PREFACE ...................................................... xiii
CONTRIBUTORS ................................................. XVII
1 FUNDAMENTALS OF ELECTRIC POWER SYSTEMS
Xiao-Ping Zhang
1.1 Introduction of Electric Power Systems .................. 1
1.2 Electric Power Generation ............................... 2
1.2.1 Conventional Power Plants ........................ 2
1.2.1.1 Fossil Fuel Power Plants ................ 2
1.2.1.2 CCGT Power Plants ....................... 3
1.2.1.3 Nuclear Power Plants .................... 3
1.2.2 Renewable Power Generation Technologies .......... 4
1.2.2.1 Wind Energy Generation .................. 4
1.2.2.2 Ocean Energy Generation ................. 5
1.2.2.3 Photovoltaic Generation Systems ......... 6
1.2.2.4 Bioenergy ............................... 6
1.2.2.5 Geothermal Energy ....................... 7
1.2.2.6 Hydrogen ................................ 7
1.3 Structure of Electric Power Systems ..................... 7
1.3.1 Structure ........................................ 7
1.3.2 Benefits of System Interconnection ............... 9
1.4 Ultra-High Voltage Power Transmission .................. 11
1.4.1 The Concept of Ultra-High Voltage Power
Transmission .................................... 11
1.4.2 Economic Comparison of Extra-High Voltage and
Ultra-High Voltage Power Transmission ........... 13
1.4.3 Ultra-High Voltage AC Power Transmission
Technology ...................................... 14
1.4.4 Ultra-High Voltage DC Technology ................ 14
1.4.5 Ultra-High Voltage Power Transmission in
China ........................................... 15
1.4.6 Ultra-High Voltage Power Transmission in the
World ........................................... 17
1.5 Modeling of Electric Power Systems ..................... 17
1.5.1 Transmission Lines .............................. 17
1.5.2 Transformers .................................... 18
1.5.3 Loads ........................................... 19
1.5.4 Synchronous Generators .......................... 20
1.5.5 HVDC Systems and Flexible AC Transmission
Systems (FACTS) ................................. 20
1.6 Power Flow Analysis .................................... 20
1.6.1 Classifications of Buses for Power Flow
Analysis ........................................ 20
1.6.1.1 Slack Bus .............................. 20
1.6.1.2 PV Buses ............................... 21
1.6.1.3 PQ Buses ............................... 21
1.6.1.1 Formulation of Load Flow Solution ...... 21
1.6.3 Power Flow Solution by Newton-Raphson Method .... 22
1.6.4 Fast Decoupled Load Flow Method ................. 24
1.6.5 DC Load How Method .............................. 25
1.7 Optimal Operation of Electric Power Systems ............ 26
1.7.1 Security-Constrained Economic Dispatch .......... 26
1.7.1.1 Classic Economic Dispatch Without
Transmission Network Power Loss ........ 26
1.7.1.2 Security Constrained Economic
Dispatch ............................... 28
1.7.2 Optimal Power Flow Techniques ................... 28
1.7.2.1 Development of Optimization
Techniques in OPF Solutions ............ 28
1.7.2.3 OPF Formulation ........................ 30
1.7.2.4 Optimal Power Flow Solution by
Nonlinear Interior Point Methods ....... 31
1.8 Operation and Control of Electric Power Systems—SCAD
A/EMS .................................................. 34
1.8.1 Introduction of SCAD A/EMS ...................... 34
1.8.2 SCAD A/EMS of Conventional Energy Control
Centers ......................................... 36
1.8.3 New Development Trends of SCAD A/EMS of Energy
Control Centers ................................. 37
1.8.3.1 New Environments ....................... 37
1.8.3.2 Advanced Software Technologies ......... 38
1.9 Active Power and Frequency Control ..................... 39
1.9.1 Frequency Control and Active Power Reserve ...... 39
1.9.2 Objectives of Automatic Generation Control ...... 40
1.9.3 Turbine-Generator-Governor System Model ......... 40
1.9.4 AGC for a Single-Generator System ............... 42
1.9.5 AGC for Two-Area Systems ........................ 43
1.9.6 Frequency Control and AGC in Electricity
Markets ......................................... 43
1.10 Voltage Control and Reactive Power Management .......... 44
1.10.1 Introduction of Voltage Control and Reactive
Power Management ................................ 44
1.10.2 Reactive Power Characteristics of Power System
Components ...................................... 45
1.10.3 Devices for Voltage and Reactive Power
Control ......................................... 45
1.10.4 Optimal Voltage and Reactive Power Control ...... 47
