Decision Making Under Uncertainty in Electricity Markets (eBook)

Antonio J. Conejo full professor at the Universidad de Castilla – La Mancha, Spain, received the M.S. from MIT and the Ph.D. from the Royal Institute of Technology, Sweden. He has published over 100 papers in prestigious journals and is the author or coauthor of books published by Springer, Wiley, McGraw-Hill and CRC. He has been the principal investigator of many research projects financed by public agencies and the power industry. He is an IEEE Fellow and a member of the editorial board of the IEEE Transactions on Power Systems. Miguel Carrión received the Ingeniero Industrial degree and the PhD degree from the Universidad de Castilla-La Mancha, Ciudad Real, Spain, in 2003 and 2008, respectively. He is currently an Assistant Professor at the Universidad de Castilla-La Mancha, Toledo, Spain. Juan M. Morales received the Ingeniero Industrial degree from the Universidad de Málaga, Spain, in 2006. He is currently working toward the Ph.D. degree at the Universidad de Castilla-La Mancha.

Decision Making UnderUncertainty in ElectricityMarkets 4
Preface 8
Contents 12
Chapter 1 Electricity Markets 20
1.1 Introduction 20
1.2 Organization and Agents 20
1.2.1 Market Organization 21
1.2.2 Agents 23
1.2.3 Pool 25
1.2.4 Futures Market 28
1.2.5 Reserve and Regulation Markets 30
1.3 Time Framework and Uncertainty 32
1.3.1 Decision Sequence 32
1.3.2 Uncertainty 34
1.4 Decision Making 36
1.4.1 Consumer 36
1.4.2 Retailer 38
1.4.3 Producer 39
1.4.4 Non-Dispatchable Producer 41
1.4.5 Market Operator 42
1.4.6 Independent System Operator 43
1.5 Summary 44
1.6 Exercises 44
Chapter 2 Stochastic Programming Fundamentals 46
2.1 Introduction 46
2.2 Random Variables 48
2.3 Stochastic Processes 50
2.4 Scenarios 51
2.5 Stochastic Programming Problems 53
2.5.1 Two-Stage Problems 53
2.5.2 Multi-Stage Problems 58
2.6 Quality Metrics 67
2.6.1 Expected Value of Perfect Information 68
2.6.2 Value of the Stochastic Solution 71
2.6.3 Out-of-Sample Assessment 76
2.7 Risk 77
2.8 Solving Stochastic Programming Problems 78
2.9 Summary and Conclusions 80
2.10 Exercises 80
Chapter 3 Uncertainty Characterization via Scenarios 82
3.1 Introduction 82
3.2 Scenario Generation 85
3.2.1 Overview 85
3.2.2 Scenario Generation using ARIMA Models 87
3.2.3 Generating Scenarios for Unit Availability 94
3.2.4 Quality of Scenario Subsets 97
3.3 Scenario Reduction 99
3.3.1 Motivation 99
3.3.2 Scenario Reduction Using a Probability Distance 100
3.3.3 Algorithm 101
3.4 Scenario Generation for Dependent Stochastic Processes 111
3.4.1 Overview 111
3.4.2 Scenarios for contemporaneous or quasi-contemporaneous stochastic processes 113
3.4.3 Scenarios for non-contemporaneous stochastic processes 120
3.5 Case Studies 122
3.5.1 Scenario Generation Using ARIMA and Dynamic Regression models: Electricity Price and Demand 122
3.5.2 Scenario Generation for Quasi-contemporaneous Stochastic Processes: Wind Speeds at Multiple Sites 127
3.6 Summary and Conclusions 134
3.7 Exercises 136
Chapter 4 Risk management 139
4.1 Introduction 139
4.2 Risk Control in Stochastic Programming Problems 140
4.2.1 Risk-Neutral Decision Making 140
