Alejandro Garcés - Mathematical Programming for Power Systems Operation: From Theory to Applications in Python

Alejandro Garcs
Technological University of Pereira
Pereira, Colombia

This edition first published 2022

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Library of Congress Cataloging-in-Publication Data

A catalogue record for this book is available from the Library of Congress

Paperback ISBN: 9781119747260; ePub ISBN: 9781119747284;

ePDF ISBN: 9781119747277; oBook ISBN: 9781119747291

Cover image: Redlio Designs/Getty Images

Cover design by Wiley

Set in 9.5/12.5pt STIXTwoText by Integra Software Services Pvt. Ltd, Pondicherry, India

1. Introduction
2. Chapter 1
3. Chapter 2
4. Chapter 3
5. Chapter 4
6. Chapter 5
7. Chapter 6
8. Chapter 7
9. Chapter 8
10. Chapter 9
11. Chapter 10
12. Chapter 11
13. Chapter 12
14. Chapter 13
15. Appendix A
16. Appendix B

1. Chapter 2
2. Chapter 3
3. Chapter 4
4. Chapter 5
5. Chapter 6
6. Chapter 7
7. Chapter 8
8. Chapter 10
9. Chapter 11
10. Chapter 13
11. Appendix C

Throughout the writing of this book, I have received a great deal of support and assistance from many people. I would first like to thank my friends Lucas Paul Perez at Welltec, Adrian Correa at Universidad Javeriana in Bogot-Colombia, Ricardo Andres Bolaos at XM (the transmission system operator in Colombia), Raymundo Torres at Sintef-Norway, and Juan Carlos Bedoya at the Pacific Northwest National Laboratory (USA), who, in 2020 (during the COVID-19 pandemic), agreed to discuss some practical aspects associated to power system operation problems. The discussions during these video conferences were invaluable to improve the content of the book. I am also very grateful to my students, who are the primary motivation for writing this book. Special thanks to my former Ph.D. students, Danilo Montoya and Walter Julian Gil. Finally, I want to thank the Department of Electric Power Engineering at the Universidad Tecnolgica de Pereira in Colombia and the Von Humbolt Foundation in Germany for the financial support required to continue my research about the operation and control of power systems.

Alejandro Garcs

Electrification is the most outstanding engineering achievement in the 20th century, a well-deserved award if we consider the high complexity of generation, transmission, and distribution systems. An electric power system includes hundreds or even thousands of generation units, transformers, and transmission lines, located throughout an entire country and operated continuously 24 hours per day. Running such a complex system is a great challenge that requires using advanced mathematical techniques.

All industrial systems seek to increase their competitiveness by improving their efficiency. Electric power systems are not the exception. We can improve efficiency by introducing new technologies but also by implementing mathematical optimization models into daily operation. In every mathematical programming model, we require to perform four critical stages depicted in Figure . The first stage is an informed review of reality, identifying opportunities for improvement. This stage may include conversations with experts in order to establish the available data and the variables that are subject to be optimized. The second stage is the formulation of an optimization model as given below:

(0.1)

Where x is the vector of decision variables, f is the objective function and, is the set of feasible solutions. Going from stage one (reality) to stage two (model) is more of an art than a science. One problem may have different models and different degrees of complexity. Practice and experience are required to master this stage, as some models are easier to solve than others. Subsequently, the third stage consists of the implementation of the mathematical model into a software. After that, the fourth stage is the analysis of results in the context of the real problem.

Figure 0.1 Stages of solving an optimization problem.

This book will focus on stages two and three, associated with power system operations models. In particular, we are interested in models with a geometric characteristic called convexity, that present several advantages, namely:

• We can guarantee the global optimum and unique solution under well-defined conditions. This aspect is interesting from both theoretical and practical points of view. In general, a global optimum advisable in real operation problems.
• There are efficient algorithms for solving convex problems. In addition, we can guarantee convergence of these algorithms. This is a critical aspect for operation problems where the algorithm requires to be solved in real-time.