Power Generation, Operation, and Control

ALLEN J. WOOD joined Power Technologies, Inc., in 1969 as a Principal Engineer and Director. He was a Life Fellow of IEEE and served as an adjunct professor in the Electric Power Engineering graduate program at Rensselaer Polytechnic Institute. Dr. Wood passed away in 2011.BRUCE F. WOLLENBERG joined the University of Minnesota in 1989 and made original contributions to the understanding of electric power market structures. He is a Life Fellow of the IEEE and a member of the National Academy of Engineering.GERALD B. SHEBLÉ joined Auburn University in 1990 to conduct research in power system, space power, and electric auction market research. He joined Iowa State University to conduct research in the interaction of markets and power system operation. His academic research has continued to center on the action of the markets based on the physical operation of the power system. He is a Fellow of the IEEE. Dr. Sheble' passed away in 2021.

• Preface to the Third Edition xviiPreface to the Second Edition xixPreface to the First Edition xxiAcknowledgment xxiii1 Introduction 11.1 Purpose of the Course 11.2 Course Scope 21.3 Economic Importance 21.4 Deregulation: Vertical to Horizontal 31.5 Problems: New and Old 31.6 Characteristics of Steam Units 61.6.1 Variations in Steam Unit Characteristics 101.6.2 Combined Cycle Units 131.6.3 Cogeneration Plants 141.6.4 Light-Water Moderated Nuclear Reactor Units 171.6.5 Hydroelectric Units 181.6.6 Energy Storage 211.7 Renewable Energy 221.7.1 Wind Power 231.7.2 Cut-In Speed 231.7.3 Rated Output Power and Rated Output Wind Speed 241.7.4 Cut-Out Speed 241.7.5 Wind Turbine Efficiency or Power Coefficient 241.7.6 Solar Power 25Appendix 1A Typical Generation Data 26Appendix 1B Fossil Fuel Prices 28Appendix 1C Unit Statistics 29References for Generation Systems 31Further Reading 312 Industrial Organization, Managerial Economics, and Finance 352.1 Introduction 352.2 Business Environments 362.2.1 Regulated Environment 372.2.2 Competitive Market Environment 382.3 Theory of the Firm 402.4 Competitive Market Solutions 422.5 Supplier Solutions 452.5.1 Supplier Costs 462.5.2 Individual Supplier Curves 462.5.3 Competitive Environments 472.5.4 Imperfect Competition 512.5.5 Other Factors 522.6 Cost of Electric Energy Production 532.7 Evolving Markets 542.7.1 Energy Flow Diagram 572.8 Multiple Company Environments 582.8.1 Leontief Model: Input–Output Economics 582.8.2 Scarce Fuel Resources 602.9 Uncertainty and Reliability 61Problems 61Reference 623 Economic Dispatch of Thermal Units and Methods of Solution 633.1 The Economic Dispatch Problem 633.2 Economic Dispatch with Piecewise Linear Cost Functions 683.3 LP Method 693.3.1 Piecewise Linear Cost Functions 693.3.2 Economic Dispatch with LP 713.4 The Lambda Iteration Method 733.5 Economic Dispatch Via Binary Search 763.6 Economic Dispatch Using Dynamic Programming 783.7 Composite Generation Production Cost Function 813.8 Base Point and Participation Factors 853.9 Thermal System Dispatching with Network Losses Considered 883.10 The Concept of Locational Marginal Price (LMP) 923.11 Auction Mechanisms 953.11.1 PJM Incremental Price Auction as a Graphical Solution 953.11.2 Auction Theory Introduction 983.11.3 Auction Mechanisms 1003.11.4 English (First-Price Open-Cry = Ascending) 1013.11.5 Dutch (Descending) 1033.11.6 