery costs. Proven Energy Ltd. The wind turbine cost is based strictly on the output capacity.1 Excel None None W-200 and W-500 WES-5 23-10 Jacobs Technical Data None Blade radius = 6 m Two-blade teetering rotor Reliable and Rugged Compact and reliable Most stable and reliable Less expensive Rotor diameter = 5 m Rotor diameter = 7 m 1. and complexity of design. 1.6. Furthermore. Southwest Windpower Wind Energy Solutions Wind Turbine Industries Capacity (kW) 2 5 and 10 5 10 1 1 and 10 11 2 5 and 6 1 and 3 25 10 Model Number E110 and E442 None AVX-1000 XL. The author collected some cost data on towers and small wind turbines with output capacities not exceeding 10 kW. number of rotor blades. and required steel piping. A break-down of the total cost of a 5-kW small wind turbine are listed in Table 1. installation.4.3.5 Total Installed Cost for 5-kW Wind Turbine in 2009 The total installed cost includes the tower.Chronological History of Wind Turbine Technology ◾ 19 Table 1. These cost data are summarized in Table 1. Tower cost is also dependent on the height of the structure and the structural integrity requirements.6. rotor design complexity. The costs for towers and turbines vary from supplier to supplier. type and location of generator.
California.0 3. without steel pipes. (949) 413-7888 ◾ Wind Monkey. California. Some suppliers charge for delivery and insurance if delivery sites are distant from suppliers' premises. However. installation priorities. Table 1.6. and sequences.41/80 Note: Towers are supplied in kit form.4 2009 Total Installed Cost for 5 kW Wind Turbine Component Turbine Tower (40 ft) Installation of turbine Installation of tower DC-to-AC inverter Miscellaneous accessories Total Cost ($) 5.600 400 150 2.0 2. the author recommends that users and wind turbine purchasers insist on having installation handled by the turbine and tower suppliers because they know their system components. San Demas. Irvine. Irvine. The following companies specialize in installation projects: ◾ Solar Planet.6 Wind Turbine and Tower Installers Wind turbine customers who do not like installation costs quoted by manufacturers can contact installation companies.0 (battery charger) Retail Turbine Cost ($) 2500 3500 6212 7850 8150 Retail Tower Cost ($)/ Tower Height (ft) 308/24 495/30 687/50 935/65 11.3 Retail Cost Estimates for Wind Turbines and Associated Towers Power Output (kW) 0.20 ◾ Wind Turbine Technology Table 1. Installation costs for turbines and towers not included in retail cost estimates.900 4.000 500 13. (909) 394-4647 .3 (grid) 3.9 1.550 1. (949) 748-5774 ◾ Sustainable Power Systems. California.
The 20-kW wind turbine manufactured by Wind Turbine Industries Corporation is capable of providing electric power for a broad range of applications such as Grid Intertied or hybrid battery charging systems at remote locations. 1. industries. The expected turbine life is about 30 years. Energy Maintenance Service produces 35-kW and 65-kW turbines.6. Another intermediate turbine supplier is the Entegrity Wind System which manufactures a 50-kW (Model EW-15) best suited for hybrid applications where the end user directly consumes wind-generated power. The EW-15 is best suited for farms. and water pumping.8 meters or 29 feet and the system offers quiet. and municipal wastewater treatment facilities in gridtied applications.6. the EW-15 unit can be incorporated into a utility system to provide electricity to small villages and towns at minimum cost. schools. Intermediate turbines are widely used for on-grid and off-grid applications such as distributed generation.8 Intermediate-Scale Wind Turbines The output capacities of these turbines range from 20 to 100 kW and they are best suited for applications where small-scale and utility-scale turbines do not provide the most cost-effective operations in the long run. The rotor size is about 8. telecommunications. reliable. Several U. depending on the wind regime at the turbine site.Chronological History of Wind Turbine Technology ◾ 21 1. This system is capable of delivering 150.7 Potential Applications of Small Wind Turbines Small-scale wind turbines are best suited for applications where electrical power consumption does not exceed 10 kW. clean. village electrification. 1. companies manufacture wind turbines with moderate capacities.000 kilowatt hours per year.000 to 200. and efficient operation. for example: ◾ ◾ ◾ ◾ ◾ ◾ ◾ ◾ Remotely located homes Telecommunication transmitter sites Offshore platforms Cathodic protection Performance monitoring sites Water pumping Utility-connected homes and businesses Remote military posts.7 Wind Farm Developers Wind farm companies play critical roles in recommendations for and selections of appropriate installation sites for cost-effective operation of wind turbines needed .S. For remote communities.
PPM Energy.5 shows a residential wind turbine configuration with off-grid capability. North Carolina.5-MW turbines operating in parallel to generate large amounts of power.1 Wind Farm Dealers Some companies and dealers specialize in site selection for installation of wind turbines to meet specific electric power generating needs on a specific area of land. These experts examine the terrain features. 1. Catamount Energy. Black Mountain.22 ◾ Wind Turbine Technology to generate large amounts of electrical power (about 500 MW). A hybrid version of a residential off-wind turbine offers the most cost-effective operation and reliability.S. Such dealers employ expert site survey experts to ensure proper installation site selection. North Carolina. Asheville. North Carolina.2 Renewable Energy Professionals It will be of great interest to prospective customers to seek professional help or advice prior to selecting a Solar Panel Installation or Wind Turbine dealer to meet his electricity requirements with minimum cost and complexity.7. (828) 669-5070 ◾ Southern Energy Management. wind speeds and directions. Horizon Wind Energy. (800) 869-8824 ◾ Appalachian Energy Solutions. Raleigh.5-MW turbines. Sugar Grove. which will be more cost-effective to operate than a coal-fired plant with an identical power rating. 1. and Clipper Wind.7. Morganton. Figure 14 shows a typical wind farm configuration of ten 2. (828) 689-2080 1. Action Energy.8 Design Configurations Various design configurations of small wind turbines have potential applications where uninterrupted supplies of electricity with high load factors are required regardless of wind conditions. A wind farm will contain several 2. North Carolina. include Wing Energy Consulting and Contracting. addresses and contact phone numbers of such professionals. Blue Water Wind. (828) 773-9762 ◾ Solar Dynamics. Cape Wind. a home wind turbine configuration with . and other relevant parameters that may impact the cost-effective operation of a wind farm. which can be contacted if needed. Blue Sky Wind. (828) 665-8507 ◾ Sundance Power Systems. North Carolina. Endless Energy Corporation. (919) 836-0330 ◾ Blue Ridge Energy Solutions. Figure 1. Renewable energy professionals include: ◾ FSL Energy Management. Mars Hill. Green Professionals Directory provides the names. Such companies operating in the U. Midwest Renewable Energy Corporation. North Carolina.
energy independence. Its design includes a patented twisted high-efficiency blade. optimum angle of attack along the entire blade length at variable wind velocities.8. highest lift-to-drag ratio. enhanced reliability.8. electromagnetic braking. Grid-tied wind turbines offer design simplicity. Compared to batteryless grid-tied wind turbines. extremely efficient aerodynamics. high efficiency.Chronological History of Wind Turbine Technology ◾ 23 Wind Turbines and Solar Power Home wind turbinesHome wind turbinesgrid-tied w/backup grid-tied batteryless Residential wind turbines-off-grid Hybrid solarwind turbines (a) (b) (c) (d) Figure 1. The turbines are economical and relatively reliable. It works impressively in both high and low wind speed conditions. 1. This design exhibits improved overall performance. grid-tied devices with battery back-ups provide uninterrupted electricity at minimum cost. They are sold in kit form and are easily assembled and installed. If one has both wind and solar power systems.5(a).2 Residential Design Configurations with Grid-Tied and Back-Up Capabilities This configuration is depicted in Figure 1. and hybrid solar–wind turbine design configuration. 1.3 Residential Design Configurations with Grid-Tied and No-Battery Operation This configuration is shown in Figure 1.1 Residential Design Configurations with Off-Grid Capabilities This wind turbine configuration is shown in Figure 1.5(c).5 Residential wind turbine configurations. a home wind turbine configuration with grid-tied and battery-less operation. slightly better system performance. grid-tied and back-up capability.8. over-speed control mechanism. and easier set procedure than . and back-up power for remote off-grid sites and under unstable grid conditions. 1. These turbines are rated below 1 kW. and superior workmanship. They also offer high reliability. and aerodynamic blade speed limitation.5(b). only one inverter is needed for a grid-tied wind turbine with battery back-up.
water pumping. these systems also go down. can be installed easily. However. and has an electromagnetic over-speed control mechanism that is more reliable than the traditional furling system. This system can be used for a variety of applications including utility-connected homes and businesses. clean. According to published reports. This configuration generates electricity simultaneously from both solar and wind energy at operating conditions. This is the most serious drawback of this design.4 Hybrid Solar-Wind Turbine System Configurations The hybrid solar–wind power system configuration is shown in Figure 1. telecommunications.6 Critical components of small wind–solar hybrid system. 1. The system is light-weight. Only one inverter unit is needed for both solar and wind power modules.5(d). thereby making the hybrid cost-effective. and offshore platform lighting.8. more than 50 countries manufacture an estimated 50.24 ◾ Wind Turbine Technology grid-tied systems with battery back-up capability. remote homes. they lack back-up capability. Small wind turbine system suppliers claim that this hybrid is best suited for battery-charging applications in all climatic environments. when the grid goes down.6. . and reliability. Wind generator PV array Batteries provide electricity to home Inverter Battery bank Whisper charge controller PV panels provide electricity to batteries Whisper provides electricity to batteries Figure 1. Critical components of a small wind–solar hybrid system configuration are shown in Figure 1. sustainability. and reliable.000 small wind turbine generators for various applications. It provides high efficiency.
generator. A compact wind turbine energy system as shown in Figure 1.8. charge controllers. and essential accessories. 1. This compact configuration shown in Figure 1.Chronological History of Wind Turbine Technology ◾ 25 Mouse over numbers to see more 1 Skystream provides electricity to home 2 Home connected to utility grid 3 Figure 1. a wind turbine comes in kit form. the residential user in essence sells electricity back to the utility company. 1. the system generates more electrical energy than the residence needs and the excess electricity is fed back to the grid. The tower represents a large component of the system and is delivered directly to the customer site. In brief. when the wind is not blowing. home wind .7 provides electrical energy to both residence and utility grid. The electric meter will actually spin backward. complete with rotor blades. inverter. However. the user must maintain stocks to replace damaged or non-operating parts as required to maintain normal system operation. wind generator magnets.8. the turbine provides quiet and clean electricity.7 Skystream residential system that works in tandem with an electric utility supplier. Most of the critical components used by residential off-grid wind turbines.5 Compact Wind Turbine and Energy Systems for Dual Applications Southwest Wind Power supplies a compact and inexpensive small-scale residential wind turbine called the "Skystream" that works in tandem with an electric utility supplier.6 Critical Electrical Components In general.7 will generate electricity for a residence and utility grid and be eligible for tax rebates and incentives provided by state and federal governments. When wind speeds are high.
and 1-kW. The vertical distribution of the wind speeds experienced by a wind turbine operating from the ocean surface is based on turbine height. High-speed ocean winds are considered ideal for generating large amounts of electricity at lower cost. 1. and home wind turbines with grid-tied and battery-free capabilities are available from Windex Greenpower4less and wind power supply stores.9.26 ◾ Wind Turbine Technology turbines with grid-tied and back-up capabilities.1 Helix Wind Turbines Helix Wind offers an elegant and cost-effective solution for homes and small businesses. samarium–cobalt.9. wind–solar water pumps.8. generator magnets made of rare earth neodymium. These effects are dependent on terrain features.9. and aluminum–nickel–cobalt. 1. The maps generated by the NASA satellite can aid in planning and locating offshore wind farms for producing electrical energy. ceramic. The Helix turbines are small capacity devices. 1. home turbine kits. The vertical distribution of the wind follows an exponential law as a function of height as illustrated in the figure. charge controllers. flexible. wind generator blades. 1. solar panels for hybrid systems. 48-V small wind turbines. Ground roughness exerts critical effects on the vertical distribution of wind as shown by the curves presented in Figure 1. The kinetic energy of the wind can be converted into electrical energy using highly efficient vertical blade designs. inverters.3 Wind Turbine Design Based on Jet Engine A Massachusetts aerospace company has devised a new concept that may be at least twice as efficient as traditional turbines deploying rotor blades that force air around . towers.2 Wind Turbines Operating from Ocean Surfaces Scientific data from NASA's QuickSCAT satellite reveal that we can harness ocean wind energy to generate electricity. The next generation of small wind turbines will be powerful enough to meet electricity requirements yet harmonious with the environment.9 Next Generation Wind Turbines with Unique Features This section describes the next generation of wind turbines and their unique design features. Components include wind generators. These small turbines allow the kinetic energy of the wind to be captured by the unique and highly efficient vertical blade design configuration.
The device channels wind into a vortex that spins the blades and generates electricity. 1500 1000 500 100 3. 1.9 V~H0.4 10 mph V~H0. His website (Tom's Whirligig) provides detailed descriptions illustrations. Google Sketchup files.5 Floating Offshore Wind Turbines StatoilHydro.4 Vertical Axis Wind Turbines Tom J.U. .0 T. 1.2 4. The Massachusetts's company hopes to have a prototype turbine completed by the end of 2009. Gilmour.28 10 mph V~H0. a Canadian inventor.16 7. is working on a 2. Unfortunately its website (flodesignwindturbine.org) is not currently functional. 65-m high Siemens turbine will have lower deepwater installation costs compared to a traditional turbine installation on a fixed platform. The company planners predict that the 80-m diameter. The vertical distribution of the wind experienced by a turbine operating from an ocean surface depends on turbine height.9.8 Vertical distribution of wind dependent on ground objects and terrain features.3-MW floating wind turbine that will be attached to the top of a "Spar-buoy" and moored to the sea bed by three anchor points to provide stability to the system. recently published a new design for a wind turbine. Ft. and a system block diagram. He is optimistic about the feasibility of his design and plans to build a working model in near future.9. a patent application for the design has been filed. H. them instead of through them.Chronological History of Wind Turbine Technology ◾ 27 10 mph Height Above Ground. Buildings Trees and Houses Open Water and Plains Symbols: H = Height of the wind turbine above the ground (feet) and V = Wind speed (MPH) Figure 1. The company plans to have a working prototype completed by the end of 2009 and thereafter feasibility tests will be performed to determine reliability and performance in high wind environments. a Norwegian company. The inventor hopes to reserve worldwide patent rights for his design and believes that his windmill will be most complex ever designed.
Based on an operating height of 50 m above the ground. Each country must generate such data to determine optimum wind turbine location sites within its territory.S. estimated values of wind power density in watts per square meter of surface area (W/m2) for various wind speed zones are summarized in Table 1. Major benefits and disadvantages of alternate energy sources are summarized.1 Potential Status Fair Good Excellent Outstanding Optimum 1.0 to 7 5 7 5 to 8. Preliminary data must be screened to eliminate areas that will not generate electrical energy at reasonable costs. Critical system components and their important functions are discussed.5 Wind Power Classification Parameters Wind power density at 50 m height (W/m2) 300 to 400 400 to 500 500 to 600 600 to 800 800 to 1. .600 Wind Speed (m/sec) 6. Site selection requirements are discussed.5.4 to 7.0 that is widely used in preparation of U.0 7. Countries that participated in the early development of wind turbines are identified. Repowering schemes to yield more electrical energy from existing wind turbines are briefly described. It is not possible to estimate the wind power classification data for various locations around the world. with emphasis on reliability and longevity. At present such data is not available for various countries. site selection for the installation of wind turbines depends on wind power calculated as a function of turbine height from the ground. performance parameters of various types of wind turbines.8 8. such data will eliminate potential installation sites unlikely to be developed onshore due to specific land uses or environmental issues. Furthermore.10 Typical Wind Power Estimates for United States According to the reports from National Renewable Energy Laboratory. wind resource maps [3]. and installation requirements for turbines and towers.0 8. Note the wind speeds shown are based on a Weibull parameter k value of 2. 1.28 ◾ Wind Turbine Technology Table 1. Wind power classification is of paramount importance prior to selecting a site for turbine installation.11 Summary This chapter describes the history of wind turbine operations around the world with emphasis on installation dates.8 to 11.0 to 8. design aspects of critical components.
Microwave Magazine. Pay-off periods for utility. Tower height as a function of wind speed to capture maximum kinetic energy at various locations is discussed. Wind power classification status in terms of electrical energy generated per unit surface area occupied by the operating system (watts per square meter) is provided for a turbine height of 50 m or 164 ft. noise reduction. March 1. reliability. [3] Wind power classification. 2009. Los Angeles Times. [2] Ground zero for alternative energy. Hybrid solar–wind energy systems are briefly described. p. and tower requirements. IEEE Spectrum. Installation cost break-down for a 5-kW small-scale design is detailed. References [1] Europe replaces old wind turbine farms. and installation cost reduction. 35. February 2009. January 2009.and small-scale scale wind turbines are specified and various design configurations for small-scale wind turbines are identified.Chronological History of Wind Turbine Technology ◾ 29 Most popular wind turbines such as utility-scale and small-scale types are described along with details about efficiency. 13. Locations and phone numbers for various wind turbine suppliers and manufacturers and wind farm development companies are provided for individuals interested in procuring wind turbines. The next generation of wind turbine designs is summarized related to performance improvement. p. A-20. p. .
and lower operating costs.1 Introduction This chapter will describe various types of wind turbines with particular emphasis on design requirements and performance capabilities. For any application. The most viable application is pumping water to reservoirs associated with hydroelectric power plants. chemical. It is important to note that linking with a utility power grid requires synchronization with the grid frequency.Chapter 2 Design Aspects and Performance Requirements 2. Extraction of wind energy from wind turbines depends strictly on wind speed and direction. the energy generated by wind turbines can be converted into electrical. or operate air compressors and water pumps. First we should identify potential applications of the wind energy captured by turbines. deployment of wind turbines to generate electricity merits serious consideration to reduce dependence on fossil oils. A wind turbine drives an electrical generator whose output can be stored in batteries or linked to a utility power grid. drive heat pumps. Despite the limited availability of suitable operating sites with high annual wind energy potential. it is vital to investigate whether a specific wind turbine offers high efficiency. That means a wind turbine must be operated at 31 . thermal or potential energy. year-round reliable operation. Note that the kinetic energy produced by a wind turbine is in a thermodynamic sense the most desirable type of energy because it is readily available and can be converted in any other form of useful energy. In brief. Wind turbines can be used to produce clean fuel composed of hydrogen and oxygen. develop fuel cells.
Storage of the electrical energy generated by the wind turbines is also expensive because of the cost of batteries and the additional equipment needed to convert the alternating current to direct current.2 and Figure 2. the efficiency of the storage and retrieval of energy is about 75%.1 illustrates early and modern wind turbines. wind turbines with downwind rotors.2 Types of Wind Turbines Several types of wind turbines operate in various regions of the world. HAWT Upwind rotor Windmill Windwheel Downwind rotor High tipspeed ratio Wind turbine Savonius rotor VAWT Darrieus turbine Giromill Figure 2. . Figure 2. 2.3.1 Windmill for water pumping applications. The windmill in the figure has played a key role in energy generation. The three distinct types of VAWTs are those with Savonius rotor configurations. windmill turbines. It is interesting to note that more than one million wind wheels continue to pump water in different parts of the world. respectively. Furthermore. Darrieus wind turbines. and turbines with high tip speed ratios ranging from 1 to 8. and Giromill wind turbines. wind wheel turbines. which means that storage of wind turbine-generated electrical energy may not be cost-effective.32 ◾ Wind Turbine Technology a constant angular rate or must drive a variable input speed constant frequency output electrical generator. Wind turbines are classified into two major categories: horizontal axis wind turbines (HAWTs) and vertical axis wind turbines (VAWTs) as illustrated in Figure 2. particularly in water pumping applications. compatible with battery charging requirements. Such machines are available with power output capabilities ranging up to 60 kW but are prohibitively expensive. The HAWT category includes wind turbines with upwind rotors.
Performance capabilities and limitations of these turbines. and Dutch type turbines.4. The figure also displays power coefficients as functions of blade tip speed-to-wind speed ratio for propeller type windmills. along with details of system and installation costs. and safety will be summarized below.2 Horizontal-axis wind turbine (HAWT).Design Aspects and Performance Requirements ◾ 33 Rotor Gearbox Anemometer Generator Yaw motor Grid Transformer Control system Foundation Figure 2. reliability. turbines with Savonius rotor configurations. turbines using high-speed two-bladed rotors. . Wind turbines using specific rotor concepts are shown in Figure 2. turbines with multi-bladed rotors.
3 Vertical-axis wind turbine (VAWT). The windmill is an effective device for pumping water because a lot of water is required to get it running. The greatest advantage of a wind wheel is shown in Figure 2. . 2.34 ◾ Wind Turbine Technology Figure 2. In comparison to a conventional wind turbine with a few slender blades rotating at high speeds. a windmill starts more easily because the rotor blades cover a far larger share of the swept area.2.1 Windmills The windmill features a very robust design composed of simple and inexpensive components. The system is easy to operate and requires minimum repair and maintenance.1.
regardless of the type. modern wind turbines are classified into horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT) categories.50 and deploy propellers with two.5.2.1 Blade Tip Speed-to-Wind Speed 6 7 Figure 2.6 Ideal efficiency for propeller type windmills 0.15 to 0. Each category is further subdivided based on upwind rotor configuration. 2. As mentioned earlier.3 Modern Wind Turbines Modern types of wind turbines including the HAWT and VAWT machines will be discussed with emphasis on applications and performance capabilities.4.5 Power Coefficient. windmill design.1 Dutch four-arm type 0 1 2 3 4 5 Ratio 0.40 and 0.3 Savonius rotor 0. 2.Design Aspects and Performance Requirements ◾ 35 0. Savonius rotor design. consists of basic components: a base or . Modern turbines using propellers exhibit poor starting torques and power coefficients between 0.2 Farm Type and Dutch Type Wind Turbines The farm type and Dutch type wind turbine configurations are depicted in Figure 2. A modern wind turbine. high tip speed ratio.or three-blade configurations as illustrated in Figure 2. and wind wheel design. downwind rotor configuration.4 Rotor concepts and power coefficients. The two turbines have excellent starting torques and power coefficients ranging from 0. Cp 0.25.4 American multi-blade type 0.2 High-speed two-blade type Various rotor 0.
.2.5 Farm type and Dutch type wind turbines. The gear box and generator are connected to the horizontal shaft and the transformer is located at the base of the tower as shown in Figure 2. Most manufacturers offer several models with different hub heights and rotor diameters to tailor installation to meet customer site and power output requirements.3. gearbox.1 Horizontal Axis Wind Turbine (HAWT) If the rotor blades are connected a horizontal shaft. tower. Rotor diameter (D) is equally important because it determines the area (A) needed to meet specific output power level. 2. Major design efforts are directed toward the major components such as rotor diameter. The tower height for HAWTs is extremely important because wind speed increases with the height above the ground. control system. A horizontal axis wind turbine may be of rotor-upwind upwind design to face the wind or rotor-downwind design to enable the wind to pass the tower and nacelle before it hits the rotor. rated electrical power. rotor.36 ◾ Wind Turbine Technology Farm Type Farm Type Dutch Modern Propeller Figure 2. nacelle enclosure housing a generator. foundation.2. and control strategy. tower height. Critical components are depicted in Figure 2. and transformer. Such turbines are widely used for commercial applications. number and twist angle of rotor blades. yaw motor and other electrical mechanical accessories. Nineteenth century water pumping wind wheels deployed downwind rotors. The turbines that dominate the current markets operate at high tip speed-to-wind speed ratios ranging typically from 5 to 7 and utilize three-bladed rotors with rotational speeds of 10 to 30 revolutions per minute (RPM). Most modern wind turbines have upwind design configurations and range from prototypes in the MW class to smaller turbines with nominal power output capacities of 20 to 150 kW. the device is an HAWT.
2 Vertical Axis Wind Turbine (VAWT) The critical components of a VAWT are not shown in Figure 2. several versions utilize grid-connected wind turbines consisting of two or three rotor blades. it prevents transmission of the bending moments from the rotor to the mechanical shaft. Ensuring the stability of the flexible rotor is essential. This is called a teeter mechanism. thereby making these components easy to service and repair. HAWT systems are best suited for electrical power generation and micro-turbines composed of two to six rotor blades are most attractive for battery charging applications. Downwind turbines are noisier than upstream turbines. 2. developed the first VAWT in 1924 and it utilized what is now known as the Savonius rotor design configuration. some with the rotor-downwind and others with the rotor-upwind configurations. This operational deficiency can be overcome with a three-bladed upwind rotor design configuration. A turbine with two rotor blades is cheaper. For this reason upwind rotor designs dominate the current markets. Furthermore. thereby reducing the procurement cost. Two-bladed wind turbines are normally downwind machines. the once-per-revolution tower passage of each blade is heard as a low-frequency noise due to human ear sensitivity in the low-frequency region. a Finnish designer and inventor.. Both the Savonius and Darrieus turbines fall into this category and are available commercially. Since the 1980s. HAWT systems typically deploy two or three rotor blades. a threeblade HAWT offers smooth operation and is therefore less disturbing. the connection to the shaft is flexible because the rotor can be mounted through a hinge. The greatest advantage of a VAWT is that the generator and gear box can be installed at the base of the tower. Two-blade wind turbines are often downwind installations. these turbines have small output capacities and hence are widely used for low-power applications such as battery charging in areas where power grids are not available. This turbine consists of a vertical S-shaped surface that rotates around a . However. also the aerodynamic efficiency of a two-blade rotor is lower than that of a three-blade rotor. This type of construction is more flexible than a stiff three-bladed rotor configuration and some of its components are more compact and lighter. i. field operating data indicate that this adjustment is not possible under abrupt or sudden changes in wind direction. However. The power output performance of a HAWT can be optimized by selecting a ratio between the rotor diameter (D) and the hub height (H) very close to unity. The control system must ensure that this power is not exceeded in high-wind environments to avoid structural damage to the system. The rated power output of a wind turbine is the maximum power allowed for the installed electrical generator. In contrast.3 because of the configuration complexity. the rotor is downwind on the tower. thereby producing a visual flickering effect.Design Aspects and Performance Requirements ◾ 37 As mentioned. George Savonius.3. The major advantage of rotor-downwind design is its automatic adjustment to wind direction—an important safety and operational feature. but it rotates faster.e.
3 VAWT Operating Requirements A VAWT requires certain wind direction conditions. Savonius rotors have very limited power outputs and poor efficiencies.3. Variants of the crosswind axis types have been proposed.4. Power coefficients for various turbine rotors are illustrated in Figure 2. 2. it is necessary to sense the direction of the wind in order to time the cyclic pitch changes accurately. Note that the Darrieus rotor has a power coefficient close to 0.38 ◾ Wind Turbine Technology central axis.5.3. 2. It is evident from this figure that a Savonius has the lowest power coefficient and it operates only over a specified blade tip speed-to-wind speed ratio. Because of their limited capacities and lower efficiencies.5 to 6. VAWTs are not as efficient as HAWTs. Savonius turbines with high capacities require large amounts of materials and are not cost-effective over the long run. but their superiority over the current turbine designs has not yet been demonstrated.35 at a blade tip speed-to-wind speed ratio ranging from 5. It is important to mention that a VAWT employs an aerodynamic lifting surface to generate torque (T). Darrieus and Giromill turbines belong to this category. these turbines are best suited for battery charging applications for telecommunication masts and remote lighthouses.4 Advantages and Disadvantages of VAWTs Major advantages of a VAWT are: ◾ Elimination of yawing mechanisms ◾ High efficiency ◾ High rotational speeds that offer reduction in gear ratios In the case of Giromills with articulated blades. VAWTs overcome the difficulties of propeller-based windmills that must be pointed into the wind by orienting the axis of the rotation so that the full force of the wind can be sensed from any direction. Savonius rotors are most commonly seen as advertisement devices erected in front of businesses to increase sales. but they are reliable and easy to maintain. Such turbines may have skipping rope-curved blades or blades with variable pitch. The Savonius turbine is widely used as a starter motor for a Darrieus turbine because the Darrieus lacks self-starting capability under certain wind speed conditions. The disadvantages of a VAWT are: ◾ ◾ ◾ ◾ ◾ Tendency to stall under gusty wind conditions Low starting torque Dynamic stability problems Sensibility to off-design conditions Low installation height limiting operation to lower wind speed environments .
Computed values of power coefficient for a Darrieus rotor are summarized in Table 2. Under these circumstances.5 Operational Difficulties of VAWTs Rotation of the blades around the axis changes both the angle of attack of the aerodynamic surface and the local dynamic pressure of a VAWT.3. the load driven by the wind turbine experiences a fluctuating power input that generates a fluctuating turbine output. In the windward portion of the rotation cycle.3. The flow relationships of the various blade parameters can be realized . The calculation will yield approximate results because the analysis is based on a large number of assumptions which. Under these circumstances.6 Simplified Procedure for Predicting Darrieus Wind Turbine Performance Using the propeller theory and equating the blade forces with wake common momentum defect. the blades operate in the flow field influenced by the blade motion in the windward phase of the operation. In one quadrant of the windward portion of the rotation cycle.Design Aspects and Performance Requirements ◾ 39 2. in case of Darrieus rotors and straight-bladed turbines without blade articulation mechanisms. 2. Dynamic analysis of a VAWT is extremely difficult because of the variability of local air flow conditions as the blades rotate around the axis. This approach is as good as any other theories. A VAWT produces both drag and lift in the direction normal to the wind vector. but its ability to predict the performance parameters of a Darrieus wind turbine is not entirely satisfactory.1. the resulting flow field is very complex and it is very difficult to make accurate estimates of the inflow conditions. 2. Thus. regulation of angular rate must be performed by the load. The tip speed ratio is the ratio of the product of blade radius and angular speed of the rotor to the wind velocity. Furthermore. the extremely complex flow situation is beyond the existing analytical capabilities. the torque produced by the rotor is not steady. axial interference in flow velocity and calculated power coefficients can be calculated using first-order analytical techniques. contradict theoretical principles of fluid mechanics. A model based on this theory can be used to predict the power coefficient for a Darrieus rotor as a function of tip speed (x) and various values of initial drag coefficients. the blades advance into the wind and retreat in the other quadrant.7 Understanding Flow Phenomena of VAWTs Appreciation of the complexities involved in the flow phenomena associated with the operation of a VAWT can be obtained from a local flow vector diagram for a blade section. In addition. the blades move into a skewed flow field that undergoes very rapid variation within the installation site. in some cases. In the leeward region of the rotating cycle.3.
This model will be useful for the analysis of constant local streamline velocity.000 from a flow vector diagram for a blade section. pitch angle. Various parameters associated with a blade section include drag and lift coefficients.021 0.402 0. twist angle. and actual velocity components as a function of polar angle and twist angle. local streamline velocity.020 0.015 0. stream surface analyses connecting the forces on the blades with defects in wake momentum would probably yield reasonable approximations for power coefficients. Costeffective operation of a propeller-based wind turbine at its design point means that system parameters must allow a minimum drag-to-lift ratio to be realized over a wide range of wind speeds.175 0. rotation wind vector.315 0.353 0.370 0.375 0. This is desirable because wind speeds vary from location to location and are strictly dependent on climatic environmental parameters. small wind turbines with capacities far below 5 kW were developed by advanced European countries including Denmark.4 Off-Design Performance Off-design performance specifications offer cost-effective design configurations. off-design parameters are selected to provide high operating efficiencies at a wide range of wind speeds.374 0. The early versions of wind turbines illustrated in Figure 2.435 0. If a reasonable mathematical model could be developed for the distribution of the longitudinal and transverse interference factors.378 0.8 Early European Wind Turbines In the early 19th century. Germany. chord line. Farm types.5 had limited applications because of low power output capabilities and poor efficiencies.3.382 0.1 Calculated Power Coefficient Values of Darrieus Rotors Initial Drag Coefficient Tip Speed Ratio 3 4 5 6 7 8 0.305 0. 2.40 ◾ Wind Turbine Technology Table 2. Dutch types. and others.433 0.400 0.000 0.162 0. and two-bladed turbines constitute the early versions. . 2.010 0. Belgium.221 0.
3 Impact of Drag and Lift Coefficients on Maximum Power Coefficient Maximum power coefficient for a turbine rotor is the most critical performance parameter [2]. Preliminary studies performed by the author indicate that variations of the power coefficients of fixed pitch wind turbines occur with variations in tip speed ratios.4. even when the angular rate of the turbine may vary if the demands of electrical loads are compatible.1 Critical Design Aspects The off-design concept offers optimum performance over a wide range of wind speeds. but are readily discernible. 2. and angular rate. deployment of such generators is limited to medium wind turbines with outputs from 50 to 60 kW. These maxima tend to be less sharply defined at lower values of this ratio. the variations in Reynolds numbers introduce deviations from the anticipated optimum turbine performance. variable input speed. When wind turbines are used to generate large amounts of electricity.2 Impacts of Variations in Design and Operating Parameters Wind turbine performance parameters are affected by variations in tip speed ratio.Design Aspects and Performance Requirements ◾ 41 2. Because of high costs. constant frequency output generators. These generators are widely used in military and commercial aircraft.4. However. This situation may be alleviated somewhat by the recently developed. Large propeller-based wind turbines achieve such control by implementing blades with pitch variability. It is interesting to note that considerable latitude exists in the combinations of airfoil characteristics and tip speed ratios that will result in high operating efficiencies over a wide range of wind speeds.4. Small wind turbines with fixed angles operate at off-design conditions whenever wind speeds deviate from the nominal value. Designs of wind turbines incorporating some selected airfoil sections with a particular . it is necessary to deliver the electrical power at a fixed voltage and frequency compatible with utility grid operating requirements. but these are of secondary importance in turbines with high capacities. fixed pitch angle. The studies further indicate that a tip speed ratio greater than unity means that a constant angular rate turbine is operating at wind speeds below the nominal value. 2. electronically controlled. under these operating conditions. This coefficient determines the optimum performance of a turbine under all operating and design parameters. Maximum power coefficient for a turbine rotor can be achieved at increasing values of the tip speed ratios as the drag coefficient-to-lift coefficient ratio (CD/CL) decreases. Large wind turbines are designed to link to main electrical power grids and thus the frequency must be synchronized precisely.
. Turbine designers have proposed four distinct augmentation schemes: ◾ ◾ ◾ ◾ Concentrator Aerodynamic lift auxiliary Ejector and diffuser Shrouds Each augmentation scheme includes an almost unlimited number of variations as new concepts appear continuously. and 0.0. 0. The operation of such turbines under off-design conditions presents an interest engineering problem that heavily influences the overall system design considerations. this illustrates the extreme sensitivity of relatively inefficient wind turbines to variations in operating conditions.1 radian or 5.03. At first glance. These curves will indicate the off-design procedures that must be followed to arrive at an acceptable design for achieving optimum performance. Both the low energy density of the winds and the relatively low theoretical upper limit on the extraction of wind power have generated considerable interest in augmentation of the power output levels of the rotors. 2. However. the concentrator schemes involve additional weight that will add to tower and foundation cost and may force a turbine installer to consider another option for the ground plane location. respectively. and 3. the angle of attack must be selected close to 0.0. Concentrators must be viewed as techniques to gain additional power from a given rotor through the use of passive and inexpensive aerodynamic surfaces.5926 [2]. The three distinct values of this ratio of 0. Typical configurations channel large quantities of flow into the rotor assembly and thus increase its output power because both flow rate and flow speed are increased.01. For airfoil sections capable of achieving minimum drag-to-lift ratios.4.42 ◾ Wind Turbine Technology drag-to-lift coefficient ratio over the entire length of a blade would select tip speed ratios corresponding to the maximum values of system performance. 3. a variation of the power coefficient of a turbine may occur through variation in the tip speed ratio. which sets the upper limit on the flow rates that can be handled.4 Performance Enhancement Schemes It is important to remember that the kinetic energy of the wind is used to drive a wind turbine. Because of the inlet and fractional losses.05 are associated with design tip speed ratios of 5. that correspond approximately to the maxima. However. comprehensive examination revealed that the overall momentum and the energy balances limit the power coefficient of the projected inlet area to the Betz-Lanchester limit of 16/27 or 0. Curves representing the power coefficient versus the tip speed ratio depend strictly on the airfoil sections and demonstrate the trend of the power coefficient. this limit cannot be achieved in theory because the air flow exiting the rotor must be diffused to ambient pressure.73 degrees.5. Furthermore. this appears an easy method for increasing the output power of a turbine rotor.
All these concepts are intended to provide more efficient and reliable operation of a wind turbine. a 10-ft radius wind turbine with a 50-ft radius blade and a 285-ft long diffuser with a divergence angle of 8 degrees will not likely be competitive with a 50-ft radius simple propeller. However. desirable terrain features. on the basis of the projected area of the recommended device it is important to note that the upper limit on wind energy extraction is limited by the laws of physics. ◾ Ejector ducts: duct dimensions must be selected to facilitate the mixing of spent flow from the turbine with the incoming wind stream and send the mixture through a diffuser in the anticipation that the average energy of the flow will be sufficient for diffusion to the free stream pressure.5 Techniques for Capturing Large Amounts of Wind Energy Techniques capable of capturing the large amounts of wind energy will be investigated with emphasis on costs and safety factors. visual impacts will eliminate various forms of shrouds from serious consideration. To meet this operational criterion. the main effect is to increase the wind energy capture area. For example. and annual energy capture. Note that the ratio for actual energy captured by a wind turbine to that which could be captured is very critical. Selection of an ideal location for a wind turbine installation is very important. Furthermore. The precise alignment of such a device to ensure optimum wind input poses a serious and risky challenge.Design Aspects and Performance Requirements ◾ 43 Certain augmentation concepts must be explored to improve starting torques and power coefficients over a wide range of tip speed ratios: ◾ Stationary surfaces: flow is channeled into the active elements. If the above devices are considered stationary but include orientation provisions to achieve a certain turbine power output with a small rotating element. . the wind speeds must be within the optimum range throughout the year at the designated location to enable the turbine to operate at its maximum power coefficient. ◾ Diffuser ducts: they are attached downstream of the turbine in the hope that the spent flow will diffuse to ambient wind pressure more efficiently than it would on its own accord. then their implementation may be justified. The selection process must consider factors such as wind speed and direction. the additional cost and weight imposed on tower and foundation represent serious disadvantages. nearby residential areas. 2. While some of these augmentation devices offer some improvement in turbine performance. ◾ Inlet ducts: dimensions of the inlet ducts must be selected to capture a larger stream tube or wind energy. In addition.
AT = Turbine blade area.6 Power coefficient as function of total blade area and blade tip speedto-wind speed ratio. and other issues.6. blade parameters. Note that large blade areas yield both greater power outputs and improved power coefficients but over a narrow range of tip speed ratios as illustrated in Figure 2. they all play important roles in efficient capture of wind energy by a wind turbine. airfoil characteristics. Power coefficient is dependent on several factors such as installation site features. rotor blade areas. CP Total blade area = 1000 Ft2 600 Ft2 300 Ft2 Ratio of Blade Tip Speed-to-Wind Speed Figure 2. flow rate. Impact on power coefficient and power delivered due to rotor blade area. pressure drop at turbine. Vo = Wind speed. flow rate. wind speeds from 20 to 30 m/min are recommended by installers—this is the most important site selection requirement. Other selection parameters include installation height. Cp = Power Delivered/½ρATVo3 Turbine Blade Area Small Large Optimum Flow Rate High Low Optimum Pressue Drop at Turbine Small Large Optimum Power Delivered Low Low Optimum Cp <0 59 <0 59 0 59 Symbols: p = air density (Kg/meter3). Turbine blades with smaller areas provide lower power coefficients over a wider range of tip speed ratios. and aerodynamic requirements. and pressure drop at the turbine can be seen in Figure 2. .7 Impacts on power coefficients. angle of attack.7. Figure 2. Power Coefficient.44 ◾ Wind Turbine Technology Power Coefficient.
O = 0.01.5X.1 Impacts of Blade and Angle Parameters on Performance Capabilities It is important to mention that the pitch angle is variable in an articulated blade Giromill wind turbine. The drag coefficient C d for a blade can be written: Cd = [CD. performance deteriorates at low Reynolds numbers. πA R = 30 and Nc/2R = 0. and A R is the area of the rotor.2) where R is the blade radius. which is strictly a function of the tip speed ratio (x). x is equal to 1.0.2. the variation of the relative flow about the blade section can be seen in the four quadrants of the flow cycle for an identical local streamline velocity. The aerodynamic performance of the rotor blades is a function of Reynolds numbers. Calculated values of power coefficient [2] for a VAWT at an optimum as a function of tip speed ratio are shown in Table 2.Design Aspects and Performance Requirements ◾ 45 2. Actual velocities vary significantly as a function of polar angle.0 + (CL2/πA R)] (2. and θ is the polar angle that exerts a significant impact on the velocity variations in the leeward portion of the cycle. 0 is the initial value of the drag coefficient. X is the tip speed ratio and is equal to (Rw/V).3) allows calculation of power coefficients for a VAWT. and V is the wind velocity experienced by the rotor blades. C is the local blade cord.5. The important performance parameter for a VAWT is the power coefficient. The equation for the power coefficient [1] for a vertical axis wind turbine is very complex and can be written as: C = (Nc/2R) (Xw) [CL sin(θ) – (CD. Various parameters involved in Equation (2. but no variation is present in a Darrieus rotor.0+CL2/πA R) (x + cos(θ)] (2. R is the blade radius. CL is the coefficient of lift. The slope of the lift coefficient CL is strictly dependent on the angle of attack and its typical value is about 0. The expression for the tip speed ratio can be written as: X = [Rw/V] (2. Furthermore.075 Inserting these parameter values in Equation (2.67 for a Darrieus rotor. CD. Since the Reynolds numbers range from low to high based on wind environments. w is the angular velocity of the rotor.3) have typical values as follows: CL = 4. the current analytical techniques in vertical axis wind turbine engineering are far from satisfactory. .3) where N is the number of rotor blades. particularly in the leeward portion of a cycle.1) where CD.
435 0.416 0.168 It is important to note that the values of the power coefficients for VAWTs are generally lower than those for HAWTs for a given drag-to-lift ratio (ε) because of the reasons cited above.01. All these calculated values of power coefficient assume an angle of attack equal to 0.03. At a drag-to-lift ratio of 0.335 0.2 Calculated Values of Power Coefficients at Optimum Drag-to-Lift Ratios for VAWTs Tip Speed Ratio (X) 2 3 4 5 6 7 8 Power Coefficient 0.55 and better is possible when the drag-to-lift ratio is maintained at 0. Calculated values of power coefficients for a HAWT as a function of tip speed ratio (X) and drag-to-lift ratio (ε) are shown in Table 2. Furthermore. It is evident from tabulated data [2] that the maximum power coefficient of 0. Based on these findings.45 occurs when the tip speed ratio has a value of 3 and the drag-to-lift ratio equals 0. An angle of attack equal to 0. Power coefficients for HAWTs are higher than those for VAWTs irrespective of the drag-to-lift ratios and tip speed ratios.46 ◾ Wind Turbine Technology Table 2. Note that the power coefficient for a horizontal axis wind turbine still maintains an acceptable value even when the tip speed ratio varies from 2 to 10.347 0. Note that at a drag-to-lift ratio of 0. the power coefficient retains a minimum value of 0. VAWTs are generally less efficient than HAWTs.05. In a HAWT case.73 degrees offers optimum performance for a HAWT.1 radian or 5.05 drag-to-lift coefficient (ε).3.247 0. acceptable power coefficient values are possible only over a very limited range of tip speed ratios. angle of attack (α) plays a critical role in shaping performance.1 radian or 5. It is evident from these data that as power coefficient of 0.73 degrees . This is the most critical design issue for choosing between VAWT and HAWT systems. we can conclude that maximum values of power coefficients are possibly only for HAWT systems operating over a wide range of tip speed ratios when the angle of attack is kept close to 5. In brief.418 0. acceptable power coefficient can be achieved over a tip speed ratio between 2 and 5.73 degrees. at the 0.5 over a wide range of tip speed ratios.01.
Design Aspects and Performance Requirements ◾ 47 Table 2. One can now visualize the advantages of HAWT installations.45 0.45 0.38 0. wind speed.01 0. and highvelocity wind flow regions such the Gobi Desert in China.3 Power Coefficient (CP) as Function of Various Parameters of HAWTs Drag-to-Lift Ratio (ε) Tip Speed Ratio X 2 3 4 5 6 7 8 9 10 0.53 0. ridges. The studies further indicate that power coefficients depend strictly on blade area and blade tip speed-to-wind speed ratios.53 0.44 0.3 Installation Site Requirements for Optimum Performance Most desirable installation sites for wind turbines include hills.05 0.34 – – – – 0. and wind energy captured.44 0.43 0. Note the exit pressure coefficient and interference factor to some extent are dependent on the .8. 2.03 0. maximum annual capture of wind energy is possible only when a wind turbine can operate over a wide range of tip speed ratios.6. flow rate. pressure drop at the turbine.01.31 and the drag-to-lift ratio equals 0. In addition. Studies performed by the author indicate that the power coefficient is dependent on turbine blade area.55 0.5.49 0.5.27 – – – – – 0. Power coefficients for wind turbines as a function of total blade area and blade tip speed-to-wind speed ratio are shown in Figure 2.56 0. Impacts of terrain features on desirable locations for wind turbines are shown in Figure 2.46 0 51 0 50 0.2 Techniques for Achieving High Power Coefficients A selected installation site must provide a blade tip-speed-to-wind speed ratio between 5 and 7 throughout most of the year to catch maximum wind energy needed for higher power coefficients.55 0. 2. The overall impacts on the power coefficient from various parameters can be seen in Figure 2.7.
3. Increases in wind speeds close 200% have been observed at the peak of a ridge. turbine installation parameters. It is critical to mention considerable variations in wind speed as wind travels over ridge sections. The power coefficient is also dependent on these two parameters as illustrated in Figure 2.5. 2. .48 ◾ Wind Turbine Technology Smooth surface High velocity (a) Well rounded hill or ridge (suitable site) High velocity Reverse flow (b) Hill or ridge with abrupt sides (unsuitable site) High velocity Reverse flow region (c) Sharp peak-could be suitable Figure 2. The winds accelerate as they pass over the ridge.1 Wind Parameters over Ridges and Hills Significant improvements in speed and direction may be noted as wind approaches hills and ridges. wind speeds may double as the flow accelerates up the gradual slope of a long ridge.8 Impacts of terrain features. Studies by wind turbine designers indicate that wind speed increases near the summit of a long ridge lying across the wind path. and accelerate even more when they pass around the end regions of the ridge [3]. The studies further indicate that the wind speed increases as it approaches the front of the ridge and attains its highest speed as it reaches the peak.9.
high wind speeds are highly desirable for wind turbines with output capacities ranging from 2.15 2.05 1.25 3.5 to 3. Regions with higher wind speeds are considered prime sites for wind turbine installations and are best suited for high-power installation.2 0. CP 3. In brief.5 MW. It is important to mention that average wind speeds of 20 to 30 mph are most desirable for safe operation of high-power turbines. but also have stronger wind environments.20 Interface Factor.0 0.5 0.Design Aspects and Performance Requirements ◾ 49 0. Terrain . Farmers living in ridge regions observed that this enhancement occurs only in the top third of the slope near the crest.9 Impacts of exit pressure coefficient and interference factor on power coefficient.3 Exit Pressure Coefficient' C 0 Pr Figure 2.5 0.10 1.0 0. a 2.0 0.5 0.0 0.1 0.5 0 0.5 Power Coefficient. Mountain passes can accelerate winds up to 100 mph (50 m/sec) during storms associated with the cold fronts. Ridge tops may not only experience more frequent winds.35 4.30 4.
