Power System Economics

Transcription

1 Power System Economics Designing Markets for Electricity Steven Stoft IEEE / Wiley

2 Cover painting by W. Louis Sonntag, Jr. ( ), The Bowery at Night, c Early deregulated electricity market with trolleys powered by Westinghouse s AC and shops probably illuminated with Edison s DC. The houses may still be lit by gas. The Third Avenue Elevated (1878), whose noise and shadows contributed to the decline of New York s onceelegant theater district, will soon be electrified. (Uncle Tom s Cabin was first staged in the Bowery Theatre visible at the extreme left.) Arc lights, brought to New York streets in 1880 by Charles Brush, transformed night life. Sonntag frequently depicted the resulting sense of glamour and excitement. The watercolor was a Gift of Mrs. William B. Miles to the Museum of the City of New York.

3 For my mother, whose writing inspired me to think I could, and my father who taught me to test high voltage with one hand behind my back

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5 Contents in Brief List of Results and Fallacies Preface Acronyms and Abbreviations Symbols xiv xviii xx xxii Prologue 2 Why Deregulate? 6 What to Deregulate 17 Pricing Power, Energy, and Capacity 30 Power Supply and Demand 40 Part 1. Power Market Fundamentals What Is Competition? 49 Marginal Cost in a Power Market 60 Market Structure 74 Market Architecture 82 Designing and Testing Market Rules 93 Part 2. Reliability, Price Spikes and Investment Reliability and Investment Policy 108 Price Spikes Recover Fixed Costs 120 Reliability and Generation 133 Limiting the Price Spikes 140 Value-of-Lost-Load Pricing 154 Introduction 202 The Two-Settlement System 208 Day-Ahead Market Designs 217 Ancillary Services 232 The Day-Ahead Market in Theory 243 Defining Market Power 316 Exercising Market Power 329 Modeling Market Power 337 Power Transmission and Losses 374 Physical Transmission Limits 382 Congestion Pricing Fundamentals 389 Congestion Pricing Methods 395 Congestion Pricing Fallacies 404 Part 3. Market Architecture Part 4. Market Power Part 5. Locational Pricing Operating-Reserve Pricing 165 Market Dynamics and the Profit Function 174 Requirements for Installed Capacity 180 Inter-System Competition for Reliability 188 Unsolved Problems 194 The Real-Time Market in Theory 254 The Day-Ahead Market in Practice 264 The Real-Time Market in Practice 272 The New Unit-Commitment Problem 289 The Market for Operating Reserves 306 Designing to Reduce Market Power 345 Predicting Market Power 356 Monitoring Market Power 365 Refunds and Taxes 411 Pricing Losses on Lines 417 Pricing Losses at Nodes 424 Transmission Rights 431 Glossary 443 References 455 Index 460

6 Contents List of Results and Fallacies xiv Preface xviii Acronyms and Abbreviations xx Symbols xxii Part 1. Power Market Fundamentals Prologue 2 Reading to Different Depths 3 Reading Out of Order Why Deregulate? 6 Conditions for Deregulation 9 Problems with Regulation 10 The Benefits of Competitive Wholesale Markets 12 The Benefits of Real-time Rates 13 Problems with Deregulating Electricity What to Deregulate 17 Ancillary Services and the System Operator 19 Unit Commitment and Congestion Management 22 Risk Management and Forward Markets 25 Transmission and Distribution 25 Retail Competition Pricing Power, Energy, and Capacity 30 Measuring Power and Energy 32 Measuring Generation Capacity 33 Pricing Generation Capacity 33 Technical Supplement Power Supply and Demand 40 Describing the Demand for Power 41 Screening Curves and Long-Run Equilibrium 44 Frequency, Voltage, and Clearing the Market 45

