computational Methods for Electric Power Systems MariesQ L. Crow, Editor, CRC Press, 2010, second edition ISBN 978 1 42008660 7 This book, intended for the graduate level, has seven chapters, Each chapter covers the relevant mathematical methods followed by power system applications, Chapter I gives a brief introduction on the increasingly complex nature of the power grid and the purpose for writing this book as a text for a graduate course on steady-state and dynamic studies, Chapter 2 provides an overview of solution methods for linear systems. The solution methods come in two types: direct and iterative. It starts with direct methods by introducing Gaussian elimination and then moves to LU factorization. Iterative methods, such as relaxation, conjugate gradient, and generalized minimal residual algorithms, are covered after a brief discussion of condition numbers and error propagation. Each method is mathematically explained and then implemented in several examples. Chapter 3 provides an introduction to systems of nonlinear equations for steady-state analysis. Three principal issues that arise with iterative methods are discussed: I) if the iterative process is well defined, 2) if the iterations converge to a desired solution, and 3) how economical is the entire solution process. It then covers fixed-point iteration and Newton-Raphson iteration in great detaiL Continuation methods are covered as ways to widen the region of convergence for a given iterative method, The second method, which can be considered an approximation of the Newton-Raphson method, is covered as DIKilai Ohjt'c/ Idenrijier 10. JJ09lMPE. 2010
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to multistep methods with extra time spent on Adams' and Gear's methods. Accuracy, error. and numerical stability analyses are then covered in greater detaiL Stiff systems with a wide range of time-varying dynamics are explained, The issue of stepsize selection is addressed as well as differential-algebraic equations, The chapter ends with two power systems applications of numerical integration methods: transient stability and midterm stability analyses. Chapter 6 is an overview of some optimization methods commonly used in power systems analysis. It begins with least squares state estimation, including weighted least squares and bad data detection. It then covers linear programming and explains the simplex method and interior point method. Some nonlinear programming methods are covered, limited to quadratic programming, steepest descent, and sequential quadratic programming. It ends with two important power system applications of optimization: optimal power flow and state estimation. Chapter 7 provides an overview of eigenvalue problems, which are important in the small-signal stability of a system. The chapter begins by introducing the power method, one of the most common methods of finding the dominant leo els of power systems, such The eigenvalue of a matrix. It as those used in Newtonnext covers the QR algoRaphson methods, are composed of very large rithm that solves the eigenvalue problem based sparse matrices. Such aprcle\!dnt plications are discussed at on a sequence of simisimple, larity transforms with the end of the chapter. The pictorial depiction of spare orthogonal matrices. The it matrix representation Arnoldi method is disis excellent. cussed as a way to compute a certain number of Chapter 5 is an overview of numerical inteeigenvalues on large ingration methods. These terconnected systems like methods are required to solve for the power system. The chapter then dynamic systems when modeled by covers singular value decomposition ordinary differential equations. Each followed by modal identification. Apmethod is evaluated on the criteria plications to the power system are only of numerical accuracy, stability, and briefly covered at the end, focusing on efficiency. The chapter begins with participation factors. one-step methods such as forwardThis 289-page book ends with a list of Euler and Runge-Kutta, It then moves 58 references and an appendix of terms,
it is often faster. Since Newton-Raphson iteration can require the computation of many partial derivatives, numerical differentiation is covered as well. The remainder of the chapter is devoted to the application of Newton-Raphson algorithms to power systems including decoupled and fast decoupled power flow, Modeling of regulating transformers is covered, as they are the most common controllers found in the power system network, Continuation me thods for the Newton-Raphson power flow using PV curves are discussed as the Newton-Raphson method often fails to converge for heavily loaded systems. The extension of the Newton-Raphson method to unbalanced three-phase power flow is briefly mentioned. Chapter 4 provides an overview of sparse matrix solution techniques including storage methods, representation, and ordering schemes, Three main ordering schemes, 0, I, and II, are covered with a brief mention of additional modification to these schemes for increased computation time. Sparse matrix techniques are important as many mathematical mod-
