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: www.springer.com/series/6161
Antonio J. Conejo Miguel Carrión Juan M. Morales Decision Making Under Uncertainty in Electricity Markets
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 13071 Ciudad Real, Spain 45071 Toledo, Spain Antonio.Conejo@uclm.es Miguel.Carrion@uclm.es Juan M. Morales Department of Electrical Engineering University of Castilla La Mancha Campus Universitario s/n 13071 Ciudad Real, Spain JuanMiguel.Morales@uclm.es ISSN 0884-8289 ISBN 978-1-4419-7420-4 e-isbn 978-1-4419-7421-1 DOI 10.1007/978-1-4419-7421-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010935724 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 (www.springer.com)
To Olaia, Mireia and Núria To Mayte, Toño, Miguel and Toñi To my parents, Cloti and Pepe
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
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.
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,
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 2010. A. J. Conejo M. Carrión J. M. Morales
Contents Preface....................................................... vii 1 Electricity Markets........................................ 1 1.1 Introduction.......................................... 1 1.2 Organization and Agents............................... 1 1.2.1 Market Organization............................ 2 1.2.2 Agents........................................ 4 1.2.3 Pool.......................................... 6 1.2.4 Futures Market................................. 9 1.2.5 Reserve and Regulation Markets.................. 11 1.3 Time Framework and Uncertainty....................... 13 1.3.1 Decision Sequence.............................. 13 1.3.2 Uncertainty.................................... 15 1.4 Decision Making....................................... 17 1.4.1 Consumer..................................... 17 1.4.2 Retailer....................................... 19 1.4.3 Producer...................................... 20 1.4.4 Non-Dispatchable Producer...................... 22 1.4.5 Market Operator............................... 23 1.4.6 Independent System Operator.................... 24 1.5 Summary............................................. 25 1.6 Exercises............................................. 25 2 Stochastic Programming Fundamentals.................... 27 2.1 Introduction.......................................... 27 2.2 Random Variables..................................... 29 2.3 Stochastic Processes................................... 31 2.4 Scenarios............................................. 32 2.5 Stochastic Programming Problems....................... 34 2.5.1 Two-Stage Problems............................ 34 2.5.2 Multi-Stage Problems........................... 39 xi
xii Contents 2.6 Quality Metrics........................................ 48 2.6.1 Expected Value of Perfect Information............ 49 2.6.2 Value of the Stochastic Solution.................. 52 2.6.3 Out-of-Sample Assessment....................... 57 2.7 Risk................................................. 58 2.8 Solving Stochastic Programming Problems................ 59 2.9 Summary and Conclusions.............................. 61 2.10 Exercises............................................. 61 3 Uncertainty Characterization via Scenarios................ 63 3.1 Introduction.......................................... 63 3.2 Scenario Generation.................................... 66 3.2.1 Overview...................................... 66 3.2.2 Scenario Generation using ARIMA Models......... 68 3.2.3 Generating Scenarios for Unit Availability......... 75 3.2.4 Quality of Scenario Subsets...................... 78 3.3 Scenario Reduction.................................... 80 3.3.1 Motivation..................................... 80 3.3.2 Scenario Reduction Using a Probability Distance... 81 3.3.3 Algorithm..................................... 82 3.4 Scenario Generation for Dependent Stochastic Processes.... 92 3.4.1 Overview...................................... 92 3.4.2 Scenarios for contemporaneous or quasicontemporaneous stochastic processes............. 94 3.4.3 Scenarios for non-contemporaneous stochastic processes...................................... 101 3.5 Case Studies.......................................... 103 3.5.1 Electricity Price and Demand.................... 103 3.5.2 Wind Speeds at Multiple Sites................... 108 3.6 Summary and Conclusions.............................. 115 3.7 Exercises............................................. 117 4 Risk Management......................................... 121 4.1 Introduction.......................................... 121 4.2 Risk Control in Stochastic Programming Problems......... 122 4.2.1 Risk-Neutral Decision Making.................... 122 4.2.2 Risk-Averse Decision Making..................... 126 4.3 Risk Measures......................................... 128 4.3.1 Variance....................................... 129 4.3.2 Shortfall Probability............................ 132 4.3.3 Expected Shortage.............................. 135 4.3.4 Value-at-Risk.................................. 139 4.3.5 Conditional Value-at-Risk....................... 142 4.3.6 Stochastic Dominance........................... 145 4.4 Summary and Conclusions.............................. 152