4.2.2 Risk-Averse Decision Making 144
4.3 Risk Measures 146
4.3.1 Variance 147
4.3.2 Shortfall Probability 150
4.3.3 Expected Shortage 153
4.3.4 Value-at-Risk 157
4.3.5 Conditional Value-at-Risk 160
4.3.6 Stochastic Dominance 163
4.4 Summary and Conclusions 170
4.5 Exercises 172
Chapter 5 Producer Pool Trading 175
5.1 Introduction 175
5.2 Decision Framework 176
5.3 Uncertainty Characterization 179
5.3.1 Day-ahead, Regulation, and Adjustment Prices 179
5.3.2 Scenario Tree 181
5.4 Pool Structure 184
5.4.1 Day-Ahead Market 184
5.4.2 Regulation Market 187
5.4.3 Adjustment Market 189
5.5 Producer Model 193
5.5.1 Unit Constraints 193
5.5.2 Expected Profit 194
5.5.3 Risk Modeling 195
5.6 Formulation 196
5.7 Producer Pool Example 197
5.8 Producer Pool Case Study 204
5.9 Summary and Conclusions 209
5.10 Notation 209
5.11 Exercises 212
Chapter 6 Pool Trading for Wind Power Producers 213
6.1 Introduction 213
6.2 Decision Framework 215
6.3 The Key Issues 218
6.3.1 Mechanism for Imbalance Prices 218
6.3.2 Revenue and Imbalance Cost 224
6.3.3 Certainty Gain Effect 227
6.4 Uncertainty Characterization 228
6.4.1 Day-ahead, Adjustment, and Imbalance Prices 229
6.4.2 Wind Power Production 232
6.4.3 Scenario Tree 234
6.5 Wind Producer Model 239
6.5.1 Basic Model 239
6.5.2 Offering Curves 243
6.5.3 Risk Modeling 244
6.5.4 Adjustment Market 245
6.5.5 Formulation 247
6.6 Wind Producer Example 249
6.7 Wind Producer Case Study 257
6.8 Summary and Conclusions 264
6.9 Notation 266
6.10 Exercises 268
Chapter 7 Futures Market Trading for Producers 270
7.1 Introduction 270
7.2 Decision Framework 270
7.3 Uncertainty Characterization 273
7.3.1 Pool Prices 273
7.3.2 Unit Availability 274
7.3.3 Scenario Tree 275
7.4 Market Structure 276
7.4.1 Futures Market 276
7.4.2 Pool 279
7.5 Producer Model 280
7.5.1 Unit Constraints 280
7.5.2 Unit Availability 281
7.5.3 Energy Balance 282
7.5.4 Expected Profit 282
7.5.5 Risk Modeling 283
7.6 Formulation 284
7.7 Producer Futures Market Example. No Unit Unavailability 285
7.8 Producer Futures Market Example. Unit Unavailability 290
7.9 Producer Futures Market Case Study 293
7.10 Summary and Conclusions 298
7.11 Notation 300
7.12 Exercises 302
Chapter 8 Medium-Term Retailer Trading 303
8.1 Introduction 303
8.2 Decision Framework 305
8.3 Uncertainty Characterization 307
8.4 Market Structure 308
8.4.1 Futures Market 309
8.4.2 Pool 311
8.5 Retailer Model 312
8.5.1 Client Modeling 312
8.5.2 Price-Quota Curve 313
8.5.3 Revenue from Selling to Clients 315
8.5.4 Energy Balance 317
8.5.5 Expected Profit 318
8.5.6 Risk Modeling 318
8.6 Formulation 320
8.7 Retailer Example 321
8.8 Retailer Case Study 325
8.9 Summary and Conclusions 334
8.10 Notation 334
8.11 Exercises 337
Chapter 9 Energy Procurement by Consumers 338
9.1 Introduction 338
9.2 Decision Framework and Uncertainty Model 339
9.2.1 Decision Framework 339
9.2.2 Pool Price and Demand 341
9.3 Model 343
9.3.1 Bilateral Contracts 343
9.3.2 Pool 346
9.3.3 Self-Production 347
9.3.4 Energy Balance 348
9.3.5 Non-anticipativity 349
9.3.6 Expected Cost 351
9.3.7 Risk 352
9.4 Formulation 352
9.5 Consumer Example 354
9.6 Consumer Case Study 359
9.7 Summary and Conclusions 366
9.8 Notation 367
9.9 Exercises 369
