Preface to the Third Edition xvii
Preface to the Second Edition xix
Preface to the First Edition xxi
Acknowledgment xxiii
1 Introduction 1
1.1 Purpose of the Course 1
1.2 Course Scope 2
1.3 Economic Importance 2
1.4 Deregulation: Vertical to Horizontal 3
1.5 Problems: New and Old 3
1.6 Characteristics of Steam Units 6
1.6.1 Variations in Steam Unit Characteristics 10
1.6.2 Combined Cycle Units 13
1.6.3 Cogeneration Plants 14
1.6.4 Light-Water Moderated Nuclear Reactor Units 17
1.6.5 Hydroelectric Units 18
1.6.6 Energy Storage 21
1.7 Renewable Energy 22
1.7.1 Wind Power 23
1.7.2 Cut-In Speed 23
1.7.3 Rated Output Power and Rated Output Wind Speed 24
1.7.4 Cut-Out Speed 24
1.7.5 Wind Turbine Efficiency or Power Coefficient 24
1.7.6 Solar Power 25
Appendix 1A Typical Generation Data 26
Appendix 1B Fossil Fuel Prices 28
Appendix 1C Unit Statistics 29
References for Generation Systems 31
Further Reading 31
2 Industrial Organization, Managerial Economics, and Finance 35
2.1 Introduction 35
2.2 Business Environments 36
2.2.1 Regulated Environment 37
2.2.2 Competitive Market Environment 38
2.3 Theory of the Firm 40
2.4 Competitive Market Solutions 42
2.5 Supplier Solutions 45
2.5.1 Supplier Costs 46
2.5.2 Individual Supplier Curves 46
2.5.3 Competitive Environments 47
2.5.4 Imperfect Competition 51
2.5.5 Other Factors 52
2.6 Cost of Electric Energy Production 53
2.7 Evolving Markets 54
2.7.1 Energy Flow Diagram 57
2.8 Multiple Company Environments 58
2.8.1 Leontief Model: Input-Output Economics 58
2.8.2 Scarce Fuel Resources 60
2.9 Uncertainty and Reliability 61
Problems 61
Reference 62
3 Economic Dispatch of Thermal Units and Methods of Solution 63
3.1 The Economic Dispatch Problem 63
3.2 Economic Dispatch with Piecewise Linear Cost Functions 68
3.3 LP Method 69
3.3.1 Piecewise Linear Cost Functions 69
3.3.2 Economic Dispatch with LP 71
3.4 The Lambda Iteration Method 73
3.5 Economic Dispatch Via Binary Search 76
3.6 Economic Dispatch Using Dynamic Programming 78
3.7 Composite Generation Production Cost Function 81
3.8 Base Point and Participation Factors 85
3.9 Thermal System Dispatching with Network Losses Considered 88
3.10 The Concept of Locational Marginal Price (LMP) 92
3.11 Auction Mechanisms 95
3.11.1 PJM Incremental Price Auction as a Graphical Solution 95
3.11.2 Auction Theory Introduction 98
3.11.3 Auction Mechanisms 100
3.11.4 English (First-Price Open-Cry = Ascending) 101
3.11.5 Dutch (Descending) 103
3.11.6 First-Price Sealed Bid 104
3.11.7 Vickrey (Second-Price Sealed Bid) 105
3.11.8 All Pay (e.g., Lobbying Activity) 105
Appendix 3A Optimization Within Constraints 106
Appendix 3B Linear Programming (LP) 117
Appendix 3C Non-Linear Programming 128
Appendix 3D Dynamic Programming (DP) 128
Appendix 3E Convex Optimization 135
Problems 138
References 146
4 Unit Commitment 147
4.1 Introduction 147
4.1.1 Economic Dispatch versus Unit Commitment 147
4.1.2 Constraints in Unit Commitment 152
4.1.3 Spinning Reserve 152
4.1.4 Thermal Unit Constraints 153
4.1.5 Other Constraints 155
4.2 Unit Commitment Solution Methods 155
4.2.1 Priority-List Methods 156
