Research & Management Science

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1 EInternational E Series in Operations Research & Management Science Series Editor: Frederick S. Hillier Stanford University, CA, USA Special Editorial Consultant: Camille C. Price Stephen F. Austin State University, TX, USA This book was recommended by Dr. Price For further volumes:

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3 Antonio J. Conejo Miguel Carrión Juan M. Morales Decision Making Under Uncertainty in Electricity Markets

4 Antonio J. Conejo Miguel Carrión Department of Electrical Engineering Department of Electrical Engineering University of Castilla La Mancha University of Castilla La Mancha Campus Universitario s/n Campus Fábrica de Armas s/n Ciudad Real, Spain Toledo, Spain Juan M. Morales Department of Electrical Engineering University of Castilla La Mancha Campus Universitario s/n Ciudad Real, Spain ISSN ISBN e-isbn DOI / Springer New York Dordrecht Heidelberg London Library of Congress Control Number: Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 To Olaia, Mireia and Núria To Mayte, Toño, Miguel and Toñi To my parents, Cloti and Pepe

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7 Preface Most relevant decisions to be made by market agents within an energy market involve a significant level of data uncertainty. For agents to make informed decisions within such a context, it is fundamental to model properly the nature and consequences of the uncertainty involved. Stochastic programming provides an appropriate mathematical modeling framework both to characterize the uncertainty and to derive informed decisions. Additionally, decision outcomes need to be characterized not only by their expected values but also by their variability levels, thus risk control of outcome volatility is needed and can be achieved using appropriate risk measures. This book provides a number of stochastic programming models for optimal decision making under uncertainty in electricity markets. Risk control is embedded into most of the presented models, which involve producers, retailers, consumers, and the market/system operator. Particular attention is paid to electric energy systems with a large integration of non-dispatchable sources, such as wind power plants. The contents of this book are briefly summarized below. Chapter 1 describes the organization of electricity markets, which encompasses short-term trading in the pool and long-term commerce through the futures market and bilateral contracting. It provides a description of the role and aim of each of the market agents, including producers, retailers, consumers, the market operator, and the independent system operator. From this chapter, it is inferred that most decisions to be made by market agents involve a significant amount of uncertain data. Chapter 2 provides a summary of stochastic programming techniques that enable informed decision making under a significant level of uncertainty on problem parameters. Both two-stage and multi-stage problems are addressed. Indexes to characterize the advantages of an stochastic programming approach vs. a deterministic one are defined and illustrated. Chapter 3 describes diverse techniques to characterize via stochastic processes the uncertainty plaguing the data needed for decision making. Specifically, it provides procedures for scenario generation and scenario reduction, vii

8 viii Preface being a scenario the actual realization of uncertain parameters along the time. Techniques to take into account spatial correlations among uncertain data are also provided. Chapter 4 presents and analyzes different risk measures that allow controlling the level of profit variability of producers and retailers, and the level of cost variability of consumers. In other words, it provides techniques to resolve the trade-off between the expected value of the profit/cost and the variability of such a profit/cost. Chapter 5 provides techniques and procedures to construct offering curves for power producers participating in an electricity pool. Diverse trading floors within the pool are considered, in particular, the day-ahead market, the regulation market, and one adjustment market. Chapter 6 complements Chapter 5 providing offering curves for producers of an intermittent non-dispatchable nature, such as a wind power producer. It describes strategies to build optimal offering curves for the day-ahead market and the adjustment markets, placing particular emphasis on the effect of the balancing mechanism. Such a mechanism is required to restore energy balance as a result of the intermittent nature of non-dispatchable production units. Chapter 7 analyzes the involvement of power producers in long-term markets, such as a futures market. It describes how a producer can hedge its profit volatility using futures market products, e.g., forward contracts. It also analyzes the effect on forward contracting of the unexpected failure of any production unit. Specifically, it provides algorithms to select optimally which forward contracts to sign. Chapter 8 considers an electricity retailer that buys energy through the futures market and in the pool to supply the electricity needs of its clients. It analyzes the complex task of any retailer that needs to offer its clients the lowest possible prices while facing both the volatility of pool prices and the inflexibility of the futures market commitments. It provides algorithms to calculate client prices and to select the forward contracts to be signed. Chapter 9 addresses the electricity procurement problem faced by a large consumer that may buy energy in the pool at volatile prices or through bilateral contracts. Bilateral contracts are long-term agreements that eliminate price volatility, but prevent taking advantage of particularly low pool prices. This chapter provides algorithms to make informed decisions on contract signing and pool involvement. Chapter 10 describes and analyzes a multi-commodity market-clearing procedure based on stochastic programming to clear a day-ahead electricity market involving both energy and reserve. The reserve determination is based on an endogenous probabilistic criterion. Equipment failures are taken into account. Chapter 11 complements Chapter 10 by considering a multi-commodity market-clearing procedure particularly adapted for an electric energy system embedding a large amount of non-dispatchable producers. The uncertainty pertaining to these intermittent producers is comprehensively treated.