Contents xiii 4.5 Exercises............................................. 154 5 Producer Pool Trading.................................... 157 5.1 Introduction.......................................... 157 5.2 Decision Framework.................................... 158 5.3 Uncertainty Characterization............................ 161 5.3.1 Day-ahead, Regulation, and Adjustment Prices..... 161 5.3.2 Scenario Tree.................................. 163 5.4 Pool Structure........................................ 166 5.4.1 Day-Ahead Market............................. 166 5.4.2 Regulation Market.............................. 169 5.4.3 Adjustment Market............................. 171 5.5 Producer Model....................................... 175 5.5.1 Unit Constraints............................... 175 5.5.2 Expected Profit................................ 176 5.5.3 Risk Modeling.................................. 177 5.6 Formulation........................................... 178 5.7 Producer Pool Example................................ 179 5.8 Producer Pool Case Study.............................. 186 5.9 Summary and Conclusions.............................. 191 5.10 Notation.............................................. 191 5.11 Exercises............................................. 194 6 Pool Trading for Wind Power Producers................... 195 6.1 Introduction.......................................... 195 6.2 Decision Framework.................................... 197 6.3 The Key Issues........................................ 200 6.3.1 Mechanism for Imbalance Prices.................. 200 6.3.2 Revenue and Imbalance Cost..................... 206 6.3.3 Certainty Gain Effect........................... 209 6.4 Uncertainty Characterization............................ 210 6.4.1 Day-ahead, Adjustment, and Imbalance Prices..... 211 6.4.2 Wind Power Production......................... 214 6.4.3 Scenario Tree.................................. 216 6.5 Wind Producer Model.................................. 221 6.5.1 Basic Model................................... 221 6.5.2 Offering Curves................................ 225 6.5.3 Risk Modeling.................................. 226 6.5.4 Adjustment Market............................. 227 6.5.5 Formulation.................................... 229 6.6 Wind Producer Example............................... 231 6.7 Wind Producer Case Study............................. 239 6.8 Summary and Conclusions.............................. 246 6.9 Notation.............................................. 248 6.10 Exercises............................................. 250
xiv Contents 7 Futures Market Trading for Producers..................... 253 7.1 Introduction.......................................... 253 7.2 Decision Framework.................................... 253 7.3 Uncertainty Characterization............................ 256 7.3.1 Pool Prices.................................... 256 7.3.2 Unit Availability............................... 257 7.3.3 Scenario Tree.................................. 258 7.4 Market Structure...................................... 259 7.4.1 Futures Market................................. 259 7.4.2 Pool.......................................... 262 7.5 Producer Model....................................... 263 7.5.1 Unit Constraints............................... 263 7.5.2 Unit Availability............................... 264 7.5.3 Energy Balance................................ 265 7.5.4 Expected Profit................................ 265 7.5.5 Risk Modeling.................................. 266 7.6 Formulation........................................... 267 7.7 Producer Futures Market Example. No Unit Unavailability.. 268 7.8 Producer Futures Market Example. Unit Unavailability..... 273 7.9 Producer Futures Market Case Study.................... 276 7.10 Summary and Conclusions.............................. 281 7.11 Notation.............................................. 283 7.12 Exercises............................................. 285 8 Medium-Term Retailer Trading............................ 287 8.1 Introduction.......................................... 287 8.2 Decision Framework.................................... 289 8.3 Uncertainty Characterization............................ 291 8.4 Market Structure...................................... 292 8.4.1 Futures Market................................. 293 8.4.2 Pool.......................................... 295 8.5 Retailer Model........................................ 296 8.5.1 Client Modeling................................ 296 8.5.2 Price-Quota Curve.............................. 297 8.5.3 Revenue from Selling to Clients................... 299 8.5.4 Energy Balance................................ 301 8.5.5 Expected Profit................................ 302 8.5.6 Risk Modeling.................................. 302 8.6 Formulation........................................... 304 8.7 Retailer Example...................................... 305 8.8 Retailer Case Study.................................... 309 8.9 Summary and Conclusions.............................. 318 8.10 Notation.............................................. 318 8.11 Exercises............................................. 321