1.10.5 Reactive Power Service Provisions in
Electricity Markets ............................. 47
1.11 Applications of Power Electronics to Power System
Control ................................................ 48
1.11.1 Flexible AC Transmission Systems (FACTS) ........ 48
1.11.2 Power System Control by FACTS 49 References ..... 50
2 RESTRUCTURED ELECTRIC POWER SYSTEMS AND ELECTRICITY
MARKETS ..................................................... 53
Kwok W. Cheung, Gary W. Rosenwald, Xing Wang, and David
I. Sun
2.1 History of Electric Power Systems Restructuring ........ 53
2.1.1 Vertically Integrated Utilities and Power
Pools ........................................... 54
2.1.2 Worldwide Movement of Power Industry
Restructuring ................................... 54
2.1.2.1 Nordic Countries ....................... 55
2.1.2.2 Great Britain .......................... 55
2.1.2.3 Continental Europe ..................... 55
2.1.2.4 New Zealand ............................ 56
2.1.2.5 Australia .............................. 56
2.1.2.6 United States .......................... 57
2.2 Structure of Electricity Markets ....................... 58
2.2.1 Stakeholders .................................... 58
2.2.2 Market Evolution ................................ 60
2.2.3 Market and Reliability Coordination ............. 62
2.2.4 The SMD Framework ............................... 64
2.2.4.1 Transmission Service ................... 64
2.2.4.2 Energy Market .......................... 64
2.2.4.3 Ancillary Service Market ............... 64
2.2.4.4 Market Monitoring and Mitigation ....... 64
2.3 Design of Electricity Markets .......................... 65
2.3.1 Market Design Objectives ........................ 65
2.3.1.1 Secure and Reliable Operation of
Power System ........................... 65
2.3.1.2 Risk Management Facilities for Market
Participants ........................... 65
2.3.1.3 Open and Transparent Market
Performance ............................ 66
2.3.1.4 Phased Implementation of Market
Migration .............................. 66
2.3.2 Market Design Principles ........................ 66
2.3.2.1 Establish Trading Mechanisms for
Energy Resources ....................... 67
2.3.2.2 Establish Open Access for
Transmission Services .................. 67
2.3.2.3 Harmonize System Operation with
Market Operation ....................... 68
2.3.3 Energy Market Design ............................ 68
2.3.4 Financial Transmission Rights Market Design ..... 69
2.3.5 Ancillary Service Market Design ................. 70
2.4 Operation of Electricity Markets ....................... 72
2.4.1 Criteria for Successful Market Operation ........ 72
2.4.1.1 Power System Reliability ............... 72
2.4.1.2 Market Transparency .................... 73
2.4.1.3 Financial Certainty .................... 73
2.4.1.4 Operational Market Efficiency .......... 74
2.4.2 Typical Business Processes Timeline ............. 75
2.4.2.1 New Zealand Electricity Market ......... 75
2.4.2.2 PJM Markets ............................ 78
2.5 Computation Tools for Electricity Markets .............. 81
2.5.1 SCED and Associated Market Business Functions ... 83
2.5.1.1 Classic OPF ............................ 83
2.5.1.2 SCED for Market Clearing ............... 84
2.5.1.3 Joint Optimization of Energy and
Ancillary Services ..................... 85
2.5.1.4 SCED Formulation Example ............... 86
2.5.2 Optimization-Based Unit Commitment .............. 88
2.5.2.1 Market-Oriented Unit Commitment
Problem ................................ 88
2.5.2.2 Advances in Unit Commitment Methods .... 89
2.5.2.3 SCUC Example Problem: Reliability
Commitment ............................. 91
2.5.2.4 SCUC Performance Consideration ......... 92
2.5.3 System Implementation ........................... 93
2.5.4 Future Direction ................................ 94
2.6 Final Remarks .......................................... 95
References .................................................. 96
3 OVERVIEW OF ELECTRICITY MARKET EQUILIBRIUM PROBLEMS AND
MARKET POWER ANALYSIS ....................................... 99
Xiao-Ping Zhang
3.1 Game Theory and Its Applications ....................... 99
3.2 Electricity Markets and Market Power .................. 110
3.2.1 Types of Electricity Markets ................... 100
3.2.1.1 Bid-Based Auction Pool / PoolCo /
Spot Market ........................... 100
3.2.1.2 Bilateral Agreements, Forward
Contracts, and Contracts for
Differences ........................... 101
3.2.2 Competition Types .............................. 102
3.2.2.1 Perfect Competition ................... 102
3.2.2.2 Imperfect or Oligopolistic
