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Space Vector Pulse Width Modulation Based Indirect Vector Control of Induction Motor Drive

The electrical machine that converts electrical energy into mechanical energy and vice versa, is the workhorse in a drive system. Induction motors have been used for over a century because of their simplicity, ruggedness and efficiency [1]. The asynchronous or induction motor is the most widely used electrical drive. Separately excited dc drives are simpler in control because independent control of flux and torque can be brought about [2]. In contrast, induction motors involve a coordinated control of stator current magnitude and the phase, making it a complex control. The stator flux linkages can be resolved along any frame of reference. This requires the position of the flux linkages at every instant. Then the control of the ac machine is very similar to that of separately excited dc motor. Since this control involves field coordinates it is also called field oriented control (Vector Control) [1,2]. Depending on the method of measurement, the vector control is divided into two subcategories: direct and indirect vector control. In direct vector control, the flux measurement is done by using the flux sensing coils or the Hall devices. The most common method is indirect vector control. In this method, the flux angle is not measured directly, but is estimated from the equivalent circuit model and from measurements of the rotor speed, the stator current and the voltage [2].


Introduction
The electrical machine that converts electrical energy into mechanical energy and vice versa, is the workhorse in a drive system. Induction motors have been used for over a century because of their simplicity, ruggedness and efficiency [1]. The asynchronous or induction motor is the most widely used electrical drive. Separately excited dc drives are simpler in control because independent control of flux and torque can be brought about [2]. In contrast, induction motors involve a coordinated control of stator current magnitude and the phase, making it a complex control. The stator flux linkages can be resolved along any frame of reference. This requires the position of the flux linkages at every instant. Then the control of the ac machine is very similar to that of separately excited dc motor. Since this control involves field coordinates it is also called field oriented control (Vector Control) [1,2]. Depending on the method of measurement, the vector control is divided into two subcategories: direct and indirect vector control. In direct vector control, the flux measurement is done by using the flux sensing coils or the Hall devices. The most common method is indirect vector control. In this method, the flux angle is not measured directly, but is estimated from the equivalent circuit model and from measurements of the rotor speed, the stator current and the voltage [2]. The Main purpose of two level inverter topologies is to provide a three phase voltage source, where the amplitude, phase, and frequency of the voltages should always be controllable [3]. PWM methods, the carrier-based PWM is very popular due to its simplicity of implementation, known harmonic waveform characteristics, and low harmonic distortion [3]. Space vector pulse width modulation (SVPWM) technique is widely used in inverter and rectifier controls [4,5]. In a space-vector PWM inverter, which is widely used, the voltage utilization factor can be increased to 0.906, normalized to that of the six step operation [6]. In the conventional Space Vector PWM technique complexity is involved due to sector identification and angle calculation. To reduce this complexity various discontinuous algorithms are proposed [5,6]. This paper presents the different Space Vector PWM techniques, which can be applied to the three phase VSI fed indirect vector controlled induction motor (IM) drive. The performance of the Induction Motor (IM) is analyzed in steady state and transient conditions.

Induction Motor Modelling
The steady-state model and equivalent circuit are useful for studying the performance of machine in steady state. This implies that all electrical transients are neglected during load changes and stator frequency variations. The dynamic model of IM is derived by using a two-phase motor in direct and quadrature axes, where ds−qs correspond to stator direct and quadrature axes, and dr −qr correspond to rotor direct and quadrature axes [3].
The dynamic analysis and description of revolving field machines is supported by well established theories. An Induction Motor of uniform air gap, with sinusoidal distribution of mmf is considered. The saturation effect and parameter changes are neglected [7].

Abstract
This paper presents the implementation of a different SPACE VECTOR PWM techniques applied to the indirect vector controlled induction motor (IM) drive involves decoupling of the stator current into torque and flux producing components of an induction motor. The drive control generally involves a fixed gain proportional-integral controller. Space vector pulse width modulation technique is widely used in inverter and rectifier controls. The electromagnetic torque obtained from machine flux linkages and currents is as: Where Te, P, Ψdr, Ψqr are the electromagnetic torque, number of poles, rotor d-q axes fluxes respectively. The electromagnetic dynamic equation describing the mechanical model of the induction motor is given by Where J, T L , B, ω m are the moment of inertia of motor and the load torque, the friction coefficient and the mechanical speed. The equations (1) to (7) form the mathematical model equations of a three phase induction motor.