Normal air flow prevails above an inversion layer.5.4 Fundamental Properties of Wind Energy Performance capabilities absolutely depend on the properties of wind energy. Turbulent installation sites must be avoided in the interest of preventing personal injuries and structural damage.3. The average wind speed can change as much as 25% from one year to the next. winds are generally light during the summer and fall and increase during the winter. thereby producing higher acceleration conditions which can create dynamic instability for a turbine tower structure. Convective circulation leads to a dramatic difference between daylight and night wind speeds. It is interesting to note that increased wind speeds have been observed during late afternoons because of convective heating effects. winds are dominated by storm systems that can produce turbulent conditions. Generally the average wind speeds vary by season and by month. Meteorological data indicate that the average wind speed consistently exceeds 12 m/sec from April to August. Convective circulation is poor in winter. while the summer is not. Accurate information on wind speed and direction gathered over 10 years or more should be reviewed by meteorologists before a site can be selected for a wind turbine installation. reaching the maximum in the spring. During winter and spring. Mountains and ridges offer higher winds for reasons cited above other than channeling effects. Inversions are most common during fall and winter in northern latitudes. early spring in March is windy. Turbulence can seriously damage tower structures and turbine components.5. Sometimes an inversion layer may accelerate the wind. This means one can expect more wind energy to be captured by a wind turbine during those months. For example. 2. The air beneath an inversion layer may be completely cut off from air circulation within a weather system moving through the area. Wind turbines operate on the theory of fluid mechanics [3] and therefore preliminary .50 ◾ Wind Turbine Technology features that enhance wind speeds can also create turbulence that may wreak havoc on wind turbines. Both regions are notorious for their air pollution episodes. 2. Wind turbines may succumb in consistently turbulent environments. Temperature inversions cause stratification of the atmosphere near the surface and can affect wind environments. For most interior regions in North America. The wind is an intermittent resource. below the layer the winds are stagnant—a condition detrimental to the efficient operation of a wind turbine. Prominent peaks often pierce temperature inversions that can blanket valleys and low-lying plains.2 Variations in Wind Speed and Direction Wind speed and direction are subject to change over most measurement durations and under different weather seasons. This can total more than 2 mph (1 m/sec) in a moderate wind regime where average wind speed of 10 mph (5 m/sec) is the norm. Temperature inversions are common in hilly and mountainous terrains such as Southern California and Western Pennsylvania.
and V is the wind speed.1 Available Wind Power The kinetic energy of the wind (EK) can be written as: EK = [(1/2) mV2] (2. 2.225 Kg/m3).4.6) 2.7) that available wind turbine power is directly proportional to air density at the installation location and the area intercepted by the wind (swept area of blade).4. approximately equal to the length of the blade. they are often used synonymously.4). The expression for mass can be written as: m = [ρ A V t] (2.5.4) where m is the mass of the air and V is the wind speed (velocity).5) where ρ is the air density (1. Although speed and velocity have distinct connotations and distinct meanings. As the blades of the wind turbine move through the air.Design Aspects and Performance Requirements ◾ 51 knowledge of the fundamental principles of fluid mechanics is necessary for thorough understanding of wind turbine operation. A is the area through which the wind passes during a given period t. the power available from the wind is P = [(1/2) ρ A V3] (2.8) where A is the swept area of the turbine blade and R is the radius of the rotor. Based on this definition. the kinetic energy of the wind is converted into mechanical energy that drives the turbine coupled to an electric generator to produce electricity. Inserting Equation (2. This can be also defined as the rate of wind energy passes through an area per unit time.7) It is evident from Equation (2. As noted in Chapter 1. The swept area is be defined as: A = [π R 2] (2. the kinetic energy of the wind is used to drive turbines. the expression for kinetic energy can be written as: EK = [(1/2) ρ A t V3] (2. The rotor blades spin about the .2 Power Generated from Wind Energy A wind turbine designer is extremely interested in the amount of power he can generate from the wind energy available. The available power is proportional to the cube of wind speed V.5. Note power is defined as the rate of wind energy available per unit time.5) into Equation (2.
On a yearly average.2.5.2. is best suited for a wind turbine installation. which is located at higher altitude but at lower altitude. a power increase of 95. Wind turbines with large rotors intercept more wind than those with smaller rotors and consequently capture more power from the wind. assuming 100% air density at sea level. at the same wind speed. Close examination of the parameters of Equations (2.2.8) reveals that significant wind power can be generated by deploying longer blades at installation sites where high winds are prevalent. seasonal changes in temperature produce negligible effects on the power available from wind. 2. In other words. Even if the wind speed increases by 25%. Note that air is less dense in summer than in winter.2 Impact of Swept Area on Power from Wind Any variation in the swept area of a wind turbine will influence the power available from wind.5.3% is achieved. That is why the Chinese installed several wind turbines capable of producing more than 10. Doubling the area swept by a wind turbine rotor will double the power available from wind according to Equation (2. Thus. more wind power is available at a coastal site than a site in Denver.4. Colorado.7). In other words.5. a place like the Gobi Desert. increasing altitude has more effect on air density than average temperature. power available from wind is proportional to the third power of the wind speed. the power available will increase by a factor of eight (2 × 2 × 2 = 8). located 5000 feet above sea level.7).3 Impact of Wind Speed and Distribution on Power Available According to Equation (2. This indicates that even a slight change .4. and 94% at 610 m. For example. It is important to mention air density exerts negligible impacts on performance because most high-power wind turbines are installed at heights around 250 ft. if the wind speed is doubled. 2.000 MW annually in that region. 97% at 305 m. doubling the rotor radius will increase both the power from the wind and the swept area by a factor of four.52 ◾ Wind Turbine Technology horizontal axis and sweep a disc-shaped area equal to the area of a circle with a radius equal to R. This principle is fundamental to understanding the wind turbine design concept.7) and (2. 2. Meteorological data reveal that air density changes little as installation height increases.4. Furthermore. The relative change in air density is about 99% at an installation height of 152 m.1 Impact of Air Density on Power from Wind Meteorological data indicate that air density decreases with increasing temperature and increasing altitude. This means higher air density occurs at turbine sites located at lower altitudes with cooler temperatures.
Wind speed distribution studies performed by the author indicate that speed distribution plays a very important role in determining the power from wind and it is always preferable to use an actual measured distribution at a specific site to achieve more accurate and reliable power estimates.5.5. Clearly. 2.10) V is the average wind speed at sea level. where V is expressed in meters per second (m/s) (2.7) and (2. Some wind turbine project managers claim that their estimates using Rayleigh distribution were only about 5% less than the power actually produced. the monthly estimates were found less reliable.1 Rough Estimate of Power Density—Exact calculation or estimate of the power density from a wind turbine is very difficult because of variations in wind speed as a function of time.0547) V3]. Under these conditions.2. This relationship holds for many sites with moderate to strong average annual wind speeds.4.9) can provide a rough estimation of power density.2. wind turbine installation sites with higher average annual wind speeds must be given priority because of the availability of higher wind power levels throughout the year. However.Design Aspects and Performance Requirements ◾ 53 in the average annual wind speed can produce a significant boost in power from the wind. where V is expressed in miles per hour (mph) (2. The Rayleigh distribution produces fairly reliable estimates when used to project annual power generation from small wind turbines.8).4. an empirical formula defined by Equation (2. 2.9) P/A = [(0. but in general follows a bell-shaped curve for a family of Rayleigh distributions at sites with different wind speeds. Assuming a sea level air density of 1.225 Kg/m3and a temperature of 60°F and inserting these values in Equations (2. Note these two equations are valid up to turbine heights close to 150 feet because the error in air density is less than 1%.6125) V3]. For .4 Rayleigh and Weibull Distributions for Estimating Wind Speeds The distribution of winds at various speeds differs from one site to the next. the expression for the power density (P/A) in watts per square meter (W/m2) may be written as: P/A = [(0. Estimates prepared based on measured distribution and Rayleigh distribution curves can exhibit huge differences. It is interesting to mention that the power density (P/A) calculated from the Rayleigh distribution curve for a given average wind speed is almost twice that derived from the average wind speed alone.4. Note the Rayleigh distribution is a hypothetical distribution of wind speeds based on a mathematical formula that tends to approximate the real world. The Rayleigh distribution tends to overestimate power generation by 10 to 20%.
5 Models for Calculating Power Density Power density from a wind turbine can be calculated in two ways.9(0.9. but meteorologists often prefer a more flexible mathematical formula called the Weibull distribution that more closely models wind turbine speeds at a wide range of installation sites.12) Using Equations (2. the curve shifts toward the higher wind speeds on the right side of the curve. The relationship between the power density derived from the average speed alone and that from a speed distribution curve is commonly known as the cube factor or energy pattern factor. Note the average annual wind speed defines the shape of the Rayleigh distribution curve.9 cube factor into Equations (2. Rayleigh distribution at high-wind locations tends to overestimate power density by 10 to 20%.2. .10). It is well established that the cube factor for the Rayleigh distribution is 1. Inserting the 1.9. One can also use the average wind speed and the cube factor for the Rayleigh distribution of 1. where V is in m/s (2.0547)] V3. 2. The power density calculated from the Rayleigh distribution curve for a given average wind speed is almost twice that derived from the average wind speed alone.5. a measured distribution produces a power density of 320 W/m2.12).54 ◾ Wind Turbine Technology example.4. As stated before. twice the result from a Rayleigh distribution (160 W/m2) under the same average speed of 5.9(0.4 instead of 1.6125)] V3.3 m/sec (12 mph).11) (2.9) and (2. one knows the average annual power density at a prospective site and can quickly estimate how much power a typical wind turbine can extract from the wind at that location. Close examination of this curve indicates that as the average annual wind speed increases. It is interesting that the Rayleigh distribution is a member of the Weibull family of speed distribution concepts. That is why the relevant cube factor is 2. where V is in mph Average annual P/A = [1.4. Rayleigh distribution remains a useful tool for most wind turbine sites. Note that site C is located in mountain passes subjected to funneling effects that cause more occurrences of winds at high speed than would be predicted by the Rayleigh distribution curve. One can sum a series of power density calculations for each wind speed and its frequency of occurrence (number of hours per year the wind blows at that speed) for the prospective site's distribution of wind speeds.11) and (2. The impact of speed distribution on power density for various sites with the same average annual speed is evident from the data summarized in Table 2.9. average annual power density (W/ m2) can be estimated using the following modified equations: Average annual P/A = [1.
However. When temperature inversion occurs in calm wind environments.4 2. buildings and other obstructions in its path. thereby yielding significant performance in terms of annual output power.3 6. the change in wind speed as a function of height known as wind shear is less pronounced and more erratic. Friction effect is higher around tall trees and building structures than it is over the smooth surface of a lake or coastal region. and thus detrimental to turbine performance. wind speeds more than 200 ft (60 m) above the ground decreased with increasing height.4 1. The following equation is useful for estimating the increase in wind speed as a function of tower height: V/V0 = [H0/H]α (2. when the average the wind shear is positive. wind moving across the earth's surface encounters friction caused by turbulent flows over and around mountains. trees. The studies further indicate that at low wind speeds.3 6. wind speed increases with height. In certain mountain passes.5. In general.13) .4 Comparison of Impact of Speed Distribution on Power Density at Sites with Same Average Annual Wind Speeds Site A B C Average Annual Wind Speed (m/s) 6. Brief studies of wind characteristics performed by the author indicate that wind speed and installation height above the ground affect the power generating capability of a wind turbine.3 Power Density (W/m2) 220 285 365 Cube Factor 1. This means that the changes in wind speed with height are not constant. In addition.Design Aspects and Performance Requirements ◾ 55 Table 2. Wind speeds increase with height at a greater rate than wind speed rates over hilly and mountainous terrains. wind speeds may increase slightly between the ground and certain tower height and then begin to decrease. These effects generally decrease as height above the ground increases until unhindered air flow is restored. the rate at which the wind speed increases with height varies with the degree of surface roughness. In brief. It is interesting to mention that frictional effects are strictly dependent on surface roughness.9 2. That is why taller towers offer higher wind speeds and permit the deployment of larger turbine blades. hills.4.3 Impacts of Wind Speed and Installation Height on Performance The combined impacts from wind speed and installation height are very complex. wind speed increases as both the friction and turbulence decrease.
Furthermore. Note that the increases in both the speed and the exponent of wind shear (α) occur at the installation location C. A typical increase in wind speed as a function of height can be related to the anticipated increased surface roughness exponent or parameter α. Changes in the wind speed as a function of height and frictional coefficient at various locations can be seen from the data summarized in Table 2. or 25.1 Increase in Speed 1. wind speed increases more dramatically with height than the 1/7 law predicts.35 1. Wind turbine installers claim that over smooth. 2. hedges.4 6. In these situations.3 8.4.13 0.29 Parameter α 0. particularly when the wind passes over corn crops.14 or 1/7.3. When the exponent of 0. level. grass-covered terrain. V0 is the wind speed at the original height or the height of the anemometer attached to the turbine nacelle.13 0.10 0.8 5.25).6.2 6.3 150 ft 7. .24 1.20).14 is applied to the ratio of two heights of 150 and 30 ft. exceptions occur.4 7. Obstructions significantly reduce wind speeds near the ground. the result is 1. and scattered trees. indicating that the wind speed at the new height (H) of 150 ft will be 1.1 Variations in Wind Shear Law Although wind shear often follows the 1/7 (0. The increase in wind speed as the installation height increases can be related to the surface roughness exponent as illustrated by Table 2.253.7 8.56 ◾ Wind Turbine Technology Table 2.29 1.5 6.18 0.5.14) law. indicating that the ground obstructions have peculiar terrain footprints compared to other locations. and α is the frictional coefficient that varies with surface roughness and measures the friction encountered by the wind as it moves across the terrain.4 8.3% greater. the wind shear exponent may increase to 1/4 (0. the parameter α or exponent for wind shear is very close to 0.253 times that at the original height of 30 ft.5.5 Changes in Wind Speed as Function of Height and Anticipated Value of Parameter α Speed at Height (m/s) Location A B C D E 30 ft 6.16 where V is the wind speed at the new height H.24 1. When the surface is even rougher and the wind passes over more trees and few buildings. the wind shear could rise to 1/5 (0.
1 5 1.00 1.14.22 1.2 Impact of Wind Shear Exponent on Output It has been already demonstrated that the velocity at the new height will be equal to the wind shear exponent on the ratio of new height to initial height. If P0 is the power at the original height of 30 ft and P is the power at the new turbine height of 150 ft.32 1.22 1. one can expect greater power outputs at higher installation sites. 2.27 0. Note that power is a cubic function of wind speed.5 Global Wind Power Capacity Using High-Power Turbines Based on a wind turbine manufacturers' survey.20 1.966] Thus.4.10 1.26 1.Design Aspects and Performance Requirements ◾ 57 Table 2.5.00 1.3.6 Increase in Wind Speed with Installation Height Height (ft) 20 30 60 80 100 120 150 160 (m) 6 9 18 24 30 37 46 49 0.42 = [1.7). as evident from Equation (2.25 1.14) where the wind shear exponent for this particular site α is equal to 0. That is why the wind turbines with outputs exceeding 2.966 times the power at 30 ft.40 0.5. the turbine output power at a height of 150 ft will be 1.10 1.10 1. This means that the power ratio for this site can be written as: P/P0 = [150/30]0.19 1.42 = [5]0. the ratio of these two powers based on Equation (2.13 1.14.00 1.15 1.14 1.27 1.38 1.28 1.15 1. The wind shear exponent used is equal to 0.35 1.5 MW require higher installation. Present-day .17 1.19 1.00 1. General Electric and Mitsubishi are deeply involved in the manufacture of high-capacity wind turbines. Based on this sample calculation.18 Surface Roughness Exponent 0.13) can be written as: P/P0 = [H/H0]3α (2.41 1 50 1 52 2.07 1.
Data on global wind turbines operating in the high.and medium-capacity ranges are summarized in Table 2.125 4.7 Global Wing Turbine Capacities (MW) at Higher Outputs Year of Operation Country Germany Spain United States India Denmark Italy United Kingdom China Netherlands Japan Others Total 2005 12.127 9.040 7.533 high-capacity wind turbines operate in the range of 2.226 11.800 11.260 1.533 MW during 2008. A comprehensive study is required to estimate the value of .088 MW in 2005 [3].572 1.512 1.58 ◾ Wind Turbine Technology Table 2. 2.6 Annual Energy Acquisition from Specified Wind Turbine Site The question of how much annual energy can be acquired from a specific wind turbine site must be answered before any decision to proceed is made.718 1.331 8.920 72. The worldwide installed wind turbine capacity was 59.927 1.125 4. India. The power capacity numbers for 2008 are based on realistic projections and good engineering judgment.689 1.435 3.353 1.088 2008 16.436 59.975 6.6 MW. China. The answer to this question is a critical economic judgment.128 1.7. The projected worldwide installed capacity increased to 72.5 to 3.885 10.219 1. and Germany added more wind power capacity between 2005 and 2008 than other countries.482 1. A realistic answer requires preliminary engineering judgment and an economic feasibility study for the specific site.
cost-effective operation and high wind conditions are critical considerations for choosing an installation site. The maximum energy-content region for this particular wind turbine with 100-kW capacity extends from 18 to 25 mph. The estimated power output levels are depicted in Table 2. one will find a bell-shaped curve showing the maximum energy content wind region in the middle of the curve and the low energy content regions at the ends of the curve. intermediate energy content regions exist between the maximum Table 2. This curve was plotted for wind speeds from 0 to 70 mph. the design. The total wind energy available depends on the installation location and the annual variations in wind speeds and directions. 2. installation.6. and operating costs warrant detailed long-term wind surveys. development. This is the most fundamental requirement for selecting an installation location.2 Impact of Wind Speed on Wind Energy Density If a wind energy density in kilowatt hours per square foot per year (kWh/ft2/year) is plotted as a function of wind speed (mph). Detailed data on the distribution of wind speeds and directions over a period of several years at the specific site must be examined to allow accurate long-term predictions of wind energy capture.8 Estimated Power Output from Turbine with 125-Foot Diameter Rotor Wind Speed (mph) 10 15 20 25 30 Wind Turbine Power Output (kW) 22 65 185 375 596 . 2. If very large and expensive wind turbines are involved. Turbine designers have estimated wind turbine power output levels for a 125-ft diameter turbine rotor as a function of annual wind speed.1 Requirements for Long-Term Capture of Wind Energy Appreciable annual wind energy acquisition requires high wind conditions 24 hours a day every day. while the minimum energy content regions extend from 0 to 5 mph and from 45 to 70 mph. However.Design Aspects and Performance Requirements ◾ 59 the wind energy to be captured in a wind turbine lifetime relative to the initial investment.8 and demonstrate a trend in turbine output power with increases in wind speed for that specific site and rotor size.6. operating. and maintenance costs. In brief.
2. Wind turbine designers claim that the highest wind energy capture per hour or per year can be achieved when the speed at which power limiting is initiated is about 50% of the average wind speed. The energy integral is defined as the ratio of wind energy captured at final wind speed (E) to the wind energy captured at initial wind speed (E0) and it varies from rotor to rotor [1]. Y is a constant (its value varies from 0.6. the unsteady nature of the wind involves the transient responses of the wind turbine system that cannot be determined from the time integrals of wind speeds and turbine power outputs.25 m/sec in the U. Note that calculations of the energy integrals as a function of wind speed ratio provide useful information on wind energy captured per hour..6. and structures. Furthermore. The total wind energy available per hour or per year depends on the installation site. At an average wind speed of 9. Note these parameters apply only to a 100-kW system with a rotor diameter of 125 ft. the total annual . and λ is the wind speed ratio varying from 1 to 3 for this particular rotor. trees and surface conditions in the vicinity of the turbine site. fluctuations in wind speeds.5 mph or 4.3 Annual and Hourly Extraction of Wind Energy by Wind Turbine It is extremely difficult to estimate the wind energy that can be captured per hour or per year when a wide range of wind conditions is encountered. Energy content regions for wind turbines will exhibit different wind speed ranges compatible with characteristics of the bell-shaped curve of wind energy density versus annual wind speed for high-power turbines and other installation locations. 2. The energy ratio (E/E0) curve as a function of wind speed ratio (λ) can be determined for a given rotor configuration and is used to indicate whether an energy ratio near to or greater than unity can be achieved for Savonius turbine rotors.15) where z is equal to 1/λ.7 for a Savonius rotor).6 to 0. unpredicted variations in wind directions.4 Energy Integrals for Savonius Rotor in VAWT Calculations of energy integrals for Savonius rotors widely used for VAWTs can be performed using the following equation: F = [4 Y z (1 –Yz)] (2. However.S.60 ◾ Wind Turbine Technology and minimum regions. this criterion is not cost-effective because a turbine designed for such low speed would have to be very large and expensive for its nominal power output. It is extremely important to mention that the constant Y will have a very limited range of values because the upper and lower portions of the curve represent extreme wind conditions that cannot be tolerated by this particular rotor.
In brief.242 1. Assuming a maximum power coefficient of 0.7 0.9. Augmentation concepts for rotors will be discussed in detail in Chapter 3.168 0.122 0.445 1.5 Use of Vortices for Creating Regions of High Wind Velocity As noted. higher wind speed of velocity will cause a wind turbine to generate more power. wind tips.474 0. In brief. or delta wings. Similarly values of the energy integrals can be obtained for other types such as upwind or downwind rotors deployed by HAWTs.0 15 2.6 0.692 1.6.102 0.8 0.393 1. 2.4 energy flow is around 38. The approach of using the ejectors or ejector–diffusers incorporating aerodynamic surfaces has been most successful for augmenting the power output of a turbine by increasing the pressure drop across the rotor as shown in Figure 2.205 1. the total annual wind energy capture by a wind turbine would be about 11. Higher wind speeds can be achieved by increasing tower heights or using augmentation techniques incorporating aerodynamic surfaces or vortices generated by buildings. Since the maximum power coefficient for a HAWT is close to 0.427 1.9.425 0.Design Aspects and Performance Requirements ◾ 61 Table 2.654 1.6 kWh/ft2 of swept area.0 25 3.6 kWh/ft2 of swept area. thus increasing wind speed and enhancing the power output capability of the turbine.732 1. this is considered as an approach to augmenting the power output of a rotor. A more promising approach seems to be the use of tip vanes—aerodynamic surfaces placed on the tips of the blades at such an angle that their lift tends to turn the wind into the rotor.77 kWh/ft2 of swept area.59 as illustrated in Figure 2. the total annual wind energy captured by a HAWT would be 1.3 (typical for a Savonius rotor). The potential effectiveness of such augmentation elements can be easily estimated when the Bernoulli equation is written for the flow ahead of the rotor and then for the .9 Energy Integral as Function of Wind Speed Ratio for Savonius Rotor Values of Constants Wind Speed Ratio (λ) 1.967 times more than that achieved by a Savonius rotor with the same average wind speed of 9.5 mph.7. the HAWT would capture total annual wind energy close to 22. The energy integral (E/E0) values for a Savonius rotor as a function of wind speed ratio (λ) are shown in Table 2.214 1.0 0.
respectively.10. The expression for calculating power coefficient can be written as: CP = [4a (1 –a)2 – (1 – a) cpr] (2. respectively. Computations of power coefficient require appropriate values of interference factor (a).16b) where P0.6. The result is: [P´ – P˝] = (ρ V02/2) [(2 q/V0) (1 – q/2 V0) – cpr] (2. Its expression can be written as: Cpr = [(P1 – P0)]/[ρVo2/2] (2.6 Maximum Power Coefficient as Function of Exit Pressure Coefficient and Interference Factor (a) Power is defined as the rate of work done by the fluid moving through the rotor. V0 and P1.333 (1 + cpr)2] (2. The parameters P´ and P˝ are the pressures immediately ahead of and immediately behind the rotor.16a) (2. 2.6.17) where cpr is the exit pressure coefficient across the rotor. Computed values of the interference factor a as a function of exit pressure coefficient are depicted in Table 2. the maximum power coefficient occurs at a value of interference factor a whose empirical expression can be written as: a = [2/3 – 1/3 (1 + cpr)2] = [ 0. V´ are the pressure and wind velocities very far ahead of and very far behind the rotor.62 ◾ Wind Turbine Technology downstream flow in the same form.20) .7 Computations of Power Coefficients Power coefficients are functions of exit pressure coefficients and interference factors. When these two Bernoulli equations are solved for the pressure drop without the assumption of P0 equal to P1. The velocity of the rotor is denoted by V´. However.19) where cpr is the exit pressure coefficient. The Bernoulli equations for both flow conditions can be written as: [P0 + PV02/2] = [P´ + ρV´2/2] [P1 + ρ (V0 – q)2/2] = [P˝ + ρV´2/2] (2. The velocity deficit at the location of P1 is defined by the parameter q.18) 2.666 – 0.
332 0.054 0.396 0.014 By inserting various values of interference factor a.3 0. but the power coefficient referenced to the enormous area was inferior to that of a free turbine system.448 0. Techniques involving ejectors for the wind turbines must be first analyzed in terms of energy and momentum balances.266 0.1 0. power coefficient can be computed as a function of exit pressure coefficient.6.432 0. The enormous size and additional weight of an augmentation device could be justified.272 0.3 0 588 0 518 0.144 0.378 0.186 0.4 Interference Factor (a) 0.2 0 512 0.2 0.308 0.4 0.7. Computed values of power coefficients are summarized in Table 2.11.10 Computed Values of Interference Factor as Function of Exit Pressure Coefficient Exit Pressure Coefficient (cpr) 00 0.324 0.336 0.234 0. 2.215 0. High potential gains from the use of diffuser–ejector schemes may be illusory if a complete wind turbine system study is not performed.008 .Design Aspects and Performance Requirements ◾ 63 Table 2. A comprehensive study can be performed within a shroud that acts like an ejector with a constant area mixing duct followed by a diffuser. Studies performed by various wind turbine scientists [4] indicate that the power outputs of wind turbines could be augmented by a factor of 10 to 20.1 0.1 0.103 0. Table 2.333 0.2 0.3 0.4 0 576 0 516 0.456 0.1 Techniques for Enhancing Power Output and Power Coefficient Certain potential augmentation techniques using aerodynamic surfaces may be deployed to enhance the power output levels and the power coefficients of wind turbines.11 Wind Turbine Power Coefficients Interference Factor (a) Exit Pressure Coefficient (cpr) 00 0.
21) allows annual hours to be calculated. and various values for c in Equation (2.27.10(d) shows annual hours when c equals Table 2. Inserting a fixed value of 8760 for a. this particular augmentation technique confines the turbine installation to ground level. Figure 2. 0. Table 2.7738 for maximum hours. and c values range from 1 to 5. Wind energy captured hours have been plotted as a function of wind speed and various values of parameter c.7738 for b.12 shows calculated annual hours for capturing wind energy. Figure 2.12 Annual Hours for Capturing Wind Energy Values of Parameter c Wind Speed Ratio (λ) 0 1 2 3 1 8760 7188 5894 4834 2 8760 7188 3964 1470 3 8760 7188 1792 41 4 8760 7188 366 00 5 8760 7188 15 00 .10(a) shows annual hours when parameter c equals 1. a represents the annual hours (8760 = 365 days × 24 hours).7 Estimating Annual Hours of Capturing Wind Energy Preliminary estimation of annual hours that could be expected to capture the wind energy at a potential installation site is critical for justifying the capital investment and ensuring cost-effective operation.10(c) shows annual hours when c equals 2. b has a typical value of 0.10(b) shows annual hours when c equals 2. z (λ) is a function of wind speed and is equal to λc. 2.7. thus reducing the kinetic energy available from the wind due to lower wind speeds. Figure 2.1 Annual Hours Estimation Using Empirical Method The annual hours to capture wind energy can be calculated from the following empirical expression: H (λ) = [a bbz(λ)] (2.21) where λ is the wind speed ratio that typically varies from 1 to 3 for maximum hours. Annual hours to capture the wind energy from a particular site are based on wind speed ratio and other variables.64 ◾ Wind Turbine Technology However. Figure 2. 2.
5 λ 2 2.10(a) Plot of annual hours as function of wind speed ratio when factor c is: (a) equal to 1.5 1.103 ?? 1 1.5 3 Figure 2.Design Aspects and Performance Requirements ◾ 65 H(λ) 0.5 4 Figure 2.10(b) (continued) Plot of annual hours as function of wind speed ratio when factor c is: (b) equal to 2. H(λ) 1.5 λ 3 3. .5 2 2.
10(d) (continued) Plot of annual hours as function of wind speed ratio when factor c is: (d) equal to 3.5 λ 3 3. . 100 H(λ) 10 0.1 0.5 4 Figure 2.01 1 1.27.10(c) (continued) Plot of annual hours as function of wind speed ratio when factor c is: (c) equal to 2.66 ◾ Wind Turbine Technology H(λ) 100 10 1 1.5 2 2.5 2 2.5 4 Figure 2.5 λ 3 3.
10–12 1. From this function the probability [f (Vi < V0 < Vi+1)] that the wind speed lies between Vi and Vi+1 can be computed. the principal objective of a wind turbine installer is to select an installation site that offers maximum annual hours for capturing wind energy over a wind speed ratio between 1 and 2.27 at wind speed ratios between 1 and 2.5 2 λ 2.10–3 1.5 3 3. and Figure 2.10–11 1. The plots indicate that the maximum duration of annual hours as a function of wind speed ratio can be achieved when parameter b is unity instead of 0. We can conclude from these plots that maximum hours to capture wind energy are possible when parameter c varies from 1 to 2.10–4 1.10(g).10–9 1.10–10 1.10–13 1.104 1. 3.10–16 1.2 Annual Energy Production Estimate Using Blade Element Momentum Method It is possible to generate a power curve using the blade element momentum (BEM) method to estimate shaft power as a function of wind speed V0. In summary.7.10–14 1. Note these plots merely provide preliminary estimates for the annual hours over which wind energy can be captured.10–18 1. To compute annual wind energy production.10–8 1. .10(e) shows annual hours when c equals 4.10–6 1.10–5 1. it is necessary to combine the production curve with a probability density function of the wind. 2.10(e) shows annual hours when c equals 5.7738 and parameter c equals 2 as in Figure 2.10–15 1.5 4 Figure 2.10–17 1.10–7 1.10–19 H(λ) 1 1.1 0.Design Aspects and Performance Requirements ◾ 67 1.01 1.103 100 10 1 0. Figure 2.10(e) (continued) Plot of annual hours as function of wind speed ratio when factor c is: (e) equal to 4.
10–13 1.10–15 1.10–11 1. .10–12 1.10–14 1.103 100 10 1 0.1 0.5 2 2.5 3 Figure 2.10–4 1. H(λ) 0.10(g) (continued) Plot of annual hours as function of wind speed ratio when factor c is: (g) equal to 2.10–8 1.10–3 1.10–6 1.10(f) (continued) Plot of annual hours as function of wind speed ratio when factor c is: (f) equal to 5.5 λ 1.10–16 1.10–5 1.5 3 Figure 2.68 ◾ Wind Turbine Technology 1.10–9 1.01 1.10–17 H(λ) 0 0.10–7 1.10–10 1.5 1.5 λ 2 2.104 1.
Histogram and Weibull distribution function. the probability density function for the wind can be written as: f(Vi < V0 < Vi+1) = [ exp(-(Vi/A)k)] – [exp(-(Vi+1/A)k)] The total annual energy production (AEP) can be calculated as: AEP = [∑I = 1N-1(1/2) P (Vi+1) + P (Vi) × f (Vi < V0 < Vi+1) × 8760] (2.23) (2. The probability density function of the wind is determined by a Rayleigh or Weibull distribution. From the Weibull distribution.N). with a typical speed interval of 1 m/sec. vegetation. Multiplying the probability function by the power (in kilowatt hours) produced by the wind speeds ranging from Vi to Vi+1. Multiplying this with the total hours per year (8760) yields the number of hours per year that the wind speed lies in the interval Vi < V0 < Vi+1. In brief. a probability density function that the wind speed lies between Vi and Vi+1 and a shaft power curve are needed to compute annual energy production for a specific wind turbine at a particular site. one can determine the contribution of total production (in kilowatt hours) for this speed interval. and structures can be modeled through a scaling factor A and form factor k. It is important to mention that the Weibull offers a more accurate probability density function because some corrections for landscape. The combined efficiency of these two components is approximately 90%.Design Aspects and Performance Requirements ◾ 69 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Profitability (%) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Wind Speed (m/s) Figure 2.22) . Note that wind energy production must be corrected for the losses at the generator and gear box.I = 1. The wind speed can be discretized into N discrete values (Vi.11 Wind speed defined by widths of columns.
Based on these tabulated shaft power data.5 m ◾ Rotational speed = 27. However. except at very low wind speeds. significant engineering skill and design and development experience are necessary to calculate reliable data for thick airfoils with high angles of attack including three-dimensional factors such as the rotational effect. it is desirable to use a very thick airfoil of approximately 40% of the chord at the roots of each blade to absorb the high bending moments. V0 (m/sec) 5 10 15 20 25 Turbine Shaft Power (kW) 42 318 516 562 570 . In brief.13. air density. Typical turbine mechanical shaft power (kilowatt) levels as a function of wind speed (meters per second) are summarized in Table 2. the BEM method provides turbine shaft power levels with minimum differences between measured and calculated data collected on a wind turbine having the following design parameters: ◾ Rotor radius = 20.1 rpm Table 2. It is interesting to mention that the Coriolis acceleration due to the rotation of the earth causes the flow from the equator to the poles that affects wind parameters and leads to the formation of trade winds. if a new blade is designed with a completely new airfoil.70 ◾ Wind Turbine Technology Mechanical shaft power is a function of wind speed. the secondary layers on the rotating blades are affected by the centrifugal and Coriolis forces that alter the post-stall lift and drag coefficients from those measured in wind tunnel tests. When the power curve showing the actual wind turbine shaft power (kilowatts) as a function of wind speed V0 (meters per second) is obtained from the measurements. it is then desirable to calibrate the airfoil data to achieve better agreement between the measured and computational data. and relevant parameters of the airfoil. If a new blade very similar to the blades for which the airfoil data were calibrated is fabricated. Clearly. To maintain structural integrity of the rotor blades. the computed results should be used carefully. it is possible to predict the power curve with high accuracy. The data available in the literature specify an airfoil not thicker than 20% of the chord and moderate angles of attack. Furthermore. the actual geometry and airfoil data for the blade are required to extrapolate the data for a high angle of attack.13 Mechanical Shaft Power as Function of Wind Speed Wind Speed.
14.07 0.46 0. and ω is the angular velocity of the rotor blade.295 0.45 0.45 0.47 0.43 0. directional data.05 0.42 0.25 5 0 585 0 542 0.03 0. daily.128 7 0 592 0 527 0.7. According to meteorological statistics. As noted earlier. and annual variations.3 Parameters Affecting Performance Wind turbine blades designed for optimum performance require variations of the airfoil sections along the radius of the blade to ensure that each blade element operates at its minimum drag-to-lift ratio (ε) that represents the ratio of drag coefficient to lift coefficient.3. The tangential speed ratio (X) also plays a key role in the improvement of the power coefficient and is equal to Rω/V0.41 2 0 56 0 55 0.Design Aspects and Performance Requirements ◾ 71 ◾ Number of blades = 3 ◾ Hub height = 35 m ◾ Air density = 1.38 3 0.185 6 0 590 0 535 0.39 0.4.068 8 0 594 0 52 0.46 0.32 0.41 0.34 0.224 0. coastal regions. the highest wind speeds are generally found at hill tops. and wind parameter changes as functions of height must be known for a Table 2.142 0.372 0. short-term variations (gusts).225 Kg/m3 2.264 0. Variations in power coefficient as functions of various parameters will be discussed in Chapter 4. the power of the wind is proportional to the cube of the wind speed or velocity.56 0.341 0.1 Impact of Wind Characteristics on Power Coefficient The amount of wind energy that can be captured depends on wind characteristics.377 0.01 0.50 0.45 0.174 0.57 0.00 0.44 0.406 0.371 0. 2. Various parameters such as mean wind speed.012 .52 0. seasonal.10 1 0. Variations of the power coefficient and axial interference factor (a) as a function of tangential speed ratio are evident from the data summarized in Table 2.7.32 4 0 58 0 55 0.314 0. where V0 is the wind speed. and out at sea.14 Impacts of Drag-to-Lift Coefficient and Tangential Speed Ratio on Power Coefficient (Cp) Tangential Speed Ratio (X) Drag-to-Lift Ratio (ε) 0. It is therefore essential to have detailed knowledge of the wind characteristics if the performance of a wind turbine is to be estimated accurately. R is the blade radius.
At about 2 km above the ground. The fluctuation of the flow can be expressed in terms of the root mean square (RMS) value of the mean fluctuating wind velocity component (dv2).1 Effects of Atmospheric Boundary Layer on Performance Microflow is influenced by local features such as trees. These wind parameters must be determined with sufficient accuracy through measurements over a sufficiently long period to accumulate reliable wind characteristic data that are essential to determine the performance and economics of a wind turbine plant. wind velocity varies over time and space. the turbulence intensity for very rough terrain consisting of trees and buildings is about 0. 2. and terrain features in the vicinity of an installation site.20.7. The water surface of a lake or river or sea exerts important effects on wind characteristics. An anemometer located at the nacelle of a turbine is capable of recording wind velocity data with great accuracy. structures.1.2 Impact of Vertical Wind Speed Gradient on Power Coefficient The vertical wind speed gradient can affect the power coefficient of a wind turbine. The resulting changes in friction at the surface produce variations in wind velocity.3.3. The vertical variations in wind speed and wind speed profile can be expressed by appropriate functions.1. Note the wind speed at the surface is zero due to the friction between the air and ground surface.26) .25) According To wind turbine installers.7.15 to 0.72 ◾ Wind Turbine Technology specific installation site. 2.24) where Vm is the mean wind speed typically determined over a 10-min interval over a long period and dv is the fluctuating wind speed component. the change in wind speed becomes zero. The change in mean wind speed with height in the form of a power exponent function can be written as: V(z) = Vr [ (z/zr)α] (2. The wind speeds increases with height most rapidly near the ground and less rapidly at greater heights. The expression for the instantaneous wind speed can be written as: V = [Vm + dv] (2. Also. Some variation in wind velocity arises from turbulence created by the wind turbine rotor and nacelle. This fluctuation velocity component is defined as turbulence intensity and can be written as: Tint = [RMS value of dv2/Vm] (2.
Computed values of this exponent with an error of ±5% are summarized in Table 2.001 0. 2.1487] = 22.1.1] = [20 × 1.10 to 0. and α is an exponent that depends on the terrain roughness whose typical value varies from 0.27) .15.7.05 0.4 Impact of Temperature Gradient on Wind Speed The major factors affecting wind speed have been considered.3. Sample Calculation: If wind speed at 10 m height = 20 m/s.7.12 0.1. what will be the wind speed at 40 m height? Wind speed at 40 m height [20 (40/10)0.15 Values of Exponent Parameter as Function of Surface Roughness Terrain Type Water surface or area Open countryside Farm land with buildings Village Roughness Class 0 1 2 3 Roughness Length (m) 0.28 (2.29 Roughness Exponent (α) 0.16 0. Now the strong influence of the vertical temperature gradient on the speed and the speed difference will be discussed. Note exact values are difficult to predict because of significant variations in surface roughness from calms and turbulent winds.15.974 or ~23 m/sec 2.3. Vr is wind speed at the reference height at turbine height zr above the ground.3 Value of Exponent Parameter as Function of Roughness Class and Length The values of the exponent parameters are strictly dependent on surface conditions of the terrain in the vicinity of the wind turbine installation sites. It is customary in meteorology to correlate wind speed measurements using the following equation: V h = [V1 (h/h1)m] Table 2.12 0.01 0.Design Aspects and Performance Requirements ◾ 73 where z is the height of the turbine above the ground.
1. R is defined as the ratio of average power output of a turbine to nominal power due to wind speed gradient.28) where r is the blade element at radius R on the arm whose axis is located at height h0 and the arm makes angle θ with the horizontal axis.4% or 0. and m is the exponent that varies approximately between 1/5 and 1/7.996 0. This exponent is depends on local atmospheric conditions. In other words.958 0.984 0.5. etc. (2. the histogram becomes a continuous function known as the probability density function that indicates the probability of a wind speed at a 1 m/sec interval centered on the value of the wind speed V.910 where V h is the horizontal component of the wind velocity at height h. 4.960 1. V1 is the horizontal component at height h1. This function can demonstrate where the wind speed falls within the interval defined by the widths of the columns as illustrated in Figure 2.7.990 0.897 0.5 m/sec is approximately 10.5 Wind Statistics Histograms of wind velocity covering several years are available and these data allow the probability density function to be determined.74 ◾ Wind Turbine Technology Table 2. Meteorology scientists have noted the strong influence of the vertical temperature gradient and also indicate that the vertical temperature gradient affects the wind speed gradient. Under these conditions.00 1.50 0.5.983 0. thus reducing turbine average output power by a reduction factor R as illustrated in Table 2.11. The figure shows the histogram and Weibull distribution function of the probability for a given speed. It is evident from the curve in Figure 2. . The sum of the height of the columns is generally assumed as unity or 100%.11 that the probability of a wind speed between 4.25 0.5 to 4.5 and 5.5. It is important to mention that the tips of the rotor blades of a propeller turbine would not be permitted to operate very far below the r/h0 ratio equal to 0.3.104.5 to 6. 5. This ratio is calculated using the following equation: R = (1/2π) ∫ [(1 + (r/h0) (sin θ)]3m dθ with integration limits between 2π and 0. Speed data are measured in meters per second "bins" such as 3.5 to 5. the influence of the wind speed gradient observed is insignificant. When the width of a column becomes very small.16. 2.000 0.5.16 Reduction of Average Power Output by Wind Speed Gradient Parameter (r/h0) Exponent (m) 1/7 1/5 0.000 1.75 0.00 0.
C is the scale parameter of the wind speed. It is important to note that shape parameter k could be equal to 10 m/s or 5 m/s.Design Aspects and Performance Requirements ◾ 75 the probability of the wind offers annual energy (0. regardless of Rayleigh or Weibull distribution. These variations will be discussed in Chapter 4. Estimated values of power coefficients for a turbine rotor blade with an angle of attack equal to 0.17. regardless of values of the other two parameters. Rotor blade designers claim that very efficient blade sections with drag-to-lift coefficient ratios equal to 0. percentage probability is much accurate. The probability density function can be fitted to a Weibull distribution function written as: P (V) = [(k/V) (V/C)k-1] [exp{– (V/C)k}] (2. At higher angles of attack.01 demonstrate a maximum when X is approximately equal to 3. The design and development of rotor blades with low angles of attack is a complex endeavor. the result is called a cumulative Rayleigh distribution.73 degrees must be selected for blade design if maximum power coefficients are desired over a wide range of tip speed ratios. It is interesting to mention that the drag-to-lift coefficient ratio effects both turbine power coefficients and variations in rotor torque grading coefficients and blade loading coefficients as a function of tangential speed ratio. Note the histogram accounts for seasonal and annual variations for the years covered by the statistics. However. the result is known as a cumulative Weibull distribution.104 × 8760) of 910 hours. Trade-off studies of rotor blades performed by the author indicate that an angle of attack equal to 0.29) P (V) is the frequency of occurrence function of the wind speed V.4 Combined Impact of Rotor Tip Speed Ratio and Drag-to-Lift Ratio on Power Coefficient The impact of tip speed ratio and drag-to-lift coefficient ratio on the turbine power coefficient as a function of angle of attack is a serious issue. It should be noted that peak values of the power coefficient tend to occur at lower values of tangential speed ratio as the drag-to-lift coefficient ratio (ε) increases.7. These facts can be verified from the calculated data summarized in the previous tables. and k is the shape parameter. 2.1 radian [1] for various tip speed ratios and drag-to-lift coefficient ratios are shown in Table 2. Similar trends have been observed for variations of the axial interference factor. The author's studies of angle of attack reveal that low angles are necessary for higher turbine outputs and power coefficients. when shape parameter k is equal to 5 m/s parameter. The impacts . A typical value for k is close to 2 and when k equals 2.1 radian or 5. the power coefficient deceases rapidly. If k has a value other than 2.
45 0.46 0 51 0 50 0. a rotating wind turbine will not completely prevent the flow of air. and the electrical power losses in the transmission line.38 0 53 0 55 0 56 0 56 0 53 0 50 0. so it can only extract a portion of the kinetic energy from wind.34 000 000 000 000 0. This is the main reason that none of the power coefficient values summarized in the above table approached or exceeded 0. all its energy will dissipate. The wind speed onto the rotor at which the energy extraction is a maximum and the wind speed will lie somewhere between the windstream speed and zero wind speed. Thus the maximum resulting value of the power coefficient or coefficient of turbine performance theoretically is 0. most modern wind turbines deployed for electricity generation operate at power coefficient (CP) levels close to 0.59. The Betz limit was formulated in 1919 and it applies to all types of wind turbines. It is critical to mention that if the air is brought completely to rest.44 0. The reduction in the power coefficient limited by the Betz is due to the losses from the viscous drag on the rotor blades. losses at the gear box. and step-up transformer at the tower base. In practice.05 0.4.59.76 ◾ Wind Turbine Technology Table 2. Calculated values of power coefficients never exceed 0.01 0.47 0. Furthermore. the swirl imparted to the airflow by the rotor structure.27 000 000 000 000 000 of these variations on various rotor and blade performance parameters will be discussed in detail in Chapters 3 and 4.17 Power Coefficient (Cp) for Rotor as Function of Tip Speed Ratio and Drag-to-Lift Coefficient Ratio at Optimum Angle of Attack (0.1 Radian) Tip Speed Ratio (λ) 1 2 3 4 5 6 7 8 9 10 Drag-to-Lift Coefficient Ratio (ε) 0.44 0.43 0.37 0. .59 because this value is limited by the mathematical derivation of the Betz limit. electrical generator.03 0.
Energy integrals capable of providing power coefficients for wind turbines as a function of wind speed ratios are identified and the impacts of exit pressure and interference factor on maximum power coefficient are explained.8 Summary This chapter describes the various types of wind turbines with emphasis on their fundamental operating principles. The accuracy of these data is within ±5%. and energy available as a function of rotor diameter. wind speed. The effects of wind speed and installation height on performance are identified with emphasis on turbine output. The impact of wind shear on turbine performance as a function of wind characteristics and surface roughness factors is briefly discussed. pitch angles. dynamic stability. Wind characteristic requirements to enhance turbine performance are identified in relation to installation site environments. along with information about penalties due to additional weight. Annual wind energy production estimates using the blade element momentum (BEM) method are summarized. Impacts of drag-to-lift coefficient ratios on maximum power coefficients as functions of wind tip ratios were discussed. power density. Computed values of wind turbine power output. and wind distribution are summarized. Computed values of turbine mechanical shaft power as a function of wind speed are provided. Wind energy models are briefly discussed in terms of wind speed and installation terrain. Estimates of annual hours to capture wind energy from a specific installation site and as a function of wind speed ratio are provided. Practical techniques to capture large amounts of wind energy are outlined with emphasis on reliability and turbine dynamic stability. and swept area are provided. Sample calculations of wind turbine power output levels in relation to installation height. Potential rotor blade articulation mechanisms to regulate the angular rate of a rotor are identified with emphasis on reliability and dynamic stability of the turbine. Potential augmentation techniques involving aerodynamic lift surfaces. installation site height. annual wind energy capture is discussed. Important applications of Rayleigh and Weibull distribution functions to estimate the long-term average wind speed for a specific installation site are identified. and diffuser ducts to enhance performance were summarized.Design Aspects and Performance Requirements ◾ 77 2. and performance capabilities and/or limitations. The effect of vertical wind speed gradient on the wind turbine power . The impacts of blade dimensions. and design complexities. Advantages and disadvantages of both types of wind turbines are briefly mentioned. Performance capabilities of modern HAWTs and VAWTs are summarized. and angles of attack on performance along with details about cost and design complexity are covered. Estimated values of power coefficients for HAWTs and VAWTs are provided. critical design aspects. Worldwide data concerning installed wind power capacity from 2005 through 2008 are summarized. Performance capabilities of propeller-based wind turbines as a function of drag-to-lift coefficient ratios and tangential speed ratios are briefly mentioned. ejector ducts. size and cost.
p. 37. 107. p.O.J. [2] A. [3] M. 1983. Aerodynamics of Wind Turbines. VA. 2nd ed.L. Wortman. 13. p. [4] T. Performance parameters based on tip speed ratios and drag-to-lift coefficient ratios are summarized with emphasis on reliability and maintenance-free operation.78 ◾ Wind Turbine Technology coefficient is highlighted in relation to turbine height and terrain roughness. 1938. IEEE Spectrum. p. London. Earth Scan Publishing. Sterling. 18. 2009. 2007. Wizelius. Jan. Histograms of wind speed data collected over a long period play a critical role in providing reliable information on wind speed and direction for a specific installation site. References [1] Europe replaces old wind farms. Jane Science.. Introduction to Wind Turbine Engineering. Hansen. Boston. . Butterworth. Reduction of average power output as a function of wind speed and wind speed gradients is discussed. Developing Wind Turbine Projects.
Critical circular control flow parameters will be identified along with their effects on axial velocity. Initially. with emphasis on rotor classification. and three-dimensional (3-D) aerodynamic analyses will be undertaken on wind turbine rotors with a focus on power and thrust coefficients [1]. and the axial component of the pressure forces acting on the control volume. two-dimensional (2-D). One-dimensional (1-D). and critical design requirements. The axial momentum equation for an ideal rotor will be derived using certain assumptions. Use of the Bernoulli equation will be justified for the far upstream area to just in front of the rotor and from just behind the rotor. incompressible. particularly with regard to design simplicity and reliability. a simple 1-D model for an ideal rotor design configuration will be evaluated to identify the critical roles of axial velocity. design aspects. Reasons for velocity jumps in the wake will be cited. pressure drops across the rotor. 79 . The expression for the rotational speed of a rotor will be developed as a function of axial induction and axial wind velocity. Various types of rotors widely used for modern wind turbines will be described.1 Introduction This chapter is dedicated to wind turbine rotors and associated components. Conditions and parameters required for stationary. and frictionless flow will be identified.Chapter 3 Design Aspects and Performance Capabilities of Wind Turbine Rotors 3. performance capabilities.
but it improves when the tip speed ratio exceeds 3. Design configurations and performance requirements for the rotor blades are different for HAWTs and VAWTs. The rotor efficiency is about 53 and 57 at tip speed ratios of 3 and 4. 57.1. 5. 3. and mechanical integrity of a rotor during its design phase. The efficiency of the Savonius rotor is generally poor over tip speeds ranging from 1 to 2. respectively. 2.5. The rotor blades must follow all the principles of aerodynamic and fluid mechanics to achieve optimum performance regardless of wind environment. a wind turbine extracts mechanical energy from the kinetic energy of the wind and the rotor plays a key role in accomplishing this objective.8. Tip speed ratio is defined as the ratio of blade tip speed to undisturbed wind speed.80 ◾ Wind Turbine Technology 3. The studies further indicate that all the blade sections must be pitched to ensure a minimum drag-to-lift ratio. and 58% at tip speed ratios of 1. Preliminary studies performed by the author indicate that the maximum efficiency or maximum power coefficient is possible at increasing values of tip speed ratios as the drag-to-lift coefficient ratio diminishes. safety. with a maximum efficiency of 33% at a tip speed ratio of 6.1 Rotor Blades The propeller blade is the most critical element of a wind turbine rotor. 6 and 7. respectively. 57. Design configurations and performance requirements for rotor blades will be discussed in detail in Chapter 4. The Savonius rotor has demonstrated a constant efficiency better than 58% over tip speed ratios between 5 and 10. A rotor in a simple 1-D model is a permeable circular disc.2.5.1. 3.2. 51. 4.1 Rotor Types and Their Performance Capabilities Wind turbine rotors and their performance capabilities and critical performance parameters will be briefly described. Upwind and downwind rotors have demonstrated higher efficiencies and are generally deployed by HAWTs and propeller type windmills. Upwind and downwind rotors are widely used by HAWTs while the Savonius and Darrieus rotors are best suited for VAWTs. The efficiency of a Darrieus rotor varies roughly from 28 to 32% over tip speed ratios from 5 to 7. Both upwind and downwind rotors are best suited for high-capacity turbines operating at high tip speed ratios. The ideal efficiency for rotors on windmills is high: 41. The disc is considered an ideal example because it is frictionless and . Because of its relatively poor efficiency.1. As stated earlier. Considerable importance is attached to performance.2 One-Dimensional Theory for Ideal Rotor A simple 1-D model for an ideal rotor must be examined before use of the blade element momentum (BEM) method. 3.5. the deployment of the Darrieus rotor is restricted to low-capacity wind turbines. 54.