9 Preface ix It is relevant to note the interrelation of the chapters in this book. Chapter 1 describes the electricity marketplace that allows the interaction of producers, consumers, and retailers under the coordinating role of both the market and the system operators. The producer decision making is analyzed in Chapters 5, 6 and 7. Complementarily, the retailer decision-making process is examined in Chapter 8, while the decision making of the consumer is studied in Chapter 9. Chapters 10 and 11 describe the tools needed by the market/sytem operator to clear pool markets. Providing an appropriate background, Chapters 2, 3 and 4 give a detailed introduction to decision making under uncertainty using stochastic programming. Finally, Appendix A provides GAMS codes for some of the examples considered throughout the book, Appendix B describes the 24-bus system used in Chapters 10 and 11, and Appendix C provides solutions to selected endof-chapter exercises. For both teaching and learning purposes, the material in this book can be arranged in different manners depending on the interest of the reader, as indicated in the following: 1. Chapter 1 is recommended for readers not particularly familiar with electricity markets and their features. 2. Chapters 2-4 providing introductory material on stochastic programming and risk analysis are relevant for readers interested in the mathematical tools for decision making under uncertainty in electricity markets. 3. Chapters 5-7 on producer strategies for selling energy (and some ancillary services) in both short- and medium-term markets are relevant for readers interested in decision making under uncertainty for producers. 4. Chapter 8 on retailer trading strategies in futures markets is relevant for readers interested in decision making under uncertainty for retailers. 5. Chapter 9 on strategies for energy procurement by consumers in a medium-term time frame is relevant for readers interested in decision making under uncertainty for consumers. 6. Chapters 10 and 11 providing background and models to develop marketclearing tools to be used by market and system operators are relevant for readers interested in market-clearing algorithms. 7. Chapters 5, 6, 10 and 11 on short-term decision making problems involving the pool and pertaining to all market agents are relevant for readers interested in decision making in the pool. 8. Chapters 7-9 on medium-term problems involving futures markets and pertaining to all market agents are relevant for readers interested in decision making in futures markets. A course on decision making for producers may include Chapters 1-4 and Chapters 5-7, for retailers Chapters 1-4 and Chapter 8, and for consumers Chapters 1-4 and Chapter 9. A course on market-clearing algorithms may comprise Chapters 1-4 and Chapters 10 and 11. A course on short-term decision making (pool involvement) may include Chapters 1-4 and Chapters 5,