7 Contents ix 1-5 What Is Competition? 49 Competition Means More than Struggle 51 The Efficiency of Perfect Competition 52 Short- and Long-Run Equilibrium Dynamics 56 Why Is Competition Good For Consumers? Marginal Cost in a Power Market 60 The Role of Marginal Cost 62 Marginal-Cost Fallacies 63 The Definition of Marginal Cost 65 Marginal Cost Results 67 Working with Marginal Costs 69 Scarcity Rent Market Structure 74 Reliability Requirements 76 Transmission 77 Effective Demand Elasticity 78 Long-Term Contracts 80 Supply Concentration Market Architecture 82 Listing the Submarkets 84 Market Types: Bilateral through Pools 86 Market Linkages Designing and Testing Market Rules 93 Design for Competitive Prices 95 Design to Prevent Gaming 98 Auctions 99 Testing a Market Design 101 Technical Supplement: Example of a Bottom-Line Test 103 Part 2. Reliability, Price Spikes, and Investment 2-1 Reliability and Investment Policy 108 Price Regulation is Essential 111 The Profit Function 114 Side Effects of Reliability Policy 116 Inter-System Competition 117 Demand-Side Effects of Price Limits Price Spikes Recover Fixed Costs 120 The Fixed-Cost Fallacy 121 Optimal Price Spikes for Peakers 123 The Lumpiness of Fixed Costs 129

8 x Contents 2-3 Reliability and Generation 133 Operating Reserves and Contingencies 134 Adequacy and Security 135 The Simple Model of Reliability 136 The Fundamental Reliability Question Limiting the Price Spikes 140 Normal Market Operation with Limited Demand Elasticity 142 Market Failure with a steep load-duration curve 144 Suppressing the Balancing Market to Avoid Regulating Price 145 Setting Price to the Last Clearing Price 148 How Real-Time Price Setting Caps the Forward Markets 150 Technical Supplement: The Condition for Failure Value-of-Lost-Load Pricing 154 Valuing Lost Load 155 VOLL Pricing is Optimal in the Simple Model of Reliability 157 Practical Considerations 159 Technical Supplement Operating-Reserve Pricing 165 Less Risk, Less Market Power 166 How Can OpRes Pricing Be Better than Optimal? Market Dynamics and the Profit Function 174 Calculating Profit Functions 175 Interpreting the Profit Function Requirements for Installed Capacity 180 The Capacity-Requirement Approach 181 Short-Run Profits with a Capacity Requirement 182 Combining a Capacity Requirement with a Price Spike 184 Comparing the Two Approaches Inter-System Competition for Reliability 188 Price-Cap Competition 189 Competition between Price Spikes and Capacity Requirements Unsolved Problems 194 High Marginal Costs and Low Price Caps 195 Pricing Supply and Demand Separately 197 Price-Elastic Demand for Operating Reserves 197 The Psychology of System-Operators 198 Part 3. Market Architecture 3-1 Introduction 202 Spot Markets, Forward Markets and Settlements 203 Architectural Controversies 204 Simplified Locational Pricing 206

9 Contents xi 3-2 The Two-Settlement System 208 The Two-Settlement System 209 Ex-Post Prices: The Trader s Complaint Day-Ahead Market Designs 217 How Day-Ahead Auctions Determine Quantity and Price 218 Summaries of Four Day-Ahead Markets 223 Overview of the Day-Ahead Design Controversy Ancillary Services 232 The List of Ancillary Services 233 Real-Power Balancing and Frequency Stability 236 Voltage Stability for Customers 238 Transmission Security 238 Economic Dispatch 240 Trade Enforcement The Day-Ahead Market in Theory 243 Equilibrium Without a Clearing Price 244 Difficulties with Bilateral Day-Ahead Markets 247 Settlement, Hedging, and Reliability 250 Other Design Considerations The Real-Time Market in Theory 254 Which Trades Are Part of the Real-Time Market? 255 Equilibrium Without a Market-Clearing Price 258 Why Real-Time Markets Are Not Purely Bilateral The Day-Ahead Market in Practice 264 Arbitrage vs. Computation 265 Efficiency 268 Reliability and Control 269 Risk Management The Real-Time Market in Practice 272 Two Approaches to Balancing-Market Design 274 The Marginal-Cost Question As Decided by FERC 277 Making Sense of the Marginal-Cost Pricing Charade 279 The Power Exchange Approach The New Unit-Commitment Problem 289 How Big Is the Unit-commitment problem? 291 Unit Commitment in a Power Exchange 294 Investment Under a Power Pool The Market for Operating Reserves 306 Types of Operating Reserve 307 Scoring by Expected Cost 309 Scoring Based on the Capacity Bid Only 310 Opportunity-Cost Pricing 313

