Computational Methods for Electric Power Systems  book cover
3rd Edition

Computational Methods for Electric Power Systems

ISBN 9781498711593
Published November 18, 2015 by CRC Press
345 Pages 87 B/W Illustrations

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Book Description

Computational Methods for Electric Power Systems introduces computational methods that form the basis of many analytical studies in power systems. The book provides the background for a number of widely used algorithms that underlie several commercial software packages, linking concepts to power system applications. By understanding the theory behind many of the algorithms, the reader can make better use of the software and make more informed decisions (e.g., choice of integration method and step size in simulation packages).

This Third Edition contains new material on preconditioners for linear iterative methods, Broyden’s method, and Jacobian-free Newton–Krylov methods. It includes additional problems and examples, as well as updated examples on sparse lower-upper (LU) factorization. It also adds coverage of the eigensystem realization algorithm and the double-shift method for computing complex eigenvalues.

Table of Contents


The Solution of Linear Systems
Gaussian Elimination
LU Factorization
Condition Numbers and Error Propagation
Stationary Iterative Methods
Conjugate Gradient Methods
Generalized Minimal Residual Algorithm
Preconditioners for Iterative Methods

Systems of Nonlinear Equations
Fixed-Point Iteration
Newton–Raphson Iteration
Quasi-Newton Methods
Continuation Methods
Power System Applications

Sparse Matrix Solution Techniques
Storage Methods
Sparse Matrix Representation
Ordering Schemes
Power System Applications

Numerical Integration
One-Step Methods
Multistep Methods
Accuracy and Error Analysis
Numerical Stability Analysis
Stiff Systems
Step Size Selection
Differential-Algebraic Equations
Power System Applications

Least Squares State Estimation
Linear Programming
Nonlinear Programming
Power System Applications

Eigenvalue Problems
The Power Method
The QR Algorithm
Arnoldi Methods
Singular Value Decomposition
Modal Identification
Power System Applications


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Mariesa L. Crow is a professor of electrical engineering at the Missouri University of Science and Technology, Rolla, USA. Dr. Crow is director of the Energy Research and Development Center. Her areas of research include computer-aided analysis of power systems; dynamics and security analysis; voltage stability; computational algorithms for analyzing stressed, non-linear, non-continuous systems; power-electronic applications in bulk power systems (FACTS); and parameter estimation.


"This book analyzes the most relevant mathematical tools for power system analysis. It is well written, well balanced, and treats the mathematical issues with a good degree of rigor and clarity. The numerical examples are illustrative and useful. ... I’m considering to adopt this book for my course, since it condenses in a unique reference the mathematical backbone of the most important power system analysis tools."
—Alfredo Vaccaro, University of Sannio, Benevento, Italy

"This book fits well into my short circuit analysis course (ECE610). ... The textbook flows, and it is a good reference book even if it is not used as a textbook. ... This book is a must for any power systems faculty. ... This textbook can be a great complement to other textbooks that do not cover the material in depth. The sequential examples presented make this book quite friendly to the students."
—Bruno Osorno, California State University, Northridge, USA

"… presents a nonconventional approach to teach or understand power system analysis: mathematics first, then each topic is related to power system applications. … This approach is ideal for researchers and graduate students, and can immediately lead them into the power system field. … Algorithms, however sophisticated, are explained with clarity, along with numerical examples to help the reader get the point."
—Lingling Fan, University of South Florida, Tampa, USA

"… an excellent combination of topics regarding computational aspects and numerical algorithms for power system analysis, operations, and control. … very useful for me to teach ECE530 [on analysis techniques for large-scale energy systems]."
—Hao Zhu, University of Illinois, Urbana-Champaign, USA

"… an excellent textbook … for a graduate-level course in electric power engineering. … covers a broad range of topics related to computational methods for power systems. … contains very good problems for students’ homework. I highly recommend this book for graduate teaching in electric power."
—Fangxing Li, University of Tennessee, Knoxville, USA

"This book is complete in respect to the tools used for power system engineering. ... It is compact and nicely written. ... Many commercial packages are available in the market. They are just used in input-output form. Students never get the feeling of the methods used inside. It is required to understand the methods. [Thus,] this book is very useful."
—Professor SN Singh, Department of Electrical Engineering, Indian Institute of Technology Kanpur