10 x Preface 6, 10 and 11, and on medium-term decision making (futures market involvement) may encompass Chapters 1-4 and Chapters 7-9. The exposition of the material in this book relies on many elaborated examples that enhance its clarity and facilitates the always hard learning process. Theoretical developments and formulations are motivated by these examples of illustrative, clarifying, or computational nature. Due to the widespread implementation of electricity markets worldwide, we feel that a book like this one is much needed within the energy engineering and economics communities. It may help graduate students and practitioners to learn the fundamentals of decision making under uncertainty in energy markets. We are grateful to a number of colleagues that have provided insightful comments and inspiring observations for the different chapters of this book. Particularly, we are grateful to Prof. Baldick from the University of Texas at Austin, US; Prof. Bouffard from the University of Manchester, UK; Dr. Barroso from PSR, Inc., Brazil; Prof. Fleten from the Norwegian University of Science and Technology, Norway; Prof. Kirschen from the University of Manchester, UK; Prof. Rosehart from the University of Calgary, Canada; Prof. Shahidehpour from the Illinois Institute of Technology, US; and Prof. Schultz from the University of Duisburg-Essen, Germany. We are particularly thankful to Antonio Canoyra, Ángel Caballero and Antonio de Andrés from Unión Fenosa Generación for many years of fruitful industry-university collaboration and for providing us with insightful comments, relevant observations, and pertinent suggestions throughout these years. We also thank our colleagues and students interested in decision making and electricity markets for providing us with a stimulating and creative interaction. We are grateful to Camille Price for encouraging us to write this book and to Fred Hillier for supporting this endeavor. Neil Levine from Springer, New York, has been most helpful with all practical matters. We are thankful to the Government of Castilla-La Mancha, Spain, for providing us with an outstanding research environment. We have dedicated a significant amount of resources, time and enthusiasm to create this book in the hope that it will be useful for the next generation of graduate students and practitioners interested in the fascinating topic of decision making under uncertainty in electricity markets. Ciudad Real and Toledo, Spain June A. J. Conejo M. Carrión J. M. Morales

11 Contents Preface vii 1 Electricity Markets Introduction Organization and Agents Market Organization Agents Pool Futures Market Reserve and Regulation Markets Time Framework and Uncertainty Decision Sequence Uncertainty Decision Making Consumer Retailer Producer Non-Dispatchable Producer Market Operator Independent System Operator Summary Exercises Stochastic Programming Fundamentals Introduction Random Variables Stochastic Processes Scenarios Stochastic Programming Problems Two-Stage Problems Multi-Stage Problems xi

12 xii Contents 2.6 Quality Metrics Expected Value of Perfect Information Value of the Stochastic Solution Out-of-Sample Assessment Risk Solving Stochastic Programming Problems Summary and Conclusions Exercises Uncertainty Characterization via Scenarios Introduction Scenario Generation Overview Scenario Generation using ARIMA Models Generating Scenarios for Unit Availability Quality of Scenario Subsets Scenario Reduction Motivation Scenario Reduction Using a Probability Distance Algorithm Scenario Generation for Dependent Stochastic Processes Overview Scenarios for contemporaneous or quasicontemporaneous stochastic processes Scenarios for non-contemporaneous stochastic processes Case Studies Electricity Price and Demand Wind Speeds at Multiple Sites Summary and Conclusions Exercises Risk Management Introduction Risk Control in Stochastic Programming Problems Risk-Neutral Decision Making Risk-Averse Decision Making Risk Measures Variance Shortfall Probability Expected Shortage Value-at-Risk Conditional Value-at-Risk Stochastic Dominance Summary and Conclusions

13 Contents xiii 4.5 Exercises Producer Pool Trading Introduction Decision Framework Uncertainty Characterization Day-ahead, Regulation, and Adjustment Prices Scenario Tree Pool Structure Day-Ahead Market Regulation Market Adjustment Market Producer Model Unit Constraints Expected Profit Risk Modeling Formulation Producer Pool Example Producer Pool Case Study Summary and Conclusions Notation Exercises Pool Trading for Wind Power Producers Introduction Decision Framework The Key Issues Mechanism for Imbalance Prices Revenue and Imbalance Cost Certainty Gain Effect Uncertainty Characterization Day-ahead, Adjustment, and Imbalance Prices Wind Power Production Scenario Tree Wind Producer Model Basic Model Offering Curves Risk Modeling Adjustment Market Formulation Wind Producer Example Wind Producer Case Study Summary and Conclusions Notation Exercises