10 xii Contents Part 4. Market Power 4-1 Defining Market Power 316 Defining Market Power 318 Defining Price-Quantity Outcomes 319 Three Stages of Market Power 321 Using Price-Quantity Outcomes to Show Market Power 323 Monopoly Power in a Power Auction 326 Market Power on the Demand Side Exercising Market Power 329 Market Power and Forward Markets 330 Long-Run Reactions to Market Power 331 Marginal and Nonmarginal Generators 332 The Two Effects of Market Power 333 Long-Run and Short-Run Market Power 334 Is a 1000% Markup Too Much? Modeling Market Power 337 Monopoly and the Lerner Index 338 The Cournot Model 340 Unilateral Action and the HHI 342 Technical Supplement: Markup Determination Designing to Reduce Market Power 345 Demand Elasticity and Supplier Concentration 346 What Keeps Prices Down? 347 Forward Contracts and Obligations 347 Demand Uncertainty and Supply-Curve Bidding 351 Technical Supplement: Calculations for Section Predicting Market Power 356 Four Factors that HHI Ignores 357 Why the Lerner Index Is Unreliable 358 Estimating Market Power 361 Technical Supplement: Market Power and Forward Contracts Monitoring Market Power 365 FERC s Ambiguous Standard 366 Market Monitoring 368 Part 5. Locational Pricing 5-1 Power Transmission and Losses 374 DC Power Lines 375 AC Power Lines Physical Transmission Limits 382 Thermal Limits on Power Lines 383 Reactive Power and Thermal Limits 384 Stability Limits on Power Lines 386

11 Contents xiii 5-3 Congestion Pricing Fundamentals 389 Congestion Pricing Is Competitive Pricing 390 Benefits of Competitive Locational Prices Congestion Pricing Methods 395 Centralized Computation of CLPs 396 Bilateral Pricing Compared to Centralized Pricing Congestion Pricing Fallacies 404 Are Competitive Locational Prices Too High? 404 Congestion Taxing Refunds and Taxes 411 Pricing Versus Taxing 412 Energy Taxes Pricing Losses on Lines 417 The Competitive Price is Twice the Average Cost 418 Competitive Losses Pricing 419 Inefficiency of Average-Cost Loss Pricing Pricing Losses at Nodes 424 Nodal Loss Prices 425 Full Nodal Pricing: Loss, Congestion and Reference Prices 427 Three Common Restrictions on Losses Pricing Transmission Rights 431 The Purpose of Transmission Rights 432 Using Financial Transmission Rights 435 Revenues from System-Issued Financial Rights 437 Physical Transmission Rights 440 Glossary 443 References 455 Index 460