These are the two fundamental conditions for an ideal rotor. it is possible to establish mathematical relationships among the various wind velocities involved. the air density is constant. and the axial wind velocity decreases from V0 to u1 as illustrated in Figure 3. pressure Velocity Vo Xrotor x po xrotor Figure 3.Under these conditions.1. The disc acts as a drag device and slows the wind speed from the initial wind speed V0 far upstream of the rotor to wind speed u at the rotor plane and finally to u1 as illustrated in Figure 3. A small pressure rise is expected upstream of the rotor. and the final wind speed at the rotor plane u1 which will be evident from the expression for the pressure drop across the rotor. has no rotational velocity component in its wake. Based on the assumptions for an ideal rotor. the pressure returns continuously to the atmospheric level. the thrust (T) generated.1 Drag dynamics. This pressure drop depends on the air density (ρ). The expression for the thrust generated can be written as: T = [Δp A] (3.1) . increasing from pressure p1 to p before a discontinuous pressure drop (Δ p) over the rotor. initial wind speed (V0). the Mach number is very small. Note during the downstream action of the rotor.1. and the absorbed shaft power (P). During this process. the streamlines must diverge as shown in the figure. Drag develops from the pressure drop over the rotor.Design and Performance Capabilities of Wind Turbine Rotors ◾ 81 Vo po u u1 po Vo u u. The relationship between the pressure and axial velocity is also illustrated in the figure.
The area can be expressed as: A = [πR 2] (3. Under these conditions.3b) Combining these two equations. Under the assumptions of an ideal rotor.z) dx dy dz +∫∫cv u(x.3a) (3. Equation (3.1. the expression for the change in pressure is: Δp = [(1/2)ρ (V02 – u12)] (3.2. and frictionless.82 ◾ Wind Turbine Technology where Δp is the pressure drop across the rotor and A is area of the rotor. Note the force from the pressure has no axial component on the lateral boundary of the control volume (cv) as shown in Figure 3. 3. V is the wind speed vector normal to the area of the element involved. and Fext is the external force component parallel to the pressure force. Since the flow is assumed to be stationary.6) .2. u is the wind speed at the rotor plane as illustrated in Figure 3.2) where R is the radius of the rotor .1 Axial Momentum Equation in Integral Format The axial momentum equation in integral format [1] can be applied to the circular control volume with the cross-sectional area of Acv as shown by a dashed line in Figure 3. Because the flow is stationary. expressions for the pressure upstream and downstream of the rotor can be written as: [p0 + (1/2)ρV02] = [p + (1/2)ρu2] [p – Δp – (1/2)ρu2] = [p0 + (1/2)ρu12] (3.z)ρV. incompressible.y. and u1 is the wind speed in the wake. the first term in Equation (3.T ] (3. V0 is the wind speed far upstream of the rotor.5) can be rewritten as: [ρu12A1 + ρV02 (Acv – A1) + (dmside/dtV0) – ρV02Acv] = [ . p is the pressure rise from the atmospheric pressure level at p0. no external force acts on the fluid upstream or downstream of the rotor.5) is zero and the last term is also zero because the pressure has the same atmospheric magnitude at the end planes and acts on same area of the rotor.225 Kg/m3).y. Fpress is the axial component of the pressure forces acting on the control volume.dA] = [Fext + Fpres] (3.4) where ρ is the air density (1. the Bernoulli equation is valid.2 and can be written as: [∂/∂t∫∫∫cvρu (x.5) where dA is a vector pointing in the normal direction of an infinitesimal portion of the control surface with a length equal to the area of this element.
9a) (3. . where T is the thrust acting in the opposite direction generated from the pressure drop over the rotor which reduces the original wind speed V0 to u1 as mentioned earlier. the expression for the torque can be written as: T = [ρ u A (V0 – u1)] = [(dmside/dt) (V0 – u1)] Using and rearranging Equations (3.10) (3.11) (3.7) Using the conservation of mass concept and combining Equations (3.9b) It is evident from Equation (3. The expression for the conservation of the mass can be written as: [ρA1u1 + ρV0Acv – ρV0A1 + dmside/dt] = [ρV0Acv] This equation provides the expression for (dmside/dt) which can be written as: [dmside/dt] = [ρ A1 (V0 – u1)] (3.Design and Performance Capabilities of Wind Turbine Rotors ◾ 83 Vo T A u1 At Acv CV mside Vo Figure 3.11) that wind velocity in the rotor plane (u) is the mean of the wind speed V0 and the final speed in the wake (u1).2 Axial momentum.1) and (3. (demised/dt) is the parameter derived from the conservation of the mass equation.8).6) and (3.8) (3.9 a): [(1/2) ρ A (V02 – u12)] = [ρ u A (V0 – u1)] This equation after rearrangement can be rewritten as: [(ρ u A (V0 – u1)] = [(1/2) ρ A (V0 + u1) (V0 – u1)] This means the expression for the wind velocity at the rotor plane can be written as: u = [(1/2) (V0 + u1)] (3.
3. there is no mass fluid flow through the lateral boundary of the control volume due to its alignment with the streamlines as illustrated in Figure 3. The axial momentum equation for the torque (T) in this case can be written as: T = [ρ u A (V0 – u1) + Fpress] (3. Because of frictionless flow.3.3.12) The force created by the pressure on the control volume following the streamlines is zero as depicted in Figure 3.13). the expression for shaft power can be written as: P = (dm/dt) (1/2)[V02 + (2P0 /ρ) – u12 – (2P0/ρ)] = [(1/2 dm/dt) (V02 – u12)] (3. The expression for the turbine shaft power P can be written as: P = [energy/time] = [(1/2) m V2]/[time] = [watts second/second] = [watts] (3.2 One-Dimensional Momentum Theory Using Alternate Control Volume Wind turbine configuration with an alternate control volume is shown in Figure 3.14) .3 Wind turbine with alternate control volume.5) on the control volume as shown in Figure 3. the wind energy does not change from inlet port to outlet port.3 into Equation (3. 3.13) The shaft power can be obtained by using the integral energy Equation (3. In the case of alternate control volume.84 ◾ Wind Turbine Technology p(x) Vo T CV U1 At A x Vo Figure 3. The force generated by the pressure distribution along the lateral walls of the control volume Fpress is unknown except the force generated by the net pressure contribution Fpress.2. Inserting the parameters shown in Figure 3.3.
16) inserting Equation (3.19) into Equation (3.11) and rearranging the terms yields: u1 = [2 u – V0] = [(2 u/V0) – 1] V0 = [2 (1 – If ) – 1] V0 = [1 – 2 If ] V0 (3.19) into Equation (3.9 a) and (3.19) (3. the expression for shaft power is reduced to: P = [(1/2) ρ u A] [V02 – u12] If the induction factor If is defined as: If = [1 – (u/Vo)] because [u = (1 – If ) V0] (3.20) Inserting Equation (3.14).9 b).21) .15) Inserting Equation (3.17) (3.9 a) yields the expression for torque: T = [(ρ u A)] [V0 – (1 – 2 If ) V0] = [(ρ A) (u/Vo) (V02) (2 If )] = [2 ρ A V02] [If (1 – If )] (3. the derivative of mass can be written as: [dm/dt] = [ρ u A] (3.15) into Equation (3.16) allows the expression for shaft power to be written as: P = [(1/2) ρ u A] [V02 – (1 – 2 If )2 V02] = [(1/2) ρ A (u/V0)] [1 – (1 – 2 If )2] [V03] = [(1/2) ρ A (1 – If )] [1 – 1 – 4 If2 + 4 If ] V03 = [(1/2) ρ A V03] [(1 – If ) (4 If ) (1 – If )] P = [2 ρ A V03] [I f (1 – I f )2] (3.17) into Equation (3.17) and (3.18) Inserting Equations (3.Design and Performance Capabilities of Wind Turbine Rotors ◾ 85 From Equations (3.
4.22) 3.25 0.28 0.32 0 Figure 3.4 Relationship of power coefficient variable for 1-D wind turbine.27 0.23) 3.4 Thrust Coefficient for Ideal OneDimensional Wind Turbine The expression for the thrust coefficient for an ideal 1-D wind turbine is: 6 4 Cp 2 0 0.29 If 0.31 0.22)] = [2 ρ A V03] [If (1 – If )2] / [(1/2) ρ A V03] = [4 If (1 – If )2] = [8 If (1 – If )] The numerical relationships of the various variables are visible in Figure 3.3 Power Coefficient for Ideal OneDimensional Wind Turbine The power coefficient (Cp) of the turbine can be written as: Cp = [shaft power/available power] = [Equation (3.2.2. .3 0. The available power in a cross-section equal to swept area A by the turbine rotor can be given as: Pavail = [(1/2) ρ A V03] (3. (3.20)/Equation (3.86 ◾ Wind Turbine Technology where If is the axial induction factor and ρ is the density of the rotor material (mass/ volume).26 0.
036 000 Torque Coefficient (CT) 000 0.5.500 0.128 0.3.9 1.2 0.24) Calculated values of torque coefficients are summarized in Figure 3.324 0.0 0.840 0.3 0.512 0.1 Computed Values of Power Coefficient and Torque Coefficient as Function of Axial Induction Factor Axial Induction Factor (If) 0.4 0. These maximum values of coefficients can be Table 3. These computed values indicate that the maximum power coefficient occurs when parameter If is 0.960 0.6 0.25) Computed values of power coefficients and torque coefficients for an ideal 1-D wind turbine as a function of axial induction factor (If ) are summarized in Table 3.000 0.21)]/[(1/2) ρ A V02] = [2 ρ A V02] [If (1 – If )]/[ (1/2) ρ A V02] = 4 If (1 – If )] (3.5.588 0.8 0.640 0.360 0.360 000 . The maximum power coefficient for the ideal 1-D wind turbine can be obtained by differentiating Equation (3.840 0.7 0.640 0. while the maximum value of torque coefficient occurs when the axial induction factor is equal to 0.1.384 0.1 0.576 0.5 0.960 1.Design and Performance Capabilities of Wind Turbine Rotors ◾ 87 CT = [thrust generated by shaft]/[thrust available] = [Equation (3.252 0.0 Power Coefficient (Cp) 000 0.23) with respect to axial induction factor: [dCp / dIf ] = 4[(-2If ) (1 – If ) + (1 – If )2] = 4[(1 – If ) (–2If + 1 – If )] = 4[(1 – I f ) (1 – 3I f )] (3.
It is important to mention the theoretical maximum power coefficient is equal to 16/27 or 0.6 0.2 0 CP(If) CT(If) 0 0. and vortex ring state.5.5 and by the calculations summarized in the figure.4 is that the free shear layer at the edge of the wake becomes unstable when the velocity jump (V0 – u1) becomes too high and eddy currents are formed (Figure 3.3 for an ideal wind turbine. In other words. a high thrust coefficient (CT ) and thus a high axial induction factor If present a case for a wind turbine capable of operating at low wind speeds.2 0. the momentum theory is not valid in the turbulent wake state and the wind velocity V0 would become negative. verified from the curves shown in Figure 3.19). the wind velocity in the wake state would become negative.8 0. if the axial induction factor exceeds 0. as shown by Equation (3. this is known as the Betz limit. the theoretical maximum torque coefficient of unity occurs when the axial induction factor equals 0.4.6 0. Based on the forgoing arguments.88 ◾ Wind Turbine Technology 0. Note that the measured data on thrust coefficients obtained by various aerodynamic scientists [2] indicate slightly higher values as a function of axial induction factor for different rotor states including windmill state. turbulent wake state.6). Furthermore.4 0. The measured data further indicate that if the momentum theory were valid for higher values of induction factor. It is interesting that the turbulent wake state is produced by unstable shear flow at the wake edge as illustrated by Figure 3. this can be seen readily in Equation (3.5 as shown in Figure 3.5926 when If is to equal 0. On the other hand. . the expansion of the wake increases with the increase in the thrust coefficient CT and also the velocity jump from V0 to u1 in the wake state.7.19).8 Figure 3.4 Axial Induction Factor If 0. The reason that the momentum theory is not valid for inductor factor values greater than about 0.5 Calculated values of torque coefficients.
Unstable wake caused by velocity jump that generates eddy Vo = Wind velocity Figure 3.Design and Performance Capabilities of Wind Turbine Rotors ◾ 89 Ao u1 A1 Ao Vo Ao u1 Figure 3. Turbulent wake state produced by unstable shear flow at wake .7 edge.6 current.
When this equation is applied to an infinitesimal control volume of thickness (dr). Since the axial velocity V0 through the rotor is defined by Equation (3. C θ. ω is the angular velocity or rotational speed. . where these absolute velocity components are parallel to the radius. Since a modern wind turbine consists of a single rotor without a stator. in terms of axial induction factor. and axis.8 Absolute velocity components.5 Effects of Rotation The wake of an ideal rotor exhibits no rotation.17). r is the radius. u is the axial wind velocity through the rotor. the expression for the power contained by the infinitesimal control volume is: dP = [(dm/dt) ω r C θ] = [(2 π r)2 ρ u ω C θ dr] (3. The blade has a tangential velocity component C θ in the opposite direction of the blade as shown. the wake will possess some rotation that can be verified from the Euler equation for wind turbines.90 ◾ Wind Turbine Technology 3.26) where m is the mass.2.28) Co = Azimuth velocity component in the wake Ca = Axial velocity of the rotor C = Absolute velocity of the blade in the down-stream Vrot = Rotor velocity µ = Axial velocity through rotor Figure 3. the azimuthal velocity component C θ in the wake decreases with the increase in the rotational speed ω of the rotor. It is necessary for a wind turbine to have a high rotational speed of the rotor to achieve high efficiency and minimize the kinetic energy loss contained in the rotating wake. ρ is the air density. For a given power level P and wind speed. The figure shows the velocity triangle for a section of the rotor and identifies various velocity components downstream of the blade.1 u C Vrel. The expansion of the wake and the velocity jump for the 1-D ideal wind turbine can also be observed in the figure. this means the axial induction factor is zero. Ca).27) (3. the rotational speed in the wake can written: C θ = [2 If´ω r] [V0 (1 – If )] Cθ ca = u Vrot Vrel.2 Vrot (3. shown on page 85. and C θ is the azimuthal component of the absolute velocity C = (Cr. as illustrated in Figure 3. respectively.8. azimuth.
27 0.33 Figure 3.32 0.5. 0.5 to 7.27) into Equation (3.5 for parameter If´ and various values for λ.3 for parameter If.9 Parameter x as function of axial induction factors. which is derived for zero rotation in the wake when the parameter If´ is equal to zero.29 If 0.5 1 0.3 0. .26) yields: dP = [4 π ρ ω2 V0 If '(1 – If ) r3] dr The total rotor power can be determined by integrating dP from 0 to R as: P = [4 π ρ ω3 V0∫ If´ (1 – If ) r3 dr] Local angles of attack below stall conditions based on the potential flow theory in which the reacting force is perpendicular to the local wind velocity as seen by the rotor blade [3]. it can be written: Cp = [(8/λ 2) ∫ If (1 –If ) x3 dx] λ = [ω R/V0] (3. The power coefficient in a non-dimensional form can be obtained by integrating the following expression with λ ranging from 0. Inserting the values of 0.29a) (3. Computed optimum power coefficient including the 3 2. Iff) 1.5 for modern wind turbines and V0 is the wind speed.5 0 0.29b) (3.29) where λ is the tip speed ratio that can vary from 0. one can obtain the optimum power coefficient with the Betz limit of 16/27.31 0.25 0.28 0.5 2 x(If. Inserting Equation (3.26 0.5 to 7.Design and Performance Capabilities of Wind Turbine Rotors ◾ 91 where If´ indicates the induction factor in the wake.
35) (3.30) Computed values and a plot of parameter x as a function of axial induction factors are depicted in Figure 3.32) Inserting Equation (3. The major advantage of fewer blades is the resulting decrease of weight and the costs of the rotor and components.31) (3. Inserting these values into Equation (3. There are.9 that parameter Iff denotes a variable If´.30) produced values of x plotted as a function of If as illustrated in Figure 3.6 Tip Speed Ratio of Rotor The tip speed ratio of a wind turbine rotor depends on the number of blades deployed by the rotor. maximum capture of wind energy is only possible with a large number of blades. the result is: [1 + 2 If´/1 + If´] = [(1 – 2 If ) / If ] Solving this equation and rearranging the terms yields: If´ = [ (1 – 3 If )/(4 If – 1)] (3.92 ◾ Wind Turbine Technology wake rotation effect with the Betz limit will be different from the previous computed value of power coefficient with zero wake effect. one gets: [(1 + 2 If´) (dIf´/dIf ) x 2] = [1 – 2 If ] (3. x 2 If´ (1 + If´) = [If (1 – If )] where x = [ω r/V0] (3.8 and 3. 3.34) Inserting various values of If in Equation (3. However.35) allowed values of If´ to be obtained. wind turbines with two blades and also with single blades.9.33) (3. Note in Figures 3.8.33) and comparing the coefficients of this new equation with those of Equation (3. and plotted as a function of If in Figure 3.9. one can write an expression involving parameters If and If´ as: [(1 – If ) dIf´/df ] = If´ Differentiating Equation (3.30) with respect to parameter If.30). For local angles of attack below rotor stall conditions and to meet the optimization requirements.2.32) into Equation (3. summarized. Most commercial wind turbines have three-bladed rotors. however. Trade-off analysis of the number of blades .
correct rotor diameter and the wind speed. Computed values of tip speed as a function of rotor radius and rotational speed are summarized in Table 3. In case of a wind turbine with one or two blades.37) where ω is the rotational speed (rpm) and R is the rotor radius or length (m). Figure 3. the rotor must have an appropriate rotational speed relative to its size. for wind turbines with the same rotor diameters. The author's studies of tip speed requirements indicate that the tip speed ratio of a wind turbine is strictly dependent on the number of blades deployed by the rotor. When the blades of a wind turbine rotate. For example. In other words. In other words. This means that expression for the tip speed ratio can be written: λ = [Vtip/V0] (3.2. An intimate relationship exists among tip speed ratio (λ).Design and Performance Capabilities of Wind Turbine Rotors ◾ 93 and turbine efficiency must be performed to ensure cost-effective performance. Rotational speed (ω) is usually expressed in revolutions per minute (rpm) and tip speed and the wind speed are expressed as meters per second (m/sec). two blades can teeter a few degrees across the hub. rotational speed (ω). three and two blades. the tip speed will be 60 m/sec but the speed at the middle of the blade will be only 30 m/sec.e. Note that large-capacity wind turbines have longer blades that operate at rotational speeds significantly below 50 rpm to reduce environmental noise level and maintain structural integrity of the turbine. which reduces the loads on the turbine.10 shows the relationships between number of blades and tip speed for wind turbines with six. thereby yielding higher dynamic stability of the system. for a wind turbine with a 20-m blade length and a rotational speed of 30 rpm. and rotor size (R). the speed at the tip of the blade is higher than speed in the middle of the blade. The tip speed can be written as: Vtip = [ω 2 π R/60] m/sec (3. The studies further indicate that fewer blades should increase the tip speed ratio. which in turn need higher rpm values than three-bladed turbines and also need sophisticated gear box design. To extract wind energy in an efficient way. the connection of the blades and the hub must be rigid to assure mechanical integrity of the system under a variety of wind conditions. Since the speed of the blade segments increases from the root of the blade to the tip of the blade. the apparent wind direction will also change. i. one-bladed turbines need higher rotational speeds than two-bladed turbines. For high-capacity wind turbines.. the rotor must have an efficient tip speed ratio. If one moves .36) It is important to remember that at a given rotational speed the tip speed increases with the length or radius of the blade. On a so-called teetering hub. proper mounting can ensure that they are flexible in the vertical plane. The tip speed ratio is defined as the ratio between the speed at the tip of the rotor blade and the undisturbed wind speed (V0).
38) where α is the angle of attack (kept as small as possible) and β is the blade angle. 3. Apparent wind direction along the rotor blade axis with a wind speed of 9 m/sec is evident due to blade twist. to achieve the same angle of attack along the entire blade axis.10. R (m) 10 20 30 40 50 10 10 20 30 40 50 15 15 30 45 60 75 20 20 40 60 80 100 25 25 50 75 100 125 30 30 60 90 125 150 from root to tip of the blade.94 ◾ Wind Turbine Technology Table 3. These test results first show .3. Estimated values of angle of apparent wind direction with respect to the vertical plane and the magnitudes of undisturbed wind speed at various blade locations are summarized in Table 3.2 Tip Speed of Rotor as Function of Radius and Rotational Speed Rotational Speed. This means that centrifugal forces and the bending moments will be enormous at the tip of a blade. the apparent wind direction will move toward the vertical plane. It is important to point out that by twisting the blade so that the angle φ decreases toward the tip. The angle (φ) of the apparent wind direction with respect to the vertical plane varies from 27 degrees at the root of the blade to 6 degrees at the tip of the blade as shown in Figure 3. the angle of attack (α) can be kept constant for a given wind condition.10. the blade must be twisted as illustrated in Figure 3.1 Properties of Airfoils Efficient design of a wind turbine is strictly dependent on the airfoil configuration and properties. normally referred to as pitch angle. It is clear that wind speed is at maximum at the tip and minimum at the root.2. ω (rpm) Rotor Radius. Therefore. It is important to mention that the undisturbed wind speed (Vundist) will decrease to about 2/3 from the assumed wind speed of 9 m/sec just in front of the rotor disc. The properties of an airfoil can be obtained from a diagram based on results of the profiles obtained from a wind tunnel. The angle of apparent wind direction can be expressed as: φ = [α + β] (3. These tabulated values provide estimates of undisturbed wind velocities at various locations along the blade radius or length.6.
the airstream cannot stick to the airfoil surface. At such a large angle of attack. which reaches a maximum at 15 degrees. and second. lift coefficient. 3 blades. It is important to point out that the angle of attack plays a critical role in determining the stall point in an airfoil diagram in which lift coefficient is plotted as a function of angle of attack. the relationship between the angle of attack and the coefficient of lift (CL). drag coefficient. a gliding ratio diagram showing the relationship between lift coefficient and drag coefficient (CD).10 Relationship of number of blades and tip speed. An airfoil diagram describes the starting lift with an angle of attack as small as –4 degrees. then decreases. and gliding ratio will change continuously at different parts of the blade along the blade axis.Design and Performance Capabilities of Wind Turbine Rotors ◾ 95 λ=3 λ=7 λ=9 (a) Tip speed ratios for a wind turbine using 6 blades. thereby creating a turbulence effect under which the . and 2 blades =6 Tip =7 =9 = 14 o = Flow angle Flow angle = [Pitch angle + angle of attack] = 27 Hub (b) Approximate wind directional flow along the axial length of the rotor blade Figure 3. the angle of attack. If the blade angle and the rotational speed are constant.
Unity list coefficient is possible with an attack angle as high as 7 degrees where an airfoil is most efficient. but circumferential force is not the same as lift force. The magnitude of the circumferential force is small compared to that of thrust. The circumferential force is considered useful because. The thrust force perpendicular to the plane of rotation is called Fthrust.6 radius 0. Note that a blade profile can have several different thicknesses.e.3 Undisturbed Wind Speed in Front of Rotor Disc as Function of Blade Radius Location at Blade Radius Blade tip 0. . Some wind turbine designers prefer to use an angle of attack equal to 0. Vundist (m/sec) 60 48 36 26 12 airfoil begins to stall.4 radius 0. These two forces have a resultant force Lres Consisting of two components: the useful or circumferential force and the useless force called thrust. with emphasis on the structural integrity of the rotor blades. In case of a wind turbine. For example. thickness with respect to width) expressed as a percent. the maximum thickness of the airfoil is 12% of the width. it provides rotational capability to the rotor.2 radius Angle β (degrees) 6 7 9 14 27 Undisturbed Wind Speed. for airfoil configuration NACA4412. the lift from the rotor blades is used to make the rotor revolve..8 radius 0. These forces are responsible for the development of a circumferential force FCIRC acting in the plane of rotation.11. Because of rotational capability. Various airfoil design configurations have been investigated and developed for wind turbine designs. when applied in the plane of rotation.73 degrees to achieve efficient and safe turbine performance with no possibility of stall regardless of the wind conditions. creation by an airfoil of a strong circumferential force is the principal requirement of a wind turbine. When a stream of air passes an airfoil. A rotor blade has a certain angle to the plane of rotation. the lift is always applied perpendicular to the apparent wind direction.96 ◾ Wind Turbine Technology Table 3.1 radian or 5. drag (D) is created in the apparent wind direction and the lift (L) is perpendicular to the drag.11. while the airfoil offers some friction or drag (D) that is applied to the apparent wind direction as illustrated in Figure 3. Furthermore. The last two digits in the type number of an airfoil indicate relative thickness (i. but the power produced is large because the rotational speed is very high as shown in Figure 3.
3. Note that the two-dimensional flow represents a plane and if this plane is described by the x.11(A). it is assumed in many aerodynamic models that the air flow at a given radial position is two-dimensional and that two-dimensional airfoil data can be applied. z coordinate system illustrated in Figure 3.1 Airfoil Configuration for TwoDimensional Aerodynamic Model It is necessary to extrude an airfoil into a wind of infinite span to realize a 2-D flow.11 Components of circumferential force. The wind starts at the hub and ends at the tip. The span-wise velocity component is much lower than the stream-wise velocity component. y.3. 3.Design and Performance Capabilities of Wind Turbine Rotors ◾ 97 Leading edge stagnation point Trailing edge y Stagnation streamline z x (a) Two-dimensional flow showing the trailing edge and leading edge Decreasing pressure Low pressure High pressure Increasing pressure (b) Physical explanation for the lift forces Figure 3. for long slender wings used in wind turbines. In actual practice. However. aerodynamic scientists have shown that local 2-D data on the forces can be used if the angle of attack is corrected according to the trailing . the chord and twist in a real wing section change along the span.3 Two-Dimensional Aerodynamic Model Wind turbine rotor blades are long structures. Under these conditions. the flow velocity component in the z direction will be zero.
They further claim that the 2-D aerodynamic model is practical for wind turbine rotor design. ρ is the air density. it is easy to compute the force distribution on the blades. The chord is defined as the line from the trailing edge to the nose. Since atmospheric pressure P0 is present far from the airfoil. The smaller the drag. Since this theory is not .4 Three-Dimensional Aerodynamic Model for Wing of Finite Length This section describes qualitatively the flow over a 3D wing and how the span-wise lift distribution changes the upstream flow and local angle of attack. the smaller will be the required engine.11(B).40) where D is the drag force.11(B). The BEM method may be used to compute the axial and tangential induction factors as well as the loads on the wind turbine. For airfoils designed for applications to wind turbines. the lift-to-drag (L/D) ratio should be maximized.98 ◾ Wind Turbine Technology vortices behind the wing. Global loads such as power output and the root bending moments of a blade can be determined by integrating this distribution along the span. 3. as described in various textbooks. If an airfoil is designed for an aircraft. If the lift and drag coefficients applied along the blades are known. L is the lift force. The pressure gradient acts like the centripetal force resulting from the circular motion of a particle.39) (3. and V0 is the flow velocity. Vortex methods can be used to calculate the induced velocities involved in computations of induction factors. The reacting force from the air flow has two components. pressure below atmospheric must be on the upper side of the airfoil and pressure above atmospheric on the lower side of the airfoil as shown in Figure 3. Basic fluid mechanics theory states that a pressure gradient is necessary to curve streamlines at a radius of curvature r and at a speed of V. Basic vortex theory. The physical explanation for lift is that the shape of the airfoil forces the streamlines to the curve around the geometry as illustrated in Figure 3. plays a key role for this model. Drag and lift are dependent on the angle of attack. The expressions for the drag (CD) and lift (CL) coefficients can be written as: CD = [D/(1/2) ρ V02 c] CL = [L/(1/2) ρ V02 c] (3. the drag-to-lift ratio should be maximized and the drag must be balanced by a propulsion system to maintain a constant speed. namely a component perpendicular to the flow velocity and a component parallel to the flow velocity. c is the chord or length of the airfoil.
lift can be defined using the Kutta-Joukowski equation: L = [ρ Vα X Г] (3. The classic literature on theoretical aerodynamics reveals that a vortex filament of strength Г can model the flow past an airfoil for small angles of attack. The difference in pressure generates lift force.Design and Performance Capabilities of Wind Turbine Rotors ◾ 99 directly used in the BEM method.12 Trailing vortex. thereby creating a pressure difference between the lower and upper sides of the wing. Therefore at the trailing edge there will be a jump in the tangential velocity due to the leakage at the tips. at the wing tips are leakages where air flows around the wing tips from the lower side to upper side of the wing. The streamlines flowing over the wing surface are deflected inward and streamlines flowing under the wing are deflected outward. 3.41) (a) Vortices stemming from a'three-dimensional wing Γ ds r. only its basic concepts will be applied. P W (b) Induced velocity from a vortex line shown by arrow Figure 3. . This velocity jump will create a continuous sheet of stream-wise velocity in the wake behind the wing and this sheet is called the trailing vortices as shown in Figure 3. The material presented here may be abstract for readers with limited knowledge of vortex theory.4. Furthermore. For this particular case.12. This is due to the fact that the flow for small angles of attack has zero viscosity and is strictly governed by the linear Laplace equation.1 Parameters Affected by Streamlines Flowing over Wing A wing is simply a beam of finite length with airfoils as cross-sections.
a complete wind can be modeled using a series of vortex filaments. Since the flow is locally 2-D. the induced velocity (w) at a specific point can be obtained as illustrated in Figure 3.4. the velocity and the momentum are relatively small compared to the centrifugal force that starts to pump fluid in the span-wise direction toward the tip. . The effect of the centrifugal and Coriolis forces is to alter the 2-D airfoil data after stall. It is important to point out that at the tips of the wing the induced velocity has a value that ensures zero lift. demonstrated the computed limiting streamline on a modern wind turbine blade moving at a moderately high wind speed. 3. Hansen et al. Limited streamlines are flow patterns very close to the surface. The model based on discrete vortices offers reasonable solution. In a separated boundary layer. One method to determine the value and the associated induced velocities of the vertices qualitatively is the solution of Prandtl's integral equation. an airfoil can be thus substituted by one vortex filament of strength Г and the lift L produced by the wing can be modeled for small angles of attack using a series of vortex filaments oriented in the span-wise direction of the wing [4]. while the trailing (free) vortices model the vortex sheet stemming from the three-dimensionality of the wind. one cannot apply the geometric angle of attack when estimating the forces on the wind. lift is reduced compared to a 2-D wing with the same angles of attack and drag forces. the 2-D data can be used if the geometric angle of attack is modified by the downwash. This assumption is reasonable for long slender wings such as those on a wind turbine. a vortex filament cannot terminate in the interior of the fluid but must either terminate on the boundary or be closed.12. The vortices of the wind known as bound vortices model the lift (L). Note the relative velocity (V) for a section of a wing is the vector sum of the wind speed and the induced velocity (w).100 ◾ Wind Turbine Technology where α is the air density and Vα is the flow velocity at the angle of attack α.2 Coriolis and Centrifugal Forces Rotating blade Coriolis and centrifugal forces play an important role in the separated boundary layers that generally occur after a stall condition. the Coriolis force points toward the trailing edge and acts as a favorable pressure gradient. Since the three-dimensionality is limited to the downwash and the span-wise flow is very small compared to the stream-wise velocity. Based on the above conclusions. In brief. When the fluid moves radially toward the tip. It is important to understand that the vortex system produced by a 3-D wing changes the local inflow conditions. However. it can be stated that for a 3-D wing. Note both effects are due to the downwash induced by the vortex system associated with a 3-D wing configuration. Based on this equation. For a vortex filament of strength Г.
Design and Performance Capabilities of Wind Turbine Rotors ◾ 101 3.14. respectively. A HAWT rotor is comprised of a number of blades shaped like wings. the tangential induced velocity in the dr (a) Wind turbine rotor configuration with three blades α φ θ Vr Vre Vr Va Rotorplane (b) Cascade of aerofoils in the radial direction from the axis Figure 3.13(A).42) where φ is the flow angle and Va and Vrot are the axial and rotational velocities. a vortex system similar to the linear translating wing must be present. Since the flow does not rotate upstream of the rotor. The induced tangential velocity in the rotor wake is defined by a tangential induction factor a´ as (2 a´ ω r).4.13(B). the axial velocity Va and the rotational velocity Vrot are related as: Tan φ = [Va/Vrot] (3. The induced velocity in the axial direction is specified through the axial induction factor a or If as aV0 where V0 is the undisturbed wind speed. If a cut is made at a radial distance r from the rotational axis as shown in Figure 3. . The local angle of attack α is given by the pitch angle θ of the airfoil.3 Vortex System behind Modern Wind Turbine HAWTs are used widely to generate large amounts of electrical energy at minimum cost and complexity. a cascade of airfoils can be observed as illustrated in Figure 3. at the rotor plane. Since a HAWT consists of rotating blades. The strong vortices are located at the edge of the rotor wake and the root vertices mainly in a linear path along the axis of the rotor as illustrated in Figure 3.13 HAWT rotor. A vortex sheet of the free vortices is oriented in a helical path behind the rotor. The vortex system oriented helically behind the rotor induces an axial velocity component opposite to the direction of the wind and a tangential velocity component opposite to the rotation of the rotor blades.
3. A single-bladed rotor with a counterweight for mechanical balance exhibits a further small drop in efficiency that may be about 6% below that of a two-bladed rotor. Weight and procurement costs for three-bladed rotors are higher than those for single or two-bladed rotors. rotors with fewer blades must run faster and that can . For similarly proportioned blades. 3. As far as the cost and design complexity are concerned.13.5 Rotor Design Requirements for Wind Farm Applications Rotor design requirements and configurations vary from application to application. Rotor requirements for wind turbines with lower or moderate capacities not exceeding 10 kW or so are not severe. where ω is the angular velocity of the rotor and r is the radial distance from the rotational axis as shown in Figure 3.102 ◾ Wind Turbine Technology Vo VO = Wind speed Figure 3.14 Vortices around HAWT rotor. The studies further indicate that a two-bladed rotor is 2 to 4% less efficient compared to a three-bladed rotor. both factors increase with an increase in the number of rotor blades.5.1 Rotor Performance Studies performed by the author on wind turbine rotors indicate that a threebladed rotor has a tip speed ranging from 45 to70 m/sec to meet high-capacity power levels and yields the best rotor efficiency. a three-bladed rotor is roughly 8 to 10% more efficient than a single-bladed rotor. rotor plane is thus approximately equal to (a´ ω r). In brief. The number of blades required seldom exceeds two. a 2-D equivalent angle of attack may be determined. If the induction factors a and a´ are known. On the other hand. requirements for two or three blades apply to wind farm applications and tip speeds range from 50 to 70 m/sec when power output exceeds 1 MW.
but the results are not encouraging. glass-reinforced plastic (GRP). In other words. operating wind conditions. the blade requirements are more stringent in terms of mechanical integrity and operational reliability. It is important to point out that with a teetered hub. One. the rotor is hinged at the hub in such a way as to allow the plane of rotation of the rotor to tilt a few degrees backward and forward from the mean plane position. selection of the rotor blade material depends totally on the mechanical and structural properties of the fabrication materials. On the other hand.Design and Performance Capabilities of Wind Turbine Rotors ◾ 103 cause problems such as excessive tip noise and erosion. carbon fiber-reinforced plastic (CFRP). . In brief. The author will discuss potential ways to use GRP technology to reduce weight and increase the stiffness of the rotor blades in Chapter 4. and other design requirements. Some designers have considered high-performance resins such as epoxy in fabrication of rotor blades. CFRP blades have been made successfully in prototypes and limited production runs. stiffness. severe dynamic imbalance may pose a serious threat to the safe operation of a wind turbine installation. It is hoped that the cost of carbon fiber will decrease in the near future as demand increases but the current price of this material is rising steadily. The deployment of this material will not have widespread use for rotor blades until its price drops. For small wind turbine rotors (diameters smaller than 5 m).2 Material Requirements for Rotor Blades The properties of the rotor blade materials depend strictly on the blade dimensions. They have demonstrated the lowest weight and highest stiffness factors but unfortunately the material is costly. Note that reduction of weight and increase in stiffness are the critical design requirements for longer blades. a threebladed rotor is considered most pleasing esthetically and offers optimum dynamic system stability. steel. These aspects will be discussed in detail in Chapter 4. 3. the choice of fabrication material is driven by production efficiency and fabrication cost rather than weight. and aluminum. Rotor blades for high-capacity wind turbines are constructed from wood laminates. the forces acting on the rotor are more evenly balanced and the hub mechanism is simple with a three-blade rotor configuration. For high-capacity turbine rotors.5. The rocking motion or the teetering of the rotor during each revolution significantly reduces the loads on the rotor blades due to gusts and wind shear and may disturb the dynamic balance of the rotor. A serious dynamic imbalance can damage a wind turbine under severe operating wind environments. and stresses on the hub structure arising from bending moments.and two-bladed rotor hubs often present the complications of teetering to limit fluctuating forces as the rotor blades sweep the wind through a varying wind velocity field. Furthermore.
shapes can be approximated by any particular stream surface.5. In other words. U is the flow speed at infinity.1 Two-Dimensional Flow Analysis over Sphere The expressions for the potential (φ) and stream (ψ) functions for the flow over a sphere [5] can be written as: φ = [(U a3/2 r2) cos (θ) + u r cos (θ)] ψ = [– (U a3/U r) sin2(θ) + (U r2/2) sin2(θ)] (3. It is important to mention that the analysis is not limited to hills shaped as spheres or cylinders. in such an analysis.43) (3. Improvement of rotor performance depends on the following factors: ◾ High lift-to-drag ratio to improve rotor efficiency over a wide range of wind environments ◾ Improved stall characteristic ◾ Low noise production ◾ Insensitivity to roughness ◾ Optimum shape for enhanced performance 3. Similarly.45) (3. The equations for the tangential (Vθ) and radial (Vr) components of the velocity can be written: Vθ = U sin(θ)[1 + (1/2) (a/r)2] Vr = – U cos(θ)[1 – (a/r)2] (3.104 ◾ Wind Turbine Technology 3. stream surfaces can be replaced by solid surfaces so that the sphere stream surface will represent the flow over a spherical hill.46) . a is the radius of the sphere.6 Hydrodynamic Analysis of Flow over Rotor Hydrodynamics flow analysis over a sphere or cylinder is capable of predicting the performance of a wind turbine rotor.6. a cylindrical stream flow surface can correspond to flow over a long ridge.44) where the radial distance r is measured from the origin of the coordinate system that coincides with the center of the sphere. and θ is an angle measured from the axis of symmetry and the wind is toward the sphere in the direction when angle θ is equal to 180 degrees. This analysis will able to predict the air movement over a solitary spherical hill.3 Impacts of Airfoil Characteristics on Rotor Performance The characteristics of an airfoil significantly impact wind turbine rotor performance. 3.
Surfaces of the constant dimensionless stream function (ψ/U a 2) and constant speed (q/U) can be plotted. .47) The surfaces of the constant flow speed (q).49a) (3.50a) (3.51a) The lines of constant speed known as isovelocity contours can be calculated as follows: [(r/a)–4 + 2(1 – 2 cos2θ) (r/a)-2] = [(q/U)2 – 1] (3. This is a quadratic equation in the cube of x or (a/r) and can be solved using standard methods.51b) Calculated values of the lines of constant velocity or isovelocity contours for 2-D flow over the sphere and cylinder are shown in Figure 3. normalized by the flow at infinity (U) can be determined from the solution of the following equation: [x-6 + 4 x-3{1 – 3 cos2θ/1 + 3 cos2θ}] = [4 (q/U)2 – 1/(1 + 3 cos2θ)] (3.5 (3.15(A) and Figure 3.6.2 Two-Dimensional Flow Analysis over Cylinder Solutions for flow over a cylinder can be given by the potential (φ) and stream (ψ) functions: Φ = [U (r + a 2/r) cosθ] Ψ = [U(r – a 2/r) sinθ] (3. can be calculated directly from the solution of Equation (3.15(a).Design and Performance Capabilities of Wind Turbine Rotors ◾ 105 The expression for the surfaces of constant flow speed (q) is: q = [Vθ2 + Vr2]0.5 (3. The 2-D flow over a sphere for constant speed is shown in Figure 3.49 b) in the following form: [r/a] = [A/2 sinθ] + [1 + (A/2 sinθ)2]0. which is equal to variable. 3. Streamlines defined by the constant value of (ψ/Ua).48) where x equals the ratio of sphere radius to radial distance (a/r).49b) The tangential velocity (Vθ) and radial velocity (Vr) components can be written: Vθ = [U {1 + (a/r)2} sinθ] Vr = [– U { 1 – (a/r)2} cosθ] (3.50b) where a is the radius of the cylinder and r is the distance as defined earlier.15(B).
3 1. Such devices may .15 Contours for two-dimensional airflow over sphere and cylinder. ejector shrouds.2 1. Precise classification is further complicated by machines that combine some or all of the basic features.0 (b) Isovelocity contours around a cylinder Figure 3.2 1. further distinction can be drawn between machines whose axes of rotation are parallel to the incoming wind and those whose axes are normal to the wind direction.4 1.0 (a) Isovelocity contours around sphere 2 1 1 2 0 1. but most fall into two main classes of wind turbines that extract power by employing lift of the surfaces and turbines that strictly depend on the drag of the rotating elements known as rotors or translating elements. Additional complications are introduced by machines that employ some form of stationary or moving augmenting devices such as inlet ducts.1 1. Aerodynamic scientists have presented various concepts for wind turbines and associated rotors. In case of rotors.106 ◾ Wind Turbine Technology 0 2 1 1 2 q/U = 1. or diffuser ducts.1 q/U = 1.
development. Design requirements and performance specifications for Savonius and Darrieus rotors are discussed. 3. Under certain circumstances. efficiency. 3. regardless of turbine axis configuration. Specific details on the penalties of augmentation devices are discussed in Chapter 2. the structural integrity. size. The studies further indicate that hills or ridges with abrupt sides are not suitable sites for augmentation.6. A rotor design must offer continuous operation with no maintenance. and 3-D aerodynamic models for wind turbine rotors are described. However. but impose additional weight. Power generated in the windstream can be determined using the following empirical formula: P (MW) = [(ρ π/8) D2 V3] (3.Design and Performance Capabilities of Wind Turbine Rotors ◾ 107 improve rotor performance. It is important to note that the rotor diameter must be less than the windstream diameter to capture maximum wind energy. dynamic stability. D is the windstream diameter (meters). even a sharp peak could be found suitable for such augmentation.52) where ρ is the air density (kilograms per cubic meter). and evaluation of a wind turbine system.4. and safe operation. and V is the wind speed in meters per second. and cost penalties.7 Summary Performance capabilities and limitations of various types of rotors used by wind turbines are summarized. testing.3 Power Generated by Windstream The power generating capability of a wind turbine is based on windstream diameter and the undisturbed wind speed in the vicinity of the turbine location. It should be noted that any repair or maintenance of a high-capacity wind turbine rotor will be extremely costly and time consuming because such rotors are located about 100 ft above the ground level. along with details concerning power coefficient and cost-effective operation. Analytical capabilities of 1-D. weight. emphasis is on reliability. The . dynamic stability. As mentioned. the rotor is the most critical element of a wind turbine. size. and efficiency of a rotor must be given serious consideration during design. Terrain studies performed by the author for the purpose of augmenting the average wind speed at a turbine installation location indicate that well rounded-hills and ridges are best suited for augmentation. Critical aerodynamic aspects of a rotor must be closely examined to ensure cost-effective performance and safe operation under a variety of wind environments. Computed values of power generated by the windstream as a function of wind speed are summarized in Table 3. 2-D. Rotor design configuration and performance requirements are different for HAWTs and VAWTS.
077 2 552 4.48 0.080 0. The 1-D axial momentum theory for an ideal wind turbine is described using the integral energy equation with emphasis on axial components of pressure forces.41 40/17.250 100/30.424 5. The effects of Coriolis and centrifugal forces on rotor performance are identified and shaft power developed by a rotor under various wind conditions is explained.219 200/60.72 0. The impact of thrust coefficient variation as a function of axial induction factor and the corresponding rotor states is discussed.35 50/15. Effects of rotation on streamlines and flow parameters are identified for modern high-capacity turbine rotors.984 150/45. Computed values of undisturbed wind speed as a function of blade length and blade angle are provided for readers who require comprehensive knowledge of wind turbines. 96 1.94 30/13.932 blade element momentum (BEM) theory and its applications to rotor blades are briefly discussed. conservation of mass theory.640 1.270 0.319 1.744 11.276 4. Wind turbine performance parameters affected by streamlines flowing over a rotor are summarized. Tip speed calculation as a function of rotor size or diameter and rotational speed is explained.718 2. and the forces generated by pressure distribution along the lateral walls of the control volume. 2-.208 19. Airfoil configurations most appropriate for all three types of aerodynamic models are identified. Factors that affect the tip speed of a rotor are identified. The importance of Euler equation parameters that affect the axial induction factor and axial rotor velocity is discussed briefly. expansion of the wake increases and causes a velocity jump from the incoming undisturbed wind speed to the wind speed past the rotor. Vortex theory applicable to a 3-D wing of finite length is reviewed with a focus on trailing vortices. and 3-D wind turbines are summarized. control volume around a wind turbine.4 Megawatts Generated by Windstream as Function of Diameter and Wind Speed Windstream Diameter (ft/m) Wind Speed (mph/m per sec) 20/8.24 0. A cascade of airfoils in a vortex system may be observed as function of .88 50/22. Expressions of power coefficient and thrust coefficient for an ideal one-dimensional wind turbine are derived in terms of rotor design parameters. Potential characteristics of airfoils best suited to represent the performance capabilities of 1-.307 10. As thrust coefficient increases. The vortex system behind a wind turbine is examined as are limiting streamlines on a modern wind turbine rotor under high wind speed environments.108 ◾ Wind Turbine Technology Table 3.
[4] S.L. Brentwood. Chichester. Introduction to Wind Turbine Engineering. 1983. Essentially. axial velocity. Rotor performance requirements are defined. isovelocity contours are obtained by solving the equations to determine the axial and tangential components of the rotational and axial speeds of a rotor. Butterworth. Earth Scan Publications. Wind Energy Technology. 2002. [5] J. Hydrodynamics analysis of the wind flow over a rotor is performed in terms of wind conditions and rotor design parameters. Mertems. VA. [3] T. Two-dimensional flow analysis using both potential and stream functions is performed over spherical and cylindrical rotor surfaces to determine isovelocity contours as functions of wind and other variables.F. Wind turbine designers feel that this type of analysis is vital for understanding the theoretical aspects and operating principles of wind turbines. Boston. London. airfoil pitch. and rotational velocity at the rotor plane. John Wiley & Sons. . Hansen. Walker and N. Wortman. 2nd ed. 8.. Wind Engineering in Building Environments. p. 18. These contours are determined from the lines of constant speeds of rotors as the function of an angle measured from the axis of symmetry. References [1] A. p. 46. 1989. Sterling. Development of Wind Turbine Projects. Aerodynamics of Wind Turbines. 2007. Multiscience Publications. Wizelius.K. 1992.O. [2] M.Design and Performance Capabilities of Wind Turbine Rotors ◾ 109 local angle of attack.J. Jenkins. U. James & Jane. p.
Chapter 4 Wind Turbine Blade Design Requirements 4.1 Introduction Understanding the blade theory applicable to a wind turbine blade is vital because the performance of a wind turbine is based on the number of blades assigned to a rotor and the design parameters of the blade elements. and relative wind speed. This chapter will investigate potential models of actual flow conditions to determine aerodynamic characteristics and predict performance. The Bernoulli equation for a stream tube ahead of the propeller disc between the plane very far in front of the propeller and a plane immediately in front will be derived in terms of axial interference factor. flow angle. This means aerodynamic considerations and properties of the fabrication materials require comprehensive examination during the design and development of the propeller or rotor blades. Aerodynamic analysis of an element of an airfoil will be undertaken to predict performance under a variety of flow environments. The blade theory states that the outer contour of the blade must be follow aerodynamic considerations and the materials used in its fabrication must be capable of providing the needed structural strength and stiffness. Expressions for the torque coefficient and power coefficient as a function of tip speed ratio. tangential interference factor. drag-to-lift coefficient ratio. and drag-to-lift coefficient ratio will be derived. Computed values 111 . drag and lift forces. blade loading coefficient. Situations under which the purely aerodynamic considerations of the blade area distributions are inevitably modified by the structural considerations to achieve safe and optimum blade performance will be explored. undisturbed wind speed.