First-Price Sealed Bid 1043.11.7 Vickrey (Second-Price Sealed Bid) 1053.11.8 All Pay (e.g., Lobbying Activity) 105Appendix 3A Optimization Within Constraints 106Appendix 3B Linear Programming (LP) 117Appendix 3C Non-Linear Programming 128Appendix 3D Dynamic Programming (DP) 128Appendix 3E Convex Optimization 135Problems 138References 1464 Unit Commitment 1474.1 Introduction 1474.1.1 Economic Dispatch versus Unit Commitment 1474.1.2 Constraints in Unit Commitment 1524.1.3 Spinning Reserve 1524.1.4 Thermal Unit Constraints 1534.1.5 Other Constraints 1554.2 Unit Commitment Solution Methods 1554.2.1 Priority-List Methods 1564.2.2 Lagrange Relaxation Solution 1574.2.3 Mixed Integer Linear Programming 1664.3 Security-Constrained Unit Commitment (SCUC) 1674.4 Daily Auctions Using a Unit Commitment 167Appendix 4A Dual Optimization on a Nonconvex Problem 167Appendix 4B Dynamic-Programming Solution to Unit Commitment 1734B.1 Introduction 1734B.2 Forward DP Approach 174Problems 1825 Generation with Limited Energy Supply 1875.1 Introduction 1875.2 Fuel Scheduling 1885.3 Take-or-Pay Fuel Supply Contract 1885.4 Complex Take-or-Pay Fuel Supply Models 1945.4.1 Hard Limits and Slack Variables 1945.5 Fuel Scheduling by Linear Programming 1955.6 Introduction to Hydrothermal Coordination 2025.6.1 Long-Range Hydro-Scheduling 2035.6.2 Short-Range Hydro-Scheduling 2045.7 Hydroelectric Plant Models 2045.8 Scheduling Problems 2075.8.1 Types of Scheduling Problems 2075.8.2 Scheduling Energy 2075.9 The Hydrothermal Scheduling Problem 2115.9.1 Hydro-Scheduling with Storage Limitations 2115.9.2 Hydro-Units in Series (Hydraulically Coupled) 2165.9.3 Pumped-Storage Hydroplants 2185.10 Hydro-Scheduling using Linear Programming 222Appendix 5A Dynamic-Programming Solution to hydrothermal Scheduling 2255.A.1 Dynamic Programming Example 2275.A.1.1 Procedure 2285.A.1.2 Extension to Other Cases 2315.A.1.3 Dynamic-Programming Solution to Multiple HydroplantProblem 232Problems 2346 Transmission System Effects 2436.1 Introduction 2436.2 Conversion of Equipment Data to Bus and Branch Data 2476.3 Substation Bus Processing 2486.4 Equipment Modeling 2486.5 Dispatcher Power Flow for Operational Planning 2516.6 Conservation of Energy (Tellegen’s Theorem) 2526.7 Existing Power Flow Techniques 2536.8 The Newton–Raphson Method Using the Augmented Jacobian Matrix 2546.8.1 Power Flow Statement 2546.9 Mathematical Overview 2576.10 AC System Control Modeling 2596.11 Local Voltage Control 2596.12 Modeling of Transmission Lines and Transformers 2596.12.1 Transmission Line Flow Equations 2596.12.2 Transformer Flow Equations 2606.13 HVDC links 2616.13.1 Modeling of HVDC Converters and FACT Devices 2646.13.2 Definition of Angular Relationships in HVDC Converters 2646.13.3 Power Equations for a Six-Pole HVDC Converter 2646.14 Brief Review of Jacobian Matrix Processing 2676.15 Example 6A: AC Power Flow Case 2696.16 The Decoupled Power Flow 2716.17 The Gauss–Seidel Method 2756.18 The “DC” or Linear Power Flow 2776.18.1 DC Power Flow Calculation 2776.18.2 Example 6B: DC Power Flow Example on the Six-Bus Sample System 2786.19 Unified Eliminated Variable Hvdc Method 2786.19.1 Changes to Jacobian Matrix Reduced 2796.19.2 Control Modes 2806.19.3 Analytical Elimination 2806.19.4 Control Mode Switching 2836.19.5 Bipolar and 12-Pulse Converters 2836.20 Transmission Losses 2846.20.1 A Two-Generator