12 List of Results and Fallacies 1 The Efficient-Competition Result 10 The Price-Cap Result 2 The Marginal-Cost Pricing Result 11 The Contracts-for-Differences Result 1 3 The Marginal-Cost Fallacy 12 The Contracts-for-Differences Result 2 4 The Ambiguous-Price Fallacy 13 The Efficient-Auction Result 5 The System-Marginal-Cost Pricing Result 14 The HHI Result 6 The Fixed-Cost Fallacy 15 The Market-Power Fallacy 7 The Weak Fixed-Cost Fallacy 16 Locational-Pricing Result 1 8 The Reliability Fallacy 17 Locational-Pricing Result 2 9 The Regulatory-Price-Spike Result 18 The Locational-Pricing Fallacy Part 1. Power Market Fundamentals Why Deregulate? Result Savings from Real-Time Rates Would Be Small 14 Pricing Power, Energy, and Capacity Fallacy Fixed and Variable Costs Are Measured in Different Units 34 Result Energy, Power, and Capacity Are Priced in $/MWh 36 Power Supply and Demand Result Supply Equals Consumption but May Not Equal Demand 48 What Is Competition? 1 Result Competitive Prices Are Short- and Long-Run Efficient 54 2 Result Competitive Suppliers Set Output So That MC = P 57 Result 1-5.3a Under Competition, Average Economic Profit Is Zero 58 Result 1-5.3b Under Competition, Fixed Costs Are Covered 58 Result 1-5.3c A Supplier with a Unique Advantage Can Do Better 58 Marginal Cost in a Power Market 3 Fallacy Marginal Cost Equals the Cost of the Last Unit Produced 64 4 Fallacy When Marginal Cost Is Ambiguous, so Is the Competitive Price 65 Result Competitive Suppliers Set Output so MC LH < P < MC RH 5 Result Competitive Price Equals System Marginal Cost 68 Result Supply Intersects Demand at the Competitive Price 69 Market Architecture Result The Forward Price Is the Expected Future Spot Price 90 Designing and Testing Market Rules Fallacy Scarcity Rents Are Unfair 95 Result Changing the Market s Rules Changes Behavior 97 Result Design Market Mechanisms to Induce Truth Telling 99 Result Four Types of Auctions Produce the Same Revenue 100 Result A Vickrey Auction Is Incentive Compatible 100

13 List of Results and Fallacies xv Part 2. Reliability, Price Spikes, and Investment Price Spikes Recover Fixed Costs 6 Fallacy Marginal-Cost Prices Will Not Cover Fixed Cost 121 Result In the Long-Run, Suppliers Recover Their Fixed Costs 123 Result Long-Run Equilibrium Conditions for Two Technologies Fallacy Marginal-Cost Pricing Causes a Capacity Shortage 129 Result Marginal-Cost Prices Induce the Optimal Mix of Technologies 129 Result Inefficiency Caused by the Lumpiness of Generators Is Negligible 131 Reliability and Generation Result Optimal Duration of Load Shedding Is D * LS = FC peak 'V LL 139 Limiting the System s Price Result A Small Amount of Elastic Demand Can Make the Market Efficient 143 Result Too Little Demand Elasticity Can Cause the Real-Time Market to Fail 145 Result Suppressing the System Operator s Balancing Market Is Inefficient Fallacy The Market Will Provide Adequate Reliability 111, Result Regulatory Policy Determines the Height and Duration of Price Spikes 114, 147 Result Do Not Cap Prices at the Highest Demand Bid Result The Real-Time Price Limit Effectively Caps the Entire Market 113, 152 Result Conditions for the Failure of a Power Market 152 Result Conditions for an Efficient Power Market 153 Value-of-Lost-Load Pricing Fallacy VOLL Cannot Be Usefully Defined 156 Result Within the Simple Model of Reliability, VOLL Pricing Is Optimal 159 Result Inaccuracy of Estimation Does Not Rule Out the Use of VOLL 159 Fallacy Risk from VOLL Pricing Is Beneficial 161 Operating-Reserve Pricing Result Many Different Price Limits Can Induce Optimal Investment 116, 168 Result A Lower, Longer-Duration Aggregate Price Spike Is Less Risky 169 Result High Price Caps Invite the Exercise of Market Power 171 Result Reliability Policy Should Consider Risk and Market Power 117, 173 Market Dynamics and the Profit Function Result The Higher the Price Spikes, the Steeper the Profit Function 177 Result Steeper Profit Functions Increase Risk and Market Power 178 Requirements for Installed Capacity Result Energy and Capacity Prices Together Induce Investment 115, 181 Result A Capacity Requirement Can Eliminate the Need for Price Spikes 184 Result VOLL Pricing Induces Optimal ICap Even When ICap Is Random 185 Result Profit Functions Are Additive, But Resulting Profits Are Not 186 Inter-System Competition for Reliability Result Competition Between System Operators Induces High Price Spikes 118, 190 Result Trading between Markets with Different Policies Can Reduce Reliability 191 Result Capacity-Requirement Markets Need Annual Requirements 192 Unsolved Problems Result The Price of Operating Reserves Should Increase When They Are Scarce 198

