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Power System State Estimation-Theory and Implementations [Book Review]

Power System State Estimation—Theory and Implementations by Ali Abur and Antonio Gómez Expósito, Marcel Dekker, Inc., 2004. ISBN: 0-8247-5570-7. This is a comprehensive book on state estimation intended for students and practitioners in power engineering. It is also of high interest for applied mathematicians working in statistics and operations research. Easy-to-read and enjoyable in most chapters, the book is well structured and most theoretical developments are illustrated with insightful examples. State-of-the-art developments as well as historical references are provided. Certainly, this book constitutes a fundamental addition to the state estimation literature by two well-known experts on the subject. No such comprehensive, detailed, and readable book was previously available. The book assumes basic knowledge of power system analysis, calculus, algebra, and statistics. Chapter 1 provides an insightful overview of the security framework where the state estimation tool is a key requirement. The energy management system of a modern electric energy system is briefly described and the need for state estimation naturally established. Chapter 2 is devoted to the formulation and the basic solution technique for the state estimation problem, i.e., the problem of finding the most likely values for voltage magnitudes and angles (system state) throughout a power network, given an appropriate set of measurements. This set of measurements typically includes voltage magnitudes and active and reactive power injections in nodes and flows in lines. The state is normally estimated by minimizing measurement errors in a least squares sense and weighting measurements according to quality; hence, the denomination weighted least squares algorithm. First, component modeling is reviewed and measurement assumptions are established. Then, technicalities pertaining to the efficient solution of the resulting system of nonlinear equations, denominated normal equations, are orderly considered and include: characterization of the measurement Jacobian, the gain matrix, Cholesky factorization, and the efficient solution of sparse linear systems of equation. The chapter concludes with the decoupled formulation of the weighted least squares algorithm and the dc formulation. Chapter 3 addresses alternative weighted least squares formulations to the state estimation problem. Those alternative formulations are justified for the potential problems encountered when solving the normal equations. These alternative methods either consider a different factorization procedure to solve the normal equations or propose a modified formulation. Alternative factorizations include: orthogonal factorization, hybrid Choleskyorthogonal factorization, and others. Particularly relevant among the modified formulations is the equality constrained weighted least squares model, which implicitly includes equality constraints for all or a subset of measurements. Variations of this method are discussed. The chapter closes with a discussion on the advantages and disadvantages of the different formulations. Chapter 4 is devoted to observability; i.e., the problem of identifying if the set of available measurements is enough to estimate the state of the system. Note that observability is related to not only the number of measurements but also to their types and locations. Two numerical techniques are provided, one based on branch variables and the other on nodal variables. Procedures to identify observable islands are provided if the system under analysis is not observable. Furthermore, a technique bo ok re vi ew