4.2.2 Lagrange Relaxation Solution 157
4.2.3 Mixed Integer Linear Programming 166
4.3 Security-Constrained Unit Commitment (SCUC) 167
4.4 Daily Auctions Using a Unit Commitment 167
Appendix 4A Dual Optimization on a Nonconvex Problem 167
Appendix 4B Dynamic-Programming Solution to Unit Commitment 173
4B.1 Introduction 173
4B.2 Forward DP Approach 174
Problems 182
5 Generation with Limited Energy Supply 187
5.1 Introduction 187
5.2 Fuel Scheduling 188
5.3 Take-or-Pay Fuel Supply Contract 188
5.4 Complex Take-or-Pay Fuel Supply Models 194
5.4.1 Hard Limits and Slack Variables 194
5.5 Fuel Scheduling by Linear Programming 195
5.6 Introduction to Hydrothermal Coordination 202
5.6.1 Long-Range Hydro-Scheduling 203
5.6.2 Short-Range Hydro-Scheduling 204
5.7 Hydroelectric Plant Models 204
5.8 Scheduling Problems 207
5.8.1 Types of Scheduling Problems 207
5.8.2 Scheduling Energy 207
5.9 The Hydrothermal Scheduling Problem 211
5.9.1 Hydro-Scheduling with Storage Limitations 211
5.9.2 Hydro-Units in Series (Hydraulically Coupled) 216
5.9.3 Pumped-Storage Hydroplants 218
5.10 Hydro-Scheduling using Linear Programming 222
Appendix 5A Dynamic-Programming Solution to hydrothermal Scheduling 225
5.A.1 Dynamic Programming Example 227
5.A.1.1 Procedure 228
5.A.1.2 Extension to Other Cases 231
5.A.1.3 Dynamic-Programming Solution to Multiple Hydroplant
Problem 232
Problems 234
6 Transmission System Effects 243
6.1 Introduction 243
6.2 Conversion of Equipment Data to Bus and Branch Data 247
6.3 Substation Bus Processing 248
6.4 Equipment Modeling 248
6.5 Dispatcher Power Flow for Operational Planning 251
6.6 Conservation of Energy (Tellegen's Theorem) 252
6.7 Existing Power Flow Techniques 253
6.8 The Newton-Raphson Method Using the Augmented Jacobian Matrix 254
6.8.1 Power Flow Statement 254
6.9 Mathematical Overview 257
6.10 AC System Control Modeling 259
6.11 Local Voltage Control 259
6.12 Modeling of Transmission Lines and Transformers 259
6.12.1 Transmission Line Flow Equations 259
6.12.2 Transformer Flow Equations 260
6.13 HVDC links 261
6.13.1 Modeling of HVDC Converters and FACT Devices 264
6.13.2 Definition of Angular Relationships in HVDC Converters 264
6.13.3 Power Equations for a Six-Pole HVDC Converter 264
6.14 Brief Review of Jacobian Matrix Processing 267
6.15 Example 6A: AC Power Flow Case 269
6.16 The Decoupled Power Flow 271
6.17 The Gauss-Seidel Method 275
6.18 The "DC" or Linear Power Flow 277
6.18.1 DC Power Flow Calculation 277
6.18.2 Example 6B: DC Power Flow Example on the Six-Bus Sample System 278
6.19 Unified Eliminated Variable Hvdc Method 278
6.19.1 Changes to Jacobian Matrix Reduced 279
6.19.2 Control Modes 280
6.19.3 Analytical Elimination 280
6.19.4 Control Mode Switching 283
6.19.5 Bipolar and 12-Pulse Converters 283
6.20 Transmission Losses 284
6.20.1 A Two-Generator System Example 284
6.20.2 Coordination Equations, Incremental Losses, and Penalty Factors 286
6.21 Discussion of Reference Bus Penalty Factors 288
6.22 Bus Penalty Factors Direct from the AC Power Flow 289
Problems 291
7 Power System Security 296
7.1 Introduction 296
7.2 Factors Affecting Power System Security 301