Under these conditions. inertial loading. 4. and the deflections at the leading and trailing edges. compressive stress. drag-to-lift coefficient. Since no specialized theories cover the operation of a propeller-based wind turbine. Important sources of loading on turbine rotor blades resulting from the earth's gravitational field. Also shown are all the wind component parameters and aerodynamic forces acting on the blade element under consideration. and blade tip speed ratio will be summarized.1) where ρ is the air density (1. V is the undisturbed wind velocity.1 Aerodynamic Performance Analysis of Blade Elements The flow at an element of width dr located at radius r on a propeller blade rotating at an angular rate of ω is shown in Figure 4. Furthermore. 4. with emphasis on aerodynamic considerations.112 ◾ Wind Turbine Technology of variations of pitch angle as a function of dimensionless radius. and aerodynamic loading on the mechanical integrity of a blade section will be described with a focus on tensile stress. vortex blade element analysis essentially involves an infinite number of blade models and yields surprisingly good analytical results. It is important to mention that the radial velocity is very small and the propeller does not induce any tangential velocity component u. and p0 is the pressure in front of the propeller. Materials and their properties best suited for the fabrication of the rotor blades will be identified along with discussions about strength and stiffness required to ensure high structural integrity under severe wind environments. Studies performed by the author reveal that the best engineering model is the one that involves the actuator disc analysis of airfoil elements. the Bernoulli equation for the planes in front of the propeller and far downstream.225 kg/m3). p is the pressure immediately in front.2 Analysis of Performance of Propeller Blades It is interesting to mention that propeller-based wind turbines span a very wide range of designs from relatively low angular rate Dutch windmills at one end and very high-speed slender propellers at the other end. The expression for the Bernoulli equation for a stream tube ahead of the propeller disk element between a plane very far in front of the propeller and plane immediately in front can be written: [(ρ/2) V2 + p0] = (ρ/2) [V2 (1 – a)2 + Vrad2] + p (4. using the assumptions . Vrad is the radial wind velocity. Beam theory applicable to blade design will be discussed in detail.1. it is necessary to rely on appropriate models of flow situations best suited for the flow characteristics and other parameters that must be analyzed to predict wind turbine performance. Equations for the deflections and bending moments at specific points along the blade length will be derived.2. a is the axial interference factor.
and each radial velocity is equal to zero. that u is equal to u1.1 Relationships of blade element parameters.3) .2) where p´ = [(–ρ V) (V – V1/2] and V1= [2 a V] (4.Wind Turbine Blade Design Requirements ◾ 113 POS 2 Leading edge POS 1 Tensile stress Tensile stress ω Trailing edge Trailing edge Compressive stress Compressive stress Leading edge mg (a) Loading effects from the earth's gravitational field Fc = ω2rmdr dr dF = ωrmdr r T Fccosθcone r Fccosθcone T = Braking torque to rotor dF = Force experience by blade r = Radius from the rotating axis V θcone m = Mass per unit length of blade. can be written as: [(ρ/2){V2(1 – a)2 + Vrad2 + u2} + p + p´] = [(ρ/2){(V – V1)2 + Vrad2 + u12} + p1] (4. p0 is equal to p1.4) (4. I = Moment of inertial (b) Effects of inertial loading on turbine blades Figure 4.
5) and (4.7) and Equations (4.12a) where X = [r Vang/V] (4.8) When the corresponding terms in Equations (4.1. and φ is the flow angle.8) are equated. the expression for the elemental torque and power [1] for N rotor blades of chord dimension c is: dT = [(ρ/2) Vrad2 N c (CL cosφ + CD sinφ) dr] dP = [(ρ/2) Vrad2 N c (CL sinφ – CD cosφ) r Vang dr] (4. ε is the drag-to-lift coefficient ratio. the result is: [(a/1 – a)] = [λ (1 + ε tanφ) cotφ cscφ)] [(a´/1 + a´)] = [λ (1 – ε cotφ ) secφ] (4.114 ◾ Wind Turbine Technology Note that parameter u is the tangential velocity component ahead of the propeller. The expression for the power coefficient can be written as: CP = [(dP/dr)/(2 π r ρ V3/2] = [{4 a(1 – a) X}(tanφ – ε/1 + ε tan φ)] (4. and CL is the coefficient of lift. a´ is the tangential interference factor. r is the radius of the blade.2. The blade loading coefficient is defined as: λ = [N c CL/8 π r] (4.5) Since the moment imparted to the fluid equals the torque (dT). 4.12b) .7) (4. C is the chord length.11) where N is the number of blades.6) and (4.9) (4.10) where λ is the blade loading coefficient.6) Based on the relationships shown in Figure 4. a is the axial interference factor. expression for the power in this infinite annular area can be written as: dP = [(4 π r3ρ V Vang2] [a´ (1 – a) dr] (4.2 Thrust and Power on Annular Area of Blade The expression for the thrust on an annular area (2 π rdr) can be written as: dT = [(4 π r3 ρ V2 a) (1 – a) dr] (4.
Wind Turbine Blade Design Requirements ◾ 115 R L w Di αi Symbols: L = Length of blade R = Radius of rotor αe αg Figure 4.15) leads to: [tanφ] = [sinφ – (X´. Equation (4.15) .ε) CDL´]/[(X´ – ε) sinφ + CBL´] where X´ = [X (1 + ε tanφ)] and CBL´ = [CBL ( 1 + ε tan)] (4.2 shows the impact of angle of attack on the lift produced and induced drag on a 3-D wing section.13) By eliminating a´ using Equations (4.2 Impact of angle of attack and induced drag.2. Vang is the angular blade speed and V is the undisturbed wind speed.14) (4.16b) (4.12a) is maximized for a given value of the tangential speed ratio X. Figure 4.3 Conditions for Maximum Power Output Maximum power output can be achieved when the right side of Equation (4.10).13) can be rewritten as: [X tanφ] = [1 – ( a sec2φ/1 + ε tanφ)] Elimination of parameter a from Equation (4. 4.16a) (4.9) and (4. Based on the geometrical relationship: [tanφ] = [(1 – a)/(1 + a´)]/X or [cotφ] = X [(1 +a´)/(1 – a)] (4.
4.22 0.05 .25 0.21 0.3 Blade Performance Optimum blade performance for a given drag-to-lift ratio is critical. particularly when calculated as a preliminary estimate.32 0. which may be impossible under certain wind conditions.43 0.116 ◾ Wind Turbine Technology 4.12 0. The calculated values indicate that the maximum values of power coefficients occur for the tangential speed ratio (X) when it varies between 1 and 4 regardless of the values of ε.43 0.075 0. maximum values of power coefficients occur when ε is equal to zero.47 0. Therefore.3.38 0. Blade performance is measured in terms of power coefficient CP.03 0. any variation of either parameter will affect the variation in the axial interference factor or coefficient a. Computed values of the power coefficient as function of tangential speed ratio (X) for various values of ε are summarized in Table 4. Any variation in axial interference may affect the mechanical integrity of a blade.1 Power Coefficient Calculation as Function of Tangential Speed Ratio (X) and Drag-to-Lift Coefficient Ratio (ε) Drag-to-Lift Coefficient Ratio (ε) Tangential Speed Ratio (X) 1 2 4 6 8 10 0.48 0.41 0.42 0.46 0. which is a function of the tangential speed ratio X for a given range of values of drag-to-lift coefficient ratio ε.2 Axial Interference Factor Axial interference factor a plays a key role in derivation of other parameters that are vital for the design and development of a turbine blade.1.33 0.1 Power Coefficient Power coefficient defines the performance of a wind turbine in terms of relative power level as a function of tangential speed ratio and drag-to-lift coefficient ratio. Calculated values of variation in the axial interference factor as a Table 4.33 0.01 0 51 0 55 0 56 0 53 0 52 0 50 0.05 0. However. 4.3. Studies of aerodynamic scientists indicate that the axial interference factor or coefficient depends on the drag-to-lift coefficient ratio (ε) and tangential speed ratio (X) values.47 0 51 0.
257 0. both the blade loading coefficient .01 0.303 0.2.274 0. moderate variations in the torque grading coefficient are seen at a given tangential speed ratio when the drag-to-lift coefficient varies from 0 to 0.242 0.3.331 0.333 0.10 0.05 0. Note very large variations in torque grading coefficient occur when the tangential speed ratio exceeds about 8.1. The rate of torque generated is strictly dependent on the torque grading coefficient. Based on these values.3. which is a function of tangential speed ratio (X) and drag-to-lift coefficient (ε).01. the variation in the axial interference coefficient is extremely small when the tangential speed ratio varies from 1 to 10 at a drag-tolift coefficient ε equal to 0.322 0.317 0.335 0.284 0.285 0. As mentioned previously. regardless of the values of the dragto-lift coefficient.294 0.328 0.318 0.325 0. This conclusion also applies to power coefficient variations.3 Torque Grading Coefficient Wind turbine output is a function of torque generated by a turbine rotor.311 0.234 – 0.334 0. It is evident from these calculated values that large variations in the torque grading coefficient occur over a wide range of tangential speed ratios for a given drag-to-lift coefficient. irrespective of the magnitude of drag-to-lift coefficient.270 0.Wind Turbine Blade Design Requirements ◾ 117 Table 4.242 0.2 Computed Values of Variations in Axial Interference Coefficient (a) Drag-to-Lift Coefficient (ε) Tangential Speed Ratio (X) 1 2 3 4 5 6 7 8 9 10 0. 4.328 0.274 0.296 0.334 0. However.212 0.290 0. Calculated values of torque grading coefficient variations as a function of these two parameters are summarized in Table 4.304 0.175 – – – – function of drag-to-lift coefficient and tangential speed ratio are summarized in Table 4.322 0.318 0.03 0.285 0.297 0.312 0.320 0.280 0. The variations in the axial interference coefficient increase as a function of tangential speed ratio.
082 0.072 0.10 0.062 0.085 0.092 0.048 0. observed particularly at lower tangential speed ratio (X).05 0.034 0. particularly at lower values of the tangential speed ratio (X) as illustrated by Table 4.074 0.103 0.18) (4.065 0. The blade loading coefficient is the most critical parameter because its impacts the mechanical integrity of a blade under severe mechanical environments.118 ◾ Wind Turbine Technology Table 4.205 0.03 0.5% near the blade tip.4 Blade Loading Coefficient The author's preliminary aerodynamic studies of rotor blades indicate that both the blade loading coefficient λ and the relative flow angle are insensitive to large variations in the drag-to-lift coefficient.4. Blade sections with .072 0.295 0.059 0.026 – 0.165 0.023 – – – – and the relative flow angle are insensitive to large variations of the drag-to-lift coefficient.039 0.165 0.128 0.3.256 0.057 0.169 0. The blade loading coefficient as defined by Equation (4.3 Variations of Torque Grading Coefficient as Function of Tangential Speed and Drag-to-Lift Coefficient Drag-to-Lift Coefficient (ε) Tangential Speed Ratio (X) 2 3 4 5 6 7 8 9 10 0 0.034 0.11) can be rewritten: λ = S [CL/4] where S is the solidity parameter and: S = [N c/2 π r] (4.128 0.158 0.056 0.238 0.17) The theory of wind turbines reveals that solidity can be approximated by seven times the blade loading coefficient (λ) during the preliminary design analysis. 4.041 0. this corresponds to a solidity of about 1. For a wind turbine with a drag-to-lift coefficient of zero and a tip speed ratio of 10.033 0.196 0.
aero-elastic effects. and blade loading are shown in Figure 4. and fatigue conditions.5 to 0.046 0. Turbine blades with high solidities must be discarded if efficient and stable operation is the design goal.014 0. Computed values of variation of the blade loading coefficient as a function of tangential speed ratio (X) and drag-to-lift coefficient (ε) are summarized in Table 4.020 0.005 0.1 and tip speed ratios of 2 will be very inefficient and the corresponding solidities will be close to 45%.0035 0. regardless of the magnitude of the drag-to-lift ratio (λ).0028 0.11).8.0022 – 0.011 0.05 0. It must be stressed that that the purely aerodynamic design considerations for blade area distributions may be modified by structural considerations that may introduce centrifugal loads.Wind Turbine Blade Design Requirements ◾ 119 Table 4.125 0.023 0.10 0. The various parameters were defined under Equation (4. It is obvious from these tabulated data that only moderate .0038 0. These computed values indicate little change in blade loading coefficient over a tangential speed ratio ranging from 1 to 3.125 0. namely Earth's gravitational loading.015 0.0023 0. the solidity parameter (S) can be approximated by 7λ.1.009 0.4 Variations of Blade Loading Coefficient as Function of X and ε Parameters Drag-to-Lift Coefficient Tangential Speed Ratio (X) 1 2 3 4 5 6 7 8 9 10 0 0. Various types of loadings involved in wind turbine design.004 – – – – drag-to-lift coefficients of 0.0046 0.007 0.4.006 0. Under these parametric conditions.The aerodynamic theory of a blade reveals that the distribution of the blade loading coefficient (λ) as a function of dimensionless radius and coefficient of load can be achieved.125 0. The theory further reveals that for representative airfoil sections.0027 0. Various forces and torques generated by these loading effects are also illustrated. minimum value of drag-to-lift coefficient (ε) occurs when the coefficient of lift (CL) varies from approximately 0.045 0.008 0.025 0. internal loading.044 0.
However. irrespective value of the drag-to-lift coefficient. Table 4.5 Variation of Relative Flow Angle (φ) as Function of Tangential Speed Ratio and Drag-to-Lift Coefficient Drag-to-Lift Coefficient (ε) Tangential Speed Ratio (X) 1 2 3 4 5 6 7 8 9 10 0 32 17 13 9 7 6 5 4 3 4 0.5. Variations in wind speed as a function of flow angle along the axial length of the rotor blade are shown in Figure 4.10 34 19 15 11 9 8 – – – – . This means that flow is least affected from the variations in the magnitudes of tangential speed ratio and the drag-to-lilt coefficient.5 Variations of Flow Angle as Function of Tangential Speed Ratio and Flow Angle Analytical studies by the author revealed that minute variations in flow angle occur as a function of tangential speed ratio and drag-to-lift coefficient.3.05 33 18 14 10 8 7 6 5 4 – 0.120 ◾ Wind Turbine Technology variations occur in the blade loading coefficient when the tangential speed ratio varies from 4 to 10.3. 4. the difference between the relative variations is small at a given drag-to-lift coefficient and given tangential speed ratio. Note that the flow angle is the sum of the blade pitch angle (β) and the angle of attack (α). These tabulated data indicate that the variation of the relative flow angles decreases with the increase in the tangential speed ratio regardless of the value of drag-to-lift coefficient. this may be verified from the computed data summarized in Table 4.
3.6. regardless of the value of the drag-to-lift coefficient. If the plots for power coefficient versus tip speed ratio (X0) are drawn for various values of ε. The variation of the power coefficient . It is important to mention that the maxima of the overall power coefficients occur over tip speed ratios ranging from 2 to 5.6R 0.3 Impacts of variations in wind speed. 7 9 14 27 Figure 4.2R Wind speed (m/s) 60 48 36 26 12 Flow angle 60 deg. then the peaks of the curves will be found optimum for the tip speed ratios for wind turbines whose blades have a pitch distribution along the radius that corresponds to the optimum turbine operation for a particular tangential speed ratio and the drag-to-lift coefficient.Wind Turbine Blade Design Requirements ◾ 121 =6 =7 =9 = 14 = 27 Wind speed as a function of flow angle and at various blade locations Blade radius Or (blade tip) 0. Based on these tabulated data. The speed ratio and drag-to-lift coefficient are the most critical parameters affecting wind turbine power. also known as power coefficient. is a function of tip speed ratio and drag-to-lift coefficient. irrespective of the magnitude of drag-to-lift coefficient. The power coefficient continues to maintain optimum values over a tip speed ratio ranging from 1 to 10. The impact of tip speed ratio and the drag-to-lift coefficient on the power coefficient is evident from the computed values in Table 4.6 Impact of Tip Speed Ratio and Drag-to-Lift Coefficient on Wind Turbine Power Coefficient Wind turbine efficiency.8R 0.4R 0. the maximum values of the power coefficient occur when the tip speed ratio varies from 2 to 6 approximately. 4.
428 0.122 ◾ Wind Turbine Technology Table 4.05 0.464 0.7 Variations in Pitch Angle as Functions of Radius The pitch angle of a blade plays a key role in maintaining a near-uniform rotor speed under variable wind speed environments—a requirement to achieve optimum power output from a wind turbine. which means that ε is equal to ε 0.448 0.1 radian (5. However.491 0.01 0. . The value shown under the 0.537 0.386 0. These computations assume a minimum drag-to-lift coefficient of zero.492 0.486 0.502 0.417 0.422 0. It is evident from these results that the variations in pitch angle decrease rapidly as a function of tip speed ratio.450 0.01 and 5. moderate variations in pitch angle occur at a given tip speed ratio when the drag-to-lift coefficient varies from 1 to 10.445 0.531 0.545 0.449 0.550 0.532 0.7.333 – with tip speed ratio increases rapidly with increasing magnitudes of the drag-to-lift coefficient and this indicates the high sensitivity of inefficient rotor blades to offdesign conditions. If the distribution of the turbine power output is plotted as a function.01/5 column means that the variation in the pitch angle is optimum when the drag-to-lift coefficient and the tip speed ratio are 0. Computed values of variations in pitch angles at a given angle of attack of 0.6 Impacts of Tip Speed Ratio and Drag-toLift Coefficient on Wind Turbine Power Coefficient (CP) Drag-to-Lift Coefficient (ε) Tip Speed Ratio (X0) 1 2 3 4 5 6 7 8 9 10 0 0.402 0.03 0.3.430 0 513 0 555 0 562 0 550 0 578 0 580 0 585 0 586 0 587 0.358 0. regardless of the value of the drag-to-lift coefficient.535 0.402 0.452 0.412 0.528 0. one will notice that about 5% of the total wind power is produced in the disc area corresponding to 20 to 25% of blade radius.477 0. 4.73 degrees) and as a function of dimensionless radius r/R are summarized in Table 4.552 0.428 0.
the performance of a complete blade corresponds to an interval of one of the curves as illustrated in Figure 4. these computations were carried out for an angle of attack of 5. For any value of a drag-to-lift coefficient (ε).01/5 35 17 12 8 7 5 4 3 2 0. Similarly. All these numerical data are vital aspects of the design and development of blades for wind turbine applications. It is important to point out that blades must be designed for optimum power generating performance and improved mechanical integrity under severe wind conditions.2. . Drag-to-Lift Ratio. As stated earlier. Optimum performance requires a variation of the airfoil sections along the radius to ensure that each element operates at its minimum drag-to-lift coefficient—the principal design consideration.05 and 3.7 Degrees of Variation in Pitch Angle as Function of Dimensionless Radius. but such fine points of design optimization will not be considered here. It is not uncommon to use different airfoil sections in the inner and outer regions of the blade. the value shown under the 0.05/3 column indicates that the variation in the pitch angle is optimum when the drag-to-lift coefficient and the tip speed ratio are 0. and Tip Speed Ratio Drag-to-Lift Ratio/Tip Speed Ratio (ε0/X0) Dimensionless Radius (r/R) 1 3 4 5 6 7 8 9 10 0.03/3.05/3 43 26 22 17 14 12 10 8 7 respectively. Note this interval starts at a very low value of the tangential speed ratio (X) corresponding to the hub of the blade and terminates when X equals the tip speed ratio (X0) of the wind turbine and is often used to characterize the particular design.Wind Turbine Blade Design Requirements ◾ 123 Table 4. respectively.5 39 24 19 14 12 9 8 6 5 0.73 degrees—considered ideal for blades used in wind turbines. The structural considerations at the hub constitute a different design problem and no attempt is made to assess or achieve aerodynamic performance there. The author's studies of blade performance indicate that the effects of tip losses and hub blockage barely degrade wind turbine performance—no more than 3 to 5% and these effects will not be discussed in detail.
5 can be modeled as a beam.Specific details on simple beam theory are Figure 4. and circumferential force as shown in Figure 4. Note the lift and the circumferential force components acting on the blade play an important role in the performance of a wind turbine rotor. 4. . forward thrust. A section of the blade illustrated in Figure 4. The magnitudes of these forces depend on the plane of rotation and flow angle. and geometrical parameters of the blade. The roles of these forces and aspects of stiffness and mechanical integrity will be discussed.5 Calculation of blade stresses and deflections.124 ◾ Wind Turbine Technology Lres L D j Wres Lres j = α + β [sum of blade angle and angle of attack] = Flow angle Fthrust Fcirc Plane of rotation Fcirc = Circumferential force Figure 4. the simple beam theory can be applied to compute the stresses and deflections at various locations on the blade.3.4.4 Forces exerted on wind turbine blades. drag.8 Forces Acting on Blades A wind turbine blade is subjected to several forces that depend on pitch angle. When the stiffness factors EI and GI at different span levels are calculated as a function of geometric parameters and fabrication material properties. residual lift. Parameter E is the modulus of elasticity (Young's modulus). G is the modulus of shear elasticity. and I represents moments of inertia at various locations along the blade as shown in Figure 4. These forces include lift.5. angle of attack.
The flap-wise bending is mostly produced by aerodynamic loads that vary with the turbulent wind fields and is relatively less serious than adverse effects produced by the earth's gravitational field and inertial loading as illustrated in Figure 4. and shear resistance under extreme thermal and mechanical environments. and other factors required to ensure blade integrity under severe thermal and mechanical environments. Fiberglass offers high stiffness.Wind Turbine Blade Design Requirements ◾ 125 Foam Webs Gelcoat Glass fibre mats and epoxy Figure 4. the wind speed at the hub of the blade. exothermic properties. Gelcoat. Various materials used in the fabrication of a blade are described in Figure 4. readily available in basic books on mechanics of materials such as Timoshenko's 1972 text. The most common materials used include foam. the aerodynamic loading as a function of wind speed conditions. upon which is superimposed some small high-frequency signals originating from atmospheric turbulence conditions. If epoxy materials are used. 4. glass fibers. The structural parameters are described as follows: . and the gravitational loading on the blade all affect the mechanical integrity and consequently the reliability of rotor blades.1 Structural Parameters and Stresses Figure 4. The tilt of the nacelle.3. The effect of gravitational loading is very severe on the edge-wise bending moment as a dominant sinusoidal vibration.9.3. it is vital to select an optimum housing metal (steel or aluminum) and evaluate the critical performance characteristics of the embedding resins such as viscosity.6.3. and epoxies that have unique characteristics. flexural strength.9 Mechanical Integrity Structural reliability and mechanical integrity must be given serious consideration during the design phase. the flap-wise and edge-wise bending moments of the blade.6 Blade fabrication details. 4.7 illustrates the main structural parameters and various stresses or forces acting on a section of a beam.
126 ◾ Wind Turbine Technology EI1 Chord β+ν Reference point Xs c/4 Symbols: v = Angle between first principal axis and chord line. EA = longitudinal stiffness ESXR = moment of stiffness about the axis X R (X R. Y R) = reference coordinate system as indicated by black dot EI XR = moment of stiffness about axis X R (Figure 4.7 Structural parameters and stresses. The impacts of critical quantities such longitudinal stiffness (EA) and moment of centrifugal stiffness (EDXYR) defined in terms of reference coordinate system on the blade must be described in detail. EI1 = bending stiffness about the first principal axis EI2 = bending stiffness about second principal axis GIv = torsional stiffness X E = distance of the point of elasticity from the reference point shown in Figure 4. The moment of inertia (I) about one of the principal axes plays a key role in the blade deflection. The s point where the shear stress is concentrated will not give rise to a deflection under shear stress and will not rotate the airfoil. The reference coordinate system (X RY R) is illustrated in Figure 4. EI2 = Second principal axis EL1 = First principal axis c = Chord length XS´ Xe and Xm various force components acting on the blade EI2 Second principal axis First principal axis ν XE Xm Figure 4.8) EI YR moment of stiffness about axis Y R (Figure 4.6 X m = distance of the center of the blade mass from the reference point X s = distance of the shear center from the reference point β = angle of twist of airfoil section measured with respect to the reference line v = angle between chord line and first principal axis The point of elasticity is defined as the point where the normal plane will not give rise to a bending moment of the beam.7.8) EDXYR = moment of centrifugal stiffness .
8 Forces acting on wind turbine blades. Using these quantities. the point (X E.Wind Turbine Blade Design Requirements ◾ 127 y y´ X yE PE α X´ XE Figure 4. The angle of attack (α) between the X´ axis and first principal axis and the bending stiffness about the principal axes can be calculated from these equations. Shear center and the torsional rigidity can be calculated using computer analysis. which is parallel to the reference system (X R. Since a wind turbine blade is generally very stiff in torsion. the torsional deflection is normally neglected.22) (4.21) where the constant σ.y) = [E (x.Y´). Also the stress equation can be written as: Σ (x. the expression for the point of elasticity can be easily written.y)] where the expression for the strain can be written as: Σ (x.y) = M1 y/[EI1] – M2 x/[EI2] + N/[EA] (4.20) Using E (Young's modulus) and ρ (material density). ε.8.y)][ε (x.Y E) can be calculated in the reference system as: X E = [ESYR] Y E = [ESXR] (4.8.Y R) as shown in Figure 4. the point of elasticity PE (X E . .Y E) represents the center of mass for the section illustrated in Figure 4. These parameters now can determine the main structural characteristics.19) (4. and N are positive for tension and negative for compression and the normal Force N can computed from the loadings on the blade. If the moment of stiffness inertia and moments of centrifugal stiffness are moved to the coordinate system designated as (X´.
The shearing forces and the bending moments can be calculated using the following equations [3]: [dTz/dx] = [– pz(x)] + [m(x) d 2U(x)/dz2] [dTy/dx] = [– py(x)] + [m(x) d 2U(x) / dy2] [dMy/dx] = Tz (4.2 6. and bending moments of the blade are shown in Figure 4.30 8.44 9.5 7500 362 328 207 92.91 0.83 1.128 ◾ Wind Turbine Technology Table 4.25) .76 2.0 12. Deflections.9.82 0.0 15.7 12.0 21. See Figure 4.6 24.0 36.0 6.4 0.9 is different from the system shown in Figure 4.32 12000 1725 1940 1490 905 557 349 221 131 65.23 (4.0 18.83 0.10.82 5.8 3.2 00 2 54 59 63 58 51 45 41 40 47 82 00 2 159 165 170 158 137 121 110 102 108 136 00 0 11 13 18 15 15 16 17 16 14 10 00 5.9.3. Note the coordinate system used in Figure 4.8.0 9.63 0.8 47.33 1.83 2.04 1.7 24.14 5.2 Shearing Forces and Bending Moments in Presence of External Forces The magnitudes of shearing forces (Tz) and Ty) and bending moments (My and Mz) acting on a blade in the presence of external forces are different from those in the absence of the external forces (py and pz).21 0.10 4.8 Structural Parameters of 2 MW Tjaereborg High-Performance Wind Turbine Radius EA EI1 EI2 GIy Mass XE Xm Xs v β+V (m (GN) (MNm)2 (MNm)2 (MNm2) (Kg/m) (mm) (mm) (mm) (deg) (gdeg) 1.84 0.21 12000 1630 1080 623 2 55 129 64.9 6.4 9.5 6.86 086 0.8. 4.24) (4.0 24.94 1. various forces acting on the blade.1 9.0 27.33 2.18 1700 330 389 347 283 235 196 166 172 90.09 0.16 –0 52 Various structural data for a 30-m turbine blade used on a 2-MW Tjaereborg wind turbine are summarized in Table 4.3 52.09 6.7 28.63 1.86 4.4 15.63 0.3 1.8 32.06 3.86 5.0 4.0 30.23 2 57 0.91 3.16 –0 52 00 14.
10. z x R pz (x) [N/m] y i i+1 N Figure 4.23) and (4. respectively. Although these equations have been taken from Walker [4].Wind Turbine Blade Design Requirements ◾ 129 z y x (a) Locations of various axes of the blade pdx T + dT M M + dM T (b) Various bending moments and forces acting on the blade Figure 4.26) where m is the mass and d2Uz/dz2and d2Uy/dy2 are the accelerations along the z and y directions.9 Deflections and bending moments.24) approach zero. [dMz/dx] = Ty (4.10 Shearing forces and bending moments. and U(x) is the velocity in the x direction as illustrated in Figure 4. If the blade is at equilibrium. the final (inertial) terms on the right sides of Equations (4. the expressions can be derived using the Newton's second law on an infinitesimal section of beam and using the parameters .
4. tensile strength. Specific details on their mechanical and aerodynamic specifications are contained in the latest hand books on material science.6 Critical Features of Blade Section Specific features of an actual turbine blade section can be seen in Figure 4.5 Material Requirements for Blades It is extremely important to mention that the selection of the blade material depends on several parameters including mechanical strength. This section describes how a rotor blade whose outer contour adheres strictly to aerodynamic considerations is fabricated to be sufficiently strong and stiff to withstand various forces under unusual wind conditions. Materials used in the past such as wood. Newton's second law is best suited to solve fluid dynamics problems. Simple beam theory can be applied to compute various stresses and deflections as shown in the figure. aluminum. blade geometrical parameters. 4.130 ◾ Wind Turbine Technology illustrated in Figure 4.9(B). the fatigue properties of the material are vital. and angle of attack. stiffness factor. and carbon-fiber-reinforced plastic (CFRP) have not demonstrated the required strength and stiffness under extreme wind environments. A turbine blade can be modeled as a simple 3-D beam when the stiffness factors EI and GI as illustrated in Figure 4. 4. glass fiber-reinforced plastic (GFRP). and I is the moment of inertia for different sections of the blade.4. Several blade materials now available are capable of meeting specific structural and aerodynamic requirements.5 at different span-wise stations are computed. deflections and bending moments as functions of the materials used in fabricating the blade elements. and fatigue properties of the material. Note that E indicates the modulus of elasticity of the material. A computer model is available to compute structural parameters of a turbine blade with emphasis on rigidity. G represents the modulus of elasticity for shear. According to turbine blade designers. Structural parameters must be determined for blade materials considered for turbines operating in harsh . airfoil configuration. weight and price per unit of length.4 Application of Beam Theory to Various Turbine Blade Configurations Aerodynamic studies performed by the author indicate that beam theory can be applied successfully to design various blade configurations.
It is absolutely essential to compute the deflections of the blade for a given load condition or as an input to a dynamic simulation using aeroelastic codes recommended by blade designers as best suited to provide high mechanical integrity in adverse wind conditions. Sometimes under extreme wind conditions. If the total induced velocity is in the same direction as the force and perpendicular to the local velocity. A device such as the triangle installed on a turbine blade element as illustrated in Figure 4. In addition. angle of attack. 4. Because computation of structural parameters similar to those summarized in Table 4.27) (4. the flap-wise and edge-wise bending moments.26) (4. two bending moments at the root of the tower will tend to disturb mechanical stability even at a moderate wind speed of 11 m/sec.Wind Turbine Blade Design Requirements ◾ 131 mechanical environments to avoid catastrophic damage to tower and the turbine components. the following performance expression for a small wind turbine can be written: [ x 2 a´ (1 + a´)] = [a´(1 – a] where x = [w r V0] a´ = [ (1– 3a)/(4a –1)] (4. axial interference factor (a). 4. radius (r).25) .6. The yaw motor movement tries to turn the nacelle back on the tower. the electrical performance of small wind turbines with optimum power output can be determined by the following equations so long as the angle of attack is below stall level and parameters a and a´ are not independent.1 Impacts of Bending Moments and Blade Instability on Performance It is interesting to mention that any rotor blade movement or instability will try to tilt the nacelle over the tower. tilt motor and yaw motor bending moments. wind speed (V). Flap-wise bending is somewhat reduced by the aerodynamic loads that vary with the turbulence wind field.2 Role of Wind Triangle A wind triangle on a turbine blade element plays key role in predicting the preliminary performance of wind turbines with output capacities not exceeding 10 kW.8 will not be cost-effective because of 10 × 10 matrix elements. and atmospheric turbulence may affect turbine blade stability.11 can provide a preliminary indication of blade performance as a function of flow angle (φ).6. and axial interference factor for turbines with output power levels not exceeding 10 kW.
and x) and wind triangle configuration for a wind turbine are shown in Figure 4.02 0. a´.31 0.27 0. Computed values of performance parameters (a.33 0.34 Axial Interference Factor a´ (a) Performance parameters for an ideal windmill Q´ a Performance Parameters a´ X X2 dCp/dx W φ α V (1 – α) ζ Ωr (1 + α´) (b) Wind triangle for a wind turbine blade Figure 4.07 0.32 0.04 0.03 0.132 ◾ Wind Turbine Technology 10 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 0.28 0. The figure illustrates the absolute velocity of the blade and hence is referred as the velocity triangle downstream .30 0.333 which is consistent with the optimum power coefficient. The optimum value for the axial interference factor tends to be 0.06 0.29 0.25 0.08 0.26 0.01 0.11. where w represents rotational speed.11 Wind triangle on turbine blade.05 0.
From an efficiency view.12 Performance curve as function of axial interference. Note that the axial velocity through the rotor is expressed by the axial induction factor or axial interference factor (a). and r is the blade radius [5]. Aerodynamics aspects and fluid dynamics considerations have been discussed in detail.5 2 x(If. Figure 4. 4. For a given power level P and wind speed.Wind Turbine Blade Design Requirements ◾ 133 3 2. Critical aspects of the blade theory have been described for the benefit of graduate students and blade design engineers.31 0.7 Summary This chapter focuses exclusively on wind turbine blade design.3 0.28 0. The blade theory states that the design of the outer contour of a blade must be based on aerodynamic considerations and the materials used in blade fabrication . The performance curve of a turbine is expressed in terms of parameter x that denotes the ratio between the local rotational speed and the wind speed. w is the rotation speed of the blade in the wake. the azimuthal velocity component in the wake decreases with the increasing rotational speed w of the rotor.25 0. Iff) 1.33 Figure 4. of the blade.27 0. The performance of a wind turbine is strictly dependent on the number of blades attached to the rotor and their geometrical dimensions.5 0 0.29 If 0. The rotation speed of the blade in wake is given as (2 a´ w r) where a´ is the axial induction factor in the wake.26 0.5 1 0. axial induction factor in wake (a´) and the power optimization term (x 2dCp/dx) where Cp denotes the power coefficient.12 depicts a typical wind turbine performance curve as a function of axial interference factor along with computed values of a and a´ parameters. it is highly desirable for a wind turbine to have a high rotational speed to minimize the kinetic energy loss in the rotating wake.32 0.
This means that aerodynamic considerations and mechanical properties of the fabrication materials must be evaluated carefully during the design and development of a rotor blade.134 ◾ Wind Turbine Technology should provide the needed structural strength and stiffness under all operating conditions. In summary. Workman. specifically in relation to mechanical strength and stiffness under extreme wind environments [6]. drag-to-lift coefficient ratio.O. . Equations for computing deflection and bending moments at specific points along the blade length are provided. Proven models of actual flow conditions must be investigated for an engineer to predict aerodynamic performance of an airfoil accurately and under a variety of flow conditions. Butterworth. Fabrication materials and properties best suited for turbine blades are described. flow angle. rotor blade dimensions are strictly dependent on output capacity.J. compressive strength. and stiff resistance of the materials used to fabricate the leading and trailing edges. Expressions for the torque coefficient and power coefficient as a function of tip speed ratio. and operating environment in the vicinity of the installation site. torsional strength. 1992. drag-to-lift coefficient. pp. Important sources of loadings on rotor blades resulting from the earth's gravitational field and inertial and aerodynamic factors are identified and their effects on the mechanical integrity of blades and rotor stability are discussed in detail. and relative wind speed. Mechanical strength and rotational stability of blades are vital and must be considered early in the design phase. 1983. Computed values of variations in pitch angle as a function of dimensionless radius. and drag-to-lift coefficient have been derived. and blade tip speed ratio are provided. 8 and 107. drag and lift forces. Mechanical integrity of a rotor blade is dependent on its tensile strength. James. blade loading coefficient. Introduction to Wind Turbine Engineering. tangential interference. Beam theory applicable to blade design is discussed in detail. wind speed. with emphasis on aerodynamic considerations and mechanical integrity under a variety of wind conditions. undisturbed wind speed. [2] M. This chapter also identified situations under which purely aerodynamic considerations may be modified by structural considerations to achieve safe and optimum blade performance under all speed environments. References [1] A. Mechanical integrity of the blades and turbine installations are critical under conditions of severe winds. Aerodynamics of Wind Turbines. London. The Bernoulli equation for a streamtube ahead of a propeller disc between a plane very far in front of the propeller and a plane immediately in front of it must be derived in terms of axial interference. p. Boston.L. Hansen. 57. Methods for maintaining mechanical stability and rotor operational safety have been recommended.
Wind Turbine Blade Design Requirements ◾ 135
[3] T. Wizelius, Developing Wind Turbine Projects, Earth Scan, Sterling, VA, 2007. [4] J.F. Walker, Wing Energy Technology, 1996, John Walker & Sons, West Essex, U.K. [5] A.R. Jha, Technical report: preliminary design aspects for wind turbine rotors, Jha Technical Consulting Service, Cerritos, CA, 1999, p. 7. [6] C.A. Harper, Ed., Handbook of Materials and Processes, McGraw Hill, New York, 1984, p. 79.
Chapter 5
Sensors and Control Devices Required for Dynamic Stability and Improved Performance under Variable Wind Environments
5.1 Introduction
Suitable sensors and controlling devices are required to maintain wind turbine dynamic stability and enhance performance under variable wind conditions. Stall regulation, pitch control, and yaw control mechanisms will be described, with emphasis on reliability, safe operation, and improved turbine performance. Control mechanisms deploying micro-electro-mechanical systems (MEMS) and nanotechnology-based devices will receive serious consideration due to their fast response, accuracy, and minimum size and weight. For high-capacity wind turbines, the connection between the blades and the hub must be extremely rigid under variable wind environments if mechanical integrity is the principal design objective. It is important to note that a teetering hub design reduces the loads on the turbine, thereby yielding improved dynamic stability. However, the advantages and
138 ◾ Wind Turbine Technology
Rotor Gearbox Anemometer
Generator Yaw motor
Control system
Figure 5.1
Horizontal axis wind turbine.
disadvantages of this hub design must be examined in terms of cost and design complexity. Monitoring sensors to record efficiency and turbine dynamic stability data must be collected randomly. Critical components such as rotor, generator, transmission system, and other components responsible for overall system efficiency, reliability, safety, and dynamic stability will be discussed in detail. Performance, reliability, structural integrity, and safety aspects will be investigated. Note that rotor dynamic stability is vital and depends on the number of blades and their airfoil characteristics. Theoretical studies performed by the author indicate that two- and three-bladed wind turbines exhibit lower tip speeds and lower rotational speeds. High-capacity wind turbine systems such as horizontal axis wind turbines (HAWTs, Figure 5.1) require gear boxes to reduce the rotational speed to maintain dynamic stability under high tip speed conditions. Note that the tip speed (X) is the ratio between
Sensors and Control Devices ◾ 139
Low-speed shaft Gear box Generator
Wind direction
Controller Brake
Yaw drive Wind vane Yaw motor Blades Tower High-speed shaft Nacelle
Figure 5.2
Nacelle components.
the rotor speed at the tip and the undisturbed wind speed. It is extremely important to mention that abrupt and ultrahigh rotational speeds are highly undesirable as far as the safety and dynamic stability of the turbine are concerned [1]. Most of the monitoring sensors and safety devices are located at the nacelle as illustrated in Figure 5.2. Critical elements of the wind turbine are located on the top of a tower as shown in Figure 5.3. Various techniques to reduce the rotational speeds under variable wind environments will be identified. Since high-capacity wind turbines will have longer blades and consequently higher towers, the system's dynamic stability and safety of both turbine and tower must be given serious consideration during the design phase. The author's aerodynamic studies of 2-D and 3-D wing designs indicate that the flow angle (φ), which is the sum of the angle of attack (α) and pitch angle (β), varies at different locations along the rotor blade length.
5.2 Regulation Control Systems
Regulation control systems [2] with fast feedback loops, microprocessor-based control mechanisms, and control algorithms are widely used by high-capacity wind
The flow angle (sum of the pitch angle and angle of attack) changes under variable wind speed conditions.2. Generator 8. Blades 2. Pitch regulation control requirements indicate that the angle of attack must be kept below 5. Controller 9.1 Pitch Regulation Control Preliminary studies of dynamic stability indicate that pitch control is necessary for dynamic stability and reliable performance of a rotor. controller. Low-speed shaft 6. Rotor 3. High-speed shaft 13. Pitch 4. The pitch angle must be adjusted at various locations along blade length to meet the flow angle requirements. The pitch angle must be adjusted by the pitch control mechanism comprised of a pitch motor.140 ◾ Wind Turbine Technology 3 2 5 1 4 12 7 13 14 6 8 9 10 1.3 Critical elements at top of tower. Nacelle 12.7 degrees if optimum power coefficient and dynamic stability are to be maintained under a variety of wind environments. The studies of a 30-m blade length reveal that both the flow angle and wind speed vary at locations along the blade length as shown in Table 5. Tower 11 15 Figure 5. Anomometer 10. Wind vane 11.1. turbines to maintain dynamic stability and reliable operation under variety of wind conditions including turbulence. Yaw drive 14. Brake 5. and drive accessories to meet the flow angle requirements as summarized . It is important to stress that both the pitch regulation and yaw control systems are required to achieve dynamic stability and safe and reliable operation of a rotor under a variety wind environments. Yaw motor 15. Gear box 7. 5.
Sensors and Control Devices ◾ 141 Table 5.7 21. It is evident from the table data that the flow angle.7 1.4 R 0.7 in the table. Note in general that the undisturbed wind speed will decrease to 67% in front of the rotor blade [2].1 Pitch Angle Adjustments to Meet Flow Angle Requirements along 30-Meter Blade Radius Radial Distance Blade tip (R = 0) 0. which in turn reduces the aerodynamic forces on the rotor blades and maintains dynamic stability of the rotor. As stated earlier. and pitch angle all increase from blade tip to hub location.2 R Wind Speed (m/sec) 60 48 36 26 12 Flow Angle (deg) 6 7 9 14 27 Pitch Adjustment (deg) 0. A reduction in aerodynamic forces on the rotor assembly will Network A Actuator Controller + – Power transducer Power set point Figure 5. the pitch angle must be changed to reduce the angle of attack. The flow angle and pitch angle adjustments will vary as a function of blade radius or length. wind speed.2 Description of Pitch Regulation Control System The pitch regulation control system as illustrated in Figure 5.4 Pitch regulation system.7 8. It permits the blades to rotate about their radial axes as wind velocity changes during operation. It is therefore theoretical possible to have an almost optimum pitch angle adjustment at all wind speeds and at a relatively low cut-in wind velocity.2. .7 3.6 R 0.4 is the most critical wind turbine subsystem and is relatively expensive.8 R 0. the values of these parameters change as a function of blade radius [2]. Note that at high wind speed conditions. 5.
and reliability of the response.142 ◾ Wind Turbine Technology improve the dynamic stability of the entire turbine. To maintain dynamic stability in turbulent environments. The rotation of the blades must be achieved smoothly and precisely. downwind rotors suffer from increased noise and cyclic loads due to the tower "shadow" and are less common than upwind rotor designs. The measured electrical signal is compared with the precision set point device and the error signal is then passed to the microprocessor-based controller. a system to control yaw must be added in addition to a pitch control system. The power generated by the wind turbine is measured using an electrical power transducer normally located in the base of the tower. Several types of actuators including hydraulic. Under these conditions.3 Yaw Control System The block diagram of a yaw regulation control system is similar to that of a pitch regulation control system. and this may jeopardize the dynamic stability of a turbine. when operating . Under turbulent winds. actuator. In some wind turbine designs. the rotor blades can be coned outward to increase tower clearance. a pitch regulation control system is not enough to maintain dynamic stability under turbulence conditions. and MEMS devices will be investigated with emphasis on the speed. 5. electromechanical. electro-optical. With downwind installation. The figure is a block diagram of a widely used control system for pitch-regulated wind turbines. The feedback loop of the control system must operate continuously to regulate the power above the rated wind speed. Implementation of yaw control is also essential to ensure dynamic stability and structural protection of a wind turbine system in a turbulent environment. but the dual control system is necessary to main dynamic stability and safe operation of high capacity wind turbines regardless of wind speeds and turbulence environments. the mechanical power output from the rotor is limited to the rated power of the electrical generator. However. it is common to encounter significant transient power fluctuations or excursions well above the set point. A turbine rotor can be mounted on the upwind or downwind side of the tower. Furthermore. control algorithm. power set point device.4 is more expensive and is inherently more efficient and reliable than stall regulation. A downwind rotor configuration will align itself with the wind direction and thus eliminate the need for a yaw drive mechanism. The challenge or the difficulty is to change the pitch of the blades on a rotor that rotates constantly. The critical elements of this regulation control system are the actuator. except yaw control is less sophisticated. only the outer part of the blade is moveable and under this design configuration the aerodynamic load on the rotor is reduced compared to a stall-regulated rotor.2. A control algorithm is used to obtain the required dynamic response for the actuator to rotate the blades in the desired direction. and power transducer. dynamic range. As noted earlier. The pitch regulation system shown in Figure 5. microprocessor-based controller. Thus deployment of both pitch and yaw regulation systems adds to the cost and makes a system more complex.
1 through 5. MEMS and nanotechnology-based devices are available if fast response and large dynamic range of microprocessor-based control systems are the principal design requirements. if fast and accurate wind response is a requirement. it allows the input and output shafts to be in line. Early wind turbines deployed wind vane devices to monitor the wind direction. Dynamic loads can be controlled by adding mechanical compliance and damping capabilities into the drive . However. The gear box is located at the top of the tower as illustrated in Figures 5. It is important to point out that shaft compactness and smooth shaft operation are the principal requirements for dynamic stability and reliable rotor operation.3. Accurate measures of these wind parameters are essential for optimum effectiveness of pitch and yaw control systems. thus providing optimum compactness. Modern direction monitoring devices for high-capacity wind turbines provide high accuracy and fast response. perhaps a clutch. They are essential to maintain dynamic stability and reliable operation under varying wind environments including turbulence. Both these devices play key roles in providing instant wind parameters needed by the pitch and yaw regulation control systems.4 Transmission Systems The mechanical power produced by a rotor is transmitted to an electrical generator by a mechanical system consisting of a gear box.2. These devices are reasonably accurate. 5. these regulation control systems cannot operate. output shaft design for high-capacity wind turbines is more sophisticated and expensive. but nanotechnology-based devices are highly recommended. It may be a simple parallel-shaft box in which the output shaft is offset in a low-capacity wind turbine. A direction monitor is located near the anemometer in Figure 5. 5. The two shafts in a gear box must provide vibration-free and reliable operation.Sensors and Control Devices ◾ 143 under turbulent conditions. Turbine designers must concentrate on high dynamic loads due to the fluctuating power output from a rotor under variable wind environments. Without wind parameter data. and a braking system to bring the rotor to a rest position in an emergency situation. a downwind turbine rotor cannot provide the dynamic stability and reliable operation required.3 Sensors for Monitoring Wind Parameters Early wind turbine designs utilized wind vane and anemometer devices to monitor wind direction and speed. Anemometers are widely used on wind turbines to record wind speeds. The gear box is required to increase the speed typically from 20 to 50 revolutions per minute (rpm) to the 1000 to 1500 rpm required to drive most types of generators.
The stators of both synchronous and asynchronous generators have three-phase windings on laminated iron cores to generate a magnetic field rotating at a constant speed. While both types of generators contain similar stators. and compactness of the gear box components. The stator windings produce a magnetic field that rotates at a constant speed. 5.5 Electrical Generators Several types of generators are commercially available for deployment in wind turbine systems. In some earlier low-capacity wind turbine designs. Thus the rotor always rotates at a constant speed in synchronism with the stator field and the network frequency. asynchronous generators are called induction generators. reliability. the rotor magnetic field was produced by permanent magnets. Note all grid-connected wind turbines are coupled to three-phase AC generators to convert mechanical power to electrical power. Induction generators. this was not a common practice for large wind turbines. synchronous generators. A synchronous generator rotor has a winding through which a direct current flows. the rotor magnetic field is produced by permanent magnets that are not suited for large electrical generators. variable-speed generators using fast transistor-based switching elements. Asynchronous generators are also known as induction generators and synchronous generators are generally known as alternators. However. Generators fall into two categories: synchronous and asynchronous generators. the performance of the transmission system depends on the efficiency.144 ◾ Wind Turbine Technology train mechanism. Induction generators and synchronous generators have non-rotating component called stators. In summary. Each stator consists of a three-phase winding on a laminated iron core to reduce noise and electrical losses in the core. In some generator designs. The design of the rotor of an induction generator is different from that of a synchronous generator. . This field winding creates a constant magnetic field that interfaces into the rotating field created by the stator winding. The rotor always rotates at a constant speed in synchronism with the stator magnetic field and the network or grid operating frequency. The rotors in modern high-capacity turbines use the magnetic field windings to generate magnetic fields. and constant-frequency generators are commercially available. The rotor of a synchronous generator has a field winding to carry a direct current. 5. The device is called a field winding because it generates a constant magnetic field that locks into the rotating field created by the stator winding. Stators in both types of generators are connected to the network or load.1 Induction Generators As stated previously.5. their rotor configurations are very different. This technique is particularly important for high-capacity wind turbines that encounter high dynamic loads and the induction generator provides less damping.