Competition ........................... 103
3.3 Market Power Monitoring, Modeling, and Analysis ....... 103
3.3.1 The Concept of Market Power .................... 103
3.3.2 Techniques for Measuring Market Power .......... 104
3.3.2.1 The Price-Cost Margin Index ........... 104
3.3.2.2 The Herfindahl-Hirschan Index ......... 104
3.3.2.3 Estimation of Pricing Behavior
Through Simulation Analysis ........... 105
3.3.2.4 Oligopoly Equilibrium Analysis ........ 105
3.3.3 Oligopolistic Equilibrium Models .................... 105
3.3.3.1 Bertrand Equilibrium .................. 106
3.3.3.2 Cournot Equilibrium ................... 106
3.3.3.3 Supply Function Equilibrium ........... 106
3.3.3.4 Stackelberg Equilibrium ............... 107
3.3.3.5 Conjectured Supply Function
Equilibrium ........................... 107
3.3.4 Market Power Modeling Using Equilibrium
Models ......................................... 107
3.4 Application of the Equilibrium Models in the
Electricity Markets ................................... 109
3.4.1 Bertrand Equilibrium Model ..................... 109
3.4.2 Cournot Equilibrium Model ...................... 109
3.4.3 Supply Function Equilibrium Models in
Electricity Markets ............................ 111
3.4.3.1 Application of Supply Function
Equilibrium Models .................... 111
3.4.3.2 Electricity Network Modeling .......... 113
3.4.3.3 Modeling of Contracts ................. 114
3.4.3.4 Choosing the Appropriate Strategic
Variable .............................. 114
3.4.3.5 Conjecture Supply Function
Equilibrium Model ..................... 114
3.4.4 Conjectural Variation and CSF Equilibrium
Models ......................................... 115
3.5 Computational Tools for Electricity Market
Equilibrium Modeling and Market Power Analysis ........ 115
3.5.1 Mathematical Programs with Equilibrium
Constraints (MPEC) ............................. 116
3.5.2 Bilevel Programming ............................ 117
3.5.3 Equilibrium Problems with Equilibrium
Constraints (EPEC) ............................. 117
3.5.3.1 Formulation of Single-Leader-
Follower Games as an MPEC ............. 117
3.5.3.2 Formulation of Multi-Leader-Follower
Games as an EPEC ...................... 119
3.5.4 NCP Functions for MPCCs ........................ 120
3.5.4.1 The Fischer-Burmeister Function ....... 120
3.5.4.2 The Min-Function ...................... 120
3.5.4.3 The Chen-Chen-Kanzow Function ......... 120
3.6 Solution Techniques for MPECs ......................... 121
3.6.1 SQP Methods .................................... 121
3.6.2 Interior Point Methods ......................... 121
3.6.2.1 Interior Point Methods with Relaxed
Complementarity Constraints ........... 121
3.6.2.2 Interior Point Methods with Two-
Sided Relaxation ...................... 122
3.6.2.3 Interior Point Methods with Penalty ... 123
3.6.3 Mixed-Integer Linear Program (MILP) Methods .... 124
3.6.4 Artificial Intelligence Approach ............... 124
3.7 Solution Techniques for EPECs ......................... 125
3.7.1 Diagonalization Solution Methods ............... 126
3.7.1.1 Nonlinear Jacobi Method ............... 126
3.7.1.2 Nonlinear Gauss-Seidel Method ......... 126
3.7.2 Simultaneous Solution Methods .................. 127
3.8 Technical Challenges for Solving MPECs and EPECs ...... 128
3.9 Software Resources for Large-Scale Nonlinear
Optimization .......................................... 129
References ................................................. 132
4 COMPUTING THE ELECTRICITY MARKET EQUILIBRIUM: USES OF
MARKET EQUILIBRIUM MODELS .................................. 139
Ross Baldick
4.1 Introduction .......................................... 139
4.2 Model Formulation ..................................... 140
4.2.1 Transmission Network Model ..................... 141
4.2.1.1 Physical Model ........................ 141
4.2.1.2 Commercial Network Model .............. 142
4.2.1.3 Economic Model ........................ 145
4.2.2 Generator Cost Function and Operating
Characteristics ................................ 146
4.2.2.1 Physical Model ........................ 146
4.2.2.2 Economic Model ........................ 147
4.2.3 Offer Function ................................. 147
4.2.3.1 Commercial Model ...................... 147
4.2.3.2 Economic Model ........................ 148
4.2.4 Demand ......................................... 149
4.2.4.1 Physical Model ........................ 149
4.2.4.2 Commercial Model ...................... 149
4.2.4.3 Economic Model ........................ 149
4.2.5 Uncertainty .................................... 150