7.3 Contingency Analysis: Detection of Network Problems 301
7.3.1 Generation Outages 301
7.3.2 Transmission Outages 302
7.4 An Overview of Security Analysis 306
7.4.1 Linear Sensitivity Factors 307
7.5 Monitoring Power Transactions Using "Flowgates" 313
7.6 Voltage Collapse 315
7.6.1 AC Power Flow Methods 317
7.6.2 Contingency Selection 320
7.6.3 Concentric Relaxation 323
7.6.4 Bounding 325
7.6.5 Adaptive Localization 325
Appendix 7A AC Power Flow Sample Cases 327
Appendix 7B Calculation of Network Sensitivity Factors 336
7B.1 Calculation of PTDF Factors 336
7B.2 Calculation of LODF Factors 339
7B.2.1 Special Cases 341
7B.3 Compensated PTDF Factors 343
Problems 343
References 349
8 Optimal Power Flow 350
8.1 Introduction 350
8.2 The Economic Dispatch Formulation 351
8.3 The Optimal Power Flow Calculation Combining Economic Dispatch and the Power Flow 352
8.4 Optimal Power Flow Using the DC Power Flow 354
8.5 Example 8A: Solution of the DC Power Flow OPF 356
8.6 Example 8B: DCOPF with Transmission Line Limit Imposed 361
8.7 Formal Solution of the DCOPF 365
8.8 Adding Line Flow Constraints to the Linear Programming Solution 365
8.8.1 Solving the DCOPF Using Quadratic Programming 367
8.9 Solution of the ACOPF 368
8.10 Algorithms for Solution of the ACOPF 369
8.11 Relationship Between LMP, Incremental Losses, and Line Flow Constraints 376
8.11.1 Locational Marginal Price at a Bus with No Lines Being Held at Limit 377
8.11.2 Locational Marginal Price with a Line Held at its Limit 378
8.12 Security-Constrained OPF 382
8.12.1 Security Constrained OPF Using the DC Power Flow and Quadratic Programming 384
8.12.2 DC Power Flow 385
8.12.3 Line Flow Limits 385
8.12.4 Contingency Limits 386
Appendix 8A Interior Point Method 391
Appendix 8B Data for the 12-Bus System 393
Appendix 8C Line Flow Sensitivity Factors 395
Appendix 8D Linear Sensitivity Analysis of the AC Power Flow 397
Problems 399
9 Introduction to State Estimation in Power Systems 403
9.1 Introduction 403
9.2 Power System State Estimation 404
9.3 Maximum Likelihood Weighted Least-Squares Estimation 408
9.3.1 Introduction 408
9.3.2 Maximum Likelihood Concepts 410
9.3.3 Matrix Formulation 414
9.3.4 An Example of Weighted Least-Squares State Estimation 417
9.4 State Estimation of an Ac Network 421
9.4.1 Development of Method 421
9.4.2 Typical Results of State Estimation on an AC Network 424
9.5 State Estimation by Orthogonal Decomposition 428
9.5.1 The Orthogonal Decomposition Algorithm 431
9.6 An Introduction to Advanced Topics in State Estimation 435
9.6.1 Sources of Error in State Estimation 435
9.6.2 Detection and Identification of Bad Measurements 436
9.6.3 Estimation of Quantities Not Being Measured 443
9.6.4 Network Observability and Pseudo-measurements 444
9.7 The Use of Phasor Measurement Units (PMUS) 447
9.8 Application of Power Systems State Estimation 451
9.9 Importance of Data Verification and Validation 454
9.10 Power System Control Centers 454
Appendix 9A Derivation of Least-Squares Equations 456
9A.1 The Overdetermined Case (Nm > Ns) 457
9A.2 The Fully Determined Case (Nm = Ns) 462