Chapter 10 Market Clearing Considering Equipment Failures 371
10.1 Introduction 371
10.2 Stochastic Security-Constrained Market Clearing 372
10.2.1 Main Features 372
10.2.2 Introducing Security Constraints 373
10.2.3 Setting Reserve Requirements: Deterministic and Probabilistic Approaches 374
10.2.4 Solution Algorithm 374
10.2.5 Security-Related Definitions 375
10.3 Stochastic Security Metrics 375
10.3.1 Probabilistic Metrics 376
10.3.2 Security Criteria Based on the ELNS 379
10.4 Market-Clearing Formulation 379
10.4.1 Assumptions 380
10.4.2 Variables 380
10.4.3 Structure 381
10.4.4 Objective function 381
10.4.5 Electricity Market Constraints 383
10.4.6 Real-Time Operating Constraints 387
10.4.7 Linking constraints 393
10.4.8 Formulation 396
10.5 Computing Scenario Probabilities 399
10.6 Market-Clearing Example 401
10.7 Market-Clearing Case Study 409
10.8 Summary and Conclusions 412
10.9 Notation 413
10.10 Exercises 416
Chapter 11 Market Clearing under Uncertainty: Wind Energy 418
11.1 Introduction 418
11.2 Wind Power Production 419
11.2.1 A Look to the Near Future: Wind Generation 419
11.2.2 All That Glitters Is Not Gold: Wind Impact on System Security 420
11.2.3 Accommodating Wind Uncertainty in Electricity Markets 421
11.2.4 The Handicap: The Computational Burden 422
11.3 Market-Clearing Model 423
11.3.1 Assumptions 423
11.3.2 Wind Uncertainty Characterization 424
11.3.3 Wind Uncertainty vs. Equipment Failures 425
11.3.4 Breaking Down the Expected Cost 430
11.3.5 Wind Spillage Cost 434
11.3.6 Formulation 435
11.4 Wind Benefits and Costs at a Glance: Performance Metrics 438
11.4.1 Average Benefit (AB) 439
11.4.2 Average Uncertainty Cost (AUC) 439
11.4.3 Net Average Benefit (NAB) 439
11.5 Market-Clearing Example with Wind Generation 440
11.5.1 Impact of wind generator location and network congestion 442
11.5.2 Impact of wind spillage cost 446
11.5.3 Impact of wind penetration and uncertainty levels 446
11.6 Market-Clearing Case Study with Wind Generation 448
11.7 Summary and Conclusions 454
11.8 Notation 455
11.9 Exercises 458
Appendix A GAMS codes 460
A.1 Introduction 460
A.2 GAMS code for the Producer Pool Example (Section 5.7) 460
A.3 GAMS code for the Wind Producer Example (Section 6.6) 465
A.4 GAMS code for the Producer Futures Market Example. No Unit Unavailability (Section 7.7) 468
A.5 GAMS code for the Producer Futures Market Example. Unit Unavailability (Section 7.8) 470
A.6 GAMS code for the Retailer Example (Section 8.7) 473
A.7 GAMS code for the Consumer Example (Section 9.5) 476
A.8 GAMS code for the Market-Clearing Example (Section 10.6) 479
A.9 GAMS code for the Market-Clearing Example with Wind Generation (Section 11.5) 485
Appendix B 24-Node System Data 491
B.1 Network data 491
B.2 Generator data 491
B.3 Demand data 494
Appendix C Exercise solutions 497
C.1 Exercises from Chapter 2 497
C.2 Exercises from Chapter 3 501
C.3 Exercises from Chapter 4 508
C.4 Exercises from Chapter 5 512
C.5 Exercises from Chapter 6 517
C.6 Exercises from Chapter 7 520
C.7 Exercises from Chapter 8 523
C.8 Exercises from Chapter 9 526
C.9 Exercises from Chapter 10 530
C.10 Exercises from Chapter 11 534
References 539
Index 546
Biographies 549