Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry

Power industry deregulation has now generally been accepted by governments, utilities, system operators, suppliers, and customers as well as the researchers in this area. It has also been acknowledged that operational paradigms require changes. These changes have occurred, as will more in the future, as electricity markets evolve and further mature. In all of these developments, one of the major and critical tools for the analysis of electricity markets has been optimization; its potential for analyzing various complex issues of electricity markets in an optimization framework has been recognized. The optimal power flow is the best example of how classical power system models have been reconfigured for analysis of complex electricity market issues.

While these developments have been taking place, the utility professionals and power engineers in general felt the need for a better understanding of the principles of electricity markets operation and also their empowerment by the tool that is most required: optimization. Although there is excellent literature on optimization available, they have largely approached the topic with pure mathematical rigor, which often requires undertaking graduate level programs in the subject. Hence, for years the topic of optimization (with the terms such as Lagrange multipliers, Kuhn-Tucker's conditions, etc.) remained taboo to power professionals. Only a few brave ones would really venture to understand how linear programming, nonlinear programming, or, say, integer programming problems could address the power system issues and their solution methods.

It is against this backdrop that Narayan Rau's book, Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry, appears in the libraries. The text has evolved from an industrial course delivered to professionals and is therefore clearly targeted to the professionals working in the field who require, as stated by Rau in the introduction, a quick sketch of popular procedures rather than mathematical rigor. One of the major attractions of the book, which must be mentioned at the outset, is the provision of a novel self-learning environment for the professionals through the use of Excel spreadsheets to solve optimization problems. These Excel spreadsheets are available for download from Wiley's ftp site: ftp://ftp.wiley.com/public/sci_tech_med/electric_power/.

The book is divided into three parts: the first deals with mathematical background, the second with linear optimization, and the third with nonlinear optimization. The first part includes discussions on matrix theory and vector spaces, eigenvalues and eigenvectors, and linear transformations. Rau discusses a broad range of topics under a single umbrella, provides concise mathematical discussions for each, and brings forth the key mathematical relationships and concepts, those that are required by power engineers on a day-to-day basis. Another interesting feature is the introduction of Excel worksheets to solve the mathematical problems, such as the determination of eigenvalues or even to determine the eigenvectors of a matrix.

The second part of the book presents linear optimization problems including the simplex method of solution (with a substantial detail on the background to this important class of problems), the concept of duality, the transportation problem, etc. This section also provides a full chapter on solved linear programming problems, including the electricity market dispatch problem considering the transmission network, the (dc) optimal power flow problem, the inter-region dispatch problem, and so on. It must be mentioned that all the Excel files available from the ftp site are very well designed and provides a very good understanding of the text material. The reader has the full opportunity to work out the problems on his/her own and learn the topic in a very practical manner.

The third section of the book deals with nonlinear optimization and includes four chapters. In chapter 5, Rau provides a comprehensive background to this class of problems, including the concept of the gradient, the Jacobian and Hessian matrix formulations, Taylor series expansions, solution of nonlinear equations using the Jacobian matrix (for solving load flow problems), and also extreme points of multivariate functions, saddle nodes. In the subsequent chapter, Rau proceeds to discuss the unconstrained nonlinear optimization problems and their solution using the univariate method, the Powell's method based on pattern search, the steepest descent method and the Newton's method in detail, and with many nicely supported examples. Further in chapter 7, Rau discusses the class of constrained nonlinear optimization problems in which the concept of Langrange multipliers and the Kuhn-Tucker conditions are introduced and explained (as with every other problem) using Excel worksheet examples, the quadratic programming problem and its solution method using linear programs, the gradient projection methods, and the sequential linear and quadratic programming problems.

The best part of the third section is the last chapter on applications (chapter 8). Here, Rau takes up several examples on nonlinear optimization such as the transmission voltage optimization, the optimal power dispatch and the (ac) optimal power flow problem, the concept of locational marginal prices and how to determine them, the active and reactive power optimization problem, loss allocation, and even a state estimation problem. All the problems are discussed with appropriate examples, Excel worksheets, and supporting calculations.

Finally, and keeping in mind that the book could be attracting a significant readership of power utility professionals who may not be electrical engineers by training, Rau provides in the appendices an overview and background to electricity fundamentals, which should be very helpful to many readers.

It is apparent that Rau has spent years in the profession handling optimization methods and optimization applications to power system problems and has thus developed great expertise in the field, as shown in the way he simplifies the descriptions of the problems and in how he develops the basic optimization problems in easy-to-understand Excel spreadsheets.

This book is clearly an important contribution to the field of power systems analysis and in particular to the area of electricity markets analysis, and readers looking for a self-learning kit for learning optimization as well as the fundamentals of electricity markets, can expect a great deal of benefit maximization from the text. The text is lucid and very pedagogic, which increases its readability highly, and coupled with the examples and Excel worksheets should provide the reader with a pleasant learning experience.

Reviewed by
Dr. Kankar Bhattacharya
University of Waterloo, Canada