Similarly. Although induction generators are not widely. performance capabilities. By increasing the rotor field current. The rotor of a HAWT produces torque pulsations at the frequency with which the rotor blades pass the tower structure. If these torque pulsations are at the natural frequency of the spring-mass system created by the blades and their . the direct current flowing in the rotor field winding magnetizes the rotor. because they are more efficient than induction generators. reactive power going to the network can be reduced. Torque direction is the fundamental difference between an induction generator and an induction motor. the major advantage is that their reactive electrical power flow is easily controlled. millions of induction motors are currently in service throughout the world. In this way. The difference between the two speeds is called the slip and equals about 1% during normal operation. by reducing the rotor field current. and the rotor currents are induced by the relative motion of the rotor in conjunction with the rotating field of the stator winding. and limitations of both synchronous and asynchronous generators. These text books offer detailed information on the operating principles.5) and irrespective of the electrical load environments. There is no electrical connection onto the rotor assembly.Sensors and Control Devices ◾ 145 5. the reactive component of the electrical power generated can be exported or transmitted to a power grid or load network. The rotor in this case consists of a squirrel cage of bars that are shortcircuited at each end. constant voltage can be maintained at variable speeds (Figure 5. It is important to mention that most high-capacity wind turbines belong to the HAWT category.6 Performance Capabilities and Limitations of Synchronous Generators Data covering design aspects and performance capabilities of electrical synchronous generators used in commercial power generating stations can be found in standard text books.5. No relative motion is present and thus there is no induced current in the rotor. Brief studies performed by the author of the deployment of synchronous generators in electrical power plants reveal that most large electrical generators are synchronous and that synchronous generators are best suited for high-capacity wind turbine installations. However.2 Rotor Configurations for Induction Generators The rotor configuration of an induction generator is different from configurations of other generators. In a synchronous generator. Therefore an induction generator always operates at a speed that is slightly higher than the speed of the rotating field produced by the stator winding. Essentially an induction generator can be considered an induction motor with torque applied to the shaft rather than taken from it. 5. The rotor speed is exactly equal to the speed of the rotating field produced by the stator winding (as with a synchronous generator). controlling the flow of reactive power gives a firm control over the voltage of a power system. Thus.
Because of problems caused by great oscillation. network connection via the synchronous generator.17. Dutch type rotors with four blades were popular for certain applications. 5. low revolution per minute sta de Bla ll M Fixed. optimum blade angle Torque Wind velocity.7 Critical Rotor Performance Parameters Several types of rotors were introduced commercially to fit certain applications and power ratings.5 Schematic diagram of a variable-speed wind turbine generator.146 ◾ Wind Turbine Technology N S DC R Tx Figure 5. ax po we r . It is possible to provide damping of the drive train with mechanical devices such as fluid couplings.6 Early rotor designs.6 illustrates popular early rotor design configurations. This occurred with one early wind turbine. resonance frequencies and some very large oscillations of the drive train will occur. RPM 150 Figure 5. Figure 5. MPH 32 16 8 12 0 50 20 24 28 100 Shaft Speed. They demonstrated power coefficients as high as 0. high torque capability. synchronous generators are not normally used in fixed-speed wind turbine installations [3]. but this technique increases design complexity and system cost.
2.0 . The high energy losses meant poor efficiencies. Rotor performance is measured in terms of power coefficient (CP) as a function of blade tip speed-to-wind speed ratio (X). teetering to limit fluctuation forces as the rotor blades sweep varying wind Table 5.0 to 7. modern propeller rotor design was introduced.43 0 55 Range of Tip Speed-to-Wind Speed Ratio (X) 0.14 0.0 5 5 to 6 5 4 5 to 6 5 3. They were followed by farm rotors with power coefficients close to 0. high torque capability. 5. low torque capability. 5. while the Savonius.7. possibly causing serious problems from tip noise. In the early 1950s. and inefficient blade designs.32 0.85 2. These two characteristics are the most important ones for a rotor. and Giromill rotors were suggested for VAWT installations because of their unique performance characteristics. Darrieus.47.3 0.2 Dynamic Stability and Structural Integrity Attempts will be made to recommend various techniques to determine and record the dynamic stability and structural integrity of a rotor. Typical power coefficients of various rotors are summarized in Table 5. blade erosion. high rpm levels. Wind turbine designers suggest that a two-bladed rotor configuration is least expensive. and efficient blade design involving exotic airfoil designs. Upwind rotors and downwind rotors were recommended for HAWT installations.2 Power Coefficients of Various Rotors Rotor Type Savonius Dutch four-arm Darrieus Two-blade Propeller (ideal) Optimum CP 0.7.to-wind speed ratios and clearly show that propeller rotor configurations offer optimum performance in a variety of wind environments.1 Rotor Design Classifications Most rotors were classified according their potential applications for HAWTs or VAWTs.30.Sensors and Control Devices ◾ 147 rates. but low rpm rates. but it runs faster.80 to 0.0 to 3. Most modern high-capacity wind turbines deploy three-bladed rotors to achieve optimum performance over a wide range of wind conditions. The table data indicate rotor performance over a number of tip speed. It demonstrated a maximum power coefficient of 0. The safe and reliable operation of a wind turbine depends on them.
A three-blade rotor will cost about 6% more than a two-blade rotor.7 provides better efficiency and improved reliability than a twoblade rotor.7). In addition. Furthermore. Essential characteristics include insensitivity to roughness. The rocking motion or teetering of a rotor at each revolution significantly reduces the loads due to gusts and wind shear. Under such conditions. Improved aerodynamic performance requires thinner blades toward the tip. low noise production. tapers in chord and twists.7 Airfoil characteristics. fatigue strength. and structural integrity under most wind environments except turbulence. the rotor is hinged at the hub in such a way as to allow the plane of rotation of the rotor assembly to tilt backward and forward a few degrees away from the mean plane. and dynamic instability. leading to vibrations of high magnitude. Most high-performance wind turbines deploy three blades to achieve reliable and safe performance with no compromises in structural integrity and dynamic stability. stiffness. r (a) Wind turbine rotor configuration with three blades α φ θ ?? Vrel Vr Va Rotorplane (b) Cascade of aerofoils in the radial direction from the axis Figure 5. a three-blade rotor configuration as shown in Figure 5. Rotor performance depends completely on airfoil characteristics of the blades (Figure 5. velocities. Rotor performance is somewhat dependent on airfoil shape and its aerodynamic characteristics. In summary. The .148 ◾ Wind Turbine Technology R dr. a three-blade rotor offers improved rigidity. the rotor will experience serious dynamic instability. excellent stall characteristics and high lift-to-drag ratio for improved efficiency under varied wind environments. with a teetered hub.
a downwind rotor will align itself with the wind direction.7. The lift forces are reduced due to stall. Active research and development activities are continuing on both three-dimensional and dynamic stall effects. rotor designers experience some difficulty in designing stall regulated rotors. shear forces.7. Conversely. the angle of incidence onto the rotor blades increases. thereby eliminating the need for a yaw drive system under moderate wind environments.3 Monitoring of Stress Parameters Random monitoring of bending moments." Because of design complexity and unfavorable performance under gusty wind environments. downwind rotors suffer from increased noise and cyclic loads due to the tower "shadow. Deployment of these monitoring devices on remotely located wind turbines can play a significant role in monitoring structural health and system reliability in gusty and turbulence environments. However. twist. However. and blade tensile and compressive stresses using MEMS and nanotechnology-based devices will keep a turbine operator informed of the structural health of the blades.5 Factors Affecting Wind Energy Capture and Turbine Performance Several factors can affect wind energy capture and ultimately deteriorate turbine rotor performance: ◾ Orientation relative to wind vector if a turbine is not omnidirectional [3] ◾ Wind speeds at which the turbine starts and stops .7. 5. Under stall conditions. turbine reliability. Note that the blades of an upwind side rotor will be coned onward to increase power clearance. and improved airfoil characteristics of the rotor blades should combine to achieve the best possible wind energy capture for the rotor speed power and site conditions. the tensile and compressive stresses generated under gusty and turbulence environments must be carefully monitored because they can affect the dynamic stability. and structural integrity of the rotor. 5. upwind rotors are preferred by the wind turbine designers over downwind rotors. 5.Sensors and Control Devices ◾ 149 taper. but the drag forces rise and the increase in rotor power that would otherwise occur is prevented.4 Stall Regulated Rotors Stall regulated wind turbines deploy a rotor configuration in which pitch angle distribution along the blades is constant at all wind speeds. This results in large aerodynamic forces on the rotor. Particularly. Stall regulation is simple and does not require a sophisticated control system.
reliability. catastrophic failure of an entire wind turbine system cannot be ruled out. In other words. a propeller-based wind turbine could be operated at its peak power coefficient regardless of wind environments and the centrifugal stress variations in the blade angle of attack. tensile stresses. the measure of rotor performance is strictly dependent on the maximum power coefficient that can be achieved under the defined operating environments.8 if effective pitch and yaw are not controlled immediately. and shear stresses at strategic locations along the axial blade length must be calibrated to obtain accurate data on the structural health of the rotor and blades. At times. It is extremely important to mention that transient conditions affect the dynamic stability of a rotor under gusty or turbulence conditions and may pose a serious threat to rotor reliability and the structural integrity of the tower. Coriolis forces. large Coriolis forces. rotor performance can be estimated from the ratio of total energy extracted by the rotor to the total wind energy available. It is important to mention that most high-capacity wind turbines are designed to supplement the power from a utility grid system and are thus forced to operate at fixed rotational speeds to generate alternating current at the designated grid frequency. the bending moments and centrifugal forces at the tip are significant. Furthermore. constant rotational speed rotors are forced to operate at off-design conditions frequently. under transient conditions. Monitoring devices or sensors are recommended to determine the magnitudes . Because of the variability of the wind. compressive stresses. Excessive bending moments and shear forces as illustrated in Figure 5.150 ◾ Wind Turbine Technology ◾ Design wind speed if the turbine operates in a power-limited mode ◾ Performance sensitivity to off-design conditions ◾ Rotor response to transient factors such as wind gusts or turbulence From a practical view. the wind speed will be optimum at the tip of the blade and minimum at the root of the blade. rotor blades experience higher magnitudes of bending moments and shear forces as illustrated in Figure 5. under gusty wind and turbulence environments. centrifugal forces. In the case of a wind turbine with small or moderate capacity. a complete shutdown of a wind turbine under uncontrollable transient conditions should be considered to prevent personal injury and property damage. Thus. particularly. This indicates that "beefing up" of the tip section must be given serious consideration to meet dynamic stability and structural integrity requirements [4]. If the angular speed was an entirely free design parameter. compressive stresses. In case of high-capacity wind turbines. and structural integrity of the rotor. As mentioned earlier. tensile stresses. a teetering hub rotor could be advantageous because it reduces the fluctuating loads on the turbines that affect the dynamic stability of the rotor. Sensors capable of monitoring the centrifugal forces. In addition.8 can pose serious threats to the structural integrity of the blades and dynamic stability of the rotor. and transient loads on the rotor must be avoided to maintain stability. The use of converters and inverters is discouraged by the high cost of the equipment and consequent reduction in efficiency.
Sensors and Control Devices ◾ 151 pdx f M T (a) Bending moment (M) and shear force acting on rotor blade (T) T + dT M + dM y z x (b) Three-axes of the rotor blade Figure 5. At the tips of the blades are leakages that allow air flows around the tips from the lower side to the upper side. a wind turbine generates unpleasant environmental noise levels and there is no need to monitor them.8 Impacts of Airfoil Characteristics on Blade and Turbine Performance It is interest to mention that airfoil characteristics (Figure 5. the streamlines flowing over the wing will be deflected inward and the streamlines flowing under the wing will be deflected outward. . 5. of the bending moments and shear stresses for high-capacity wind turbines.7) play an important role in the performance and reliability of rotor blades. In other words.8 Bending moments and shear forces. As stated earlier. Such sensors are neither required nor justified for small or moderate capacity wind turbines to minimize system cost and complexity. These sheets are known as trailing vortices. These conditions create a jump in the tangential velocity at the trailing edge followed by a continuous sheet of stream-wise vorticity in the wake behind a wing. Essentially a wind turbine blade is a beam of finite length with airfoils as cross-sections to create a pressure difference between the lower and upper sides of the wind and give rise to lift.
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Classical aerodynamics principles demonstrate that a vortex filament of certain strength can model the flow past an airfoil for small angles of attack so long as the angle of attack does not exceed 5.7 degrees regardless of wind environment. This is because the flow for small angles of attack is mainly inviscid and governed by the linear Laplace equation. Under this assumption, an airfoil can be replaced by one vortex filament of finite strength and the lift produced by 3-D wind can be modeled for small angles of attack using a series of vortex filaments (bound vortices) oriented in the span-wise direction of the wing. In summary, blade performance is based on the vortex filament orientation and trailing vortices. However, the performance will not improve if rotating blade Coriolis and centrifugal forces are not controlled at angles of attack exceeding 5.7 degrees. At large angles of attack (more than 12 degrees), the air stream cannot stick to the airfoil surface, thereby creating a turbulence effect under which airfoil begins to stall. Aerodynamic scientists state that an airfoil is most efficient when the angle of attack remains below 7.5 degrees. However, most designers prefer to keep the angle of attack below 7.5 degrees for other reasons. Airfoil design and the relative thickness of the blade must be given serious consideration to achieve stall-free and reliable rotor performance under various wind conditions. The circumferential force must be kept small compared to the thrust to retain the high relative speed needed to produce optimum blade power.
5.8.1 Vortex System behind High-Capacity Turbine
A HAWT functions as a high-capacity wind turbine. The rotor of a HAWT consists of a number of wing-shaped blades. If a cut is made at a radial distance r from the rotational axis, a cascade of airfoils can be observed as shown in Figure 5.7. The figure illustrates the rotor of a three-blade HAWT with blade radius R. The local angle of attack is given as α by the pitch of the airfoil θ, the axial velocity is Va, and the rotational velocity at the rotor plane is denoted by Vrot. The cascade of airfoils can be seen at the bottom of the figure. The vortex system produced is located behind the HAWT. If the lift and drag coefficients are known, it is easy to compute the force distribution for the airfoils along the blades. The blade element momentum (BEM) method can be used to compute the axial induction factor, the longitudinal induction factor, and the various loads acting on the turbine. The Biot-Savart equation can be used to calculate the induced velocities in the rotor [4].
5.9 Automatic Shut-Down Capability
Automatic shut-down capability of a wind turbine in an emergency situation created by gusty winds or turbulence should receive serious consideration for safety reasons. Since no operational or maintenance personnel are usually near a wind turbine installation, a built-in provision for automatic shut-down is preferred to prevent damage to the
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turbine and nearby structures. Brief studies of turbine safety and reliability performed by the author indicate that a HAWT with a downwind design configuration could provide a built-in automatic adjustment to wind direction, serving as a safe operational feature under most wind environments. However, this adjustment is not possible when abrupt changes in wind direction occur. Under abrupt wind direction changes, a rotor with three or more blades could offer smooth and stable performance. Under turbulence conditions, there is no design provision for automatic shut-down.
5.10 Critical Design Aspects of HAWT and VAWT Rotors
Comprehensive aerodynamic studies of wind turbines performed by the author reveal that most high-capacity systems operate as HAWTs because of their superior performance and improved reliability. A HAWT offers higher output power, relatively lower environmental noise levels, and higher power coefficients. VAWTs tend to stall under gusty wind conditions and present serious dynamic stability problems. A VAWT requires lower installation height, leading to inferior operation at lower wind conditions, reducing both output power and efficiency. On the other hand, a VAWT has small blade length that prevents large bending moments and deflections and offers significant savings for the tower structure and accessories. The environmental noise level from a VAWT is lower than that from a HAWT because of low installation height.
5.10.1 Techniques for Improving Turbine Reliability and Performance
Techniques to capture maximum energy under low wind speed conditions should be explored. As explained earlier, wind energy capture depends on wind speed. Low wind speed means low energy capture; a wind turbine operation will not be cost-effective under such condition. Studies by aerodynamic scientists reveal that a variable generator excitation control technique implemented in turbine design will realize significant improvement in the amount of wind energy capture and consequently higher wind turbine power output in low wind speed environments. These scientists further note that his technique also improves the aerodynamic rotor control to ensure safety and reliability of the entire system. Turbine efficiency depends on the number of blades used and the blade efficiency. Blade performance is a function of flow angle, wind speed, blade radius, angle of attack, blade pitch angle, and axial and longitudinal interference factors. In summary, turbine performance is based on rotor and blade efficiency. Ethernet interface can provide continuous monitoring of turbine performance under low wind conditions. It is interesting that residential wind turbine systems
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deploying twisted high-efficiency blade designs offer improved turbine performance, optimum angle of attack along the entire blade length, and unique aerodynamic design features. Implementation of charge controllers would offer better system reliability and improved turbine performance. Scientists at MIT claim that a new concept based on jet engine principles offers hope for improved wind turbine design with significant improvements in efficiency and reliability. The new design concept forces the air around instead of through the rotor blades. In other words, the system works by channeling the wind into a vortex that spins the blades and generates mechanical power that can be converted into electrical power via a generator. Various augmentation schemes are available to enhance the performance of wind turbines. Most effective designs demonstrating significant improvement in performance include concentration, aerodynamic lift, and diffusers and ejectors [4]. However, performance improvement based on these schemes involves a tradeoff of additional weight, cost, and increased tower design complexity. Trade-off studies are required to determine performance improvement versus the increases in weight, cost, and complexity before an augmentation system is selected. Optimum values of critical design parameters that may achieve significant performance improvements must be given serious consideration. For example, optimum wind speeds must be within the recommended range throughout the year at an installation site. Furthermore, the maximum power coefficient—the main performance indicator of a wind turbine—requires wind speeds of 20 to 30 m/min, a drag-to-lift coefficient ratio less than or equal to 0.01, and an angle of tilt close to 5.7 degrees. The impacts of drag-to-lift coefficient ratio and tangential speed ratio (X) on power coefficient can be seen from the data in Table 5.3 indicating that the power coefficient continues to increase as the tangential speed ratio increases at the lowest value of drag-to-lift coefficient ratio. However, the power coefficient increases initially, then decreases. Note that the power coefficient values decrease rapidly at the highest drag-to-lift ratio as the tangential speed ratio increases. It is important to mention that higher power coefficients are possible at a drag-to-lift coefficient of 0.01, regardless of the tangential speed ratio. In summary, both the drag-to-lift coefficient and the tangential speed ratio significantly influence the power coefficient or efficiency of a wind turbine. It is interesting to mention that greater power is available at higher wind speeds excluding gusty and turbulence environments.
5.10.2 Sensors for Ensuring Efficiency, Dynamic Stability, and Structural Integrity
An installation site must be selected carefully, with consideration given to the adverse effects of temperature inversion and rapid variations in wind speeds. Turbine installations at sites frequently subjected to gusty winds and turbulence are undesirable
Sensors and Control Devices ◾ 155 Table 5.3 Impacts of Drag-to-Lift Ratio and Tangential Speed Ratio on Turbine Power Coefficient
Tangential Speed Ratio Drag-to-Lift Ratio 0.00 0.01 0.03 0.05 0.07 0.09 1 0 52 0 50 0.46 0.45 0.43 0.41 2 0 56 0 55 0.47 046 0.44 0.38 3 0.57 0.56 0.45 0.45 0.39 0.32 4 0 58 0 55 0.42 0.41 0.34 0.25 5 0 586 0 542 0.371 0.372 0.314 0.185
if dynamic stability and structural integrity are required. Critical installation site selection parameters should be carefully examined and evaluated prior to installation of a high-capacity wind turbine. Temperature inversions cause a stratification of the atmosphere near the surface that is detrimental to efficient operation of a wind turbine. Installations where variations in wind speed and direction exceed 25% from one year to the next should be avoided because optimum capture of wind energy is not possible. It is important to mention that wind speed and direction are subject to change at any time for any location. Rayleigh distribution and Weibull distribution techniques should be used to estimate the wind speed for a potential site. Meteorological scientists state that Rayleigh distribution provides reliable estimates to project annual power generation from small and medium capacity systems. Reliable sensors must be deployed to monitor wind speed distribution because it plays a critical role in determining the power generated. Most small and medium capacity wind turbines use anemometer devices to monitor wind speed with moderate accuracy. MEMS and nanotechnology-based monitoring sensors now available offer reliable and accurate information on wind speed. A monitoring device must be installed at an appropriate location on a nacelle where it will be free from interference from nearby objects. Wind speed and direction data monitored by the sensors is sent to the controller for transmission to other sensors or subsystems. The controller essentially directs the yaw motor to turn the rotor to face toward or away from the wind, depending on wind direction. Wind data is also sent to the braking mechanism that directs the rotor to slow down when necessary. Under certain operating environments such as turbulence, the braking mechanism will send a command to stop completely to avoid structural damage to the tower and injury to maintenance personnel nearby.
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5.10.3 Blade Twist Angle Adjustments
Adjustment of blade twist angle is necessary to optimize performance in variable wind environments. It is impossible to stop a rotor and then adjust the twist angle. As a matter of fact, adjustment of twist angle is very tricky while a turbine is in operational status. An operator must be highly experienced and make incremental adjustments accurately and quickly. A sudden or incorrect adjustment could affect dynamic stability of a rotor, producing violent vibrations that could damage the tower structure. In summary, only an experienced operator can adjust blade twist angle to maintain optimum rotor performance.
5.11 Low Harmonic Content Electrical Generators for Improving Efficiency
To achieve optimum generator efficiency, it is necessary to convert all the DC power into AC power through an inverter with an operating frequency compatible with grid frequency requirements. This enables a generator to operate over a wide range of wind speeds without disturbing the grid frequency. In addition, all the modern high-capacity wind turbines deploy high-speed transistors as switching devices to generate waveforms much closer to sine waves with fewer harmonic distortions as shown in Figure 5.5. The generator design concept shown offers high efficiency leading to improved system output. Further improvement in generator efficiency may be realized by cooling the stator windings via a forced-air system operating at a specific rate and cooling temperature. Cooling of stator windings improves generator performance and increases reliability. Forced-air cooling also keeps the graphite exciter brushes and the rotor windings at safe operating temperature. Cooler temperature increases the safety and reliability of the rotor and stator windings over extended durations. When the operating temperature is kept constant at an optimum value, the electrical losses and IR losses in the windings are significantly reduced, leading to more generator efficiency and improved reliability.
5.11.1 Bearing Reliability
Lubrication is absolutely essential for bearings used by gears, turbines, and generators operating at high rpm levels. Lubrication promotes smooth and reliable operation, particularly at high rpm conditions. A gear box in a wind turbine system is located between the rotor and an electrical generator that rotates typically between 4000 and 5000 rpm. The bearings supporting the rotor assembly and generator must be kept well lubricated with an oil that meets the room temperature viscosity requirements recommended by the American Institute of Mechanical Engineers or an equivalent authority on temperature specifications to ensure high reliability and
When a rotor blade is down-rotating.1 Impact of Gravitational Loading The gravitational field of the earth causes a sinusoidal loading on rotor blades and the stress may eventually lead to structural damage.2 Impact of Inertial Loading Preliminary aerodynamic studies by the author indicate that inertial loading occurs when a turbine is accelerated or decelerated under abrupt change in wind speed. the stresses from gravitational loading are critical for fatigue analysis of the rotors and assessment of the structural integrity of a wind turbine. and bending moments as illustrated in Figure 5. Oil level in a gear box must be checked regularly to maintain quality and optimum quantity. The gears are completely immersed in the oil to maintain efficiency. As mentioned previously.12. Since modern wind turbine blades are more than 30 m long and may weigh several tons. No scheduled maintenance requirements are recommended by wind turbine suppliers or installers. a wind turbine will be subjected to 2. It is important to mention that wind turbines are designed to operate 20 years or longer.Sensors and Control Devices ◾ 157 maintenance-free operation.9. 5. This means that rotor blades under gravitational loading conditions may be subjected to tensile stress.6 × 106 (20 years × 365 days × 24 hours × 60 minutes × 25 rpm) stress cycles from gravity. Bending moments of higher magnitudes will disturb the dynamic balance of rotor and lead to performance degradation. At the same time. 5. As long as the operating wind conditions are smooth and free from turbulence effects.12. edge-wise bending moments may develop. the trailing edge encounters compressive stress while the leading edge meets tensile stress. Inertial loading can also occur when a braking torque is applied to a rotor under . inertia. minimize wear and tear. Assuming a 25-rpm turbine speed and an operating life of 20 years. in the up-rotating position. compressive stress. and aerodynamics. The stresses and moments can seriously undermine the dynamic balance of a rotor and structural integrity of a turbine. and ensure reliable operation. the trailing edge is exposed to tensile stress and the leading edge is exposed to compressive stress. Similarly. the most important sources of loadings are gravitational forces.12 Impacts of Loadings on Structural Integrity of Wind Turbine The structural integrity of a wind turbine can be compromised by loadings. 5. Determining stresses generated by various loading sources plays important role in fatigue analysis of a system. wind turbines can run efficiently over very long periods without maintenance.
m is the mass per unit length of the blade.158 ◾ Wind Turbine Technology POS 2 Leading edge POS 1 Tensile stress Tensile stress ω Trailing edge Trailing edge Compressive stress Compressive stress Leading edge (a) Loading effects from the Earth's gravitational field Fc = ω2rmdr dr dF = ωrmdr r T Fcsinθcone r Fccosθcone V T = Braking torque to rotor dF = Force experience by blade r = Radius from the rotating axis m = Mass per unit length of blade. where m is . The centrifugal force acting on an incremental section of a rotor blade at a radius r from the rotational axis can expressed as Fc which is equal to w2 r m dr. r is the radius of the rotating axis of the blade section.9). Inertial loading of greater magnitude can stem from excessive centrifugal force acting on the blades. The braking torque (T) applied to the rotor shaft is equal to the product of the moment of inertia of the rotor and the rate of rotating speed of the rotor. which is generally applied to reduce the flap-wise bending moment (Figure 5.9 Inertial loading. and dr is the blade element length. a small section of the blade will feel a force of specific magnitude (dF = dw/dt r m dr) in the direction of rotation. Under certain braking conditions. Note that inertia loads can also stem from local acceleration that may contribute additional force acting on a rotor. where dw/dt is the rotation speed. I = Moment of inertia θcone (b) Effects of inertial loading on turbine blades Figure 5. certain operating conditions.
3 Impact of Aerodynamic Loading The theories of aerodynamics and fluid dynamics indicate that aerodynamic loading is caused by air flow past a turbine structure including the rotor blades and tower.001 0.2 0.03 0. In other words. The Z0 value varies from 10-4 m over a water surface to 1 m over city surfaces. thereby reducing the total flap-wise bending moment. It is interesting to visualize how blade coning influences bending moments in the blades. It is desirable to note that wind shear is given as a sinusoidal variation of wind speed seen by a rotor blade with a frequency corresponding to the rotation speed Table 5. which can impact the stresses on the blades and their dynamic balance under higher stress conditions. Roughness lengths and other terrain surface characteristics are summarized in Table 5.12.4 [4]. the centrifugal force has a component in the span-wise direction of the blade. Wind shear is defined as a terrain surface characteristic and is expressed in meters of roughness length (Z0). but the normal component of centrifugal force yields a flap-wise bending moment in the opposite direction to the bending moment produced by the thrust.1 0. this shear can be estimated with an error not exceeding ±10%.05 0. the mean wind speed increases with height above the ground.8 0.005 0. The wind field seen by a rotor varies in space and time due to the atmospheric factors including turbulence.0 0. It is important to mention that the wind field seen by a rotor is strictly characterized by shear [4].4 Roughness Lengths of Terrain Surface Characteristics Terrain Surface City Forest Surface with trees and bushes Farmland with closed appearance Farmland with open appearance Farmland with few buildings Bare soil Snow white Smooth sand Water Roughness Length (m) 1.Sensors and Control Devices ◾ 159 the mass of the incremental section of the blade and w is the angular velocity of the rotor.0003 0. To maintain a neutral stability condition. Due to coning.0001 . 5.
with emphasis on reliability and safety. a wind turbine may operate under a yaw condition if the direction of the wind is not measured correctly or the yaw control system malfunctions. The most important sources of loadings include gravity. The adverse effects of these loadings on the dynamic stability and structural integrity of a rotor are identified. Design aspects of pitch regulation and yaw control systems are summarized and factors such as time response and reliability are detailed. The turbulent inflow and sinusoidal variations from wind shear make yaw regulation system design more difficult. the turbulent fluctuations superimposed on the mean wind speed also produce a time variation in the wind speed and thus in angle of attack value. The structural integrity of a rotor and a complete turbine system may be compromised by loadings generated by various sources. In summary. the efficiency of a yaw regulation control system is based on sinusoidal variations of the wind speed due to shear and the roughness length of the terrain surface characteristics. Methods for improving dynamic stability and structural integrity of a rotor are discussed. it is necessary first to generate a realistic wind field and remember that a tower also contributes to variations in inflow. To simulate the behavior of a wind turbine using an aero-elastic code. Forced-air cooling for stator windings is described. the rotor moves in the same direction as the wind and the relative rotational speed is reduced at the bottom position corresponding to 180 degrees. inertia. it improves the efficiency and reliability of an electrical generator. Techniques to maintain high speed bearing reliability are also explained. If the blade at the top position corresponds to a zero degree angle. Various techniques have been described to improve the efficiency and reliability of mechanical transmission systems and methods for improving the efficiency and reliability of a generator are outlined.160 ◾ Wind Turbine Technology of the rotor. Monitoring sensors incorporating MEMS and nanotechnologies that provide accurate data on wind speed and direction are described. Pitch angle adjustment is defined to meet flow angle requirements at various locations along the length of a 30-m blade. Anemometers currently installed on wind turbines lack accuracy and fast response. However. In this case. the reduced wind speed at the rotor plane has a component normal to the rotor axis and a tangential component to the rotor. 5. Aerodynamic scientists and wind turbine designers note that the most serious impact can be expected from gravitational loading. Sensors to provide the pitch and yaw control capabilities are described. dynamic stability. Furthermore. because earth's gravitational field creates . and aerodynamics.13 Summary This chapter focuses on the sensors and devices that ensure the efficiency. These loadings play an important role in fatigue analysis of a system. Variations in the inflow differ for upwind and downwind rotor configurations. and structural integrity of various elements of a wind turbine.
. Introduction to Wind Turbine Engineering. Aerodynamic scientists state that the most efficient airfoil is a critical parameter if high efficiency and reliability of a rotor under various wind environments are required. Jenkins. [3] Ibid. p. Butterworth. 8. 47.O. . References [1] A. Aerodynamics of Wind Turbines. These values indicate that shear effect on turbine performance and dynamic stability of the rotor is most serious in a city environment. Chichester. p.01. Boston. The impacts of airfoil characteristics on rotor performance and turbine efficiency are discussed in detail. Earth Scan. Wortman.L. Preliminary studies by the author reveal that optimum wind turbine performance requires a wind speed of 20 to 30 m/min and a drag-to-lift ratio equal to or less than about 0.. John Wiley & Sons. 2007. Wind shear is defined as a terrain surface characteristic and is generally expressed in meters as roughness length (Z0) that varies from 10 –4 m over water to 1 m over a city surface. London. Hansen. Air leakage occurring at the blade tips may cause a sudden jump in the tangential velocity at the trailing edge. Walker and N. thereby producing trailing vortices that can disturb the angle of attack.F.Sensors and Control Devices ◾ 161 sinusoidal loading on the blades. Sinusoidal variations in wind speed observed under turbulent conditions may generate a shear effect that adversely impacts both dynamic stability and angle of attack. 2002. It can also generate bending moments that can further complicate the dynamic balance of a rotor. [4] M. Rotor efficiencies for various design configurations are mentioned as functions of tip speed ratio. 1983. p. p. leading to dynamic instability and structural damage. [2] J. 57. 45. 2nd ed. Wind Energy Technology. This loading can generate tensile and compressive stresses of high magnitudes.J.
Stand-alone wind turbine generators are best suited for powering remote sites. The studies further reveal that reliable and efficient inverters. and widespread availability of low-cost photovoltaic (PV) or solar panels have revolutionized stand-alone wind power systems. Data compiled by Pacific Gas & Electric Company indicate that the number of stand-alone windbased power systems continues to mushroom at a rate of 29% annually [1]. Implementation of solar cell technology into stand-alone wind turbine systems offers a cost-effective and practical choice for customers living in remote 163 . and reliability of stand-alone power systems. These light power plants deploy small or moderate capacity wind turbines and banks of batteries sized to carry electricity for household consumption during severe winter winds and summer emergency periods. Studies performed by the author reveal that the high cost.Chapter 6 Stand-Alone Wind Turbine Systems 6. state and federal tax incentives. The utility's data further indicate that the market for such systems will continue to expand in areas not served currently by commercial utility companies. and frequent maintenance requirements of early stand-alone power systems discouraged many customers. Aggressive research and development focused on critical components have demonstrated significant improvement in cost. poor reliability. efficiency. but modern wind turbine technology has solved most of the problems and people in remote locations beyond the reach of commercial utility power lines accept the stand-alone power system concept.1 Introduction Stand-alone wind turbine systems play an important role where utility-based power systems are nonexistent.
The author's studies of stand-alone power systems reveal that the electrical energy must be generated near the site of use to minimize distribution cost and transmission losses. Gradually. diesel engines and steam turbines took over Wind generator PV array Batteries provide electricity to home Inverter Battery bank Whisper charge controller PV panels provide electricity to batteries Whisper provides electricity to batteries Figure 6. wind machines can be used to generate heat for residential and other applications. without the need for inverters for specialized pumping applications. wind machines are frequently used to drive AC motors directly. Various configurations of stand-alone wind turbines can be seen in Figure 6. The modularity of photovoltaic technology transformed the remote stand-alone power system market by enabling homeowners to tailor power systems to their needs and budgets. It is important to mention that remote stand-alone power systems that depend solely on wind turbines may require back-up electrical generators or high-capacity battery systems. Historically wind turbines of moderate capacity (known as wind chargers or windmills) were used to charge batteries of remote power systems typically deployed to pump water and grind grain. Paul la Court in Denmark was one of the first people to connect a windmill to an electrical generator and gave a tutorial course for "agricultural electricians. In addition.1 Stand-alone wind turbine system. . small wind turbines are ideal for this purpose. On farms. Today. however.164 ◾ Wind Turbine Technology areas that have no commercial utility power lines.1. power consumption needs. The use of wind turbines in stand-alone applications required trade-off studies in terms of cost." He installed in his school one of the first wind tunnels in the world to investigate rotor aerodynamic principles. and availability of electrical energy at all times.
000 small stand-alone wind turbines are used by nomadic herdsmen in remote regions of Northwestern China. wind turbines are best known for generating electrical power at remote sites for decades. Surprisingly. but DC can be converted to alternating current (AC) similar to power from a commercial utility source. According to suppliers of stand-alone wind turbines. For one or two customers at a remote site. when only 10% of wind farms generated electricity for homes. Small turbines are widely used in rural areas to supply electricity to remote areas where power lines are not available.2 Historical Background: Use at Remote Sites Besides mechanically pumping water. . However. about 75% of all small wind turbines built are destined for stand-alone systems at remote sites. during the two world wars when fossil fuel was scarce. China alone builds approximately. wind turbine technology was considered as a source for generation of large amounts of electrical energy. remote applications generally require some form of alternate energy source. Some find their ways to remote locations in Canada and Alaska. Studies performed by the author indicate that a remote installation site requires an average wind speed greater than 9 mph to generate the electricity from a stand-alone power system or small wind turbine at lower cost than power from gasoline-based or diesel generators. according to energy planners.Stand-Alone Wind Turbine Systems ◾ 165 the production of the electrical energy. What is a remote site? The rules are not strict. During the1930s.000 wind machines per year. It is important to point out that the wind is an intermittent source of energy. 6. Some homeowners determined to generate their own electrical energy even though they could just as easily buy it from local utilities. These stand-alone wind turbines are small enough to be carried on horseback from one encampment to another. They represent the sole sources of electrical power available on the great Asian Gobi Desert that stretches from China to Russia. Battery systems require only direct current (DC) for charging. For this reason. Wind turbine planners claim that as many as 110. Standalone wind turbine installers feel that as a rule anyone residing more than 1 km from an existing power line will find it cheaper to install an independent power system rather than connect to a commercial utility power line. thousands of small wind turbines were used for irrigation and pumping water. a utility cannot justify the cost of running lines. At such sites. increasing numbers of stand-alone power systems are installed to serve the lower 48 United States. a small wind turbine may be more cost-effective than a photovoltaic system alone. Others serve mountain-top telecommunications sites where utility power lines do not exist. 10. battery storage becomes a necessity. Batteries store surplus electrical energy generated on windy days for later use. Commercial utility companies will build a power line almost anywhere if someone pays for it. For remote residential that require a fairly steady supply of electricity.
6. batteries to be charged.1 Hybrid System with Back-Up Capability This design for a hybrid stand-alone power system consists of a low-capacity wind turbine. battery-charging wind systems as illustrated in Figure 6.166 ◾ Wind Turbine Technology However. 60 Hz frequency. solar array as a renewable energy source. The propeller generally deploys two rotor blades (As shown) to achieve optimum economy and design simplicity. . In other words. battery charger. if the turbine cannot operate because of abnormal wind conditions.3.1 will be found more practical and cost-effective. This configuration of a hybrid stand-alone system can simultaneously charge the batteries and provide AC to power devices operating at 110 V. The hybrid system [1] offers a cost-effective approach and ensures continuous supplies of electricity if any of the two power modules becomes temporarily inactive. 6.3 Configurations of Stand-Alone Systems Potential design configurations of hybrid stand-alone power system with back-up capability and variable speed propellers are shown in Figure 6.2. solar panels will provide the DC electricity for charging the batteries and AC DC loads Wind Generator DC Source center DC/AC inverter Constant frequency AC loads Variable speed State of charge Batteries Battery charger Automatic disconnect switch Utility power line Figure 6. back-up generator. and AC load center. an inverter to convert DC to AC electricity.2 Hybrid stand-alone system with back-up capability and variable speed propellers.
These micro wins turbines are so small that they can be erected or taken down by a single person in a short time. If you wanted a wind turbine for a remote site. they can be installed for less than $2000. 6. It is interesting to . but the cost of a solar power system and possible low sunlight levels favor the micro wind turbine for certain conditions. Today most pipelines are protected by small PV modules. it protects the exposed metallic surfaces from galvanic corrosion. A micro wind turbine provides an electric charge to the surface of a metallic pipe to counteract galvanic corrosion in highly reactive soils. but in cloudy environments this protection may not be effective. Conversely. Another application of micro wind turbine technology is charging automobile batteries to power security lighting in rugged and isolated areas. wind and solar resources complement each other: the strong winds in the winter are balanced by strong sun in the summer. PV technology can be used to charge batteries. One example is cathodic protection of pipelines. storage is not needed during calm winds because corrosion is a slow process occurring over long periods. At one time all cathodic protection in rural areas was provided by wind turbines that generated few watts.3 Applications of Micro Wind Turbines Some applications of low-power wind turbines do not require storage capabilities. Such small wind turbines that output fewer than 100 W are commercially available and effective for charging batteries with minimum cost and complexity. thereby enabling the hybrid system designers to reduce the size of each component [1]. Furthermore. water.3.3. gas. A solar dealer would provide solar panels that would cover your roof with PV cells or modules with optimum power ratings. electrical energy is available from the small wind turbine. When the wind returns. Market survey date indicate that Bergey Wind Power and Northern Power Systems—small wind turbine pioneers—have successfully demonstrated wind and solar hybrids that utilize the assets of both technologies. Micro wind turbines can used to charge automobile batteries and power security lighting systems in remote locations.2 Micro Wind Turbines Micro wind turbines with very low capacities are best suited for charging the batteries on sailboats and recreational vehicles. if solar power is not available due to heavy clouds or rains. In many remote sites.Stand-Alone Wind Turbine Systems ◾ 167 electricity power to drive appliances. and other nontoxic liquids. This protection is best suited for remotely located pipes carrying oil. 6. a dealer will meet your electrical energy requirements and provide you with batteries of appropriate specifications to handle the required power load. System designers have found that these hybrids perform even better in terms of reliability and efficiency when coupled with small low-cost back-up generators to reduce the number of batteries needed. fewer batteries will provide significant savings in procurement costs.
. As the electrical loads on central power systems expand to remote villages. The new hybrid power systems generate very little power in comparison to central power plants. Many third world nations are scrambling to expand their power systems to meet demands for rural electrification. about half of the population lived without access to utility power as recently as 15 years ago.3 can be moved easily to provide power to remote villages. There are few technical reasons why micro wind turbines cannot be used if the installation cost exceeds $1500. Arabic countries. However.g. Many people in villages of India. 1 kWh (one unit) of electricity provides ten more essential services in India than it provides in Indiana. To demonstrate this point. powering security sensors. This compact stand-alone system has higher generating capability than a micro wind turbine and can be designed in any configuration shown in Figure 6. but the third world uses very little power because most of its population cannot afford to buy and operate electrical appliances due to high power costs. e.1 to suit a specific application. and generating electric power compatible with utility company specifications. China. charging electric vehicle batteries.3. this approach to rural electrification no longer makes sense since reliable hybrid power systems comprised of wind turbines and solar power systems became commercially available. Hybrid power systems that feature small or micro wind turbines because of their sufficient power output and low procurement cost.. Most countries are following the pattern set by the United States during the 1930s: building new power plants and extending transmission and distribution lines from the cities to rural areas. thus.4 Micro Wind Turbines for Rural Electrification It is important to mention that about one-third of the world's people live without electricity. 6. providing emergency lighting. rapid electrification of remote villages is possible at minimum cost and with simplicity. Developing nations' installation of hybrid power systems is more cost-effective than stretching the service areas of heavily loaded and unreliable generating plants in large cities. Some micro wind turbines have been designed to perform several tasks simultaneously. Some micro wind turbine are available capable of supplying power for all-electric modern homes located in remote areas where utility power lines do not extend. While China which has embarked on a program of rapid industrialization. Local governments using micro wind turbines can provide electricity to villages quickly in emergency situations. and African countries lack access to utility power. a compact hybrid stand-alone system as shown in Figure 6.168 ◾ Wind Turbine Technology mention that PV modules are currently deployed extensively for such applications because of lower installation costs. This compact wind turbine power system is fully capable of providing all the electricity for a home while feeding excessive electricity to commercial utility grid power lines.
For example. Hybrid power systems consisting of wind and solar power modules also permit use of smaller.6 Telecommunications Applications in Remote Areas It is difficult and economically infeasible to install power lines for telecommunications applications in remote and hostile areas where hybrid versions of micro wind turbine power systems can play a critical role. less costly components than would be needed if a system design configuration depended on only one power source. it is easier to add more solar modules to a PV array than it is to add wind machines. In brief. Recent models have power generating capabilities approaching 500 W.3 Compact hybrid stand-alone system.3.5 Power Generating Capacity Despite their advantages. PV modules can be added in smaller increments than micro wind turbines [2]. This design flexibility can . sufficient wind energy is probably available to compensate for the loss of solar power. When scaling up outputs from remote power systems. on an overcast winter day when PV generation is low due to poor solar intensity.Stand-Alone Wind Turbine Systems ◾ 169 1 Skystream provides electricity to home 2 Home connected to utility grid 3 Figure 6. Wind turbines are sized from 50 to 250 W.3. each additional wind turbine requires a separate tower and control system. Advances in solar and wind technology have eliminated the need to install expensive stand-alone power systems because remote systems do not usually depend totally on a single source. Although the output of micro wind turbines is less than that from most PV modules (typically 50 W). wind turbines are less modular than PV power modules. 6. 6. thereby adding installation and procurement costs.
Such reductions will permit users to stretch each kilowatt hour to do as much as work possible. In addition. it is easy to design a wind. 6. reliability.3. In effect. and cost. 6. After the total need is established. performance. A hybrid design could include a small and inexpensive fossil-fueled back-up generator for the same reasons. low-capacity power systems. allowing users to meet their energy needs from smaller and less costly power systems. Depending on generator size and overall power consumption. effort.8 Reducing Power Demands Reducing electrical energy consumption through conservation and efficiency measures will certainly reduce the demand for electricity. knowing how. solar. The studies further indicate that little in the way of lifestyle sacrifice is required because modern compact fluorescent lights and energy-efficient appliances need less power and less expensive wind turbines. This is particularly true at remote locations where individuals must spend time. or other energy providing system.3. Furthermore. The typical energy amounts consumed by common appliances according to Pacific Gas . 6. and when electrical energy is used is more important for a stand-alone power system than for an interconnected wind turbine. an electrical generator can "top up" discharged batteries and meet electrical needs not met by a combined wind and solar generation scheme. and money to generate electricity. one must estimate energy consumption by appliances and other devices requiring electricity. and size. where. One way to control system cost is to reduce the demand for power. However. latest technologies must be explored to improve the energy efficiency. thereby allowing the deployment of inexpensive. In addition.9 Typical Energy Consumption by Electrical Appliances To size any electrical power system. this approach would require trade-off studies to analyze performance. initial procurement costs of power systems remain high. One cost saving idea is to determine what appliances will be used at a remote site and estimate their power consumption in an effort to reduce operating times for sensors and appliances that do not contribute to system reliability and longevity.170 ◾ Wind Turbine Technology significantly lower the installation and procurement costs for a remotely located power source. a stand-alone system can replace the fuel and the maintenance expenses of a back-up generator with a larger solar and wind turbine combination.3.7 Cost Reduction Techniques The author's studies of hybrid versions of power sources author indicate that despite significant improvements in reliability. the designer of a hybrid power source is not required to size the components for worst-case operating conditions by specifying a larger turbine and storage battery bank than necessary.
the total energy consumption at a remote location may not exceed 200 W. A remote location will most likely require a 50-W lighting source.1. It is important to note that a stand-alone wind turbine in a remote location will not have to support many of the appliances cited in the table. washing machines. two fans. central air-conditioning units.10 Techniques for Reducing Energy Consumption It is always more economical to save energy than to generate it with a hybrid power system comprising of micro wind turbine and a solar power source. 6. It is wise to consider all available options to save energy consumption at remote sites. hybrid power systems are best suited for remote and unmanned locations. sizing of a stand-alone power system should be based on overall power consumption by appliances and the number of hours they operate. for example. is powering a hot water heater or stove with gas or other fuel. computer and printer. six 60-W bulbs. radio. Therefore. It is extremely important to determine the minimum energy consumption needed for the services expected if optimization of the value of a renewable power system and minimization of procurement costs are the principal deciding factors. and a small fan with a 50-watt rating.3. and a dishwasher operate simultaneously. microwave ovens. 6. Cooking with gas or propane instead of a microwave will save power and provide economical service. The electrical appliances are categorized in terms of heating. propane. a security sensor not consuming more than 100 W.Stand-Alone Wind Turbine Systems ◾ 171 & Electric of California are summarized in Table 6. Studies of stand-alone power sources performed by California's Pacific Gas & Electric Company found that remote power generation must be confined to lighting. a microwave oven. Note that most high-wattage appliances such as toasters. remote energy consumption will certainly increase if other appliances are added to the load. Therefore. However. Among alternate methods for reducing electricity consumption. Electric cooking stoves consume great amounts of energy and exert high peak power demands that determine the sizes of inverters and other hybrid components. As mentioned earlier. and water pumping uses because remote sites are seldom served by municipal water sources. The average energy consumption of a residence is about 5 kW if a window air conditioning unit. Similarly. installation of a gas line to a remote location is not economically feasible. Compact fluorescent lights can . oil. and electric ranges usually do not operate simultaneously. refrigeration. and other household functions. a refrigerator. heating with gas. or wood is far more economical at a remote site than heating with electricity. However.4 Stand-Alone Systems for Remote Sites This section discusses energy requirements for remote sites and emphasizes economic feasibility and reliability. dryers. air conditioning.
1 Typical Power Consumption by Household Appliances Appliance Consumption (W) Heating Space heater Heat pump 1500 4000 Air Conditioning 110-V window unit 220-V window unit Central unit 1500 2500 4500 Water Heating Electric heater Heat pump 350 200 Refrigeration 10-cu ft manual defrost 20-cu ft frost-free 50 145 Laundry Electric dryer Washing machine 5000 per load 250 per load Lighting Bulbs 60 to 100 Other Electrical Appliances Microwave oven Ceiling fan Portable fan Ceiling fan Air cooler Toaster 750 /1500 200/300 100/200 200/250 250–300 750/850 .172 ◾ Wind Turbine Technology Table 6.
2 Air Conditioning Units Depending on climate and house size. It is important to mention that some behavior modification may prove beneficial for optimizing the performance of a hybrid power system. A standard refrigerator may push an energy budget over the edge and require an additional wind turbine or more solar panels to meet the demand. 6. Power reduction techniques are particularly critical for remote and unmanned operating sites.) Consumption (W) 1000/1400 1100 120/150 50/150 75 225 400 significantly reduce the electricity demand. Sun-frost devices may be well worth the added cost— another trade-off to consider when designing a stand-alone power system. Energy ratings of electrical appliances including washing machines and refrigerators are available from the Consumer Guide to Home Energy Savings published by Home Energy magazine which also offers tips on saving energy without reducing comfort. If air conditioning is necessary. These techniques can cut lighting costs by two thirds. For . a trade-off study should be conducted to determine whether an evaporative cooler or air cooler can provide a comfortable temperature [2].4. Modern refrigerators consume close to 1000 W. 6.4.1 Typical Power Consumption by Household Appliances (Continued) Appliance Iron Laser printer Facsimile Personal computer Black-and-white television Color television Plasma television (52 in.Stand-Alone Wind Turbine Systems ◾ 173 Table 6. Sun-frost refrigerators exhibit the highest efficiencies (300 W) but cost about $2500. an air conditioning unit can double the energy consumption of an otherwise energy-efficient home. Swamp coolers use far less energy and work well in arid climatic environments such as the Southwestern United States. Consumption may be further reduced by lighting only areas where light is needed and by simply turning off lights when not needed.1 Refrigeration Appliances Significant energy savings can be achieved with refrigeration appliances. today's energy-efficient models consume 700 to 800 W watts in typical American homes.