Contents xv 9 Energy Procurement by Consumers....................... 323 9.1 Introduction.......................................... 323 9.2 Decision Framework and Uncertainty Model............... 324 9.2.1 Decision Framework............................ 324 9.2.2 Pool Price and Demand......................... 326 9.3 Model................................................ 328 9.3.1 Bilateral Contracts............................. 328 9.3.2 Pool.......................................... 331 9.3.3 Self-Production................................. 332 9.3.4 Energy Balance................................ 333 9.3.5 Non-anticipativity.............................. 334 9.3.6 Expected Cost................................. 336 9.3.7 Risk.......................................... 337 9.4 Formulation........................................... 337 9.5 Consumer Example.................................... 339 9.6 Consumer Case Study.................................. 344 9.7 Summary and Conclusions.............................. 351 9.8 Notation.............................................. 352 9.9 Exercises............................................. 354 10 Market Clearing Considering Equipment Failures.......... 357 10.1 Introduction.......................................... 357 10.2 Stochastic Security-Constrained Market Clearing.......... 358 10.2.1 Main Features.................................. 358 10.2.2 Introducing Security Constraints................. 359 10.2.3 Setting Reserve Requirements.................... 360 10.2.4 Solution Algorithm............................. 360 10.2.5 Security-Related Definitions...................... 361 10.3 Stochastic Security Metrics............................. 361 10.3.1 Probabilistic Metrics............................ 362 10.3.2 Security Criteria Based on the ELNS.............. 365 10.4 Market-Clearing Formulation............................ 365 10.4.1 Assumptions................................... 366 10.4.2 Variables...................................... 366 10.4.3 Structure...................................... 367 10.4.4 Objective function.............................. 367 10.4.5 Electricity Market Constraints................... 369 10.4.6 Real-Time Operating Constraints................. 373 10.4.7 Linking constraints............................. 379 10.4.8 Formulation.................................... 382 10.5 Computing Scenario Probabilities........................ 385 10.6 Market-Clearing Example............................... 387 10.7 Market-Clearing Case Study............................ 395 10.8 Summary and Conclusions.............................. 398 10.9 Notation.............................................. 399
xvi Contents 10.10 Exercises............................................. 402 11 Market Clearing Under Uncertainty: Wind Energy........ 405 11.1 Introduction.......................................... 405 11.2 Wind Power Production................................ 406 11.2.1 A Look to the Near Future...................... 406 11.2.2 Wind Impact on System Security................. 407 11.2.3 Accommodating Wind Uncertainty............... 408 11.2.4 Computational Burden.......................... 409 11.3 Market-Clearing Model................................. 410 11.3.1 Assumptions................................... 410 11.3.2 Wind Uncertainty Characterization............... 411 11.3.3 Wind Uncertainty vs. Equipment Failures.......... 412 11.3.4 Breaking Down the Expected Cost................ 417 11.3.5 Wind Spillage Cost............................. 421 11.3.6 Formulation.................................... 422 11.4 Performance Metrics................................... 425 11.4.1 Average Benefit (AB)........................... 426 11.4.2 Average Uncertainty Cost (AUC)................. 426 11.4.3 Net Average Benefit (NAB)...................... 426 11.5 Market-Clearing Example with Wind Generation.......... 427 11.5.1 Impact of wind generator location and network congestion..................................... 429 11.5.2 Impact of wind spillage cost...................... 433 11.5.3 Impact of wind penetration and uncertainty levels.. 433 11.6 Market-Clearing Case Study with Wind Generation........ 435 11.7 Summary and Conclusions.............................. 441 11.8 Notation.............................................. 442 11.9 Exercises............................................. 445 A GAMS Codes............................................. 447 A.1 Introduction.......................................... 447 A.2 GAMS code for the Producer Pool Example (Section 5.7)... 447 A.3 GAMS code for the Wind Producer Example (Section 6.6).. 452 A.4 GAMS code for the Producer Futures Market Example. No Unit Unavailability (Section 7.7)......................... 455 A.5 GAMS code for the Producer Futures Market Example. Unit Unavailability (Section 7.8)......................... 457 A.6 GAMS code for the Retailer Example (Section 8.7)........ 460 A.7 GAMS code for the Consumer Example (Section 9.5)....... 463 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)............................... 472
Contents xvii B 24-Node System Data..................................... 479 B.1 Network data......................................... 479 B.2 Generator data........................................ 479 B.3 Demand data......................................... 482 C Exercise solutions.......................................... 485 C.1 Exercises from Chapter 2............................... 485 C.2 Exercises from Chapter 3............................... 489 C.3 Exercises from Chapter 4............................... 496 C.4 Exercises from Chapter 5............................... 500 C.5 Exercises from Chapter 6............................... 505 C.6 Exercises from Chapter 7............................... 508 C.7 Exercises from Chapter 8............................... 511 C.8 Exercises from Chapter 9............................... 514 C.9 Exercises from Chapter 10.............................. 518 C.10 Exercises from Chapter 11.............................. 522 References.................................................... 527 Index......................................................... 535 Biographies................................................... 539