Since publication of the second edition, there have been extensive changes in the algorithms, methods, and assumptions in energy management systems that analyze and control power generation. This edition is updated to acquaint electrical engineering students and professionals with current power generation systems. Algorithms and methods for solving integrated economic, network, and generating system analysis are provided. Also included are the state-of-the-art topics undergoing evolutionary change, including market simulation, multiple market analysis, multiple interchange contract analysis, contract and market bidding, and asset valuation under various portfolio combinations.

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

xii contents

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