System Example 2846.20.2 Coordination Equations, Incremental Losses, and Penalty Factors 2866.21 Discussion of Reference Bus Penalty Factors 2886.22 Bus Penalty Factors Direct from the AC Power Flow 289Problems 2917 Power System Security 2967.1 Introduction 2967.2 Factors Affecting Power System Security 3017.3 Contingency Analysis: Detection of Network Problems 3017.3.1 Generation Outages 3017.3.2 Transmission Outages 3027.4 An Overview of Security Analysis 3067.4.1 Linear Sensitivity Factors 3077.5 Monitoring Power Transactions Using “Flowgates” 3137.6 Voltage Collapse 3157.6.1 AC Power Flow Methods 3177.6.2 Contingency Selection 3207.6.3 Concentric Relaxation 3237.6.4 Bounding 3257.6.5 Adaptive Localization 325Appendix 7A AC Power Flow Sample Cases 327Appendix 7B Calculation of Network Sensitivity Factors 3367B.1 Calculation of PTDF Factors 3367B.2 Calculation of LODF Factors 3397B.2.1 Special Cases 3417B.3 Compensated PTDF Factors 343Problems 343References 3498 Optimal Power Flow 3508.1 Introduction 3508.2 The Economic Dispatch Formulation 3518.3 The Optimal Power Flow Calculation Combining Economic Dispatch and the Power Flow 3528.4 Optimal Power Flow Using the DC Power Flow 3548.5 Example 8A: Solution of the DC Power Flow OPF 3568.6 Example 8B: DCOPF with Transmission Line Limit Imposed 3618.7 Formal Solution of the DCOPF 3658.8 Adding Line Flow Constraints to the Linear Programming Solution 3658.8.1 Solving the DCOPF Using Quadratic Programming 3678.9 Solution of the ACOPF 3688.10 Algorithms for Solution of the ACOPF 3698.11 Relationship Between LMP, Incremental Losses, and Line Flow Constraints 3768.11.1 Locational Marginal Price at a Bus with No Lines Being Held at Limit 3778.11.2 Locational Marginal Price with a Line Held at its Limit 3788.12 Security-Constrained OPF 3828.12.1 Security Constrained OPF Using the DC Power Flow and Quadratic Programming 3848.12.2 DC Power Flow 3858.12.3 Line Flow Limits 3858.12.4 Contingency Limits 386Appendix 8A Interior Point Method 391Appendix 8B Data for the 12-Bus System 393Appendix 8C Line Flow Sensitivity Factors 395Appendix 8D Linear Sensitivity Analysis of the AC Power Flow 397Problems 3999 Introduction to State Estimation in Power Systems 4039.1 Introduction 4039.2 Power System State Estimation 4049.3 Maximum Likelihood Weighted Least-Squares Estimation 4089.3.1 Introduction 4089.3.2 Maximum Likelihood Concepts 4109.3.3 Matrix Formulation 4149.3.4 An Example of Weighted Least-Squares State Estimation 4179.4 State Estimation of an Ac Network 4219.4.1 Development of Method 4219.4.2 Typical Results of State Estimation on an AC Network 4249.5 State Estimation by Orthogonal Decomposition 4289.5.1 The Orthogonal Decomposition Algorithm 4319.6 An Introduction to Advanced Topics in State Estimation 4359.6.1 Sources of Error in State Estimation 4359.6.2 Detection and Identification of Bad Measurements 4369.6.3 Estimation of Quantities Not Being Measured 4439.6.4 Network Observability and Pseudo-measurements 4449.7 The Use of Phasor Measurement Units (PMUS) 4479.8 Application of Power Systems State Estimation 4519.9 Importance of Data Verification and Validation 4549.10 Power System Control Centers 454Appendix 9A Derivation of Least-Squares Equations 4569A.1 The Overdetermined Case (Nm > Ns) 4579A.2 The Fully Determined Case (Nm = Ns) 4629A.3 The Underdetermined Case (Nm < Ns) 