14 xvi List of Results and Fallacies Part 3. Market Architecture The Two-Settlement System Result A Two-Settlement System Preserves Real-Time Incentives Result A Contract for Differences Insulates Traders from Spot Price Volatility Result Contracts for Differences Preserve Real-Time Incentives 213 Day-Ahead Market Designs 13 Result A Single-Price Day-Ahead Auction Is Efficient 220 Ancillary Services Result Strictly Bilateral Power Trading Requires Centralized Coordination 241 The Day-Ahead Market in Theory Result A Bilateral DA Market Decreases Reliability 249 Result Side-Payments in a Day-Ahead Pool Do Not Increase Reliability 252 The Real-Time Market in Theory Result Real-Time Power Is Not Bought or Sold Under Contract 256 Result Real-Time Pools Sometimes Require Direct Control of Generation 259 The Day-Ahead Market in Practice Result A Day-Ahead Power Pool Is Not Required for Reliability 269 The Real-Time Market in Practice Result SMC Unit Commitment with Elastic Demand Is Inefficient 283 Result System-Marginal-Value Pricing Provides Efficient Demand Incentives 284 The New Unit-Commitment Problem Result A Power Exchange s Unit-Commitment Inefficiency Is Less Than 1%. 293 Result Marginal Cost Prices Can Solve Some Unit-Commitment Problems 294 Result A Power Exchange Lacks a Classic Competitive Equilibrium 297 Result A Power Pool with Accurate Bids Induces the Optimal Dispatch 297 Result Two-Part Bids Can Solve Some Unit-Commitment Problems 298 Result A Power Exchange Has a Nearly-Efficient Nash Equilibrium 300 Result Side Payments in Power Pools Distort Investment in Generation 303 The Market for Operating Reserves Result Capacity-Bid Scoring for Spinning Reserves Is Optimal Part 4. Market Power Defining Market Power Result Monopoly Power Always Causes the Quantity Withheld to be Positive 325 Result When Assessing Monopoly Power, Ignore Demand-Side Flaws 325 Result Profitably Raising the Market Price May Not Be Market Power 326 Exercising Market Power Result Market Power Cannot Be Exercised in Day-Ahead Power Markets 331 Result The Bid that Raises the Price May Not Set the Price 332 Modeling Market Power 14 Result The Average Lerner Index Equals HHI Over Demand Elasticity 342 Predicting Market Power Result Price Distortion Measures Market Power Better 361 Monitoring Market Power 15 Fallacy Some Market Power Is Needed and Beneficial 370 Fallacy Market Power Cannot Be Proven 370

15 List of Results and Fallacies xvii Part 5. Basic Locational Pricing Power Transmission and Losses Result Kirchhoff s Laws 376 Result Power Equals Voltage Times Current (Volts Amps) 377 Result Ohm s Law Is Voltage Equals Current Times Resistance (I R) 377 Result Transmission Losses Are Proportional to Power 2 / Voltage Physical Transmission Limits Result Thermal Limits Depend on Real and Reactive Power Flows 385 Congestion Pricing Fundamentals Result Transmission Price AûB Is the Power Price Difference, P B! P A Result Only Competitive Locational Prices Minimize Total Production Cost 394 Congestion Pricing Methods Result Power Flows Are Approximately Additive Result Competitive Bilateral Prices Equal Centralized Locational Prices 401 Congestion Pricing Fallacies 18 Fallacy Congestion Rent > Redispatch Cost Is Unfair to Consumers 406 Refunds and Taxes Result Price for Efficiency and Not to Raise Revenue 414 Result Tax for Revenue and Not to Improve Efficiency 414 Result An Energy-Based Transfer from Generators to Loads has No Net Effect 415 Result An Energy Tax on Load or Generation Will Be Paid by Load 416 Pricing Losses on Lines Result Marginal Losses Are Twice Average Losses 418 Result The Competitive Charge for Transmission Is Twice the Cost of Losses 419 Result Competitive Bilateral Loss Prices Equal Marginal Cost 421 Result Average-Cost Loss Pricing Raises the Cost of Production 423 Pricing Losses at Nodes Result Changing the Reference Bus Changes Loss Prices Uniformly 427 Result Changing the Reference Bus Does Not Affect Bilateral Trades 427 Transmission Rights Result Trading Opportunities Are Not Blocked by Congested Lines 433 Result Revenue from a Feasible Set of TCCs Will Be Sufficient 439 Result The Feasible Set of Physical Rights Cannot Account for Counterflows 440

