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Mathematical Programming for Power Systems Operation
Mathematical Programming for Power Systems Operation
From Theory to Applications in Python
Alejandro GarcésTechnological University of PereiraPereira, Colombia
This edition first published 2022
© 2022 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.
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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
Contents
1 Cover
7 1 Power systems operation1.1 Mathematical programming for power systems operation1.2 Continuous models1.2.1 Economic and environmental dispatch1.2.2 Hydrothermal dispatch1.2.3 Effect of the grid constraints1.2.4 Optimal power flow1.2.5 Hosting capacity1.2.6 Demand-side management1.2.7 Energy storage management1.2.8 State estimation and grid identification1.3 Binary problems in power systems operation1.3.1 Unit commitment1.3.2 Optimal placement of distributed generation and capacitors1.3.3 Primary feeder reconfiguration and topology identification1.3.4 Phase balancing1.4 Real-time implementation1.5 Using Python
8 Part I Mathematical programming2 A brief introduction to mathematical optimization2.1 About sets and functions2.2 Norms2.3 Global and local optimum2.4 Maximum and minimum values of continuous functions2.5 The gradient method2.6 Lagrange multipliers2.7 The Newton’s method2.8 Further readings2.9 Exercises3 Convex optimization3.1 Convex sets3.2 Convex functions3.3 Convex optimization problems3.4 Global optimum and uniqueness of the solution3.5 Duality3.6 Further readings3.7 Exercises4 Convex Programming in Python4.1 Python for convex optimization4.2 Linear programming4.3 Quadratic forms4.4 Semidefinite matrices4.5 Solving quadratic programming problems4.6 Complex variables4.7 What is inside the box?4.8 Mixed-integer programming problems4.9 Transforming MINLP into MILP4.10 Further readings4.11 Exercises5 Conic optimization5.1 Convex cones5.2 Second-order cone optimization5.2.1 Duality in SOC problems5.3 Semidefinite programming5.3.1 Trace, determinant, and the Shur complement5.3.2 Cone of semidefinite matrices5.3.3 Duality in SDP5.4 Semidefinite approximations5.5 Polynomial optimization5.6 Further readings5.7 Exercises6 Robust optimization6.1 Stochastic vs robust optimization6.1.1 Stochastic approach6.1.2 Robust approach6.2 Polyhedral uncertainty6.3 Linear problems with norm uncertainty6.4 Defining the uncertainty set6.5 Further readings6.6 Exercises
9 Part II Power systems operation7 Economic dispatch of thermal units7.1 Economic dispatch7.2 Environmental dispatch7.3 Effect of the grid7.4 Loss equation7.5 Further readings7.6 Exercises8 Unit commitment8.1 Problem definition8.2 Basic unit commitment model8.3 Additional constraints8.4 Effect of the grid8.5 Further readings8.6 Exercises9 Hydrothermal scheduling9.1 Short-term hydrothermal coordination9.2 Basic hydrothermal coordination9.3 Non-linear models9.4 Hydraulic chains9.5 Pumped hydroelectric storage9.6 Further readings9.7 Exercises10 Optimal power flow10.1 OPF in power distribution grids10.1.1 A brief review of power flow analysis10.2