4.2.5.1 Physical Model ........................ 150
4.2.5.2 Commercial Model ...................... 150
4.2.5.3 Economic Model ........................ 150
4.3 Market Operation and Price Formation .................. 151
4.3.1 Physical Model ................................. 151
4.3.2 Commercial Model ............................... 151
4.3.3 Economic Model ................................. 152
4.4 Equilibrium Definition ................................ 152
4.5 Computation ........................................... 154
4.5.1 Analytical Models .............................. 154
4.5.2 Numerical Solution ............................. 156
4.5.3 Fictitious Play ................................ 157
4.5.4 Mathematical Program with Equilibrium
Constraints and Equilibrium Program with
Equilibrium Constraints ........................ 160
4.5.5 Specialized Solution Methods ................... 160
4.6 Difficulties with Equilibrium Models .................. 160
4.7 Uses of Equilibrium Models ............................ 161
4.7.1 Market Rules Regarding the Changing of
Offers ......................................... 162
4.7.2 Single Clearing Price Versus Pay-as-Bid
Prices ......................................... 162
4.7.3 Divestitures ................................... 163
4.8 Conclusion ............................................ 163
Acknowledgment ............................................. 163
References ................................................. 164
5 HYBRID BERTRAND-COURNOT MODELS OF ELECTRICITY MARKETS
WITH MULTIPLE STRATEGIC SUBNETWORKS AND COMMON KNOWLEDGE
CONSTRAINTS ................................................ 167
Jian Yao, Shmuel S. Oren, and Benjamin F. Hobbs
5.1 Introduction .......................................... 167
5.2 Role of the ISO ....................................... 170
5.3 The Hybrid Subnetwork Model ........................... 173
5.3.1 Two Existing Models ............................ 173
5.3.1.1 The Pure Cournot Model ................ 173
5.3.1.2 The Pure Bertrand Model ............... 174
5.3.2 The Hybrid-Bertrand-Cournot Model .............. 175
5.3.2.1 The Firms' Problems ................... 175
5.3.2.2 The Market Equilibrium Conditions ..... 176
5.3.2.3 Computational Properties .............. 178
5.4 Numerical Example for the Subnetworks Model ........... 180
5.5 Bertrand Model with Common Knowledge Constraints ...... 183
5.5.1 The Firm's Problems ............................ 183
5.5.2 The Market Equilibrium Conditions .............. 187
5.6 Numerical Example of Equilibrium with Common
Knowledge Constraints ................................. 188
5.7 Concluding Remarks .................................... 190
Acknowledgments ............................................ 191
References ................................................. 191
6 ELECTRICITY MARKET EQUILIBRIUM WITH REACTIVE POWER
CONTROL .................................................... 193
Xiao-Ping Zhang
6.1 Introduction .......................................... 193
6.2 AC Power Flow Model in the Rectangular Coordinates .... 194
6.3 Electricity Market Analysis Using AC Optimal Power
Flow in the Rectangular Coordinates ................... 195
6.3.1 Modeling of Power System Components in
Optimal Power Flow ............................. 195
6.3.1.1 Modeling of Transmission Line ......... 195
6.3.1.2 Modeling of Transformer Control ....... 196
6.3.1.3 Modeling of Generating Units .......... 197
6.3.1.4 Generator Reactive Power Capability ... 197
6.3.1.5 Modeling of Loads ..................... 198
6.3.1.6 Bus Voltage Constraints ............... 199
6.3.2 Electricity Market Analysis .................... 199
6.4 Electricity Market Equilibrium Analysis ............... 202
6.4.1 Nash Supply Function Equilibrium Model ......... 202
6.4.2 Assumptions for the Supply Function
Equilibrium Electricity Market Analysis ........ 202
6.4.3 Parameterization Methods for Linear Supply
Functions in Electricity Market Equilibrium
Analysis ....................................... 204
6.4.3.1 Intercept Parameterization ............ 204
6.4.3.2 Slope Parameterization ................ 205
6.4.3.3 Slope-Intercept Parameterization ...... 205
6.4.3.4 Linear Slope-Intercept
Parameterization ...................... 205
6.5 Computing the Electricity Market Equilibrium with AC
Network Model ......................................... 205
6.5.1 Objective Function for the Social Welfare for
Imperfect Competition .......................... 205
6.5.2 Objective Function for the Maximization of
Profit of the Generating Firm .................. 206
6.5.3 Formulation of Market Equilibrium Model ........ 206