16 Preface My original purpose in writing this book was to collect and present the basic economics and engineering used to design power markets. My hope was to dispel myths and provide a coherent foundation for policy discussions and market design. In the course of writing, I came to understand there is no received wisdom to present on two key issues: price-spikes and pools. While the majority of the book still holds to my first purpose, Parts 2 and 3 are guided as well by a second. They seek to present the two unresolved issues coherently, answer a few basic questions and highlight some of the gaps in our current understanding. The price-spike issue is how to design the market to accommodate two demandside flaws underlying the price-spikes that provide incentives for investment in generation. Part 2 shows that some regulation is required until one flaw has been mitigated. The first regulatory goal should be to ensure the revenue from the aggregate price spike is just sufficient to induce a reliable level of generating capacity. This revenue is determine by (1) the duration of the aggregate price spike which is under the influence of NERC guidelines and (2) the height of the price spike which is regulated by FERC. Currently, neither institution appears aware their policies jointly determine investment. Part 2 provides a framework for computing the level of investment induced by any combination of NERC and FERC policies. Because many combinations will work, it suggests a second goal. Price volatility should be reduced to levels that might be expected from a mature power market levels far below those observed in the current markets with their incapacitated demand sides. I hope Part 2 will clarify the regulatory options and the need to fix the market s demand side. While Part 3 presents the standard principles of bilateral markets, exchanges and pools, it is able to make little progress on the second issue, the power-pool question. An exchange is a widely used form of centralized market the New York Stock Exchange is an example while pools are peculiar to power markets. Exchanges trade at one price at any given time and location, while pools pay different prices to different generators according to their costs. The differences in transparency and operation are considerable as may be their performance. Unfortunately, little theoretical or empirical research is to be found, and Part 3 can only raise issues and show the answers are far from obvious. While three pools operate in the eastern U.S. and PJM has been deregulated for nearly four years, no evaluation of their efficiency has been undertaken. The only national effort, a shoestring operation at the Department of Energy, has been crippled by lack of access to data that FERC could easily obtain from the pools. Pro-pool forces within FERC have, for years, blocked any suggestion to evaluate the performance of pools or their potential benefits. No description of any eastern