Indirect Vector Control
In the indirect vector control the unit vector signals (Cos ε θ and Sin ε θ ) are generated in feed forward manner, indirect vector control is very popular in industrial application. The

Space Vector Pulse Width Modulation
The SVPWM technique can increase the fundamental component by up to 27.39% that of SPWM. The fundamental Voltage can be increased up to a square wave mode where a modulation index of unity is reached. SVPWM is a form of PWM proposed in the mid-1980s that is more efficient compared to natural and regularly sampled PWM three-phase mathematical system can be represented by a space space vector. For example, given a set of threephase voltages, space vector can defined by Where ( ) V t are three sinusoidal voltages of the same amplitude and frequency but with +1200 phase shifts.
In the space vector modulation, a three phase two level inverter can be driven to eight switching states where the inverter has six active states (1-6) and two zero states (0 and 7). Repeating the same procedure, we can find the remaining active non-active states.
The three-phase inverter is therefore controlled by six switches and eight inverter configurations. The eight inverter states can transformed into eight corresponding space vectors. In each configuration, the vector identification uses a 'O' to represent the negative phase voltage level and a '1' to represent the positive phase voltage level.
The relationship between the space vector and the corresponding switches states is given in Table 1 and Figure 3. In addition, the switches in one inverter branch are in controlled in a complementary fashion (1 if the switch is on and 0 if it is off). Therefore, Output patterns for each sector are based on a symmetrical sequence. There are different schemes in space vector PWM and they are based on their repeating duty distribution. Based on the equations for T a , T b , T 0, T 7 , and according to the principle of symmetrical PWM, the switching sequence in Table 1 is shown for the upper and lower switches.

Proposed Discontinuous SVPWM Technique
Continuous PWM (CPWM) suffers from the drawbacks like computational burden and inferior performance at high modulation indices. Moreover continuous PWM (CPWM) method the switching losses of the inverter are also high. Hence to reduce the switching losses and to improve the performance in high modulation region several discontinuous PWM (DPWM) methods have been reported. It uses the concept of imaginary switching times. The imaginary switching time periods are proportional to the instantaneous values of the reference phase voltages are defined as Where T S is the sampling period and V dc is the dc link voltage. V a , V b, V c are the phase voltages. The active vector switching times T 1 and T 2 may be expressed as , , x as bs cs

T T T T ∈
and is neither maximum nor minimum switching time. The effective time is the duration in which the reference voltage vector lies in the corresponding active states, and is the difference between the maximum and minimum switching times as given

Sector
Upper Switches: S1,S3,S5 Lower Switches S4,S6,S2 In the proposed method the zero state time will be divided between two zero states as T 0 μ for V 0 and T 0 (1-μ) for V 7 respectively, where μ lies between 0 and 1. The μ can be defined as μ = 1-0.5(1 + sg n (cos3(ωt + δ)) where ω is the angular frequency of the reference voltage, sgn(y) is the sign function, sgn(y) is 1, 0.0 and -1 when y is positive, zero and negative respectively. The modulation phase angle is represented by δ. When μ = 1 any one of the phases is clamped to the positive bus for 120 degrees and when and μ = 0 any one of the phases is clamped to the negative bus for 120 degrees. When μ=0 and μ=1, DPWMMAX and DPWMMIN are obtained respectively and μ=0.5 results CPWM.

Simulation Results
To validate Space Vector Based indirect vector controlled induction motor drive. Indirect Vector controlled IM drive is implemented in       Table 2).
The figure shows that the stator current response of an IM, it reaches the Steady state reaches at 0.07 sec, currents are 2 Amp and the load torque of 2.5 N-M applied at 0.7 sec.
From the speed response the IM attains steady state at 0.07 sec and the speed is nearly at its rated speed i.e. 150 rad/sec. Until load is applied at 0.7 sec (Figures 9-12).

Conclusion
In This work, indirect vector controlled induction motor drive fed from two-level 3-phase Space Vector PWM inverter is implemented. SVPWM uses the dc bus voltage than SPWM. In Continuous PWM (CPWM) technique the switching losses of the inverter are high. To reduce the switching loss and complexity in CPWM technique DPWM techniques are implemented. The modulating waveforms of different DPWM sequences are obtained based on their clamping sequences. In DPWMMAX method, the clamping of 120° takes place at the middle of