462Problems 46410 Control of Generation 46810.1 Introduction 46810.2 Generator Model 47010.3 Load Model 47310.4 Prime-Mover Model 47510.5 Governor Model 47610.6 Tie-Line Model 48110.7 Generation Control 48510.7.1 Supplementary Control Action 48510.7.2 Tie-Line Control 48610.7.3 Generation Allocation 48910.7.4 Automatic Generation Control (AGC) Implementation 49110.7.5 AGC Features 49510.7.6 NERC Generation Control Criteria 496Problems 497References 50011 Interchange, Pooling, Brokers, and Auctions 50111.1 Introduction 50111.2 Interchange Contracts 50411.2.1 Energy 50411.2.2 Dynamic Energy 50611.2.3 Contingent 50611.2.4 Market Based 50711.2.5 Transmission Use 50811.2.6 Reliability 51711.3 Energy Interchange between Utilities 51711.4 Interutility Economy Energy Evaluation 52111.5 Interchange Evaluation with Unit Commitment 52211.6 Multiple Utility Interchange Transactions—Wheeling 52311.7 Power Pools 52611.8 The Energy-Broker System 52911.9 Transmission Capability General Issues 53311.10 Available Transfer Capability and Flowgates 53511.10.1 Definitions 53611.10.2 Process 53911.10.3 Calculation ATC Methodology 54011.11 Security Constrained Unit Commitment (SCUC) 55011.11.1 Loads and Generation in a Spot Market Auction 55011.11.2 Shape of the Two Functions 55211.11.3 Meaning of the Lagrange Multipliers 55311.11.4 The Day-Ahead Market Dispatch 55411.12 Auction Emulation using Network LP 55511.13 Sealed Bid Discrete Auctions 555Problems 56012 Short-Term Demand Forecasting 56612.1 Perspective 56612.2 Analytic Methods 56912.3 Demand Models 57112.4 Commodity Price Forecasting 57212.5 Forecasting Errors 57312.6 System Identification 57312.7 Econometric Models 57412.7.1 Linear Environmental Model 57412.7.2 Weather-Sensitive Models 57612.8 Time Series 57812.8.1 Time Series Models Seasonal Component 57812.8.2 Auto-Regressive (AR) 58012.8.3 Moving Average (MA) 58112.8.4 Auto-Regressive Moving Average (ARMA): Box-Jenkins 58212.8.5 Auto-Regressive Integrated Moving-Average (ARIMA): Box-Jenkins 58412.8.6 Others (ARMAX, ARIMAX, SARMAX, NARMA) 58512.9 Time Series Model Development 58512.9.1 Base Demand Models 58612.9.2 Trend Models 58612.9.3 Linear Regression Method 58612.9.4 Seasonal Models 58812.9.5 Stationarity 58812.9.6 WLS Estimation Process 59012.9.7 Order and Variance Estimation 59112.9.8 Yule-Walker Equations 59212.9.9 Durbin-Levinson Algorithm 59512.9.10 Innovations Estimation for MA and ARMA Processes 59812.9.11 ARIMA Overall Process 60012.10 Artificial Neural Networks 60312.10.1 Introduction to Artificial Neural Networks 60412.10.2 Artificial Neurons 60512.10.3 Neural network applications 60612.10.4 Hopfield Neural Networks 60612.10.5 Feed-Forward Networks 60712.10.6 Back-Propagation Algorithm 61012.10.7 Interior Point Linear Programming Algorithms 61312.11 Model Integration 61412.12 Demand Prediction 61412.12.1 Hourly System Demand Forecasts 61512.12.2 One-Step Ahead Forecasts 61512.12.3 Hourly Bus Demand Forecasts 61612.13 Conclusion 616Problems 617Index 620

“Without a doubt, this book makes admirable progress in integrating the ­traditional with the new, and, as such, it is a worthy addition to professional libraries. It is a valuable text for a one- or two-course sequence in a graduate curriculum in power systems. Reasonable resource support for both student and instructor is available through the publisher.”  (IEEE, 1 July 2014)