17 Preface xix pool, suitable for economic analysis, can be found within FERC or in the public domain. Theoretical pool descriptions cover ex-ante pricing while knowledgeable observers indicate the eastern ISOs use ex-post pricing. This is said to be based on a philosophy of controlling quantities in real-time and computing prices after the fact. In practice, it involves proprietary calculations that apparently assume the operator s actions were optimal. I could discover no useful discussion of the theory of this critical issue, so readers of Part 3 must wait for a later edition. Competitive power markets, like regulated markets, must be designed and designed well. Because of the poor quality of many current designs and the lack of a well-tested standard, this book does not recommend a rush to deregulate. A given deregulation may succeed, but economic theory cannot predict when such a complex political process, once begun, will be out-maneuvered by the forces it seeks to harness. If a market is being designed or redesigned, this book is meant to help; if the decision is to wait, this book is meant to make the wait shorter. Acknowledgments Those who undertook to read, correct and criticize drafts provided an invaluable service and deserve thanks from all of my readers, whom they have protected from many confusions, diversions, and errors. For this difficult undertaking I am especially grateful to Ross Baldick, Joe Bowring, Haru Connally, Rob Gramlich, Doug Hale, Alex Henney, Bill Hogan, Mat Morey, Sabine Schnittger, and Jurgen Weiss. Many others have made more narrowly focused but still invaluable contributions. They provided an ongoing discussion on many topics and constantly provided fresh views and caught errors. Thanks to Darwin Anwar, Gerry Basten, Richard Benjamin, Severin Borenstein, Jason Christian, Ed Mills, Udi Helman, Mike Rothkopf, Erik Hirst, Ben Hobbs, Mangesh Hoskote, Marcelino Madrigal, Dave Mead, Joshua Miller, Alan Moran, Jim Kritikson, Dan Gustafson, Frank Felder, Carl Fuchshuber, Richard Green, Harry Singh, Alasdair Turner, Hugh Outhred, Gail Panagakis, Alex Papalexopolous, Gregory Werden, and James Wightman. Without the patient support of the IEEE/Wiley staff, John Griffen, Tony Vengraitis, and Andrew Prince, none of this would have been possible. My copy editor, Susan Ingrao, has been a pleasure to work with and tremendously informative, even answering arcane typesetting questions. Remaining errors are the result of my inaccurate corrections or last minute changes. For support and guidance on every challenge, I have turned first to my wife Pamela who has been my creative advisor, editor, and legal counsel. I thank her for her abundant patience and unerring judgement. But of all those who have contributed to this book, I owe the most to my mother, Dorothy, who brought her artistry to the dull world of power economics. Through three complete drafts, she gently but persistently corrected and shaped, guided and polished. While the quality of my writing still falls far short of my mother s, it delights me to have learned, at last, a little of her art.

18 Acronyms and Abbreviations AC ACE CA ISO CFD CLP CR DA DOJ FERC FTR FTC GT HHI ICap IPP ISO ISO-NE LBMP LHMC LMP LRMC MC NERC NYISO NYSE NE OpRes PJM PTR RHMC RT RTO SMC SMV TR UC VOLL alternating current area control error California Independent System Operator contract for differences competitive locational price capacity requirement day ahead Department of Justice Federal Energy Regulatory Commission financial transmission right Federal Trade Commission gas turbine generator Herfindahl-Hirschman index installed capacity independent power producer independent system operator ISO New England locational-based marginal price left-hand marginal cost locational marginal price long-run marginal cost marginal cost North American Electric Reliability Council the New York Independent System Operator, Inc. the New York Stock Exchange Nash equilibrium operating reserve Pennsylvania-New-Jersey-Maryland Independent System Operator physical transmission right right-hand marginal cost real time (market) regional transmission organization system marginal cost system marginal value transmission right unit commitment value of lost load

19 Acronyms and Abbreviations xxi Units Used to Measure Electricity V volt The unit of electrical pressure A amp The unit of electrical current W watt Power (Energy per hour) h hour Time Wh watt-hour Energy k kilo Used in kw, kwh and kv. M mega 1,000,000. Used in MW and MWh. G giga 1,000,000,000. Used in GW. T tera Used in TWh.

20 Symbols Units Symbol Definition e, * equilibrium and optimal superscripts peak, mid, base peakload, intermediate, and baseload generating capacity subscripts 1, 0 day-ahead, and real-time subscripts A, B bus-a, bus-b subscripts $/MWh AC E average cost of energy for a load slice $/MWh AC K average cost of purchasing and using capacity for a load slice $/MWyear ARR annual revenue requirement of a generator $/MWh CC cost of providing spinning-reserve capacity. none cf capacity factor none C cost of Production none D LS duration of load shedding (L g > K) none D PS duration of price spike (L g + OR R > K) none D peaker duration of peaker use (L g + OR R > K base ) none e price elasticity of demand MWh E energy $/MWh FC fixed cost $/MWh F T current price of a future for delivery at time T MW g generation out of service none h true probability of needing spinning reserves none h^ estimated h amps I electrical current MW K installed generating capacity (ICap) MW K n e average K in an equilibrium when K is random.

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