Those who cannot compromise a comfortable lifestyle may face a rude awakening. wash laundry on windy and bright sunny days to save electrical energy without affecting lifestyle. The author's studies of stand-alone hybrid power systems reveal that they can generate and store DC electricity. e. It is advisable to reduce your electric consumption until you are ready to make a transition to producing your own electrical power. Since most electrical loads will be supplied by the batteries most of the time. after which the procurement of the components and installation of turbine and tower can be completed.2 provides high reliability and greater design flexibility in sizing a hybrid stand-alone system. and the required voltage for operating a hybrid power system. The two major aspects of a stand-alone system are power generation and storage. It is interesting to mention that sun-frost refrigerators are built in both DC and AC versions.174 ◾ Wind Turbine Technology example.3 Selection of AC or DC Operation After the power consumption requirement is defined and AC or DC power is selected. 6. performance specifications for the hybrid system components can be established. An average American household should able to reduce its consumption to about 3600 kWh per year or about 10 kWh per day. The figure clearly identifies the inverter and storage batteries. minimizing energy-intensive discretionary electrical loads on days when power is reduced extends battery life and stores extra power for use when needed for important functions such as water pumping or additional refrigeration. but the back-up generator will increase system complexity and cost.g. . Most Europeans live comfortably with that much electricity or less. PV arrays produce DC energy. new houses are always wired for AC.. wind turbines generate AC energy that is rectified to DC energy so it can be stored in batteries. they do not need to rewire from DC to AC.4. the choice becomes whether to feed the load with DC directly or with AC though an inverter as illustrated in Figure 6.1. Conventional homes use AC electricity to operate appliances. The efficiencies of electronic inverters exceed 90% but inverters add cost and complexity to a system. If owners of stand-alone systems with inverters want to add commercial utility power or sell their properties. It is important to mention that the addition of a back-up generator as shown in Figure 6. A reduction of power consumption will determine the size of a power system that will meet your needs. Banks are sometimes reluctant to finance homes with stand-alone power systems and prefer to finance homes with conventional wiring. It is desirable to learn to synchronize weather and lifestyle. Such homes are easier to finance than those wired for DC. Furthermore. whether wiring should be for AC or DC . DC wiring is justified for refrigeration and water pumps because these appliances limit inverter losses. Turning off unneeded appliances is a very small burden for energy-conscious consumers. A back-up generator provides constant frequency AC energy needed by electrical appliances.
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6.4.4 Parameters of Generating System
Appropriate values of electrical parameters of a generating system must be defined to maintain operational continuity and reliability. Output voltage levels for solar panels, wind turbines, batteries, and a back-up generator system must be specified. Note that low-voltage operations require thicker and heavier cables or wires to carry same amount of electrical power as high-voltage systems. For the same sizes of cables, low-voltage operations waste more electrical energy in resistance losses than higher-voltage operations. Thus the voltage preferred for operating a remote hybrid power system safely and efficiently is directly proportional to the amount of power that passes through it. This is an important design consideration for a hybrid stand-alone power system. In brief, the selection of operating voltage is strictly dependent on power consumption. According to the editor of Home Power, a 12-V operation is preferred for a building requiring fewer than 2 kWh per day. Homes consuming power below 6 kWh per day should use 24-V service; those requiring more than 6 kWh per day should have 48-V systems. The author's studies of wind turbines indicate that some micro wind turbines operate at 12 V because the power output is only few watts. Most wind turbines and solar hybrids use 24 or 48 V, depending on the power output of the solar arrays and how the arrays are connected. A voltage of 120 is considered appropriate when the power consumption approaches 20 kWh per day. The initial cost for a 120-V system is extremely high. Furthermore, high-voltage systems do not permit greater design flexibility for renewable power systems than they do for 24- or 48-V systems. If you need to move a solar array into a more exposed position or move a wind turbine to a hilltop [3], a 120-V power system may be the only choice for minimizing transmission line losses and cable costs. In brief, operating voltage for a hybrid power system must be selected yield maximum economy and minimum cable losses.
6.5 Sizing of System Components
For a small load powering one transistor radio and couple of 20-W bulbs, a 12-V PV system consisting of one or two 50-W solar panels with DC output makes the most cost-effective choice. For applications such as vacation cabins, a PV power system is easier to work with and less expensive than a micro wind turbine. However, if the load increases above a few hundred watts, wind and solar hybrid power schemes become more attractive and practical. For loads exceeding 4 kWh per day, a wind turbine is far more cost-effective than PV modules. Small PV arrays typically cost about $25 per kilowatt hour. Large amounts of electrical energy can be generated from small wind turbines at lower cost. For example, a wind turbine with a 3-M rotor can generate electricity in excess of 3 kW and
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will cost about $2000. A wind turbine with a 7-m rotor can generate more than 20 kW and will cost about $10,000; errors in such cost estimates may exceed ±10%.
6.5.1 Sizing and Performance Capabilities of Solar Arrays
Sizing of solar arrays is dependent on several factors including the latitude of the installation location, peak sun hours per day, height of the array, solar intensity, climate conditions, and type of sun tracking scheme deployed. To estimate the potential electric generation from a PV array that may contain hundreds of 2-W solar modules, multiply the rated capacity of the PV array by the peak sun hours per day for the installation site region. For example, a 200-W solar array will generate about 1000 W per day in a region with five peak sun hours per day—equivalent to 365 kWh per year. Deployment of a tracking mechanism for the solar array can achieve about 45% more energy than a fixed array and may boost the annual solar energy close to 530 kWh. Specific details on sizing solar arrays are available in Solar Cell Technology and Applications.* As noted earlier, output of a solar power system depends on several factors, while output of a wind turbine depends on relatively few: wind speed and direction, rotor dimensions, and tower height. However, after a wind turbine is installed, its output depends totally on wind parameters. After the roof panels are installed for a solar system, the power output depends on the peak solar intensity (hours per day), temperature of the array surface, and the shadowing effects from the panels. Finally, the power output estimate from a solar installation will be less accurate because solar installations are more subject to parameter changes than wind turbines.
6.5.2 Sizing and Performance Capabilities of Inverters
Inverters convert DC energy into AC energy. Several types have been developed, but the electronic versions are best suited for solar-based power systems. A few years ago, the efficiency of an electronic inverter ranged from 88 to 91%; it has now significantly improved close to 95%. Compact commercial electronic inverters yield efficiencies ranging from 92 to 94%. It is important to point out that cost, reliability, and efficiency are the most critical design parameters of the electronic inverters for applications in solar power modules. Inverters operate conventional appliances, whether power is generated by a PV array, wind turbine, or hybrid power system. Most inverters produce a modified AC sine wave that can serve a variety of AC loads ranging from standard electronic components (computers and stereos) to washing machines. In cases of sensitive electronic components, inverters with low harmonic distortions are preferred to maintain optimum performance and reliability of the devices.
* A.R. Jha. Taylor & Francis, 2010, Boca Raton, FL.
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To determine the size of an inverter, it is necessary to calculate the electrical load demand in watts from all the appliances that are likely to operate simultaneously. The inverter should be sized to handle the surge requirements of induction motors in refrigerators and washing machines that operate over extended periods. Small appliances often demand 1.5 to 2 times their rated operating currents when they start. This fact must be considered during the design and development phase to ensure the stated reliability and longevity specifications are met. Large appliances such as washing machines and refrigerators can draw three to four times their rated operating currents when they are switched on. For example, a 500-W electric motor induction requires 1500 to 2000 W for start-up. Such power surge requirements are easily met with wind turbines, but present a problem for solar-based power modules. All inverter manufacturers list their continuous and surge outputs, but the continuous output rating represents what the inverter can supply over a long period without intermittent failure, overheating, or performance degradation. Few loads operate continuously, and those that do draw very small current. Sandia National Laboratories recommends sizing an inverter to 125% of the expected continuous load to avoid performance degradation and component overheating. For safe operation, a 2-kW inverter should run most minor appliances or electrical loads, while major appliances such as washing machines and microwave ovens must be operated singly. A 5-kW inverter will be required to operate a washing machine, refrigerator, well pump, and microwave oven simultaneously. A microwave oven, hair dryer, or iron will draw an individual load from 1000 to 1500 W, but they operate only for short times. They may influence the size of the inverter needed, but they contribute very little to total energy consumption. Stand-alone power system designers predict that an inverter with a capacity of 5 to 8 kW is required if all the appliances discussed above operate simultaneously. An inverter should also provide fuse protection from the various sources of generation and power factor correction for inductive loads. In addition, the inverter design should have provisions for disconnect switches on both the AC and DC sides and power management switches to limit certain loads from exceeding its capacity. It is not advisable to operate appliances such as electric dryers, electric hot-water heaters, or electric stoves on a stand-alone power system unless you are using them as dumps for excess energy generation. These electric appliances consume large amounts of electricity and place unreasonably high current demands on an inverter. Propane gas is a better answer for powering such appliances provided they operate for short durations or only in emergencies. Some inverters are designed to provide battery charging functions. A separate inverter should be available for this purpose and it should be capable of handling multiple inputs via hook-ups to renewable sources and from a back-up generator. Without a battery charger, there is no way to ensure that the batteries stay fully charged to provide electrical energy if needed.
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6.5.3 Sizing and Performance Parameters of Batteries
Two distinct types of batteries are common in hybrid stand-alone power systems: lead–acid and nickel–cadmium batteries. In addition, batteries used in trucks and golf carts can be used if their charge–discharge cycles, capacities over extended periods, and reliability under uncontrolled environments are acceptable for use in hybrid stand-alone power systems. Sustaining a rated battery charge under various temperature environments and over extended periods must be given serious consideration. Sealed batteries are preferred to achieve reliability and longevity over the long term. Lead–acid batteries have higher current capacities, but must be maintained to ensure full energy capacity at all times. Their capacity is significantly reduced at lower temperatures and thus present a maintenance problem. As to cost, lead–acid batteries are less expensive than nickel–cadmium batteries. A nickel–cadmium battery with the same capacity (ampere hours) as a lead–acid battery could cost as much as $1500; the cost of a lead–acid battery is significantly lower. Nickel–cadmium batteries are lighter, more reliable, and do not require maintenance. It is a good policy to separate batteries from inverters, switches, and service panels if longevity and reliability of the batteries are the principal requirements. In addition, this practice prolongs the lives of the electrical components while guarding against the ignition of hydrogen emitted by sparks during high-voltage charges. Nickel–cadmium batteries are more costly than lead–acid batteries, but offer other advantages. They are best suited for cold climates because they are less susceptible to freeze damage, require very little maintenance, and last longer than lead–acid batteries. Nickel–cadmium batteries are widely used in computers and other electronic devices and can be fully discharged without harm to electronic circuits or devices. Lead–acid batteries are best suited for power applications and do not suffer from "memory effects." Correct sizing of batteries is critical to ensure constant performance and reliability of the operating components of a stand-alone power system. It is advisable not to undersize the batteries, inverters, and wiring to avoid catastrophic failure of the critical elements. A lead–acid battery bank has no capability for expansion if storage is insufficient after few years of operation. More batteries cannot simply be added in small increments. Essentially, a lead–acid battery bank is a fixed-size entity. Expansion requires a complete new bank of batteries of the proper voltage wired in parallel. Suggested locations for solar panels, batteries, inverters, controllers, and fused switches are shown in Figure 6.4. A vent should be provided to remove acid fumes from the storage area. If possible, lead–acid batteries should be housed in a well-ventilated room separated from living quarters to ensure safety of the occupants.
Stand-Alone Wind Turbine Systems ◾ 179
Suggested Batteries Locations
Solar array
Vent Inverters and controller Fused disconnect switches
Insulation Batteries Rack
Figure 6.4
Components of power storage system.
6.5.4 Sizing and Performance Parameters of Solar Panels
Sizing of solar panels is relatively simple. Panels can be added to compensate for losses to a back-up generator. In other words, any power shortage in the back-up generator capacity can be made up by installing additional PV modules to an array or install a larger micro wind turbine.
6.6 Stand-Alone Systems with Utility Power Back-Up
Potential design configurations for stand-alone wind turbine power systems are illustrated in Figure 6.5. The figure shows variable speed propellers, locations of the inverters and batteries, water pumping apparatus, electrical generator with DC or variable frequency AC capability, and application for thermal loads. Hybrid versions of stand-alone power systems incorporating micro wind turbines and photovoltaic sources along with reliability and performance issues were described in Section 6.5. A stand-alone power system with utility back-up capability is useful when a utility is reluctant to implement a direct connection or when homeowners want to wean themselves gradually from a commercial utility grid system. Electronic controls are necessary to monitor continuously the performance of a battery bank. If the batteries become depleted or completely drained, an automatic switch closes the
5 Potential design configurations.180 ◾ Wind Turbine Technology Wind Generator DC DC loads Inverter Constant frequency AC loads Variable speed Batteries Wind Generator Variable frequency AC Variable frequency motors (water pumping) Variable speed Wind Gearbox Mechanical loads (water pumping. . it may be desirable to engage utility back-up power to charge the batteries.) Variable speed Wind Generator DC or variable frequency AC Heating coils and thermal storage ermal loads Variable speed Figure 6. grinding grain. If renewable power sources consistently fail to provide the necessary power and a commercial utility is nearby. in essence substituting utility grid power for a back-up generator. etc. This utility back-up power approach makes a lot of sense in regions where utility power service is not reliable. thus starting the charging process until the batteries are fully charged. utility power line to the battery charger. The independent power source (not the utility company) still handles all the electrical loads and continues to provide service to all electrical loads if the utility power is interrupted.
a stand-alone system could pay for itself in one year if its owner resides more than 1 km from utility power lines. The micro wind turbine assumes a rotor diameter of 3 m and turbine capacity equal to 13. Such users typically install remote power systems because the cost of extending utility power lines to their sites is significantly higher.1 Economic Aspects of Remote Systems In general. Output power rating.Stand-Alone Wind Turbine Systems ◾ 181 It is important to mention that utility back-up is like the uninterruptable power sources widely used to protect computers from power outages regardless of cause. Using sophisticated design techniques. Under these financial conditions. The values of the performance parameters quoted are based on extensive engineering analysis and judgment.000 W. For someone considering a stand-alone power system in the United States strictly on economic grounds.2. users of remote power system do not expect their wind turbines and solar power generation to compete with the cost of commercial utility-generated electrical energy. As a rule of thumb. Sometimes utility companies offer discounts for educational institutions and religious buildings. Pacific Gas & Electric charges about $60. Both the solar and wind systems are priced based on minimum power storage: 13 kWh for 2 days.000 per mile to bring utility lines to rural customers. Many critical computer systems are required to operate continuously from batteries. we can eliminate one inverter.6. The utility source is used only to charge the batteries. The electrical loads draw current from an inverter that is constantly fed by the batteries. thereby realizing a significant reduction in procurement cost as illustrated by Table 6.000 per mile to extend power lines. California utility companies charge new customers about $10 per foot for overhead power line extensions [2] and charge 50% more for buried power cables. The output of the solar array is assumed to be 800 W. The back-up generator selected is sufficient to handle the electrical loads for a power system of this size. The French electric companies charge rural customers as much as $32. . and procurement costs of both systems are summarized in the table. The material presented above clearly establishes the economic principles for extending commercial power lines in various situations. The situation in Europe is slightly different.6. A hybrid system allows downsizing of battery storage requirements. 6. power available per day over a 5-hour duration.2 Cost Analysis for Stand-Alone Hybrid System A cost analysis for a hybrid version of stand-alone power system comprising of a small micro turbine and a compact solar system is based on the following facts. 6. it would be cheaper to bring in a utility power line if the site is fewer than 1000 ft from existing lines. storage capacity.
0 13.6.000 with rate escalation of 10% Minimum energy purchase requirement = $1200 Annual kilowatt hour purchase order = 4500 with inflation rate of 5% Utility company charge for electricity = 10 cents per kilowatt hour 6.000 Solar Power Module 800 4.600 6000 Micro Wind Turbine 1500 8. and operational capability in severe wind environments.000 6.2 13.0 10.2 kWh Total storage requirement = 26 kWh Total system procurement cost = $25. reliability.7 Stand-Alone Wind Turbine–Based Systems for Various Applications This section discusses potential applications of stand-alone wind turbine power systems with emphasis on performance. commercial utilities charge $10 per foot to extend a power line to a customer's premises alone with additional fees summarized in Table 6.3.0 11.2 Procurement Costs and Performance Parameters of Stand-Alone Systems Parameter Power output rating of system (W) Power output per day over 5 hr (kWh) Storage capacity (kWh) Procurement cost ($) Back-up generator/charger capacity (W) Summary: Refrigerator procurement = $500 Duplicate inverter = (– $1400) Total power output = 8300 W Total power consumption requirement = 12.182 ◾ Wind Turbine Technology Table 6. As mentioned earlier. The assumed parameters and conditions are: Cost of service for 2500 foot line = $25. Performance capabilities and limitations of stand-alone .3 Cost Estimate for Extending Line from Existing Utility This section presents a cost estimate analysis for extending a utility power line located 2500 ft from a customer residence.
The author's preliminary studies of wind turbines for telecommunications applications reveal that reliability and minimal maintenance are the principal design requirements. village electrification. 6.7. Net present value of payments due utility company after 20 years = $38.Stand-Alone Wind Turbine Systems ◾ 183 Table 6. and operate continuously over extended periods (sometimes in excess of 7500 hours per year). Wind turbines deployed by the telecommunications industry encounter more extreme weather.4.1 Telecommunications Telecommunications operations demand reliability and uninterrupted energy sources. Wind turbines made by various companies listed in the table have operated at several sites and the users are impressed by the reliability of the machines even when operating at an average wind speed of 6 m/sec or 11. particularly in isolated rural environments. and building heating and water pumping applications will be summarized. only robust wind turbines using fully integrated. This demonstrates the mechanical integrity and uninterrupted performance capability of the HR 3 wind turbine.3 Estimated Cost of Extending Utility Power Line Service Year 1 2 3 4 19 20 Service Cost ($) 25. the .000 1200 1200 1200 2503 2753 Total amount paid to utility company over 20 years of service = $54. These unattended power sources are expected to function for much longer periods of time than home-based power systems and even commercial wind power plants. According to designers.7. direct-drive designs perform satisfactorily in the rugged and isolated environments characterized by telecommunications sites as shown in Table 6.000 00 00 00 00 00 Utility Power Purchased ($) 1200 1200 00 00 2503 2753 Net Payment ($) 26.035. 6.500 wind turbine systems for telecommunications.66 knots. This power system in operation installed in Antarctica to handle telecommunications worked continuously for 12 hr during a fierce Antarctic storm. However.2 Performance Capabilities of HR 3 Hybrid The HR 3 hybrid system designed by Northern Power Systems in the United States is widely used for telecommunications applications.
At Norway's Hamnjefell telecommunication . Two U.4 Continuous Load Capabilities of Reliable Wind Turbines Wind Turbine Designation NPS HR 1 (hybrid from Northern Power Systems) Bergey 1500 (wind turbine from Bergey Wind Power) NPS HR3 (hybrid from Northern Power Systems) Bergey Excel (wind turbine from Bergey Wind power) Continuous Operating Load (kW) 0.7. Their wind turbines meet the telecommunication industry's principal requirements. Since then. recharged its storage batteries. and the United States.184 ◾ Wind Turbine Technology Table 6. namely reliability and low maintenance. are the most reliable suppliers of wind turbines suited for telecommunications applications.3 Fuel Savings from Use of Hybrid Systems Based on 15 years of operation as shown in Table 6. Alternate fuels such as propane or gasoline can also operate generators.0 35 radio station temporarily went off the air when the exhaust pipe stack for the backup generator blew away during the storm. 6. high winds at the site blew the anemometers away after they recorded wind speeds of 126 mph or 56 m/sec. and fully restored all the station's telecommunications. manufacturers.5 mph.S. Twice during the first 2 years of operation.4 0. Northern Power Systems and Bergey Wind Power. The HR 3 hybrid power system consisting of an 84-kWh battery bank and a 1. the HR 3 resumed its normal operation. When the storm started to abate.2-kW solar array and operating on Calvert Island off the coast of British Columbia has cut diesel fuel consumption substantially. Other components of these systems include a PV array and an 84-kWh battery bank that significantly decreases the operating time of a diesel generator. Canada. this installation site has endured even stronger winds. The performance of the HR 3 was so impressive that three more HR 3 wind turbines were installed at the site.4.4 1. hybrid system designers claim that hybrids have been successful in reducing the fuel consumption at remotely located telecommunications sites in Antarctica. The system operator claimed that overall the hybrid system reduced fuel use nearly 90%—equivalent to half the maintenance cost of a conventional diesel engine. yielding a significant saving for costly diesel fuel for a generator. The turbines are capable of meeting the continuous electrical load requirements of telecommunications installations encountering average wind speeds close to 6 m/sec or 14.
Canada.Stand-Alone Wind Turbine Systems ◾ 185 station above the Arctic Circle. but this is not a sound scheme for bringing power to villages with populations of a few thousand. and a 40-kW inverter.2 billion people have no access to electricity. 6. each 7 m in diameter. A stand-alone power source consisting of a micro wind turbine and solar array operates successfully in the Mexican village of Xcalac on the Yucatan Peninsula. thereby eliminating the need for costly storage batteries. Extending utility power service from cities to remote villages in developing countries presents a challenge to the city utilities. This approach is attractive for villages in undeveloped African and Asian countries. The most practical and economical answer is installing high-voltage transmission lines few miles away from villages with large populations. 6.5 to 2. a 12-kW PV array tied to a large battery bank. This design configuration is cost-effective for village electrification and does not require scheduled maintenance.1 Successful Examples Since the cost of building conventional power plants is very high and villages contain no manufacturing facilities to purchase power.2 million utility power line to this remote village. Bergey Wind Power installed the hybrid power system that utilizes both wind and solar energy sources. Batteries and inverters are needed only for loads that require constant frequency AC power.8 Hybrid Systems for Village Electrification Historians believe that 1. Bergey erected the first Mexican wind farm including a 60-kW array of six micro wind turbines. . and the European Community. a stand-alone power system composed of a micro wind turbine and solar array is desirable for electrification. The complete power system cost about $500. Batteries are not needed to meet emergency conditions because wind energy is available 24 hours a day and the solar energy is available for a minimum of 6 hours on a sunny day. electrification of villages and rural regions can be accomplished by distribution lines installed by commercial power companies. In developed countries such as the United States. grinding grain. or hydroelectric power plant to electrify an individual village is both financially impossible and illogical. an HR 3 hybrid power system has met more than 70% of the site's electrical loads since 1985 [4]. In some third world countries.000 which offset the construction of a proposed $3.8. Several hybrid power schemes successfully operate in Danish and Dutch coastal villages. village electrification schemes are considered for pumping water. nuclear. and handling other tasks that do not require utility-grade electricity. Storage batteries can be added if necessary. Construction of a coal-fired.
2 Application of Village Electrification for Water Pumping Most village farmers rely on irrigation water.6 Water pumping system. The amount of water pumped depends on the wind parameters and the various heads or heights involved.8. Well outlet Friction head Total discharge head Total dynamic head Pumping head Static water level Draw down Cylinder Figure 6. total discharge head. The figure clearly identifies the critical elements of a micro wind turbine: friction head. The energy needed to pump water is a function of the volume and the height to which the water must be lifted.6. Specific details on pumping heads using wind turbine technology are shown in Figure 6.186 ◾ Wind Turbine Technology 6. static water level. water outlet pipe. . pumping head. The wind turbine takes kinetic energy available at the installation site and converts it into mechanical energy that drives the pumping motor coupled to an electrical generator. and total dynamic head from a draw down reference line.
For example.5 Sample Calculation and Breakdown of Total Dynamic Head for Wind Turbine-Based Water Pumping System Type of Head Static Draw-down level Discharge Friction head for pipe Friction head for 90-degree elbow Total dynamic head Magnitude of Head (ft) 100 5 10 12 18 145 The static head is the most important parameter and is defined in a very practical way. most of the mechanical wind pumps have been back-geared to increase the mechanical power to be generated. diameter) requires three 90-degree elbows to route the water into the storage tank. A breakdown of the total dynamic head for this system is summarized in Table 6. Unless the water storage tank is sited below the well outlet pipe as illustrated in Figure 6.8.5. In the past. Packer heads are required when an outlet is higher than a well opening. a 100-ft pipe (1-in. one plans to store water in a tank with an inlet pipe 5 ft above the ground up a small hill with a 5-ft gain in elevation or height. The packer head facilitates faster pumping above the height of the well into the storage tank. Most back-geared windmills lift the sucker rod once every . a windmill lifts the sucker rod on every revolution of the turbine rotor. Under low wind environments.6. As to the pipe and storage tank. The numbers in the table are valid only for this example. Most current windmills use a transmission technique to enhance the mechanical advantage of a rotor under light wind conditions. 6.Stand-Alone Wind Turbine Systems ◾ 187 Table 6. Thus. The sucker rod lifts a column of water in the well as illustrated in the figure. thereby bringing the system to a halt. farm windmills provided domestic water and sometimes included storage tanks in the towers.6. In recent years. Other windmill operators delivered water to a nearby tank on a raised platform of suitable height.3 Estimating Pumping Capacity of Farm Windmill Early farm windmills directly coupled the wind turbine rotor via a crank to a sucker rod not clearly shown in Figure 6. a packer head or additional head is required to pump sufficient water into the tank. the weight of the water in the well would often stall the rotor.
4 Hybrid Wind Turbines for Economic Electrification Many third world nations are scrambling to construct and install hybrid power systems to meet electricity demands in thinly populated regions. Pumping system components are shown in Figure 6.8. According to energy planners. the hybrid power systems can be removed and sent to other remote villages where electricity is badly needed. This technique slightly increases the complexity of a windmill but enables it to pump more water under light winds.188 ◾ Wind Turbine Technology Well outlet pipe Wind turbine propeller Tower foundation Base cylinder Outlet control valve Discharge head monitor Figure 6. unmanned operation. this scheme will allow electrification to expand rapidly with minimum capital investment. 6. The benefits of the electricity generated by such hybrid systems include reasonable procurement cost. 6.7 Outlet components of pumping system. reliability. three revolutions. and maintenance-free.7. A hybrid power system of a low-cost wind turbine of moderate capacity and a solar power system can provide nonstop power almost 24 hr a day. In addition. Bergey wind turbines can charge the batteries . Most coastal countries deploy wind turbines to pump water for agricultural applications [1].9 Multitasking Wind Turbines Wind turbines designed and developed by Bergey Power Systems are best suited to perform several tasks simultaneously. as central power systems expand to villages. Energy planners for village electrification schemes have performed comprehensive trade-off studies and concluded that hybrid power systems that feature small wind turbines or micro wind turbines because of their relatively low procurement cost are best suited for village electrification schemes because they can supply electricity in a short time at minimum installation cost.
The micro devices are widely used to charge automobile batteries. Furthermore. which is possible with high-capacity wind turbines. 6. power generated by wind turbines can heat homes at minimum cost and without greenhouse effects. known as a micro wind turbine. Based on a current market survey.9.1 Low-Power Turbine Applications Low-power wind turbines can handle several applications that do not require storage functions. particularly in Asia and Africa. cannot afford such systems unless the installation costs are paid by their central governments or through United Nations community development programs. provides an electric charge to the surface of a metallic pipe to counteract galvanic corrosion in highly reactive soils. pump water. The author's studies of wind parameters indicate generally that a wind speed exceeding 30 mph is necessary to generate large amounts of electrical energy. The smallest power system on the market. farms. Economic studies of energy planners indicate that a few 100-W capacity micro turbines could meet the energy requirements for a small village a minimum cost without compromising reliability and system performance. heat homes. The studies further indicate that a wind speed close to 6 mph is considered adequate for micro or small wind turbines that are best suited to charge batteries. and small businesses. Such wind turbines generally have output capacities to 1 kW with procurement costs exceeding $2500. Wind turbines from other sources are also capable of performing tasks simultaneously. the Bergey Excel wind turbine is powerful enough to meet electricity requirements of an all-electric home. when the wind returns. Small villages in third world countries. In villages in Arctic regions and other or extremely cold areas. Sophisticated electronic controls and switches generally needed for 100-watt wind turbines are not required for micro turbines. Wind turbine designers in Denmark decisively demonstrated that micro wind turbines or medium-capacity wind turbines have successfully powered homes. Small and micro wind turbines output a few watts of power. It is important to mention that successful harnessing of wind energy requires an operating site that provides sufficient wind speed that can be captured by a turbine. and generate electricity for domestic consumption. 1 kW of electricity can provide energy for ten households in an underdeveloped village. the system again protects the exposed metal. Typically. power security lighting at remote or unmanned facilities. These micro wind turbines involve minimum procurement and installation costs and do not require scheduled maintenance. a micro wind turbine can be . and pump water where supplies are not readily available.Stand-Alone Wind Turbine Systems ◾ 189 needed for various applications and generate electricity compatible with the utility specifications established by the Public Utility Regulatory Policies Act of 1978. Stored power is not needed during calm wind environments because corrosion is a very slow process.
9. the wind machine mechanically drives the well pump entirely on its own via the overrunning clutch. 6.3 Annual Energy Outputs of Wind Turbines Estimation of annual energy output (AEO) follows these steps: 1. When the wind is strong and the wind turbine is producing he full output. the conventional power source operates the water pump alone and the overrunning clutch assures that a constant volume of water is pumped regardless of the wind speed. storage is often impractical and wind turbines typically drive a well pump in conjunction with a conventional energy source. the turbine assists in driving the water pump. Calculate the wind power density (Pd) at the installation site and height where the wind turbine will operate (watts per square meter). Coupling wind turbines with conventional energy sources is fairly simple with an electric pump. In brief.190 ◾ Wind Turbine Technology installed for less than $2000 and can function as a stand-alone power system at a rugged. remote. Since the wind is an intermittent source of energy and irrigation requires large amounts of water. When the winds are weaker. and unmanned operating site.6.6 Water Pumping Requirements for Common Crops Pumping Water Requirement (gal/acre) 6400 10700 4800 6900 5900 26100 Irrigated Crop Village farm Rice Cereal Sugar cane Cotton Lawn and garden . Typical daily pumping requirements in gallons per acre for various crops at a wind speed of 6 m/sec or 12 mph are summarized in Table 6. 6. but not so easy with a diesel-driven pump.2 Design Requirements for Irrigation Most stand-alone power systems deploy small wind turbines for irrigation applications.9. Note that water requirements vary based on soil characteristics and ground temperature. Table 6. West Texas State University [1] developed an ingenious device for mechanical coupling the variable output of a wind turbine with an irrigation pump deploying an overrunning clutch mechanism device. This system is widely used in countries that face shortages of water for irrigation and is best suited for stand-alone power systems.
4. Find the product of the first three parameters above. Assume a reasonable value (percent) for the overall conversion efficiency (η) of the system. rounded up to approximately 6 m/sec.48 × 100. Values of annual energy output levels as a function of wind speed. multiply the product by the assumed overall efficiency.4) Assuming various efficiency values. total overall efficiency.48] Typical overall system efficiency can be expressed: η = [rotor efficiency] [transmission efficiency] [generator efficiency] [power conditioning efficiency including yawing and wind gust effects] (6.48 × 20% × 8760] of 17.0480. The estimated AEO values in . The swept area A can be written as: A = [π radius2] = [π 3.52] = [38. and conventional rotor diameter are shown in Table 6.1) yields an AEO [253 × 38.1) (6. Note this value applies only to the above assumed efficiency values. Use 8760 (24 hr × 365 days) as the number of hours per year.143 or 3.9. Bergey Power Systems measured an average wind speed of 5 m/sec or 11 mph at a height of 10 m above the ground.4) into Equation (6.5) (6.7. the overall efficiency can be written: η = [36%] [85%] [80%] [80%] = [20%] (6.3.143 times the initial wind speed—5.86. For a 7-m diameter wind turbine installed at a hub height of 100 ft.2) through (6.000 kWh per year. Find the swept area (A) based on a conventional turbine or HAWT rotor radius (square meters). This means that the magnitude of AEO can be written as: AEO = [step 1] [step 2] [step 3] [overall efficiency of wind power system] AEO = [Pd A 8760 η] (6.3) Inserting the values from Equations (6. According to recent data collected by meteorologists. power density.1 Wind Power Density and AEO Computations Wind power density is dependent on the average wind speed at a specified operating height. 3. wind speed increases with installation height according to the 1/7 power law. the wind speed will be about 30. The power density at 6 m/sec wind speed is about 253 W/m2.Stand-Alone Wind Turbine Systems ◾ 191 2.2) 6.
192 ◾ Wind Turbine Technology Table 6.7 Estimated Annual Energy Output from Wind Turbines (kWh/year × 1000)
Rotor Diameter (m) Wind Speed (mph) 9.0 10.1 11.2 12.3 13.4 14.6 Power Density (W/m2) 90 110 150 190 250 320 Total Efficiency (%) 28 28 25 25 21 19 4 2.3 3.4 4.1 5.2 5.8 6.7 5 3.6 5.3 65 8.2 9.0 10 6 5.2 7.6 9.3 12 13 15 7 7.1 10 13 16 18 20
the table indicate that magnitudes of AEO increase with increases of wind speed, power density, and conventional rotor diameter. It is interesting that the overall system efficiency decreases with increases in wind speed arising from abrupt variations in speed and direction. Typical average wind speed at a 100-ft hub height is about 6 m/sec or 13 mph—approximately twice the wind speed in meters per second. The parameters in Table 6.7 provide useful information about the performance of micro and small hybrid systems well suited for stand-alone installations.
6.10 Summary
This chapter is dedicated to stand-alone power systems composed of small or micro wind turbines and solar arrays to minimize system procurement cost. Preliminary studies by the author indicate that stand-alone wind turbine systems plays a critical role where commercial power lines are not readily available. These systems deploy small or moderate capacity wind turbines and banks of batteries sized to provide electricity for household consumption during the winter season and emergency periods during summers. A back-up diesel-driven generator can charge batteries during extended calms or shortages of electricity. The studies further indicate that the high cost, poor reliability, and frequent maintenance requirements for early standalone power systems discouraged customers. However, recent research, design, and development activities have solved most of the shortcomings and people who live in remote locations and or lack access to commercial utility service now accept the stand-alone power systems. The author's studies reveal that implementation of solar cell technology in conjunction with a small wind turbine at a remote site offers a cost-effective and reliable
Stand-Alone Wind Turbine Systems ◾ 193
option for customers who are interested in stand-alone power systems. Use of a diesel-based system or battery bank as a stand-by power source combined with a small wind turbine in a remote location is not a cost-effective approach. In some remote locations where high levels of power are needed badly, a diesel-driven generator or high-capacity battery bank could serve as a back-up power source, but this approach is expensive and requires scheduled maintenance. Solar cell technology is cost-effective for stand-alone systems in remove locations that lack commercial power lines. Various design configurations of stand-alone systems with emphasis on reliability, safety, installation cost, and maintenance-free operation have been described. Stand-alone power systems are suited for village electrification because of low installation cost and maintenance-free operation. A stand-alone power system consisting of a small or micro wind turbine and solar array can charge batteries in a remote location or small village, pump water for irrigation, and power mills for grinding grain [1]. Solar arrays can provide electricity for emergency lighting, security devices, and low-power appliances operating at 110 V and 60 Hz frequency in remote locations where utility grid lines are not available. When solar power is not available under cloudy conditions, a micro wind turbine with moderate capacity can provide the needed electrical energy at low cost and with minimum complexity. Recent surveys indicate that a micro wind turbine of moderate capacity can be installed for less than $2000. A micro wind turbine of lower capacity for individual residential use can be purchased for about $1500. A unique use of a micro wind turbine is applying an electric charge to the surface of a metallic pipe to counteract galvanic corrosion in high reactive soils. This protection is suitable for pipes carrying oil, gas, and other nontoxic liquids in remote areas. This chapter discussed the hybrid design concept for a stand-alone power system and focused on costs and reliability. A hybrid stand-alone system may include a small fossil-fueled back-up generator to provide electrical power for lighting, security sensors, and electronic devices, but this combination requires trade-off studies to determine performance, reliability, and installation and operation costs. Hybrid stand-alone systems (micro wind turbines and solar modules) are desirable for telecommunication installations, particularly, in remote and inaccessible areas. Reliable performance of remote telecommunications installations is vital, particularly during floods and after earthquakes and air accidents in jungles and high mountain terrains. The proposed hybrid stand-alone system with back-up power capability can provide continuous (day and night) electricity to a remote telecommunications installation. At some remote sites, wind speeds exceeding 9 mph are required to generate electricity from a stand-alone micro wind turbine system. A hybrid system combines two low-cost energy sources (a PV system and a micro wind turbine) that are capable of charging batteries at inaccessible locations. Estimated values of annual energy output levels (1000 × kilowatt hours per year) for stand-alone or hybrid versions of micro wind turbines based on wind speed, overall efficiency, power density, and conventional rotor diameter are provided for system designers or customers interested in small stand-alone systems. Critical
194 ◾ Wind Turbine Technology
issues to consider before selecting a stand-alone power source include installation costs, maintenance-free operation, and reliable guarantees of continuous electricity. Advantages and disadvantages of such systems such as cost, reliability, and design simplicity are summarized. During the 1980s, thousands of small wind turbines with capacities ranging from 10 to 40 kW were installed in California. At the same time, the Danes were installing 50-kW wind turbines in coastal regions to power homes, farms and businesses, because they depend heavily on the generation of low-cost electricity by wind turbines.
[1] P. Gipe, Wind Power for Homes and Businesses, 1993, Chelsea Green, Post Mills, VT, p. 11. [2] S. Mertens, Wind Energy in Built Environments, Multiscience, 1989, Essex, U.K., p. 29. [3] J. Walker and N. Jenkins, Wind Energy Technology, 2002, John Wiley & Sons, Chichester, p. 18. [4] M.O.L. Hansen, Aerodynamics of Wind Turbines, 2nd ed., 1992, James & James, London, p. 63.
Chapter 7
Wind Energy Conversion Techniques in Built Environments
7.1 Introduction
Installation of wind turbines in built environments presents complex problems that are rarely encountered in open environments. This chapter will provide detailed descriptions of the wind resources in built environments that can be converted into energy by deploying wind turbines. This conversion technique requires focus on maximum energy yield from a wind turbine. It deals with the integration of wind turbine and building aspects in such a way that the building structure concentrates the energy of the wind for turbine use only. Preliminary studies undertaken by the author identified three distinct principles of buildings that concentrate wind energy strictly on turbines. Wind energy concentrators fall into four categories described as follows: ◾ ◾ ◾ ◾ Wind turbines installed in ducts through adjacent buildings Wind turbines installed at the roof of a building Wind turbines installed at the sides of a building Wind turbines installed between two airfoil-shaped buildings
The aerodynamic aspects of the four distinct types of concentrators and their respective wind turbines will be investigated; integration techniques for achieving maximum energy yields of wind turbines will be covered. Aerodynamic investigations
196 ◾ Wind Turbine Technology
involve mathematical models, computer simulation of air flow, and verification of computed parameters with measured data obtained from an open jet wind tunnel if available. Computer simulation may be performed with a computational fluid dynamics (CFD) code if available. It is important to note that both verification techniques involving measurement and CFD calculation will be exploited to achieve the most accurate verification results. This subsection provides broad descriptions of the critical design concepts of the energy yield of a wind turbine installation in a built environment. The chapter offers detailed descriptions of the average global wind speed in a built environment, wind speed in the vicinity of an installation, wind speed near buildings, and verification of the mathematical models of the three possible concentrator schemes cited above. This chapter also provides useful information on appropriate wind turbines for deployment in built environments. The advantages and disadvantages of three concentrator principles (including emphasis on reliable and cost-effective design) are identified. At-the-roof configurations and variations of installations in ducts through buildings in relation to overall turbine efficiency will also be explained.
7.2 Concentrator Configuration Requirements
This section describes the configuration requirements and performance capabilities of concentrator devices used by the wind turbines in built environments. It is critical that a concentrator configuration be optimum for a specific built environment. For example, if an at-the-roof configuration is considered, a sphere-like structure will able to concentrate three to four times the energy of an omnidirectional freestream wind [1].
7.2.1 Sphere-Like Configuration
Preliminary studies performed by the author on sphere-like building structures revealed concentrator configurations that can overcome the problem of low average wind speed in built environments and provide energy yields comparable to those in rural areas where typical wind speeds exceed 15 mph.
7.2.2 In-Ducts-through-Buildings Configuration
The author's studies also show that in-ducts-through-buildings configurations involving two ducted ellipsoids in a cross with a duct at the cross center can concentrate the wind energy in an omnidirectional free stream wind by a factor of about1.5. The studies further stipulate that other concentrator configurations offer lower wind energy concentrator factors and hence this configuration will not be discussed further.
thereby reducing their dependence on utility companies. concentrators deliver the wind energy where it is needed. Cost estimates depend on the type of structure. and their energy yields represent savings on utility bills. Reduced zero energy design (ZED) and lower energy design (LED) building architectures are recognized as the most desirable renewable energy schemes. ZED and LED building owners are encouraged to use power from renewable energy sources.3 Close-to-a-Building Configuration This configuration is very efficient in using acceleration afforded by a structure.2. Studies performed by aerodynamic scientists and engineers on built environment power . which is roughly three times the price paid to commercial utilities for renewable energy sources in rural areas.3. We can conclude from these statements that wind energy conversion in built environments via concentrator effects from buildings may be recognized as a renewable energy source. This constitutes a better payback than would be available in a rural area. and characteristics of nearby structures. 7. 7. It offers the most cost-effective solution compared to the other concentrator types.2. 7. This way the building owners can be reimbursed at a price set by the utility company. Despite small size.Wind Energy Conversion Techniques in Built Environments ◾ 197 7.4 Capabilities of Various Concentrator Schemes: Summary Potential wind energy concentrator configurations in relation to the amount of wind energy converted in built environments and concentrator efficiencies have been evaluated. to the built environment. Energy planners believe that small renewable energy sources integrated into building designs will reduce consumption of energy from commercial utilities.3 Energy Design Buildings Energy design building technique offers reductions in energy consumption through the design of a structure. its height. Brief studies concluded that the wind energy yields for all the possible concentrator configurations evaluated are limited because the wind turbines can only benefit from the concentrator effects when the devices are relatively small compared to the building size.1 Requirements for Built Environments Architecture requirements and turbine installation locations must be selected to produce renewable energy with simplicity and at minimum cost. It is important to mention that the motives for integrating renewable energy sources into residential and commercial buildings are driven by environmental issues but a building must be designed to capture large amounts of wind energy for the wind turbines.
2. Further improvement in the power output of a wind turbine operating in a built environment is possible by integrating concentrating devices in a design. It is not sensible to build an expensive concentrator if a slightly bigger rotor would produce more power. MPH 32 28 150 16 8 12 0 50 20 24 100 Shaft speed. reliability. concentrators add cost and excessive weight and reduce reliability. sources indicate that the earth's surface characteristics at a built environment are critical issues to consider in designing a renewable energy source in terms of high turbine efficiency. and critical performance parameters. Aerodynamic scientists claim that wind speed around taller buildings can be significantly higher than the average free stream wind speed in a built environment. Some local acceleration of the wind is required to achieve a viable wind energy yield in a built environment.1). Based on comprehensive economic analyses.1 Requirements for renewable energy sources. Furthermore. if a concentrator po we r . improved reliability. where an average wind speed of 15 m/sec is not uncommon. Trade-off studies should be conducted before the deployment of concentrator devices to determine cost. However. It is possible to use this effect and design buildings with dedicated wind turbines that can utilize the increase of the average free stream wind speed. turbine designers conclude that a concentrator contributes a doubtful economic benefit. However. Concentrating devices enhance turbine shaft performance as a function of wind speed.198 ◾ Wind Turbine Technology sta de Bla ll Torque M ax Fixed. The studies further indicate that a built environment generally has a higher roughness property than a rural area [1]. very little improvement in shaft performance can be achieved when the wind speed exceeds 16 m/sec as illustrated in Figure 7. This high roughness produces a low wind speed (typically about 6 m/sec) compared to rural areas. RPM Figure 7. optimum blade angle Wind velocity. and torque versus shaft speed performance (Figure 7.
2 Concentrator device. In addition. They decrease when vertical height approaches 100 m or so and variations thereafter are smaller than 0. wind energy conversion. Successful installation of a BAWT power system requires comprehensive knowledge of wind energy. can be integrated into a wind turbine installation without excessive additional cost. It is important to point out that computing variations in roughness length requires lengthy mathematical calculations involving critical meteorological data spanning 10 years or more. the step should be taken. A comprehensive aerodynamics background is required to identify promising design configurations for efficient wind energy conversions in built environments.2 Impact of Roughness Length on Wind Speed Parameters Variations in roughness length are based on the type of terrain—an important parameter of wind speed and a function of boundary layer profile change.06 m/sec around 180-m operating height. This section explains the aerodynamics of BAWTs. concentration schemes. roughness varies with the terrain classification [3]. and built environments with high roughness factors. Variations in roughness factor are due to boundary layer profile changes. Analytical research tools include mathematical . Brief studies by the author reveal that roughness factor depends on turbine operating height and operating environment. cost-effective concentration schemes. Wind turbines capable of providing concentrated energy are known as building-augmented wind turbines (BAWTs). 7.3. establishing the boundary conditions for wind energy conversion in a built environment is tedious and challenging.Wind Energy Conversion Techniques in Built Environments ◾ 199 0 0 5 10 15 Wind speed VO [m/s] 20 25 Figure 7.3. Variations in wind speed arise from changes in the operating height as illustrated in Figure 7. and wind aspects in built environments.
These models can be used to design the most cost-effective concentrator device for a particular wind turbine. the roughness height can be determined using the log law applicable outside the city boundary. known as the internal boundary layer.3 Effects of operating heights.2. it experiences a step-up in roughness height from Z01 to Z02. as shown in Figure 7.5 V(z) 6 5. the roughness height hk will grow downwind of the roughness change.8 (7.4.200 ◾ Wind Turbine Technology Wind Speed V(z) as a Function of Operating Height 7 6. When air flow enters a city. The effects of the step-up in roughness height do not occur instantaneously in the whole atmosphere and are limited to the height hk of the internal boundary layer as shown in Figure 7. After the boundary conditions (wind energy. The log law can also be used to calculate wind speed in a city environment. 7. will develop a new roughness height designated Z02. models of wind energy conversion in built environments.3. Under turbulence environments. The new boundary layer. wind energy conversion. This empirical model can be described by the following expression: Hk(x) = [0.max][x/Z0. a designer can select a feasible and cost-effective option for a conversion in a built environment.1 Estimating Wind Speed in City Environment When the wind enters a city environment. and built environment) are defined.5 5 20 30 40 60 70 z Operating height (meter) 50 80 90 100 Figure 7. An empirical model was developed to reflect the growth of the internal boundary layer based on dimensional analysis and bulk research data.max]0.1) . It is evident that the atmosphere outside the internal boundary layer behaves according to the upwind roughness Z01.28 Z0.3.
Hk is the roughness height or simply the height of internal boundary layer. d is the distance between the internal and external boundary layers. where Z0.2δ and δ denotes a boundary layer height of about 1000 m for neutral air flow and strong winds.1) is valid for smooth-to-rough and rough-to-smooth variations in a wall region where Hk(x) is less than 0.Wind Energy Conversion Techniques in Built Environments ◾ 201 External boundary layer zmin z z01 Roughness 1 d + z02 hk z02 Roughness 2 Internal boundary layer x Symbols: Z01 = Initial wind speed before entering the city Z02 = Wind speed after leaving the city hk = Roughness height step of the internal boundary layer Figure 7. Z01 is the roughness height of the internal boundary layer. It is important to mention that after some transient effects closely downwind of the step-up in roughness.32 Vext) [In (hk /Z01) In(Z – d/Z02)]/[In (60/Z01) In (hk – d/Z02)] (7.1. the log law for the internal boundary layer can be applied when parameter x varies between 500 and 5000 m. Scientists claim that within the approximation of the model of the internal and external boundary layers as shown in Figure 7. Vext is the wind velocity in the external boundary layer.4 Roughness factor changes. Z02 is the roughness height of the external boundary layer. Under these conditions. and Z is the roughness height of the internal boundary layer. matching of the wind velocity above and below the parameter yields the velocity in the internal layer written as: Vint (Z) = (1. Equation (7. the internal boundary layer will be logarithmic in a neutral atmosphere.2) where Vint is the wind velocity in the internal boundary layer. Variations in roughness height .max is the higher of the Z01 and Z02 parameters.
speed variations about the mean wind speed during short intervals. The scientists further indicate that under turbulence conditions the roughness heights for the internal and external boundary layers are highly unpredictable and depend on the turbulence intensity (Iturb) which is written as: Iturb = [σ V/Vave] (7.1 Atmospheric Boundary Layers Temperatures in various atmospheric layers can affect wind speed and direction in each layer. Studies of aerodynamic engineers and meteorological scientists reveal that the highest wind speeds are generally found on hill tops. Using above equations.3 Wind Potential in Built Environments The energy available from the wind is proportional to the cube root of wind speed or velocity. and out at sea.3.5) that the turbulence intensity increases with increasing roughness and decreasing height to the surface of the earth. and variations resulting from height and temperature. Important parameters of wind include mean speed. 7.3. For a neutral atmospheric condition.5) It is evident from Equation (7.4 V0] (7.202 ◾ Wind Turbine Technology from a step-up are shown in Figure 7. direction. in coastal regions.3) where V is the wind velocity. The return flow toward the equator is deflected west and produces the trade winds. and σ V is the standard deviation of the wind speed V. Wind direction is affected by both the temperature and acceleration due to the rotation of the earth (Coriolis acceleration).3. the standard deviation can be expressed as: σv = [2. The Coriolis acceleration [3] causes the wind flow from the equator to the poles to be deflected toward the east. . the air begins to sink in the lower layers of the atmosphere. 7. Vave is the average wind velocity. At cooler temperatures.4. the modified expression for the turbulence intensity is: I = [ In (Z – d/Z0)]–1 if Z is greater than Zmin (7.4) where V0 is the wind velocity in the neutral atmosphere. Experimental data of aerodynamic scientists indicate that a value of 60 m must be taken for parameter h k because the roughness variations occur from high to low and vice versa so that their adverse effects cancel each other. seasonal and annual variations.