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Comments The title of the book is relevant and simple. though it may appear classical. Perhaps "Mathematical Foundations and Methods for Power System Analysis and Studies" could have conveyed the intent beller. The indusion of new material. namely. generalized minimal residual (GERES) methods, numerical differentiation, secant method. homotopy and continuation methods. power method for calculating dominant eigenvalues. singular-value decomposition method and pseudo-inverses, and matrix pencil method in the second edition enriches the book. In many universities, computer methods in power systems are introduced without a pre-requisite in numerical analysis. The author should be commended for including the right amount of mathematical rigor for the methods covered in the book and the logical flow
of material in all chapters is excellent. The many simple examples in each chapter are excellent because in this way the student gets a good gra~p and insight into the materiI" al in each chapter. GenerII" I ')
Though the author recommends the course at the graduate level. I would suggest that Chapters 1-4 be adopted in a senior-level course. since the material is covered in a clear and lucid manner. ally. many of these are not The book is limited resourc (' to steady-state and dycovered in standard books for power system analysis. Illdt('ritl! for namic analysis and studThe author offers ies only. The important grddudtl' many constructive sugstudy of fault analysis gestions in comparing using Zbus is missing and different methods for a studeflt in my opinion, the fault given application throughor shorl-circuit analysis out the book. This is good is fundamental for the resource material for a d qucllifving design, planning, and opgraduate student preparing eration of power systems. for a qualifying exam or e X n 1 . In addition. numerical for a practicing engineer methods for electromagand perhaps even a nonpower engineer netic transients are not covered and working in a power engineering indus- symbols. such as for inductors. are not try could use it for self-paced learning. consistently used where standard IEEE
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At Gonzaga, our courses are developed and taught by industry experts to answer the question:
What does the power industry engineer of the future need to know now?
march/april 2011
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recommended symbols would help. The results from using commercial packages are as accurate as the assumptions made and the models used. This point could be stressed so that the students could be made aware of this fact. The applications covered. and also not covered. in the book take a new meaning and deserve new approaches and treatment because of the unprecedented and complex changes taking place in the smart grid. I would strongly recommend that the author consider revising the book quickly to make it an excellent textbook for future use. This is even more important when the student interest in power and energy is increasing dramatically and rapidly_ Additionally, here are the recommendations for each chapter: v Chapter I could be expanded to give a better and global view of the nature of the power systems and the need for applications so that students and other users of the book can appreciate the material covered in it. v The potential applications for methods covered in Chapter 2 are not apparent. Which ones are widely used in practice? Perhaps a list of applications and some minimal level of description of the newer methods in the least would be welcome.
v v v
What is the purpose of including the secant method described in Chapter 3. and what is the potential application fLH this method'~ Do any of the commercial packages use if? These questions are also valid for the newer methods introduced in the book. Distribution systems are notoriously unbalanced due to many single-phase laterals and random demand profiles. They have other serious power quality issues too. I commend the author for introducing the three-phase power flow analysis, though it could be covered in greater detail. Perhaps a more detailed treatment of this ubiquitous study along with three-phase harmonic flow studies could be added in the next edition. The treatment of a regulating transformer model covered as part of Section 3.6 is excellent. Chapter 4 is covered very well and more comprehensively than other recent books. In Chapter 5, an example on small signal stability problems should have been included. The topics in Chapter 6 are covered well. The only comment I have is that the optimization section should have differentiated
between convex solving methods on convex problems like lea~t squares. linear programming. and quadratic programming. from nonconvex solving methods such as sequential quadratic programming and steepest descent methods. v The list of references at the end of the book is comprehensive. but some references do not have page numbers included. The author could consider including other textbooks on this subject by Ahmed EI-Abiad, Gerald T. Heydt Homer Brown. and other recent books in the reference list to make the reference resource richer. In summary. the book has many positive contributions to be recommended as a textbook for a senior- or graduate-level course_ I must highlight the mathematical rigor the author strived to include throughout the book and the inclusion of many simple examples and problems at the end of each chapter is creditable. Some of the applications could be described in more detail. Finally, if the author expands and modifies it for future power grid applications this book is bound to be a classic piece.
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-55 (ManiJ Venkata
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