9A.3 The Underdetermined Case (Nm < Ns) 462
Problems 464
10 Control of Generation 468
10.1 Introduction 468
10.2 Generator Model 470
10.3 Load Model 473
10.4 Prime-Mover Model 475
10.5 Governor Model 476
10.6 Tie-Line Model 481
10.7 Generation Control 485
10.7.1 Supplementary Control Action 485
10.7.2 Tie-Line Control 486
10.7.3 Generation Allocation 489
10.7.4 Automatic Generation Control (AGC) Implementation 491
10.7.5 AGC Features 495
10.7.6 NERC Generation Control Criteria 496
Problems 497
References 500
11 Interchange, Pooling, Brokers, and Auctions 501
11.1 Introduction 501
11.2 Interchange Contracts 504
11.2.1 Energy 504
11.2.2 Dynamic Energy 506
11.2.3 Contingent 506
11.2.4 Market Based 507
11.2.5 Transmission Use 508
11.2.6 Reliability 517
11.3 Energy Interchange between Utilities 517
11.4 Interutility Economy Energy Evaluation 521
11.5 Interchange Evaluation with Unit Commitment 522
11.6 Multiple Utility Interchange Transactions-Wheeling 523
11.7 Power Pools 526
11.8 The Energy-Broker System 529
11.9 Transmission Capability General Issues 533
11.10 Available Transfer Capability and Flowgates 535
11.10.1 Definitions 536
11.10.2 Process 539
11.10.3 Calculation ATC Methodology 540
11.11 Security Constrained Unit Commitment (SCUC) 550
11.11.1 Loads and Generation in a Spot Market Auction 550
11.11.2 Shape of the Two Functions 552
11.11.3 Meaning of the Lagrange Multipliers 553
11.11.4 The Day-Ahead Market Dispatch 554
11.12 Auction Emulation using Network LP 555
11.13 Sealed Bid Discrete Auctions 555
Problems 560
12 Short-Term Demand Forecasting 566
12.1 Perspective 566
12.2 Analytic Methods 569
12.3 Demand Models 571
12.4 Commodity Price Forecasting 572
12.5 Forecasting Errors 573
12.6 System Identification 573
12.7 Econometric Models 574
12.7.1 Linear Environmental Model 574
12.7.2 Weather-Sensitive Models 576
12.8 Time Series 578
12.8.1 Time Series Models Seasonal Component 578
12.8.2 Auto-Regressive (AR) 580
12.8.3 Moving Average (MA) 581
12.8.4 Auto-Regressive Moving Average (ARMA): Box-Jenkins 582
12.8.5 Auto-Regressive Integrated Moving-Average (ARIMA): Box-Jenkins 584
12.8.6 Others (ARMAX, ARIMAX, SARMAX, NARMA) 585
12.9 Time Series Model Development 585
12.9.1 Base Demand Models 586
12.9.2 Trend Models 586
12.9.3 Linear Regression Method 586
12.9.4 Seasonal Models 588
12.9.5 Stationarity 588
12.9.6 WLS Estimation Process 590
12.9.7 Order and Variance Estimation 591
12.9.8 Yule-Walker Equations 592
12.9.9 Durbin-Levinson Algorithm 595
12.9.10 Innovations Estimation for MA and ARMA Processes 598
12.9.11 ARIMA Overall Process 600
12.10 Artificial Neural Networks 603
12.10.1 Introduction to Artificial Neural Networks 604
12.10.2 Artificial Neurons 605
12.10.3 Neural network applications 606
12.10.4 Hopfield Neural Networks 606
12.10.5 Feed-Forward Networks 607
12.10.6 Back-Propagation Algorithm 610
12.10.7 Interior Point Linear Programming Algorithms 613
12.11 Model Integration 614
12.12 Demand Prediction 614
12.12.1 Hourly System Demand Forecasts 615
12.12.2 One-Step Ahead Forecasts 615
12.12.3 Hourly Bus Demand Forecasts 616
12.13 Conclusion 616
Problems 617
Index 620