3.3.6) The mean wind speed or velocity is typically determined as an average value measured over a 10-min span.3. 7.3 [3]. 7. the intensity is typically 0.7) . The two most common ones used to generate wind profiles include power exponent and logarithmic functions that were developed [3] to describe changes in mean wind speed as a function of height.3 Vertical Wind Speed Gradient Research studies conducted by meteorological scientists indicate that the wind speed at the surface is zero due to the friction between the air and ground surface. and terrain features in the vicinity of the turbine installation site.3.3. Standing crops and water surfaces introduce fluctuations in air flow characteristics.1. trees. For very rough terrain including several trees and buildings. the turbulence intensity varies between 0. Vertical variations in wind speed or wind speed profiles at a particular installation site can be expressed by different functions.3.3. The instantaneous wind speed (Vins) can be defined as a mean wind speed (Vmean) plus the fluctuating component (Vfluct) and thus its expression can be written as: Vins = [Vmean + Vfluct] (7. the fluctuations in wind speed have been considered only in the horizontal direction. The functions are based on experimental data collected by competent aerodynamic and meteorological scientists at various installation locations. the resulting changes in friction at the surface introduce fluctuations in wind speed and direction. The fluctuation of the wind speed is expressed in terms of the root mean square (RMS) value of the fluctuating velocity component and is also defined as the turbulence intensity. Wind speed history can be measured by mounting a device called an anemometer on the nacelle of a wind turbine.Wind Energy Conversion Techniques in Built Environments ◾ 203 7.1 that indicate that at a height about 2 km above the ground the change in wind speed approaches zero. For smooth terrain surfaces. To date. The studies further indicate that wind speed increases with height above the ground. increasing less rapidly at increasing height as demonstrated by the values summarized in Table 7.15 and 0.2 Impact of Atmospheric Boundary Layer on Wind Speed and Variations Wind flow is also affected by the local features such buildings. most rapidly near the ground. In brief. Variations in wind speed can also arise from turbulence effects created by the turbine rotor and the nacelle housing.1 Power Exponent Function This function can be written as V (z) = [Vr (z/zr)α] (7.
Calculated values of wind speed at the reference height are shown in Table 7.29 24.1.2 Wind Speed Parameters for Calculating Vertical Profile Terrain Water surface Open country Farmland with buildings Farmland with many trees Roughness Class 0 1 2 3 Roughness Length z0 (M) 0.204 ◾ Wind Turbine Technology Table 7. These calculations use Equation (7. However.1 Wind Speed as Function of Wind Turbine Operating Height Operating Height z (m) 40 50 60 70 80 90 100 125 150 Wind Speed at Operating Height Vz (m/sec) 22. Close examination of these calculations indicates that at lower heights the variations in the wind speed decrease as the height increases. Wind speed parameters for calculating a wind profile as a function of surface roughness and exponent are summarized in Table 7.01 0. and α is the exponent representing a function of the roughness of the terrain.92 24.91 25.28 .001 0.4 262.49 23.97 23.05 0.12 0. Table 7.7) and assume 0.16 0.12 0.62 24. the variations in wind speed increase as the operating height exceeds 100 m.2.18 257. zr is the reference height Vr is the wind speed at the reference height.1 for the exponent and a wind speed of 20 m/sec at a reference height of 10 m.31 Exponent α 0.20 where z is the height above the ground.
Roughness lengths and the exponent values for various terrain types are shown in Table 2.07 m/sec. Equation (7.5 m/ sec.3. and V (10) is the wind speed (m/sec) at a reference height 10 m from the ground.6 indicates that the probability of a wind speed between 4.3. the difference from 90 to 100 m is 0. A wind speed of 5 m/sec is assumed at a reference height of 10 m for an open country terrain with a roughness length (z0) of 0. the difference from 140 to 150 m is 0.3. 7.5. Beyond 170 m.11 m/sec. It is evident from these calculations that the difference in wind speed from 20 to 30 m height is 0. Wind flow in the boundary layer near the ground is illustrated in Figure 7. It is important to mention that the wind speed statistics are derived from data accumulated over . the difference from 160 to 170 m is 0. Such data can be obtained from a histogram and a Weibull function for the probability of a given wind speed measured in 1 m/sec "bins" as illustrated in Figure 7.5 and 5.3.Wind Energy Conversion Techniques in Built Environments ◾ 205 7.09 m/sec. the difference from 50 to 60 m is 0.3 Wind Statistics for Built Environments Accurate wind statistical data for a built environment is absolutely necessary if cost-effective performance is the principal requirement for a wind turbine in that environment.4%.5 and 5.3.2 Logarithmic Function for Calculating Wind Speed Variations Variations of wind speed as a function of operating height can be computed using the following logarithmic expression: [V (z)/V (10)] = [In (z/z0)/In (10/z0)] (7.3.20 m/sec. a bin can represent a wind speed between 4.87) are summarized in Table 7.07 m/sec. These values clearly show that the difference between two consecutive heights continues to decrease till the height approaches 170 m from the ground. Parameter z0 represents the roughness length for the type of terrain involved. It is important to point out that both functions can be used to calculate the mean wind velocity or speed at a given height if the mean wind velocity is known at the reference height (zr). These wind speed values are valid in the boundary layer near the ground as mentioned earlier. The computed values of wind speed as a function of operating height (z) for an open country terrain are summarized in Table 7.46 m/sec. the difference from 120 to 130 m is 0. the difference in wind speed remains constant close to 0.8) can be used to compute the vertical profile of the wind.12 m/sec. and the difference from 190 to 200 m is 0.5 m/sec is approximately 10. z0 is the roughness length.8) where V (z) is the wind speed at operating height z (m/sec).3.3.06 m/sec. For example.6. Close examination of the histogram in Figure 7.12. The calculated values using Equation (7.
33 8. The histogram indicates the probability if a wind speed is within the interval given by the widths of the consecutive columns.20 8.13 8. The cumulative Weibull distribution yields the probability that the wind speed will exceed a specific value.71 7. (m) 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Wind Speed (m/sec) 5. .27 8.81 7.90 7.20 7.206 ◾ Wind Turbine Technology Table 7. the histogram becomes a continuous function called the probability density function.82 7.60 7.39 several years.02 7. It considers seasonal variations and year-by-year variations over the years covered by the statistics.98 8.09 8.57 6.35 7.24 6.78 6.3 Computed Wind Speeds in Open Terrain as Function of Wind Turbine Operating Height Operating Height z.48 7. When the width of a column decreases.
air flow around buildings is characterized by the use of the Reynolds and Strouhal numbers. First. The studies further reveal that an aerodynamic building usually has a thin boundary layer attached to its entire surface.4. Second. 7. 7. building shapes such as bluff and blunt types permit characterization of aerodynamic aspects.Wind Energy Conversion Techniques in Built Environments ◾ 207 Mean profile Actual wind speed profile Figure 7.4 Local Wind Characteristics in Built Environments The flow properties arising from building shapes and aerodynamic aspects of certain building types will be described. the probability distribution function of wind velocity at a specific location around a building should be derived. While bluff buildings exhibit phenomena that combine . An aerodynamic building is characterized by a small wake.5 Wind flow in boundary layer.1 Building Characterization Brief studies performed by the author reveal that the first characterization of building shapes must distinguish aerodynamic buildings from bluff buildings. Bluff buildings are characterized by early separation of the boundary layer from the surface and a large wake. Finally.
208 ◾ Wind Turbine Technology 15 14 13 12 11 10 9 8 7 6 5 4 –3 2 1 0 Profitability (%) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Wind speed (m/s) Figure 7. Such phenomena typify a bluff building. The no-slip condition at the surface of a building yields a contribution to total drag which is known as the viscous drag component of the drag force. the viscous drag component dominates the pressure drag component at an aerodynamic building.3 Drag Force Components A building exerts two types of drag force components: pressure drag and viscous drag. flow characteristics of bluff and aerodynamic buildings.2 Streamlines around Buildings with Sharp Edges Brief aerodynamic studies of buildings with sharp upwind edges reveal that the boundary layer separates at the upwind edges and separation bubbles form on the sides and at the top. The studies further reveal that the main stream is deflected around the building and a large wake downwind of the building is formed. Computer simulations by aerodynamic scientists clearly show the streamlines around an aerodynamic body and a bluff body in a parallel flow. Aerodynamic scientists believe that the pressure drag of an aerodynamic structure can be virtually determined by assuming potential flow around the building. Based on this assumption. 7. This essentially contributes to total or pressure drag.4.6 Histogram of wind speed. 7. The viscous drag at a bluff building has the same . it is important to note that the characterization of a building as aerodynamic or bluff depends strictly on wind flow direction.4. The difference in local velocity around a structure results in pressure differences at its surface regardless of its dimensions.
Consequently. θ is the angle measured from the axis of symmetry. It is evident from this figure that a 2-D flow is approximated around bodies that have a single dimension ten times larger than another dimension.7. only their dimensions vary. Potential flow velocities at the sides of a cylinder and sphere are illustrated in Figure 7. The difference between the potential flow velocities at the sides of a sphere and a cylinder has critical implications for BAWT systems. as illustrated in Figure 7. Bodies comprising height. Aerodynamic scientists believe that flow data obtained from simple inviscid hydrodynamics analyses may be replaced by analysis of the solid surfaces of flows S 4 3 2 1 R θ/u θ 5 Cylinder Sphere Figure 7. The flow velocity at the surface of a cylinder or sphere can be determined using the potential theory. the Reynolds number.7 Wind flows around cylindrical and spherical bodies.4 Air Flow Properties Flow properties may be determined from the dimensions of the flow. 7.7. and the wind is toward the sphere when θ equals 180 degrees. the pressure drag component dominates the viscous drag component at a bluff building. A building exhibiting a single very large dimension along with one or more smaller dimensions can be characterized as a 2-D body.4. . The flow around a 3-D object (sphere) will be relatively uniform and smooth. Bodies and objects have the same basic shapes. The wind flow properties around 2-D (cylindrical) and 3-D (spherical) bodies differ.Wind Energy Conversion Techniques in Built Environments ◾ 209 magnitude as the viscous drag at an aerodynamic building but a different magnitude of the pressure drag due to the separated boundary layer. The flow can be two-dimensional (2-D) or three-dimensional (3D). Structures that have width and length are characterized as 2-D. and the Strouhal number. The flow velocity on the surface of a blunt body can be determined if the attached flow is assumed as a function of uθ where uθ is the flow velocity. and length are categorized as 3-D. These differences can be determined from a 3-D body by infinite elongation of the sphere in one direction. width. The differences in flow around a sphere and a cylinder thus provide the differences in flow between 2-D and 3-D bodies or objects.
Thus. .10) where r is the measured radial distance from the origin of the coordinate system which coincides with the center of the sphere of radius a. Stream surfaces mat be replaced by solid surfaces so that the sphere flow stream surfaces represent the flow over a solitary spherical hill and cylindrical flow stream surfaces will correspond to flow over a long ridge. It is important to point out that the flow at a 3-D bluff target or body can also move perpendicular to that plane with larger dimensions. the potential (φ) and stream (ψ) can be written [4]: φ = [(Ua3/2r2) cosθ + Ur cosθ] ψ = [(–Ua3/Ur) sin2θ + (Ur2/2) sin2θ)] (7. Surfaces of constant dimensionless stream function (ψ/Ua 2) and constant speed (q/U) are represented in Figure 7. angle θ is measured from the axis of symmetry. The hills do not have to be spherical or cylindrical and may be approximated by any stream surface. The tangential velocity vθ and the radial velocity vr components can be expressed: v θ = (U sinθ) [1 + 0. respectively.5 (a/r)3] v r = (–U cosθ) [1 – (a/r)3] (7.13) is quadratic in the cube of (a/r). it is logical to state that the flow velocities at the sides of a 2-D body will be higher. Note that constant velocity surfaces are also known as isovelocity contours and are represented in Figure 7.8 by various values of the q/U ratio.13) Equation (7. The surfaces shown in Figure 7. The boundary layer will separate at the along-wind sides of the blunt body and a wake will form. thus creating a possible difference between the potential flow resulting from the attached flow and the actual velocity at a Reynolds number exceeding unity.9) (7. and the wind flow is toward the sphere in the 180-degree direction.4.12) Surfaces with constant flow speed q = (vθ2 + vr2)0.1 Hydrodynamic Analysis of Flow over Sphere For a flow over a sphere of radius a. 7.11) (7.4.210 ◾ Wind Turbine Technology over spherical and cylindrical objects.5 normalized by the flow at infinity U can be found from the solution of the following expression: [(a/r)-6 + 4 (a/r)-3{(1 – 3 cos2θ/1 + 3 cos2θ)}] = [4 (q/U)2 – 1/1 + 3 cos2θ] (7.8 by symbols A and B. and can be solved using standard methods.8 illustrate the limited disturbance of a flow field by the presence of a spherical object.
8 2 1 1 2 0 q/u = 1.4. u0 is the free stream velocity.1 1. which is defined as: Cp = [p – p0/0.5 p u02] (7.Wind Energy Conversion Techniques in Built Environments ◾ 211 ψ Ua2 A= 0 70 60 50 40 30 20 10 C A 1.2 Impact of Pressure Coefficient on Free Stream Quantities The flow velocity at a Reynolds number much higher than unity can be computed from the measured data for the pressure coefficient (Cp).4.5] (7.2 1. which could be compared with a measured value at the pressure coefficient Cp at a separated flow .0 Figure 7. 7.0 0. the tangential velocity as a function of angle θ can be determined from a potential theory with an attached flow.2 1.3 1.14) where p is the pressure at the location where Cp is specified. and p0 is the pressure for the free stream.8 Surface functions. the tangential velocity component (uθ) at a point where the pressure coefficient Cc exists can be determined: uθ = [uθ (1 – Cp)0. Using Bernoulli's equation.15) At the surface of a cylinder and sphere.
these vortices induce a regular suction at the sides of a bluff object. In addition. a Reynolds number indicates whether the viscous effects in a fluid flow may be neglected. The Reynolds number can be defined as the ratio of inertial and viscous forces in the fluid flow. The tangential velocity at the surface of a 2-D blunt body will be higher than the velocity at the surface of a 3-D blunt body. a conventional flow pattern can be observed in the wake of a bluff body.3 Theoretical Aspects of Reynolds and Strouhal Numbers Basic knowledge of Reynolds and Strouhal numbers is necessary to visualize the flow patterns.16) where ρ is the fluid density.000. particularly for BAWT) operations. The .9 uθ (θ) Four important conclusions may be drawn from the above data: 1. the tangential velocity component at a radial distance can be given as: uθ (r) = [0.4. configurations that cause 2-D flow should be preferred above those that cause 3-D flow because the wind velocity near a 2-D building is considerably higher. For a BAWT building.15 a) 7. uc is the characteristic flow velocity. The vortices are very important for the building and BAWT installation.1 and the angle is 90 degrees. The Reynolds number for a fluid can be expressed as: Re = [ρ uc Dc/η] (7.000 and 400. Under these flow conditions. the Reynolds number varies between 200. a low one shows that the viscous forces dominate the inertial forces.212 ◾ Wind Turbine Technology according to aerodynamic scientists.1R from the surface of a sphere or a cylinder is reduced to 90% of the surface velocity. Because of their high local velocity components.4. When the ratio (r/R) is 1. (7. thereby creating a resonance at the eigenfrequency of the bluff body. 4. The scientists further believe that the Reynolds number for a sphere and cylinder with separated flow can be accurate with error rate below 10% up to a circumferential angle θ equal to 90 degrees. This flow pattern is generally known as a vortex street. η is the dynamic viscosity of the fluid. and Dc is the characteristic dimension of a body completely immersed in the fluid. The acceleration is independent of the absolute building size. The tangential velocity at distance 0. 2. vortices of opposite signs are shed from the upwind edges of the bluff object in an alternate and regular way. A high Reynolds number indicates that the inertial forces dominate the viscous forces. 3. Therefore. Brief studies of Reynolds numbers and their effects seem to indicate that at certain Reynolds numbers.
75] Rearranging Equations (7.Wind Energy Conversion Techniques in Built Environments ◾ 213 magnitude of this eigenfrequency (fe) can be determined from the following empirical formula: fe = [46/h] Hz (7.8) Cd0. the expression for the shedding frequency produced by the vortices can be written as: fs = (0.23) that the ratio (turbine diameter to characteristic size of the building) must be less than 80% of Cd0.5 to 2. It is important to note that the regular high flow velocities at the sides of a bluff body can produce alternating power in a BAWT installation. the Strouhal number may be determined from the following equation: S = [fs Dc/u0] (7.22) yields: [Dt/Dc] < [0. the S (Strouhal) number represents the frequency of the vortices leaving one side of the building. and u0 is the free stream velocity.17) where h is the building height in meters.20) If one allows the quasi-steady approach of the BAWT in the shedding region. For a 2-D building with a blunt or bluff shape. Research by BAWT .21) It is evident from Equation (7. by strict definition. a steady operation of a BAWT system can be achieved and a turbine with diameter (Dt ) is installed if: [1/fs] > [6 Dt/u0] The inverse of Equation (7.19) where fs is the shedding frequency produced by the vortices.23) (7.19).18) and (7.75] (7.21) and (7.20) can be written: [1/fs] = [4. Dc is the characteristic dimension or size of the body or building. the S number [4] can be written approximately as: S = [(0.18) where Cd is the drag coefficient.75 where Cd is the drag coefficient that may vary for blunt to bluff bodies from 0. However.75] (7.76 (Dc/u0) Cd0. In a nondimensional form.21) Cd– 0.22) (7.21) [u0 Cd–075/Dc] (7.0. From Equations (7.
214 ◾ Wind Turbine Technology engineers and aerodynamic scientists indicates that a Dd/Dc ratio below 0.1 to achieve higher system efficiency from the acceleration effects close to structures. Any structural adjustments that reduce interaction of the vortices may prevent the formation of the vortex street. Some of these parameters vary based on height and surface roughness. It is important to mention that the vortex street originates from the interaction of the flow on two sides of a building and is therefore more frequently observed behind 2-D buildings compared to 3-D buildings. For specific . This BAWT installation is most common in the Netherlands. This subsection will also show the derivation of the energy yield of a BAWT installation from this probability distribution.4 Probability Function of Wind Speed for BAWT Installations This subsection discusses the probability distribution of wind in the atmospheric layer at a specific BAWT installation site. the BAWT diameter Dt is limited to Dt/Dc less than 0.4. The input wind speed ui at the concentrator for the free stream wind from the windrose sector may be determined from the free stream wind speed u0. although the Weibull distribution works beautifully for wind speeds ranging from 4 to 16 m/sec at which the turbines operate most of the time. Effects of various parameters on the probability of distribution at the location where the wind speed is changed by a concentrator structure will be identified.I] (7.I u0.5 must be avoided if stable operation of a BAWT system is the principal requirement. Therefore. a change in free stream wind speed caused by a major building used as a concentrator is Reynolds independent. Such adjustments are generally notched at upwind edges of the building or toward the apex.I to ui.5 will yield a stable BAWT operation.i at a certain reference height using the following expression: Ui = [Cr.i yields the Reynolds-independent change of the wind speed from uo. the impact of installation height is more pronounced.24) where the parameter Cr. In such cases. a ratio above 0. In other words. Variations in wind speed occur due to: ◾ Location near a sharp-edged building ◾ Location in a duct through a sharp-edged building ◾ Entry of wind between airfoil-shaped buildings A change of the free stream wind speed in the local wind speed near a building is Reynolds-independent. It is important to note that the probability of distribution of the wind in the atmospheric boundary layer can be defined by a Weibull distribution.3. 7.. However.
At a wind speed of 9 m/sec. the allowable aerodynamic noise level (AENL) at nearby homes during the night is expected to be at the lowest level—approximately 40 dB (A) in the Netherlands. reliability and safety.5. very little energy can be generated by a wind turbine. In addition. harnessing of large amounts of wind energy requires site height capable of producing high wind speed conditions. According to aerodynamic scientists. Equations are available to compute noise levels.1 Aerodynamic Noise Levels Aerodynamic noise generated by wind turbine propellers is the most annoying factor for the people living nearby. In addition.5 Impact of Built Environment on BAWT Performance Adverse effects of a built environment on critical components of the wind turbine will be described along with details related to efficiency. higher energy is produced only by high wind speeds. all sources of vortex shedding from the turbine rotor must be avoided because the velocity differences and consequent pressure differences in the air flow are primarily responsible for aerodynamic noise generation. 7. 7. As stated earlier. However. refer to standard texts on aerodynamics or hydrodynamics. 7. a noise level of 40 dB is also equal to the noise produced by a refrigerator at a distance of 1 m. a low tip speed is highly desirable for a wind turbine in a built environment to keep aerodynamic noise to an acceptable level. the noise emission from a lift-driven horizontal axis wind turbine (HAWT) is approximately proportional to the fifth power of the tip speed. According to aerodynamic scientists. Furthermore. installation sites well above the average building height are considered most promising.5. Therefore the combination of wind energy conversion and built environment is not so logical from an energy yield view. It is important to point out that built environments generate low wind velocity conditions and wind energy conversion is feasible at higher wind speeds. In brief. Wind turbine designers recommend that stall of the propeller blades must be avoided to minimize aerodynamic noise level.2 Computation of Total Aerodynamic Noise at Installation Site Local zoning laws require that total noise levels in residential areas must stay below a specified allowable maximum that is comfortable to residents. They also note that this noise level equals the level in a rural area with a wind speed of about 9 m/sec or 18 mph. If a wind turbine is modeled as a .Wind Energy Conversion Techniques in Built Environments ◾ 215 details on parameters involved in the equation for Weibull distribution.
103 dB at 400 m.3 Noise Arising from Nearby Wind Turbines It is important to mention that the noise level from n identical sources (Np. The reduction of noise (Np) at location P can be calculated by the following: Np = [ Nan – 10 log10(4π R 2)] (7.25) where Np (in decibels. the noise at a certain distance R from the source can be computed. 106 db at 600 m. The total sound pressure level from n wind turbines operating at the same location can be calculated from the following equation: Lp.4 Computed Values of Allowable Noise Level as Function of Distance R Distance R (m) 10 20 30 40 50 60 70 80 90 100 Allowable Noise Level Nan (dB) 71 77 81 83 85 86 88 89 90 91 point source with spherical noise spreading.5. and 111 dB at 1000 m.g. Further calculations indicate that the allowable level varies.4.n) is characterized as the total sound pressure level from n noise sources operating at a specific point. The computed values of allowable noise levels of a wind turbine in a built environment as a function of R to a sound pressure level of 40 dB are summarized in Table 7. 109 dB at 800 m. Nan (dB) is the allowable noise level at distance R (in meters) from the noise generating location.26) .n = [10 log10(∑10α)] (7. 7. e. 97 dB at 200 m. dB) is the noise level at the source P..216 ◾ Wind Turbine Technology Table 7.
and the sum symbol has a bottom value of j = 1 and a top value of j = n. the higher frequencies of several kilohertz seem to have a strong directional dependency. Furthermore. in contrast to low frequencies. the total sound pressure level due to the background noise and ten wind turbines will be 50 dB. Therefore the sound pressure levels in decibels around 1000 Hz frequency are approximately equal to the sound pressure levels in dB (A). the higher frequencies may be heard only within the straight path of the source or as sound reflections from that path. variable j varies from 1 to n. A weighting does not have any impact on the noise levels generated by the turbine. Aerodynamic scientists believe that two important issues are involved in noise emission. Aerodynamic scientists claim that a wind turbine rotor generates a broadband aerodynamic noise with dominating frequencies of several kilohertz.9. The sound pressure level is an A weighted parameter denoted by dB (A) to identify the selective sensitivity of the human ear. . The second issue identifies alternating noise levels as nuisances and scientists feel that these noise emissions should be ignored.Wind Energy Conversion Techniques in Built Environments ◾ 217 Noise Allowed (dB) at a Distance R (meter) from the BAWT Installation 95 90 NA(R) 85 80 75 70 0 20 40 60 R (meter) 80 100 Figure 7. Consequently. Assuming a background sound pressure of 40 dB and ten wind turbines operating at the same location with a resulting sound pressure level at location P of 40 dB each.9 Allowable noise level. Allowable noise level from wind turbines as a function of distance (R) can be estimated from Figure.1 Lp(j). First. 7. This A weighting reduces the sound pressure with frequencies other than 1000 Hz because this particular frequency is the most sensitive of the human ear. for the dominating frequencies of a BAWT installation or a wind turbine. where exponent α is equal to 0.
5.4 Induced Vibrations from Turbine Blades Vibrations from wind turbine blades generally arise from pitch and yaw control mechanisms. they will induce a frequency equal to 2 NH ωH and so on. a HAWT system induces vibrations in the building at frequencies equal to the rotational frequency of the rotor ωR and vibration frequencies equal to i NH ωH where i is the integer and NH is the number of rotor blades. More blades on a rotor will produce low frequencies with varying amplitudes. However. mast. Any movement of the structure may produce resonance frequencies different from the blade vibration frequencies. Amplitude and frequency of vibration depend somewhat on wind turbine configuration. If the turbine blades move through two regions with a velocity different from the average.5 Shadow Flicker from Blades Situations in which wind turbine blades are in the direct path between sun rays and the eyes of an observer and reflections of sun rays on wind turbine blades should be avoided.5. It is strongly recommended to avoid frequencies of a HAWT or VAWT close to the eigenfrequencies of the support structure including the building roof. walls. This phenomenon is known as rotational sampling. and other components on which they are mounted.218 ◾ Wind Turbine Technology 7. The rotor blades move through the low-velocity region upwind or downwind of the tower. Based on these facts. Thus. turbine blades located in the direct path of the sun's rays can be a nuisance to an observe near an operating wind turbine at visible frequencies below 20 Hz. The induced vibration frequencies from a VAWT are different from those described for HAWT systems. The problem of the reflections can be solved with dull paint. Severe vibrations of blades occur during operation in gusty winds or mechanical turbulence. 7. Based on . one finds an induced frequency caused by the rotational sampling equal to i NH ωH from HAWT systems. The lowest induced vibration equal to ωH is due strictly to mass imbalance and differences in aerodynamic loads of the blades. the rotational sampling frequency of a VAWT is twice as high as that of a HAWT because the blades of a VAWT pass the mechanical turbulence structures twice—once at the upwind side of the VAWT and once at the downwind side. The tower shadow and turbulence structures generate higher vibration frequencies. For example. VAWT systems induce vibration frequencies in the building at the rotational frequency equal to ωV due to mass imbalance balance and the difference in aerodynamic loads of the VAWT blades and frequencies equal to 2 i N V ωV caused by rotational sampling. A shadow causes an induced vibration frequency equal to the product of rotational frequency of the HAWT rotor (ωH) and the number of blades (NH) at each revolution of the rotor. Note that the blades that move through a mechanical turbulence structure with a velocity that differs from the average velocity will induce a frequency equal to NH.
wind energy increases at higher installation heights. The largest turbulent structures in the wind can be scaled with this average characteristic size of the built environment. Brief studies performed by the author indicate that a minimum wind velocity of 9 m/sec is recommended to achieve high energy yield.00 25 3. This means that the average height Have of a building plays a key role in developing mechanical turbulence in a built environment.67 2. while a duration of 5 sec for mechanical turbulence is highly undesirable from mechanical stability and structural integrity viewpoints . a HAWT will most likely cause serious hindrance because of the shadow flicking problem below 20 Hz frequency. The time scale or duration of the mechanical turbulent (Tturb) structures can be found by dividing their characteristic size by the average wind velocity and writing the expression of the time scale as Tturb = [Have/u0] (7.6 Turbulent Structures Mechanical turbulence is strictly dependent on the average height or roughness of obstacles.17 5.33 4. Aerodynamic scientists claim that large turbulent structures will change the local wind direction in the built environment in terms of the characteristic size of the turbulent structures (Have) and the average wind velocity (u0). As mentioned earlier.08 2 50 2. Therefore. while a maximum time scale or turbulence duration of 4 sec is highly recommended for mechanical stability and structural integrity.92 .00 3 50 12 1.00 5.75 4.5. 7. HAWTs have more problems in avoiding the low frequencies because of the single-blade passage where the Darrieus has a double-blade passage between the sunrays and the observer instead.83 8 2 50 3.5.12 3.5 Computed Values of Turbulent Duration or Time Scale Wind Velocity(m/sec) Turbulent Structure Size (m) 20 25 30 35 6 3.Wind Energy Conversion Techniques in Built Environments ◾ 219 the preliminary studies performed by the author it can be stated that compared to the Darrieus. Note that a wind velocity of 6 m/sec is not so ideal from an energy yield view. Table 7.38 10 2.27) Computed values of turbulence duration as a function of turbulent structure size are summarized in Table 7.
ensure that the Tturb must be greater than 6 DRV/u0. Simulated studies of viscous flow by aerodynamic scientists indicate that a similar stream tube expands up to a certain diameter and then decreases in diameter due to reenergizing and speeding of the flow in and around the wake. one finds a DRV smaller than 4 m. This rotor size limitation can provides an estimate of energy yield.27) and (7. this sample calculation clearly shows that a wind turbine for a built environment is limited by rotor diameter. Based on this statement. In other words. This sample calculation provides an approximate estimate for the diameter of a wind turbine in a built environment.28): Tturb > Ts and DRV < [(1/6) Have] (7. the varying effects become very important and the Lancaster-Betz limit based on the steady flow no longer applies.5. for a viscous flow. to avoid the fast changes in load coupled with the varying effects. The stream tube length is defined by the average path of particles of very small mass in the flow. for a Turbo less than 6 DRV/u0).29) defines the critical rotor size or diameter for a wind turbine in a built environment. Therefore. This equation essentially characterizes the time needed to create a quasi-stationary stream tube for an actuator in which the Lancaster-Betz limit is applicable. Computational fluid dynamics (CFD) calculations for a BAWT with an actuator show a virtual stream tube length approximately six times the diameter of the turbine rotor in the viscous flow. . large amounts of electrical energy cannot be generated using wind turbine technology in built environments. the expression for the scale time Ts can be written as : Ts= [6 DRV/u0] (7.28) where DRV is the diameter of the rotor in the viscous flow and u0 is wind velocity. The studies further indicate that the area where streamlines of the stream tube are roughly parallel is taken as the virtual "beginning or end" of the stream tube where the wind energy is extracted. the stream tube length is finite where the wind energy is extracted.220 ◾ Wind Turbine Technology 7.7 Impact of Stream Tube Length on Wind Energy Extraction The momentum theory leads to the Lancaster-Betz limit that indicates a stream tube of finite length where the energy is extracted. In this situation. Equation (7.29) where Have is the average height of the wind turbine or BAWT. Using Equations (7. Thus. However. Based on this conclusion. Assuming an average height of 23 m.
2 Drag-Driven Wind Turbine The driving force of a drag-driven wind turbine rotor originates from the difference in drag of two rotating bodies as shown in Figure 7. while the other cup that moves downwind produces the power. .8. and built environment suitability.Wind Energy Conversion Techniques in Built Environments ◾ 221 7. the efficiency or the power coefficient of the rotor is of critical importance. The conversion of wind energy into mechanical power in the rotor axis may be realized with a drag-driven. 7. In other word.10. Wind turbine rotor design configuration for a built environment is subject to rotor size limits and restricted structural parameters. The figure clearly illustrates the concept.30) where P is the power at the rotor axis.8 Yawed Flow Requirements in Built Environment Three distinct boundary conditions must be satisfied for efficient wind energy conversion in a built environment: available wind energy. Thus. a BAWT system cannot use the same rotor used in a HAWT. wind energy conversion technique.5.10(A). it is characteristic for a drag-driven rotor that the power is produced by a body that moves downwind. The cup with the spherical upwind side has the lowest drag. the material in this section will formulate the point of justification in search of feasible and cost-effective options for wind energy conversion in built environments [4].1 Rotor Design Configurations for BAWT Systems It is important to mention that for open rural areas. Based on these boundary conditions. ρ is the air density. The author's preliminary studies reveal that three available wind turbine design configurations may be considered for a BAWT installation: ◾ Drag-driven ◾ Lift-driven ◾ Hybrid-driven The rotor design configurations for these distinct wind turbines are illustrated in Figure 7. lift-driven. Regardless of type. Consequently. The device consists of two cups. ASA or At is the swept area of the rotor.5) ρ ASA u03] (7. 7. The expression for the power coefficient of a rotor can be written: CP = [P/(0. or hybrid-driven rotor.8. the rotor used for a HAWT presents certain advantages over other types. this cup dissipates power as it moves in the direction of the incoming wind.5. and u0 is the free stream wind velocity.5.
Based on the depicted rotor configuration. and hybrid-driven wind turbines. A.10(A). uc uo Actuator (b) Lift-driven wind turbine deploying an actuator D g (c) Hybrid-driven wind turbine using a Savonius rotor Figure 7. the torque of the rotor axis per square meter of swept area can be determined. lift-driven. It is evident from the schematic that the relative velocities on the turning bodies must be used to compute the drag. When the drag of the body that moves . II. The torque (T) along the rotor axis is produced from the difference in the drag of the turning bluff bodies shown in Figure 7. The power generated on the rotor axis can be written: P = (T ω] (7.10 Rotor configurations for drag-driven.l ω Cd.h Rl (a) Drag-driven wind turbine using rotating bluff bodies Streamline on area control Ao A.222 ◾ Wind Turbine Technology Cd.31) where ω is the rotational speed of the rotor and the torque (T) produced by the rotor is the product of drag coefficients of the rotating bluff bodies and the relative velocities multiplied by the air density (ρ).
h is 1. Note the actuator is located in a stream tube in parallel flow with the entrance and exit of the stream tube at infinite distance from the actuator as illustrated. the conservation of axial momentum within the control area is assumed irrotational and the divergence-free flow shows that the thrust force acting on the actuator (Fa) can be written as: Fa = ρ [u02 A0 – ue2 Ae] (7.10(B) is bounded by the stream tube that forms the boundary of the flow through the actuator [5]. 7. The control area as shown in Figure 7. This is a working model for the rotor of a lift-driven wind turbine at infinite high value of parameter À.l = 0).8.max = [(2/27) Cd.32) where C d. and ρ is the air density. A0 is the area of the flow stream at the input. Ae is the area of the flow stream at the exit.Wind Energy Conversion Techniques in Built Environments ◾ 223 upwind is neglected (Cd.33) where u0 is the flow velocity at the input. This means a drag-driven rotor converts a maximum 11% of the power available in the free stream wind into mechanical power at the rotor axis.h indicates the higher value of drag coefficient. Based on the conservation of mass theory within the stream tube: [Mass of flow at inlet flow] = [mass of flow within tube] = [mass of flow at exit] (7. Therefore.3 Lift-Driven Wind Turbine Figure 7.h (7. The typical value of C d.10(b) is a diagram of a lift-driven wind turbine that deploys an actuator. ue is the flow velocity at the exit. Note the wind flow is normal to the actuator plane.5. When this value is inserted in Equation (7. a maximum of 10% of the electrical power is available from a drag-driven wind turbine rotor operating in a built environment— significantly lower than available power from a conventional wind turbine power source. the equation for the maximum power coefficient can be written as: CP.11. which is defined as the ratio of the tip speed of the rotor and the free stream velocity (ω R at/u0) where ω is the rotational speed of the tip of the rotor and u0 the free stream velocity. the maximum power coefficient for the drag-driven rotor is 3/27 OR 0.34) .32). If 90% efficiency is assumed for the generator and the gear box.5. which is defined as an energy-extracting device of small size dealing with a normal force on the surface that decelerates normal velocity through the disk. Hydrodynamic experts demonstrated through experiments that the pressure forces acting on the control area do not contribute to the momentum balance.
an expression for the thrust force (Ft) acting on the actuator may be written as: Ft = [(0.37) Equation (7.36) yields: Ut = [(0.37) by Equation (7.35) and Bernoulli's theorem on a streamline upwind and downwind of the actuator. The velocity through the rotor is: Ut = [u0 – a] (7. the expression for the flow velocity at the exit becomes: ue = [u0 ( 1 – 2a)] (7. is called bare actuator wake expansion by fluid dynamic scientists.8. A is the area of the flow. From Equation (7.4 Deceleration of Air by Rotor The deceleration of the air by a rotor can be expressed in terms of an induction factor. tube region.5) ρ At (u02 – ue2)] Dividing Equation (7. and exit. is twice the induced velocity (a u0) at the location of the actuator.39). .34) can be rewritten as: ρ[u0 A0] = ρ[ut At] = ρ[ue Ae] (7.224 ◾ Wind Turbine Technology Equation (7.35) where u denotes the flow velocity. respectively. 7.38) (7.36) Using Equations (7.35). The subscripts 0. one can write: Ft = [(ρ At ut (u0 – ue)] (7.38) and (7.39) where a is an induction factor.38) is strictly based on the momentum theory that becomes invalid when the exit flow velocity is less than or equal to zero. and ρ is the density of air. From Equations (7. and e indicate the input. This important conclusion that may be obtained via simplified vortex theory.40) This equation states that the induced velocity infinitely far downwind of the actuator (2 a u0). t.5.33) through (7.5) (u0 + ue)] (7.
5 ρ At u03] (7.5 ut ρ At)[u02 – ue2]/[ 0.38) into Equation (7.5)[(u0 – 1/3 u0)/u0] [(u0 + 1/3 u0)/u0]2 = (0.38).59] (7.5 ρ) [A0 u03 – Ae ue3] (7. The actuator device absorbs a maximum of 59% of the power available in free . This operation yields: ue.5 Power Absorbed by Actuator The power absorbed by the actuator cane is determined by subtracting the output power level from the input power level entering the stream tube as shown in Figure 7. The expression for the power absorbed can be written as: Pasb = (0.43).5)[2/3] [4/3]2 = [1/3][16/9] = [16/27] = [0.43) Equating (7.44) with respect to ue: CP.Wind Energy Conversion Techniques in Built Environments ◾ 225 7. the expression for the power coefficient (CP) is: CP = ( 0. the power absorbed by the actuator can be determined by multiplying the thrust force (Ft) by the flow velocity through the actuator This is another important result used by fluid dynamics engineers and scientists. the expression for the power coefficient is reduced to: CP = [Ft ut/(0.5.30) to (7.46) It is evident from this equation that a lift-driven rotor converts a maximum of 59% of the power available from the free stream wind into the mechanical power at the rotor axis—about six times more than the power available from a drag driven-rotor.42).41).5 ρ) At u03] (7.42) Inserting Equation (7.5 (1 – ue/u0)/(1 + ue/u0)2 (7. Using Equation (7.10.45) Substituting Equation (7. max = [(1/3) u0] (7.45) into the derivation of Equation (7. max = (0.8.44) The expression for the maximum power coefficient can be found by setting the derivative of Equation (7.41) From Equation (7.44) with respect to variable ue equal to zero. the expression for the power coefficient can be rewritten as: CP = 0.35) for conservation of mass in a stream tube and Equation (7.
It is evident that a drag-driven rotor requires a lot of material and also has the lowest power coefficient. Table 7.5. In contrast.6 Summary of Boundary Conditions for Wind Turbines in Built Environments Built Environment Wind Noise emission Vibration Wind Turbine Element Rotor size Yawed flow Reynolds number effects Building Acceleration Resonance Structural aspects . which characterizes this configuration as hybriddriven.24—twice as good as a drag-driven rotor.10 to 0.15. max equal to 0. The studies further indicate that a lift-driven wind turbine is effective for delivering wind energy with simplicity and minimum cost in a built environment.6 Hybrid-Driven Wind Turbines As noted earlier. Laboratory measurements of a hybrid-driven rotor demonstrated a CP. The wind turbine acts like a drag-driven device. The highest optimum power coefficient has been reported for a twobladed Savonius rotor with a gap to diameter ratio (g/Dt) ranging from 0.5.8. max) for hybrid-driven rotor than for a purely dragdriven rotor. a BAWT system with a twisted Savonius configuration has been considered for hybrid-driven application in built environments. Due to the gap in the Savonius configuration. Specific details of Savonius rotor architecture with a gap between the two turning bluff bodies are illustrated Figure 7. which yields a higher optimum power coefficient (CP. The top view of a Savonius [5] rotor shows a gap (g) between the two bluff bodies. The additional driving force is generated by suction.226 ◾ Wind Turbine Technology stream wind. The actuator concept offers a useful model for an idealized lift-driven rotor best suited for BAWT systems. Drag-driven wind turbines are therefore not in great demand.10(C). Therefore. 7.8. the bluff bodies are driven by drag and suction. 7. the projected blade area of a lift-driven rotor is typically a fraction of the area for a drag-driven rotor.7 Comparison of Wind Turbines in Built Environments The author's preliminary studies indicate that the projected area of a dragdriven rotor is close to the rotor swept area. A lift-driven rotor combines a high power coefficient with fewer material requirements. a Savonius rotor configuration offers the least compact architecture with reasonable efficiency.
Effects of induced vibrations and shadow flicker of wind turbine blades are described.6 Summary This chapter is dedicated to the performance capabilities and limitations of BAWTs. Calculated values of allowable aerodynamic noise levels as a function of distance from the source are provided. Boundary conditions are critical because they provide the contours of wind energy conversion in built environments and the contours yield useful data for projecting BAWT performance. with emphasis on built environment aspects. Impact of free stream length on wind energy extraction is briefly discussed with emphasis on the advantages of the computational fluid dynamic (CFD) method. Requirements for building structures with BAWT systems are summarized. . Eigenfrequencies of mechanical resonance due to bluff building structures are explained. Important boundary conditions for BAWTs are identified with particular emphasis on wind energy conversion efficiency and cost-effective design aspects. Important components such as pressure drag and viscous drag are briefly summarized. Wind speed parameters vital in estimating the vertical wind movements are summarized.5. The significance of vertical wind speed gradient due to build environments is discussed.8.8 Boundary Conditions for Wind Turbines in Built Environments Table 7. lift-driven. and construction. Wind speed parameters vital in calculating vertical wind profiles are summarized. Performance capabilities and limitations of BAWTs (drag-driven. critical elements. and hybrid-driven) best suited for built environments are summarized as are power coefficient (efficiency) factors. Mechanical turbulence effects and their durations as a function of building height are discussed along with details about mechanical resonance frequency.6 summarizes details of the boundary conditions of wind energy conversion in built environments. Variations of roughness length as a function of wind velocity are identified. Characteristics of atmospheric boundary conditions are discussed in detail. Critical design aspects of wind energy concentrators that are required to boost wind velocity in built environments are summarized along with discussion about cost and complexity. Effects of sharp upwind building edges on wind velocity are discussed in detail.Wind Energy Conversion Techniques in Built Environments ◾ 227 7. 7. Effects of built environments on wind speed and wind variations are identified. Potential wind energy concentrator configurations such as spherelike structures and in-duct-through-building configurations and enhancement of wind velocity are discussed. Mathematical expressions for power coefficients of BAWT systems are derived and the computed values of their power coefficients are provided.
1994.A. [2] P. Chelsea Green.J. 89. New York. Wind Turbine Technology. 35. p. 57. Multiscience. Chichester. 15. . Wind Energy Techniques. Post Mills. Jenkins.F. John Wiley & Sons. American Society of Mechanical Engineers Press. 1987. [4] D. 1989. Wind Engineering in Built Environments.228 ◾ Wind Turbine Technology References [1] S. VT. [3] J. Wortmann. U. Wind Power for Homes and Businesses.K. p. Boston. Gipe. Introduction to Wind Turbine Energy. Mertens. 1983. Walker and N. 2002. 2006. Butterworth. Essex. p. 17. Spera. p. p. [5] A.
replacement. effects on radio communications and television reception. Will a particular wind turbine be able to meet his electric consumption requirements? Will the selected system pay for itself and if so. A customer may have several questions that require accurate answers from a wind turbine installer. disturbances of local ecology. miscellaneous costs for maintenance. final checkout testing. tower design constraints.Chapter 8 Environmental Issues and Economic Factors Affecting Wind Turbine Installation 8.1 Introduction This chapter focuses on the environmental issues and economical aspects justifying wind turbine installations. transportation. The environmental matters such as physical restrictions. zoning restrictions. and finally economic feasibility for installation at a particular site must be considered. The economic aspects such as initial costs for analysis and design. It is important to note that feasibility is determined strictly on the bases of costs and the value of electrical energy generated based on preliminary estimates. installation costs for turbine and tower. within what time frame? Will the system be a sound investment? Is it worth all this 229 . and repair. cost of generation of one kilowatt of electricity compared to electricity from other sources. and impacts on bird life must be thoroughly evaluated prior to selection of an installation site. noise levels. fabrication. assembly and operational testing.
The extrapolated wind speed versus height relationship showed that the wind speed varied as 16 the power of height (H0. as H0. Furthermore. the wind speed near the surface of the earth increases close to the 1/7 power of the turbine height above the surface of the ground.2. there is no single straightforward way to analyze the economic issues surrounding installation of a wind turbine. and from the surfaces of open water and plains. river. According to aerodynamics and fluid dynamic scientists. or sea. It may be difficult or even impossible to obtain approvals from appropriate authorities to operate a wind turbine system in a restricted zoning area due to objections from residents in the vicinity of the installation site. The correct and reliable answers to these questions are based on a number of speculative variables that are not subject to precise calculation. respectively. 8. and the desired rate of return based on prevailing economical factors.to 10-year spans. inflation rate. Meteorological data should be collected over several years to ensure that wind speeds of 20 to 30 mph are available at operating heights of 20 to 30 ft.28 due to trees and homes. Utmost care should be exercised in selecting a site for a wind turbine installation. Significant amounts of shear and compression normally occur in a horizontal wind stream as it travels over the topographical contours and rough surface of the earth at any installation site. for example.2 Environmental Factors and Other Critical Issues Environmental factors and other critical issues must be seriously evaluated prior to selection of an installation site for generation of electricity from a wind turbine.1 Choice of Installation Site Installation site is the most critical choice. Wind measurements made over decades by Canadian weather bureaus at two installation sites in Southern Canada [1] at altitudes from 7 to 10 m exhibited slightly different power exponents. the free flow velocity at heights far enough from the surface to be unaffected by surface shear is significantly larger than that of the winds at the surface or at anemometer heights of 20 to 20 ft where wind speed is normally measured. and over flat plains as illustrated in Figure 8. It is interesting that the geographic distribution of average wind power density is . These wind speed-versus-height relationships are valid only for few countries where wind speed measurements have been made over 8. 8. It is clear that wind speed (V) varies as H0. In brief. These values may not be valid in desert regions due to wide temperature variations within the 20 ft above the surface of the earth.4 due to tall buildings.1. interest rate.230 ◾ Wind Turbine Technology trouble? The answers may be elusive. Shear generates lower wind speeds near the surface than at heights great enough for free wind flow to occur. where wind speed is normally measured by anemometers. over open water such as a lake.16).
20 10.2 Tall buildings 4.41 10.00 15. 8. even more skewed because it varies as the cube of wind speed.2. 1500 1000 500 100 3.16 7.28 10 mph V~H0.37 3. A horizontal wind speed from 20 to 30 mph is ideal for most installations.70 6.1 Wind speed dynamics.02 3.28 3. Computed values of vertical wind speed (V) as a height (H) for various ground roughness levels are summarized in Table 8. which is a function of installation height and surface conditions.1.63 5.31 12.4 10 mph V~H0.Environmental Issues and Economical Factors ◾ 231 10 mph Height above ground. The computed values are for the vertical wind speeds that differ from the horizontal wind speeds that drive wind turbines to generate electricity.77 3.17 V = H0.91 .16 2.62 3.2 Wind Features and Their Effects Brief studies performed by the author indicate that certain wind features produce certain effects such as maximum energy output and turbulence conditions Table 8.9 Trees and houses V~H0.1 Vertical Wind Speed as Function of Height for Various Ground Roughness Factors Height H (ft) 100 500 1000 2000 3000 4000 5000 V = H0.70 3.09 2.4 6.91 24 59 27 59 30. Ft.0 Open water and plains Figure 8.85 20. H.85 V = H0.92 8.40 9. The horizontal component of the wind is important for turbine performance.