6.5.3.1 ISO's Optimization Problem ............ 206
6.5.3.2 Nonlinear Complementarity
Constraints ........................... 208
6.5.4 Formulation of the Optimization Market
Equilibrium Problem as EPEC .................... 208
6.5.5 Lagrange Function for the EPEC Optimization
Problem ........................................ 209
6.5.6 Newton Equation for the EPEC Problem ........... 211
6.5.7 Modeling of Reactive Power and Voltage
Control ........................................ 215
6.6 Implementation Issues of Electricity Market
Equilibrium Analysis with AC Network Model ............ 216
6.6.1 Initialization of the Optimization Solution .... 216
6.6.2 Updating the Optimization Solution ............. 217
6.6.3 Solution Procedure ............................. 217
6.7 Numerical Examples .................................... 218
6.7.1 Reactive Power and Voltage Control ............. 218
6.7.1.1 Description of the Test Systems ....... 218
6.7.1.2 Test Results of the 3-Bus System ...... 218
6.7.1.3 The IEEE 14-Bus System ................ 220
6.7.1.4 Discussions ........................... 221
6.7.2 Transformer Control ............................ 222
6.7.2.1 Description of the Test Systems ....... 222
6.7.2.2 Test Results on the 5-Bus System ...... 222
6.7.2.3 Test Results on the IEEE 30-Bus
System ................................ 225
6.7.3 Computational Performance ...................... 227
6.8 Conclusions ........................................... 228
6.9 Appendix .............................................. 229
6.9.1 Second Derivatives for Power Mismatches in
Rectangular Coordinates ........................ 229
6.9.2 Second Derivatives for Transmission Line
Constraints in Rectangular Coordinates ......... 229
6.9.3 Second Derivatives in Rectangular
Coordinates .................................... 230
6.9.4 Second Derivatives of Transmission Line
Constraints in Rectangular Coordinates ......... 234
6.9.5 Third Derivatives of Power Mismatches with
Transformer Control ............................ 234
6.9.6 Third Derivatives of Transmission Line
Constraints .................................... 235
Acknowledgments ............................................ 237
References ................................................. 237
7 USING MARKET SIMULATIONS FOR ECONOMIC ASSESSMENT OF
TRANSMISSION UPGRADES: APPLICATION OF THE CALIFORNIA ISO
APPROACH ................................................... 241
Mohamed Labib Awad, Keith E. Casey, Anna S. Geevarghese,
Jeffrey C. Miller, A. Farrokh Rahimi, Anjali Y. Sheffrin,
Mingxia Zhang, Eric Toolson, Glenn Drayton, Benjamin
F. Hobbs, and Frank A. Wolak
7.1 Introduction .......................................... 241
7.2 Five Principles ....................................... 242
7.2.1 First Principle: Benefit Framework ............. 243
7.2.2 Second Principle: Full Network
Representation ................................. 245
7.2.3 Third Principle: Market Prices ................. 246
7.2.4 Fourth Principle: Explicit Uncertainty
Analysis ....................................... 247
7.2.5 Fifth Principle: Interactions with Other
Resources ...................................... 249
7.3 Palo Verde-Devers NO. 2 Study ......................... 250
7.3.1 Market Model: PLEXOS ........................... 250
7.3.2 Project Description ............................ 252
7.3.3 Input Assumptions .............................. 253
7.3.3.1 Transmission .......................... 253
7.3.3.2 Loads ................................. 253
7.3.3.3 Generation ............................ 253
7.3.3.4 Uncertainty Cases ..................... 255
7.3.3.5 Market Price Derivation ............... 256
7.3.4 Results ........................................ 259
7.3.4.1 Benefit Category 1: Energy Savings .... 259
7.3.4.2 Uncertainty in Energy Benefit
Estimates ............................. 261
7.3.4.3 Benefit Category 2: Operational
Benefits .............................. 264
7.3.4.4 Benefit Category 3: Capacity
Benefit ............................... 264
7.3.4.5 Benefit Category 4: Loss Savings ...... 265
7.3.4.6 Benefit Category 5: Emissions ......... 265
7.3.4.7 Summary of Results .................... 265
7.3.5 Resource Alternatives .......................... 266
7.4 Recent Applications of Team to Renewables ............. 266
7.5 Conclusion ............................................ 267
Acknowledgments ............................................ 268
References ................................................. 268
INDEX ......................................................... 271
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