14 xiv Contents 7 Futures Market Trading for Producers Introduction Decision Framework Uncertainty Characterization Pool Prices Unit Availability Scenario Tree Market Structure Futures Market Pool Producer Model Unit Constraints Unit Availability Energy Balance Expected Profit Risk Modeling Formulation Producer Futures Market Example. No Unit Unavailability Producer Futures Market Example. Unit Unavailability Producer Futures Market Case Study Summary and Conclusions Notation Exercises Medium-Term Retailer Trading Introduction Decision Framework Uncertainty Characterization Market Structure Futures Market Pool Retailer Model Client Modeling Price-Quota Curve Revenue from Selling to Clients Energy Balance Expected Profit Risk Modeling Formulation Retailer Example Retailer Case Study Summary and Conclusions Notation Exercises

15 Contents xv 9 Energy Procurement by Consumers Introduction Decision Framework and Uncertainty Model Decision Framework Pool Price and Demand Model Bilateral Contracts Pool Self-Production Energy Balance Non-anticipativity Expected Cost Risk Formulation Consumer Example Consumer Case Study Summary and Conclusions Notation Exercises Market Clearing Considering Equipment Failures Introduction Stochastic Security-Constrained Market Clearing Main Features Introducing Security Constraints Setting Reserve Requirements Solution Algorithm Security-Related Definitions Stochastic Security Metrics Probabilistic Metrics Security Criteria Based on the ELNS Market-Clearing Formulation Assumptions Variables Structure Objective function Electricity Market Constraints Real-Time Operating Constraints Linking constraints Formulation Computing Scenario Probabilities Market-Clearing Example Market-Clearing Case Study Summary and Conclusions Notation

16 xvi Contents Exercises Market Clearing Under Uncertainty: Wind Energy Introduction Wind Power Production A Look to the Near Future Wind Impact on System Security Accommodating Wind Uncertainty Computational Burden Market-Clearing Model Assumptions Wind Uncertainty Characterization Wind Uncertainty vs. Equipment Failures Breaking Down the Expected Cost Wind Spillage Cost Formulation Performance Metrics Average Benefit (AB) Average Uncertainty Cost (AUC) Net Average Benefit (NAB) Market-Clearing Example with Wind Generation Impact of wind generator location and network congestion Impact of wind spillage cost Impact of wind penetration and uncertainty levels Market-Clearing Case Study with Wind Generation Summary and Conclusions Notation Exercises A GAMS Codes A.1 Introduction A.2 GAMS code for the Producer Pool Example (Section 5.7) A.3 GAMS code for the Wind Producer Example (Section 6.6) A.4 GAMS code for the Producer Futures Market Example. No Unit Unavailability (Section 7.7) A.5 GAMS code for the Producer Futures Market Example. Unit Unavailability (Section 7.8) A.6 GAMS code for the Retailer Example (Section 8.7) A.7 GAMS code for the Consumer Example (Section 9.5) A.8 GAMS code for the Market-Clearing Example (Section 10.6) 466 A.9 GAMS code for the Market-Clearing Example with Wind Generation (Section 11.5)

17 Contents xvii B 24-Node System Data B.1 Network data B.2 Generator data B.3 Demand data C Exercise solutions C.1 Exercises from Chapter C.2 Exercises from Chapter C.3 Exercises from Chapter C.4 Exercises from Chapter C.5 Exercises from Chapter C.6 Exercises from Chapter C.7 Exercises from Chapter C.8 Exercises from Chapter C.9 Exercises from Chapter C.10 Exercises from Chapter References Index Biographies

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