It is evident . laminar wind flow offers constant wind energy Wind energy by nature is unsteady and may be absent and thus require a storage scheme or back-up energy source for applications that require constant power Per HAWT theory. optimum sites. taller installation towers are required on rougher ground to reach levels at which laminar flow exists. particularly in contoured areas. A single type of terrain modification may not be suitable for all installation locations.3 Terrain Modifications to Augment Wind Speeds for Improved Performance Terrain modification may be required if the average wind speed at a specified installation location is below the minimum necessary to operate a wind turbine. Potential wind features and their effects are summarized in Table 8. Extreme care should be exercised in selecting a modification scheme to ensure highly reliable performance economically and simply.2.2 Wind Features and Effects Feature Vertical wind speed variations Effect Even for level terrain. ridges. are difficult to find Wind turbine systems must be ruggedly built to operate with reliability in gusty winds and turbulence Severe wind energy fluctuations Omnidirectionality Horizontal wind speed variation from location to location Nonuniform spatial conditions due to ground roughness and terrain variation that are detrimental to the stability and structural integrity of a wind turbine. It is critical that wind turbine customers understand the effects produced by various wind characteristics.232 ◾ Wind Turbine Technology Table 8. and well rounded hills. a turbine must always be vectored into the wind direction to achieve maximum energy output Based on site surveys of meteorologists at various installations. rough ground surface may result in turbulence conditions and at low-speed winds under a height of 30 ft.2. Note how wind speed is augmented by terrain features such as hills. Potential terrain modifications are illustrated in Figure 8. Terrain modification may improve turbine performance with minimum cost and little complexity. 8.2.
4 Impact of Volumetric Flow Rate on Performance The author undertook aerodynamic of wind speed parameters that indicate that the volumetric flow rate of an air stream significantly impacts power output and power coefficient of a wind turbine. These statements confirm that an optimum blade design maximizes the product of the volumetric flow rate and the pressure drop across the turbine. Hilly terrain accelerates wind and is considered highly desirable from high wind energy yield view. The studies further indicate that for a large blade area. .2 Terrain modifications. from Figure 8. This means that any reduction in the volumetric flow rate of the windstream will affect the output power level and the power coefficient.2. 8. a large reduction of windstream velocity will occur but the volumetric flow rate of the windstream will remain low.Environmental Issues and Economical Factors ◾ 233 Smooth surface High velocity (a) Well-rounded hill or ridge (suitable site) High velocity Reverse flow (b) Hill or ridge with abrupt sides (unsuitable site) High velocity Reverse flow region (c) Sharp peak (could be suitable) Figure 8.2(a) that well rounded hill terrain offers high wind speeds and is thus well suited for wind turbine installations.
295 ρ V03] (8. For propeller-drive wind turbines using three blades. Based on this principle.59 that predicts the maximum fraction of power can be extracted by a wind turbine from a windstream.35 at a ratio of peripheral speed to wind stream speed. the power coefficient attains the highest value of 0. The equation of the power density can be written as: Pden = [Pmax/AT ] = [0. The momentum theory states that the maximum amount of energy of a wind turbine that can be extracted depends on the volumetric flow rate of the airstream and that 8/9 of the kinetic energy of the wind stream is extracted while the airflow passes through the turbine.2) that the power density increases by a factor of eight when the wind speed doubles as illustrated by Figure 8. not blade tip speed to wind stream speed ratio. the maximum loss in wind speed will be about 67 % of the initial velocity. . For the Darrieus wind turbine rotor. and V0 is the initial velocity of the windstream. the expression for the maximum power that can be extracted from a windstream by a wind turbine can be written: Pmax = [0. Note the constant (0.3. 8. the power coefficient attains a maximum of 0.6 Power Coefficient Power coefficient (PC) is the second most important performance parameter of a wind turbine.295 AT ρ V03] (8.2.5 Maximum Extractable Power The maximum power that can be extracted from a wind turbine is the principal design parameter.2.295) includes the Betz coefficient equal to 0. because the peripheral speed of a Darrieus rotor is crucial. ρ is the air density equal to 12. Rotor designs that are not listed in the table exhibit lower maximum coefficients at lower speed ratios than high-speed two-bladed horizontal axis rotors and Darrieus vertical axis rotors [2].1) where AT is the total blade area.234 ◾ Wind Turbine Technology 8.59 when the ratio varies between 7 and 8. The power coefficient also depends on the rotor configuration and number of blades deployed.2) It is evident from Equation (8.3. Typical power coefficients for a two-bladed wind turbine and various rotor configurations are summarized in Table 8.25 Kg/m3. Under these conditions. Its magnitude depends on the ratio of the blade tip speed to free flow windstream speed.
rotor axis orientation. Under these conditions. The torque developed by a horizontal axis rotor blade of fixed pitch angle varies with the wind velocity and the rotor shaft speed as shown in Figure 8. and pitch angle adjustment capability.3 Typical Power Coefficients for Two-Bladed Turbines with Various Rotor Configurations Rotor Type High efficiency High speed Darrieus Blade Tip Speed-to-Windstream Speed Ratio 7 to 8 5 to 6 5.3 Power density as function of wind speed.47 0. 8.Environmental Issues and Economical Factors ◾ 235 A = 1 Ft2 Power in a Windstream of 1 Ft2 Watts 160 140 120 100 80 60 40 20 0 0 10 20 30 V 3 P = ρV A 2 Symbols: A = Area of the windstream (sq.4.35 . wind speed.58 0. Table 8. the output torque will decrease significantly and lead to unsafe stalling. It is important to avoid blade stalling that occurs when the rotational speed of the blade is too slow in a windstream at a given velocity. ft) V = Wind speed (MPH) P = Air density Note: Doubling the speed increase the wind power by 8.2.7 Output Torque Performance Aerodynamic design engineers believe that the output torque of a wind turbine is based on the rotor type and its parameters. Wind Speed.3 CP 0.8 to 6. mph Figure 8.
Designers note that at wind speeds below rated values. the rotor speed must vary with the wind po we r .236 ◾ Wind Turbine Technology sta de Bla ll Torque M ax Fixed. MPH 32 28 Maximum power occurs at Shaft speed (RPM) Wind speed (MPH) 50 100 125 200 13 26 29 34 16 8 12 0 20 24 50 100 150 Rotor Shaft Speed. RPM Wind speed (MPH) 8 16 24 32 Rotor shaft speed (RPM) 32 62 83 126 Figure 8.4. most modern wind turbines are equipped with variable-pitch controlled blades.5. to achieve maximum output power or torque from a windstream with speed fluctuations. If the rotational speed of a blade is too slow in a windstream of a given velocity. It is clear from the curves in Figure 8.4 Torque output. These tables illustrate the impacts of rotor shaft speed and wind velocity on the maximum torque and output power levels of modern wind turbines. The maximum power levels as a function of rotor shaft speed and wind velocity are summarized in Table 8. A controlled mechanism is required to adjust the pitch angles of the blades to maintain a constant rotational speed in the event of a change in wind speed or in output load of the turbine. For this reason. Therefore. optimum blade angle Wind velocity. Estimated values of torque developed as a function of wind velocity and rotor shaft speed are shown in Table 8. the blade will stall and thus reduce the output torque.4 that maximum and maximum torque do not occur at the same wind velocity (mph) or rotor shaft speed (rpm) . the pitch angle of the blade or the rotational speed of the blade must be adjusted.
Most wind turbine power systems deploy specifically chosen synchronous alternating current (AC) generators with fixed-ratio gear trains.Environmental Issues and Economical Factors ◾ 237 Table 8.4 Maximum Torque as Function of Wind Velocity and Rotor Shaft Speed Wind Velocity (mph) 8 12 16 20 24 28 32 Rotor Shaft Speed (rpm) 32 41 62 72 83 97 124 Table 8. .5 Estimated Maximum Power Level as Function of Rotor Shaft Speed and Wind Velocity Rotor Shaft Speed (rpm ) 50 75 100 125 150 Wind Velocity (mph) 13 19 26 29 35 speed to extract maximum power. This mismatch poses a serious problem of interfacing a rotor with an electrical output generator. The most practical approach is to allow the rotor speed to vary optimally with the wind speed and employ a variable speed. This type of generator must be operated at constant input (fixed wind turbine rotor) speed to maintain synchronism with the electric current in the utility grid line to which it is tied. This way the power generated by wind turbines can be connected to commercial power grids. constant-frequency generator to achieve constant (60 Hz) electrical operation compatible with the commercial utility grid requirements. Suitable mechanical or electrical devices that can perform this task may be selected if cost and complexity factors do not undermine reliable system performance. They also indicate that this does not match the optimum operating conditions for synchronous or induction AC generators commonly used by high-power wind turbines.
3927) ρ D2 V3] (8.3 Problems Arising from Large Windstream Diameters It is important to mention that increasing the effective diameter of a rotor will increase its cost.220 0.098 0.6 Power (MW) Generated by Windstream as Function of Wind Speed and Windstream Diameter Windstream Diameter D (ft) Wind Speed V (mph/ft/sec) 10/15 20/30 30/45 40 50 0. It interesting to note that considerable power can be generated by wind spread even at a wind speed of 50 mph with a wind stream diameter of 200 ft. It is evident from Equation (8.225 kg/m3). and ambient noise level.8 Power Generated by Windstream as Function of Windstream Diameter The output power (P) generated by a windstream relies on the wind speed (V) at the installation site and the wind stream diameter of the turbine (D)—the effective diameter of the rotor capable of capturing the wind energy.888 1 562 150 0.390 100 0.000 3 512 200 0.5.6. weight.098 0.238 ◾ Wind Turbine Technology 8. Computed values of power generated by a windstream as a function of wind stream diameter and wind speed are shown in Table 8.6.3) that wind turbine power output is proportional to the cube of the wind speed. tower structural complexity. The output power generated by a wind turbine can be written as: P = [(0. but proportional to the square of the wind stream diameter. Table 8.222 0. For example.2.390 0. Since most systems operate at wind speeds ranging from 20 to 40 mph as illustrated by Figure 8. doubling the wind speed can achieve four times more power output and doubling the wind stream diameter one can produce eight times more power.888 2. However.390 1 560 3 560 6. power generated by a windstream beyond speeds above 40 mph are shown in Figure 8.242 .0245 0. no attempts were made to compute power output for wind speeds exceeding 40 mph. 8.3) where ρ indicates the air density (1.
MW 14 12 10 8 6 4 2 0 0 10 20 30 Wind Speed. mph 60 70 Figure 8. Ft 200 Symbols: P = Output power D = Wind stream diameter V = Wind speed Figure 8. and system complexity before considering significant increases in rotor size.Environmental Issues and Economical Factors ◾ 239 Wind Energy Density kWh Ft2 – Yr 0 10 20 30 40 50 Wind Speed. mph 40 50 50 100 P= ρπ 2 3 DV 8 Wind stream diameter.3.1 Higher Noise Levels Noise generated by wind turbines is very annoying [3] and the decibel (dB) level ranges from the threshold of hearing to the threshold of pain. It is 16 Power in a Wind Stream. reliability.5 Wind speed variations below 40 mph. Scientists believe that doubling the power of a noise source by installing two wind turbines will increase the overall noise level by 3 dB—the smallest change most people can detect. comprehensive trade-off studies should be performed to determine cost. 8. .6 Wind speed variations above 40 mph. Therefore.
a wind turbine with two blades spinning downwind of a tower will make a characteristic "whop-whop" as the rotor blades pass behind the tower. It is important to distinguish the ambient background noise of an installation and the noise generated by the wind turbine. the noise generated by a wind turbine must be placed within the context of noise levels from other sources. City or county noise ordinances generally specify a maximum level that must not be exceeded over a specified time frame. For example. Noise level is measured in decibels (dB)—the units commonly used to specify noise levels. Note that impulsive sounds also elicit a greater response than sounds at a constant level. If a customer selects this type of wind turbine. This complicates the task of estimating the impact from the noise of a wind turbine. If an installation is in a high wind area. Furthermore. Another element is the time duration over which turbine noise can be heard. It is interesting that many complaints about wind turbine noise in California have been directed at two-bladed downwind turbines. the wind turbine noise may not be bothersome because the ambient noise level of the windstream may impact the noise level generated by a turbine.240 ◾ Wind Turbine Technology important to mention that pain level is dependent on the pitch of the blades. . if you live near an airport or a busy highway. Some cities and counties weigh the time duration over which the noise occurs at various levels and frequencies. Another example is noise from the wind. the sound from a wind turbine may add to community unhappiness. a wind turbine may emit far less noise but does so continuously. Some may find this aspect of the wind turbine-based energy more annoying than noise generated by other energy sources. A wind turbine equipped with three blades will have a different sound profile than a two-blade turbine. The components of sound generated by a complex machine like a wind turbine are generated by many sources including the wind over the rotor blades and the whirring of the generator Furthermore. For example. making it distinctive from the other sound components. If your community is unhappy about high utility rates. The noise measurements are dependent on the way the human ears perceive sound by using a scale weighted for the frequencies best heard by the human ear. kicking a garbage can draw someone's attention lot quicker than a person humming a tune. The scale ignores sound frequencies we cannot hear. a wind turbine will barely create a noise problem. he may need to consider the inherent effects from low-frequency sound components. each sound component has a characteristic pitch. It should be the objective of the responsible authorities to limit increases in the total noise arising from a wind turbine installation in relation to noise generated by other sources [3]. Finally. Noise acceptance is affected by subjective factors. This impulsive sound may be missed by standard noise measuring equipment. Compared to noise levels from trains or airplanes that emit high levels infrequently throughout the day and night.
Next. Noise measurements made by aerodynamic engineers indicate that the ambient noise level from a 10-kW wind turbine is about 51 to 53 dB (A) at wind speeds of 25 mph (11 m/sec) [4]. It is extremely important to mention individual hearing sensitivities differ.2 Ambient Noise from Installation Site Studies performed by wind turbine design engineers indicate that the ambient or background noise from the nearby trees varies from 51 to 55 dB (A) at a distance of 40 ft (12 m under a wind speed of 15 mph). It is important to mention that the difference between the ambient noise level and the noise level generated by a wind turbine determines most people's responses. However. noise heard by nearby residents is the product of these two distinct noise levels. First. The noise generated by the turbine varies from 54 to 55 dB (A) at a distance of 323 ft (100 m) to 53 to 54 dB (A) at 643 ft (200 m). then compare the disposition of nearby residents toward your findings and anticipate the response expected from them. Under these wind speed conditions. The overall noise level from 30 wind turbines of 10 kW each will be 45 dB (A) within 500 m. while the noise generated by a wind turbine is based on the blade parameters and number of blades in the rotor. an exact estimation is impossible because decibel level changes based on several unpredictable and fluctuating parameters. This means that the estimation of sound pressure must be determined from the persons who have similar hearing sensitivities. . 8. no matter how quiet. the noise from the nearby trees can mask the noise generated by a 10-kW wind turbine operating in the same wind environment. which may not be possible in actual practice. The following procedure is recommended to estimate the noise level from a wind turbine.3.Environmental Issues and Economical Factors ◾ 241 8. The noise level estimates predicted by the European Wind Energy Association for 300-kW wind turbines indicate that the noise from operation in a wind speed environment of 18 mph will drop to 45 dB (A) within 200 m. It is also a good idea to estimate the sound pressure level those people will hear. The noise estimates indicate that no wind turbine. determine who will hear the noise and their distance from the site. The main objective of the authorities should be limiting increases in the total noise to a level that should be acceptable to the residents in the vicinity of a wind turbine site. The background noise level is subject to surface conditions. One must understand clearly the distinction between the background noise and the noise generated by a wind turbine.2. Compare this result with any applicable county or city regulation and the ambient noise under conditions when the wind turbine will most likely operate. Finally. find the estimated level of noise emitted at some distance by a wind turbine at a specific installation site.3. can achieve levels better than the ambient noise.1 Estimating Noise Levels from Wind Turbines It is difficult but not impossible to estimate the noise generated by a wind turbine.
3.3. Advise them of your installation plans and request their comments. Answer their questions as accurately as possible and make sincere attempts to incorporate their comments when designing your site. Even in such areas. 8. or fiberglass. This is no longer a problem because modern blades are made from wood. More than 5000 wind turbines operate close to the ridges of Tehachapi Pass in Southern California. but there has not been any interference with communication signals.2.2 Community Reaction to Wind Turbine Noise Community acceptance of noise levels from a wind turbine site may lead to approval of the installation of additional wind turbines until the overall noise level exceeds the acceptable magnitude. 8.3 Television and Radio Interference Electrical design engineers believe that wind turbines deploying metallic rotor blades may disrupt radio and television reception. These techniques have made newer wind turbines significantly quieter. A report prepared by Bergey Wind Power suggests that if there is any doubt whether a wind turbine installation will disturb anyone within a radius of 500 to 1000 m.000 wind turbines operating in the United States and Europe. For a comprehensive treatment of the subject. readers are advised to refer appropriate texts written by experts. wind turbine manufacturers have made significant efforts to reduce noise levels. Since the early 1980s. Small wind turbines are used worldwide to supply electricity for remote telecommunications stations for both commercial and military applications. Wind turbines would never have been selected to power such stations if the users saw any hint of electronic interference from the rotor blades. The . Of the 25. They decreased aerodynamic noise levels regardless of turbine output capacity by sharpening the trailing edges of the rotor blades and using new tip shapes.242 ◾ Wind Turbine Technology 8. Both components are expressed in decibels (dB). plastic. Bergey's report further indicates that the reaction of a community to the noise from a small wind turbine declines after the residents acclimate to the new sounds. adverse effects have been rare and localized. Design engineers reduced the mechanical noise of larger systems by isolating the gearboxes from the nacelles and installing sound-deadening insulation.4 Quantitative Description of Wind Turbine Noise Evaluating noise from wind turbines is very complex and the acceptable limits vary from country to country. only a few have adversely affected communication signals. Electronic interference has been a problem only in remote areas where television and radio signals are extremely weak. Noise generated by a wind turbine can be quantified by measuring two distinct components: the sound power level component of the source (LW ) and the sound pressure level component (LP) at the installation location.3. it is wise to be a good neighbor and contact those who might be affected.
Readers are advised to understand the clear distinctions of noise components. The sound power level (LP) varies with the wind speed at a turbine installation site. Table 8. Most sound power levels have been measured between 96 and 108 dB (A) range at wind speeds close to 8 m/sec. The sound power level component of a source such as a wind turbine can be defined as: Lw = [10 Log (PS/P0)] (8. It is important to mention that the decibel (A) weighting function depends on noise frequency. The figure shows that wind turbine noise level decreases with distance from the turbine site. This is done with a weighting filter as illustrated in Figure 8. the sound pressure level component describes the noise at a remote point. The most common technique is to weight the measurements to reflect the sensitivity of the human ear.Environmental Issues and Economical Factors ◾ 243 source power level component describes the power of the source noise. The linear increase in weighting function continues up to 500 and attains its maximum value at about 2000 Hz and decreases thereafter.7(B).7(A). Wind turbine noise pattern as a function of distance from the installation is illustrated in Figure 8.7 Computed Sound Power Level as Function of Wind Turbine Output Wind Turbine Output ( kW) 1 10 20 30 40 50 100 200 300 400 500 1000 Sound Power Level A (dB) 90 100 103 105 106 107 110 113 115 116 117 120 .4) where PS is the sound power level of the source and P0 is the reference sound power level (often 1 microwatt or 10 -6 watt). Calculated values of sound power level as a function of source power are summarized in Table 8.7.
The pascal is the unit for expressing pressure.4 dB(A) 42.3 dB(A) (a) Wind turbine noise pattern showing noise level as a function of distance from the turbine site A Weighting (dB) 0 –10 –20 31.4) and assuming a wind speed of 8 m/sec.5) where p is the root mean square (RMS) value of the sound pressure level and p0 is the reference sound pressure. One pascal equals 6895 pounds per square inch (psi). In brief. the reference sound pressure equals .9 dB(A) 44. They will vary as a function of wind speed and operating conditions. The expression for sound pressure levels [5] can be written as: Lp = [20 Log (p/p0] (8.9 dB(A) 39. which is often written as 20 μPa (micropascals) or 20 × 10 –6 Pa (pascals). These calculated values are obtained using Equation (8.7 dB(A) 150 m 45. In addition. the values may contain ±decibel (A) errors.7 Weighting filter.244 ◾ Wind Turbine Technology 400 m 200 m 160 m 300 m 36.5 250 500 1000 2000 4000 8000 Frequency (Hz) (b) Noise filter response with dB a weighting function 36 125 Figure 8.
91 8. High-Capacity Wind Turbine Sound power level data are based on wind turbine performance parameters and are generally available from the manufacturer.12 63.37 21. The operating range of 30 to 45 dB for parameter Lp is recommended for operating capacities in the range of 200 to 400 kW.49 177.09 79.87 24 54 0. the RMS value of sound pressure can be calculated.81 50.82 RMS p (lb/in 2) 4. Engineers recommend a simple model approved by the .3. the RMS of the sound pressure also increases. These data allow a user of a wind turbine to determine the sound pressure levels around the wind farm as a function of distance to ensure that the planning requirements are satisfied and no nuisance will affect nearby residents.5).8 Computed RMS Values of Sound Pressure Levels at 350 m Lp (dB) 30 32 34 36 38 40 42 44 45 (p/p0) 31. For wind turbines with output power levels exceeding 1 MW.36 5.8. Wind turbine engineers specify a typical sound pressure level ranging from 35 to 45 dB (A) at a distance of 350 m from a wind farm location.82 17.96 13. as Lp increases.138 psi. 8.43 100 125.Environmental Issues and Economical Factors ◾ 245 Table 8.49 6. The (A) indicates that this parameter is measured using an A-weighted filter.90 158. which is done by applying a filter generally referred to as dB A or dB (A).4.71 10. Calculated values of RMS sound pressure levels at a distance of 350 m from a wind farm are summarized in Table 8.1 Estimation of Noise Generated by Single. Based on the table data. Persons planning to reside near high-capacity (2. the sound pressure levels will be significantly higher. it is very common to weight the measurements to reflect the sensitivity of the human ear.5 MW) wind turbines are advised to live at least half a mile from the installation site. As mentioned earlier. Inserting various values of sound pressure level (Lp) ranging from 35 to 45 dB into Equation (8.62 39.
Inserting various values of the parameters involved into the above equation. The results obtained from Equation (8.7) yields [61 dB] = [10 Log (2 π R 2)] or [6. According to wind turbine designers.6) can be rewritten as: [LW – Lp] = [10 Log (2π R 2] (8. Any noise emanating from a gear box can be easily detected by the human ear. namely.9.9 and reveal that the larger the (LW – Lp) difference in dB. The expression for this model can be written as: Lp = [Lw – 10 Log (2π R 2) – α R] (8. the greater will be the distance at which the sound power level generated by a wind turbine will not disturb the nearby residents. Inserting these values in Equation (8. In other words. the product (αR) can be neglected for various distances from the noise generating source. according to designers.7) Inserting several values of LW and Lp in the recommended ranges and using Equation (8. Sample Calculation: LW = 95 dB (assumed). we can verify the above assumption. Equation (8.6) Lp is the sound pressure level at a distance R from the noise source with a sound power level of Lw and α is a frequency-dependent sound absorption coefficient. a typical sound pressure level can be in the range of 35 to 45 dB (A) at a distance (R) of 350 m from a wind farm.4)] = [Log (6.1] = [Log (6.7). Lp = 34 dB (assumed) and the difference (LW – Lp) comes to 61 dB.7) are summarized in Table 8. distances from a noise source can be calculated. Both Lp and Lw are expressed in dB A or dB (A).246 ◾ Wind Turbine Technology International Energy Agency (1995) for determining the propagation of noise from a single turbine unit. As mentioned earlier.2832) R 2 ] or [Log (1258925. the noise generated by a high-capacity wind turbine is acceptable to most people living at the distances specified in Table 8.2832 R 2 )] or [R 2] = [200169] yielding the distance R = 448 m. the product (α R) is small for high-capacity turbines operating at longer distances from the noise generating source compared to the difference between the parameters LW and Lp. the noise from a wind turbine may be more obvious at low wind speeds than at high speeds because the general background noise caused by the . Under this assumption. In summary. An additional noise level of 5 dB (A) is often added to the sound pressure figure for purposes of assessing acceptability.
10.4 Estimating Critical Performance Parameters Using Classical BEM Theory Comprehensive aerodynamic studies by various scientists indicate that total wind energy production. number of blades. The . 8. The mechanical noise has discrete tones. rotational speed of the turbine.Environmental Issues and Economical Factors ◾ 247 Table 8. The level reduces to about 37 dB (A) at 400 m distance. 8. The calculated results are based on rotor radius. The principal noise of wind turbines has two components: one is the aerodynamic noise from the rotor structure and the other the mechanical noise from the gear box. It is very important to install wind turbines at a minimum distance or more from nearby homes to ensure the noise level is acceptable. It is evident from these data that a minimum mechanical shaft power close to 7% of the peak value occurs at a wind speed of 5 m/sec. and other critical performance parameters of a wind turbine can be estimated using the classical blade element momentum (BEM) theory [6]. hub height.9 Sound Power Level and Sound Pressure Level (Lp) as Function of Distance (R) Sound Power Level LW (dB) 95 97 100 108 98 95 Sound Pressure Level Lp(dB) 45 45 45 50 39 35 (LW – Lp) dB 50 52 55 58 59 60 Distance from R (m) 126 159 224 317 355 399 wind trees is proportionally lower. Aerodynamic noise is a function of vortices from the trailing edges and the tips of the rotor blades. and blade parameters such as angle of twist and chord size. Computed values of mechanical shaft power as a function of wind speed are shown in Table 8. wind speed. while the aerodynamic noise is usually broadband as illustrated in Figure 8. A 300-kW modern wind turbine operating at a wind speed of 8 m/sec (or 15 mph) produces a noise level of 45 dB (A) 200 m from the installation site.1 Mechanical Shaft Power Mechanical shaft power generated by a wind turbine depends strictly on the wind parameters. mechanical shaft power.4. and other structures. generator.7(A).
Wind turbine efficiency achieves the maximum of 0. and the airfoil characteristics affect the values shown in Table 8.4. These results indicate that the BEM method captures the measurements very well at wind speeds below 25 m/sec as illustrated in Table 8.248 ◾ Wind Turbine Technology Table 8. tower.9.2 Impact of Blade Design Parameters on Performance Level The performance of a wind turbine is dependent on the blade parameters such as twist angle and airfoil characteristics (thickness and chord dimension)—both parameters are functions of rotor radius and typical values are summarized in Table 8.11. It is interesting that both the twist angle and the chord dimension decrease as rotor radius is increased. Wind turbine blades can be designed to accommodate the specific airfoil best suited for a certain type of system. The typical values of twist angle and chord dimension shown in this table apply only to airfoils not thicker than 20% of the chord. generator. 8.10 Mechanical Shaft Power as Function of Wind Speed Wind Speed (m/s) 5 10 15 20 25 30 Mechanical Shaft Power (kW) 42 318 516 562 571 512 optimum shaft power can be achieved over wind speeds ranging from 20 to 25 m/ sec but shaft power continues to decrease as wind speed approaches about 23 m/sec.5 for a tip speed ratio between 9 and 10. The rotational effects of the rotor.5 Justification of Wind Turbine Installation Based on Economics Preliminary cost estimates for a commercial wind turbine installation must be prepared with a view to procurement cost for the turbine. an airfoil of about 40% of the chord thickness at the root of the blade must be used to absorb high bending moments.5. A thick airfoil is preferred to avoid adverse effects from centrifugal and Coriolis forces acting on the rotating blades. and . the blade geometry. To maintain structural integrity of a wind turbine. 8.
956 0.86 4. If the wind slows down or stops. For example. Exact estimates of wind turbine installation cost are difficult. maintenance.5.262 associated electrical and mechanical components.02 16.45 5. particularly during the day regardless of season.420 1.Environmental Issues and Economical Factors ◾ 249 Table 8. In addition.85 1. and site surveying costs including interest must be determined along with rate of return and break-even point.06 7.294 0. power companies in Sweden save water with hydropower dams when the wind blows and use this saved hydropower when the wind speed drops below the minimum since power consumption varies continually.11 Typical Blade Parameters as Functions of Rotor Radius Rotor Radius (m) 45 55 65 75 85 95 10 5 15 5 20 5 Angle of Twist (degr) 20.627 1 597 1 540 1. Operating. A moderate share of wind power in a system does not need a back-up capacity if the absence of a designated electrical load can be tolerated for a short time. The electricity supply-and-demand proposition is critical role in determining the installed power capacity of wind turbines and estimating installation costs.30 13.1 Continuous Availability of Electrical Energy It is important to mention that wind availability is not constant.355 1.08 10. This leads to a conclusion that it is necessary to have a back-up power producing system with the same capacity as the wind turbine if a continuous supply of electricity is vital.358 0.018 Chord Dimension (m) 1. every generating system has a built-in regulating capacity to adapt power generation as a function of wind speed variations and the output of the wind turbines. because of the inherent problems associated with wind as an energy source.481 1. electrical power must be generated by other sources. 8. . if not impossible.
and associated electrical and mechanical accessories.3 13 0 23 33 7.000 20.250 ◾ Wind Turbine Technology 8. According to a survey on wind farms.4 Output (kW) 10 1 2 4 10 9 65 System Cost ($) 17. electrical generator.5 MW each. Preliminary cost surveys of megawatt class wind turbines indicate a 2.000 29.12. This method considers only the initial capital involved and Table 8. and tower structure. Calculations of the total cost of electricity produced must include the initial procurement costs of equipment. Furthermore.700 16.5. installation labor.5. electrical cables and wires. Economic experts believe that one simple method is useful for rapid and reasonably accurate estimates. and all other costs associated with operations and maintenance. the largest wind farm could include 100 wind turbines with an output power capability of 2. Methods of calculating costs range from very simple formulas to very large computer codes that generate large quantities of numbers and dazzling graphic displays. A survey of commercial systems [1] indicates that cost per kilowatt decreases for higher-capacity wind turbines. the true value of the extremely elaborate cost computations will remain questionable until sufficient data are accumulated to provide a solid and reliable basis for cost predictions.5-MW system made by the General Electric Company costs about $3. this may be verified from the cost data on propeller-based wind turbines summarized in Table 8.000 7.750 3.25 million. Equipment procurement costs include the cost of wind turbine assembly. Procurement cost includes the wind turbine.500 1. accessories.500 Manufacturer Aeolian Energy Bergey Dunlite Enertech Jacobs Wind Works Zephyr Dynamic . tower.2 Estimating Procurement Costs Procurement cost for a single wind turbine or a group of wind turbines will be very different from the cost for a wind farm utilizing 100 turbines.3 Per-Kilowatt Electrical Energy Cost It is difficult to determine the actual cost of electrical energy per kilowatt generated by a wind turbine.12 Turbines Procurement Costs for Propeller-Based Wind Blade Diameter (ft) 32 8. 8.
Both options need to be investigated with particular emphasis on procurement cost and installation complexity. the output generated by a wind turbine can be increased by locating a turbine in a region of higher wind speed and by increasing the diameter of the rotor. data in the table assume a wind speed of 8 m/sec or about 16 mph. If the cost of a wind turbine is calculated on a per-kilowatt basis (CkW ) expressed as dollars per kilowatt. That means cost per kilowatt is significantly lower for the megawatt class of wind turbines. but this factor is not included in annual energy output (EO). The actual power density of a synchronous AC generator driven by a gear train with a fixed gear ratio would be less than the density in the theoretical case.8) where Ei is the energy integral (discussed in previous chapters in detail) and the 8760 (24 hours × 365 days) represents the hours per year. 8. the total cost over N years of the wind turbine life will be approximately: Ctotal =[CkW PR + Cannual N + Cmaintenance N] (8.9) .4. gear train loss. rotor swept area. Wind turbine designers believe that it is customary to present the cost of a wind turbine in terms of cost per kilowatt of the nominal output power. and the annual maintenance cost is Cmaintenance. 8. However.1 Empirical Method for Computing Annual Energy Output of Wind Turbine Wind turbine engineers developed an empirical method to compute the annual energy output of a wind turbine based on the assumption that the specific power cost (dollars per kilowatt) is a function of the rated wind speed.5. As noted in earlier chapters.Environmental Issues and Economical Factors ◾ 251 reasonable operating and maintenance costs.5.12. the annual cost is Cannual.4 Per-Kilowatt Electrical Energy Cost from Wind Turbine As stated earlier. and the efficiency of the generator. Since the power density of a wind stream varies with both the velocity of the stream and the swept area of the rotor. exact estimation of power cost per kilowatt because of unpredictable variations in wind speed. a fraction of the initial cost.12 that the procurement cost for a wind turbine decreases as the output power rating increases. It is important to mention that the specific power cost is a function of the prevailing wind speed at the installation site. The expression of the annual energy output of a wind turbine with a power rating of PR can be written as: EO = [(PR Ei) 8760] (8. and the electrical generator type and efficiency. This is not considered for the data shown in Table 8. power density of a wind turbine is strictly dependent on the cut-in wind speed or the velocity of the wind stream. It is evident from Table 8.
one must select a .2 Cost of Electricity as Function of Turbine Cost and Life Calculations of the cost of the electricity per kilowatt hour (cents per kilowatt hour) generated by a wind turbine as a function of turbine cost per kilowatt and useful life in years (N) indicate that the cost of the electricity generated per kilowatt hour decreases as the turbine cost per kilowatt decreases and the useful turbine life increases. the calculated value of total cost of energy per kilowatt hour cannot be completely accurate because several assumptions are involved. Some turbine designers believe that a likely cost figure approaches 25 to 35 cents/kWh when realistic fabrication. High-capacity wind turbines with useful lives of 25 years are currently available.9 cents/kWh] The total cost of energy per kilowatt hour generated by a wind turbine is roughly three to four times higher than the cost generated by a coal-fired or nuclear power plant. In summary.252 ◾ Wind Turbine Technology Due to inherent uncertainties in CkW parameter. Systems of moderate and small capacities can attain operating lives close to 30 years.10) Sample Calculation: Assuming the following values of the parameters involved.0 (assumed) Ctotal= [11.5. then the total cost of the energy per kilowatt hour can be specified with an accuracy of less than ±5%. The computed value of 11. In order to further reduce the cost of electricity generated. Compared to a solar power generating source. If the values of the assumed parameters can be specified within an accuracy of less than ±2%.13. the total cost of energy per kilowatt hour generated by a wind turbine is about 50% lower. the total cost of the wind turbine per kW basis is: Cannual = 18% (assumed) Cmaintenance = 6% Turbine life = 20 years (assumed) Energy integral Ei = 1. The results obtained using the above equations and assumed parameters are summarized in Table 8.9 cents/kWh has been verified by prominent wind turbine designers on the basis of a production run of 200 units with 180-ft rotor diameters and 200-kW ratings. 8. maintenance.4. the total cost of the turbine for the life of N years can be written as: Ctotal = (CkW ) [(1/N) + Cannual + Cmaintenance ]/[(8760) PR] (8. and tower costs are included.
and yains indicates years after installation (typically 20).34 7.12) where CCRF is the capital recovery factor (8.92 7. f R is the periodic levelizing factor [Equation (8. If the annual cost of money can be reduced below 15% and the useful turbine life can be increased to 30 years. CO indicates the cost on a per-kilowatt basis. f T is the turbine equipment fixed rate charge (18%).51 9. f L is the land fixed rate (15%).13 Cost of Electricity (Cents per Kilowatt Hour) Generated as Function of Turbine Cost and Turbine Life Wind Turbine Cost (kW) Useful Turbine Life N (Yr) 20 25 30 3600 11. . CL is the land cost. COM represents operations and maintenance.9%). and fO is the annual levelizing factor.91 9. a current market survey indicates that the cost is very close to $2500 per kilowatt. the result can be a generating cost approaching 7 cents/kWh. However.66 2400 11. These parameters represent the recommended NASA accounting procedures for Mod-6H wind turbines and are considered adequate for all preliminary cost estimates pertaining to systems of moderate capacity.4.21 9. The cost of electricity generated by propeller-based wind turbines can be calculated by: CkW = [CT f T + CL f L + COM FOM + CO fO]/E (8.58 7.93 3000 11.47 wind turbine with a per-kilowatt cost as low as $2000. e is price the escalation rate (6 %). f is the multiplying factor. FR = [CCRF (1 + e)/[1 + r]yains (8. 8.5.3 More Elaborate Method of Computing Cost of Energy Generated by Wind Turbine A more elaborate expression for computing the cost of energy per kilowatt hour was proposed by various wind turbine designers [1] for high-capacity propeller-based systems.Environmental Issues and Economical Factors ◾ 253 Table 8.12)].11) where CT is the cost of the turbine.
000 including installation.4.2597] = [0.089 × 1.75] = [$135] (8.5. If a wind turbine is located on 1 acre of land worth $1000 and the annual average wind speed is 22.5 mph.14) Assuming 18%.17) into Equation (8.16) FR is defined by Equation (8. the cost of electrical energy can be easily estimated. the actual equipment cost comes to Cann.480 (8.08)3] = [0. Assuming the value of the energy integral (R).06]/[1.18) If 6% of the original cost of wind turbine ($36.06)]/[1 + 0.320] * (8. = [(18/100) (36.000] = [$4. wind speed is approximately 9. power rating of 10 kW. the annual energy output from the 10 kW wind turbine can be given as: Eout = [(10 kW) (8760) (annual average wind speed/prevailing wind speed)3 (R)] (8.565]kWh (8.0943/1.equip.9%).000) (FR) (8.07486] = [$134.07486] (8. discount rate (8%). system cost of about $36. the annual cost of equipment.S.13) = [10 × 8760 × (22.4 Sample Calculation for Estimating Cost of Electricity Generated by Wind Turbines The approximate cost of electricity generation by a wind turbine system can be determined from low-capacity systems (e.16).06 × 36.year = [(5%) (36. This means: FR = [(0.089)(1 + 0.000) is taken as the annual cost of operation and maintenance.5/30)3(0.17) Inserting Equation (8. and years after installation (three assumed). .000)] = $6. in the third year the cost of replacement defined as the periodic levelizing factor (FR) will be: CThird.8)] = 29..254 ◾ Wind Turbine Technology 8.12) in terms of capital recovery factor (8.08]20 = [0.year =[1800 × 0. and assuming prevailing wind speeds exceeding 30 mph or 15 m/sec).5 mph*. price escalation rate (6%). the third year replacement cost is: CThird.15) Assuming that the annual replacement cost is only 5% of the original cost.19) Annual U.g. the calculation is: Copera + Maint= [2 × 0.
47 cents/kWh] (8.19).6. it is possible to negotiate a lower price.6 Estimated Costs of Critical Components and Subsystems We will now attempt to identify procurement costs for critical components and subsystems.-made systems.20) The total system cost is the sum of the results of Equations (8.15).085/29. . the cost of land equals: CLand = [15% × $1000] = [$150] (8. rotor shaft. Fewer suppliers mean less room for negotiation and the possibility of paying the asking price.5 cents/kWh—roughly four times the current rate for electricity produced by conventional power plants.762 kWh and the generating cost will increase to 53.4 cents/kWh. the costs of components of small commercially available wind turbines are lower than costs for high-capacity propeller-based systems. It is interesting that critical component costs for European wind turbines are slightly different from costs for U. (8..14). If a component for a European wind turbine is not available in the U. If several suppliers can provide the same component.Environmental Issues and Economical Factors ◾ 255 Using 15% as the land fixed rate charge. 8. and pitch control unit.21) Based on dividing Equation (8.22) The cost of the electricity generated by a 10-kW wind turbine is about 37. the cost of electricity generated by this wind turbine is: Celec = [$11. will be about 20. generator. site foundation.1 Cost Estimates for Critical Components Procurement costs for critical components vary by manufacturer. the result will be a higher price and longer delivery time.18). The critical components include blades. and (8.085] (8.21) by Equation (8. Generally.585kWh] = [37. 8. gear box. nacelle. It is important to point out that the electricity generated by a wind turbine located at a site with an annual average wind speed of 15 mph.S. and miscellaneous electrical and mechanical accessories are characterized as subsystem elements. (8.20): CTotal system cost = [$6. The tower.S.480 + $4320 + $135 +$150] = [$11.
The major issue in estimating component costs for large wind turbines may be the lack of agreement about the contributions of major components to the total cost of a system. Some procurement experts are reluctant to express their opinions about costs.S. In addition. procurement costs for critical components for augmented systems are much higher than those for standard wind turbines because of large stationary surfaces and expensive rotating elements.14.2 3.4 18. cost more because of higher wages and fringe benefits.4 to 35.2 18.4 7.3 .1 8. The procurement costs for critical components of four large propeller based wind turbines are summarized in Table 8.3 to 31 5 4. Note that the procurement costs for critical components used in European wind turbines manufactured in Denmark and Switzerland with power outputs from 1 to 10 kW are somewhat less expensive. Because of this lack. Based on the table data.4 to 26.14 Estimated Procurement Costs of Critical Components Component Rotor blades Gear box and generator Hub.1 24. Due to the lack of reliable cost data and differences in estimating procedures. Some turbine designers point out that for European wind turbines and the old U. prices because of stringent quality control procedures of U.2 17.3 to 31.2 to 10. rotor costs vary from 10 to 20% of the 67% rotor cost contribution cited by Eldridge [5] for medium capacity systems. manufacturers. European prices differ from U. Critical wind turbine components manufactured in the U.2 to 11.4 5. little has been done to achieve concrete and meaningful cost data covering critical components. The author used his engineering cost projection experience to prepare a medium cost estimate for the critical components of large conventional wind turbines.S.256 ◾ Wind Turbine Technology It is difficult to determine the true procurement or replacement costs for critical components for wind turbines.4 Medium Percent Cost 7.S. Putnam machines. nacelle and shaft Control system elements Tower Site and foundation Miscellaneous engineering Percent of Total System Cost 3 to 11.2 5. different cost estimating procedures must be used for large wind turbines with output power ratings exceeding 100 kW and small wind turbines rated at 1 to 10 kW. No attempt has been made to estimate component costs for augmented systems because of the complexity of components. The rotor cost contribution varies from 67 to 40% for wind turbines with power ratings ranging Table 8. the percentage rate of the total system cost exhibits enormous spread.2 13.S.3 7.
Manufacturers prefer taller towers because they want their products operate with utmost safety and optimum performance. This company manufactures several high-capacity (2. 8.6. Wind turbine experts now understand power-robbing turbulence and its effects on performance. Major design and performance parameters of the 2-MW system [6] can be summarized as follows: Rated power capacity = 2 MW Rated and desired wind speed = 25 mph Survival wind speed = 150 mph at rotor Cut-in wind speed = 11 mph Cut-out wind speed = 35 mph Cone angle = 12 degrees Inclination of axis = 0 degrees Rotor speed = 35 rpm Blade diameter = 200 ft Blade twist angle = 11 degrees Blade ground clearance = 40 ft Operational life = 30 yr 8. the author selected the 2-MW wind turbine designed. installers learned that cost-effective power generation and optimum wind turbine performance require tall towers. The flat terrain and few obstructions at installation sites did not call for towers taller than 60 ft." By the late 1940s guyed tower heights ranged from 80 to 110 ft. developed and manufactured by the General Electric Corporation. the large number of variables of wind turbine systems make it extremely difficult to determine the true costs of individual components. the manufacturers believe . the greater the power. Designers were fully confident that wind speed capture and optimum power generation were possible only with greater tower heights.2 Typical Design and Performance Characteristics of 2-MW Wind Turbine Simply to provide general knowledge of design and performance parameters of high-capacity wind turbines.7 Wind Turbine Towers Tower structures are essential to provide the safe and reliable operation of turbines under a variety of wind conditions. In addition. In brief. despite the claim by aerodynamic engineers that "the higher the tower.5-MW) wind turbines and its units operate around the world.Environmental Issues and Economical Factors ◾ 257 from 100 to 1000 kW (1 MW). As the technology matured. During the 1930s. turbine towers in Great Britain were not very tall.
The Eiffel Tower is the best known example of a truss tower. U.2 Mechanical Strength Requirements A tower must withstand the forces and bending moments arising from high wind conditions and also provide the structural integrity to carry an expensive wind turbine and its accessories. Micro systems generally deploy rotor diameters smaller than 3 m (10 ft) and are best suited for low-power applications. As stated earlier. For small-capacity systems. Truss towers are generally more rigid than pole towers. As the output capacity of a wind turbine increases. creating loads on a tower structure must be avoided under all operating conditions.7.S. the height requirements for moderate capacity turbines vary between 100 and 120 ft. Towers are rated by the thrust loads they can endure without buckling and bending. safety standards require manufacturers to design their wind turbine systems to withstand 120-mph (54 m/sec) winds without sustaining damage.7. Wind turbine manufacturers believe that a tower structure vibrating in resonance must be avoided because such vibration can exert tremendous force on the tower and lead to a catastrophic failure of the tower and turbine. the weight. The thrust on a tower structure at this wind speed is based on the rotor diameter of the turbine and its mode of operation under the defined prevailing conditions. In brief. By today's standards. the components become bulkier and heavier. the mechanical safety and integrity of an entire wind turbine system is depends strictly on the tower structure.3 Tower Classifications Towers used for wind turbine installations fall into two major categories: freestanding (self-supporting) and guyed types.1 Tower Height Requirements Height requirements vary by turbine rating. Height requirements for micro turbines commonly used in residential settings are somewhat different. However. In brief. a minimum tower height of 80 ft is recommended for moderate capacity wind turbines.. 8. When trees are nearby.S. ensure high wind energy capture. Towers can be designed to withstand any load condition.258 ◾ Wind Turbine Technology that taller towers allow more design flexibility. cost . and more difficult and costly to move.7. the towers are not suited for turbines more than 60 ft above the ground. as the size of a wind turbine increases.and tower height increase proportionately. A tubular or pole tower is another free-standing form produced in several different varieties. a height of 100 to 120 ft (30 to 35 m) is recommended. 8. truss towers are assembled in 30-ft sections. 8. Because micro turbines are low-cost systems utilizing simple towers. In the U. and are preferable if buildings and trees are present. Tower heights for wind turbines with capacities exceeding 100 kW usually exceed 100 ft. the .
a pole tower can be hinged at the base. 8. manufacturers erect the hinged tubular towers with powerful hydraulic jacks. the tubular towers are visible at longer distances than lattice towers. guyed towers offer a good compromise of mechanical strength. and even fiberglass. For largecapacity turbines with outputs exceeding 100 kW. ground roughness coefficient. In California. and omnidirectionality are explained. Pole and tubular towers present considerably higher erection costs than guyed towers but are only modestly more costly than truss towers. For a micro turbine. then hoisted into place and bolted to the foundation using high-strength steel bolts. then bolted to the foundation. tipped into the desired place with a gin pole. Installation of truss towers generally requires a crane. and appearance. they require more space than free-standing towers and are prone to crushing under heavy winds and turbulence conditions. Steel pipes are widely used in guyed applications for small wind turbines (outputs below 5 kW). towers are shipped in parts and assembled at installation sites. erection cost. wind speed variation as a function of installation height. Pole tower installation generally requires a crane. Pole towers are best suited for low-capacity or micro turbines with output ratings below 10 kW and are generally fabricated from tapered steel tubes. inexpensive steel pipe. Potential wind features and their effects. and ground terrain features on the power generation capability of wind systems are discussed in detail. Terrain modification techniques to enhance the volumetric flow rate and wind speed vital for improving performance at sites with marginal wind speeds are detailed. The tower is assembled on the ground at the site. the lattice towers tend to blend into the background at distances above 2 mi (3 km). According to wind turbine manufacturers. Pole towers require stronger foundations than truss towers to spread overturning force over a wider base. concrete.8 Summary This chapter describes the environmental issues and critical economic aspects that justify the deployment of wind turbines to generate electricity. For small or micro wind turbines. nonuniform spatial conditions resulting in from ground roughness and terrain variation. Effects of critical factors such as free wind flow. The author's studies of tower installation indicate that towers. Free-standing pole and tube towers are more aesthetically pleasing than truss towers. must be assembled and bolted to tower foundations by experienced personnel as recommended by the turbine manufacturers. . ease of installation. horizontal wind speed variation. In Denmark and Switzerland. particularly for medium. wind energy fluctuation. namely vertical wind speed.and high-capacity systems.Environmental Issues and Economical Factors ◾ 259 sections may be pre-assembled and welded together prior to delivery. However. Both the tapered steel tubes and steel pipes can be guyed to provide additional strength.
16.J. [5] J. 1983. Calculated noise levels from large wind turbines related to distance from the source are discussed along with the effects of ambient noise level on the frequency-based noise generated by wind turbines. [2] R. [4] A. p.. The effects of wind turbine noise on television and radio signals are investigated with emphasis on quality of sound and video. The use of the blade element momentum (BEM) theorem to calculate critical wind turbine performance parameters is explained. and pitch-angle adjustment are outlined.Hansen. Estimated costs.K. and maintenance cost are included. London. Wind Energy in Built Environments. and P. 1989. Wind Energy in Built Environments. 1976. S.260 ◾ Wind Turbine Technology Expressions for optimum power output and maximum power density as a function of wind speed and wind stream diameter are developed. Walker. Chichester. Essex. p. More elaborate methods of computing cost per kilowatt hour for wind turbine energy along with realistic assumptions are discussed. operating cost. Wind Energy Technology. 1989. U. .N. Boston. 2002. Introduction to Wind Turbine Engineering.B. Aerodynamics of Darrieus rotor.. References [1] S. Multiscience. Wilson. AIAA J. [3] S. 15.E. Walker and N.. 1023. 29. are summarized. Multiscience. Jenkins. 1992. [6] O. and mechanical strength requirements are briefly discussed for various tower types and configurations. Wortman. Mertens.K. John Wiley & Sons. Procurement costs for critical components manufactured in Europe and the U. Aerodynamics of Wind Turbines. Essex. Martin and J.F. Sample calculations to predict the electricity cost per kilowatt hour as a function of turbine output power. Aircraft. Mertens. operating height. Lissaman. p. Various methods for optimizing the output torque as a function of rotor shaft parameters. 2nd ed. Estimated wind turbine procurement costs as a function of output rating and rotor blade diameter are provided. Butterworth. U. 79.S. James & James.L. wind speed.
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