steven stoft. power system designing markets for electricity - resumen capitulo 3.pdf

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Power System Economics (389p) Designing Markets for Electricity © 2001 Steven Stoft Excerpts from Part 3 Part 1: Introduction 88 p. Part 2: Price Spikes, Reliability and Investment 110 p. Part 3: Market Architecture 78 p. 3-1 Key Questions of Market Architecture 5 p. 1 Spot Markets, Forward Markets and Settlements 2 Controversies 3 Simplified Locational Pricing 3-2 The Pure Bilateral approach 5 p. 1 No central market 2 Central Coordination without Price 3 A Pure Transmission Market 3-3 Why Have a Spot Energy Exchange 7 p. 1 A Pure Spot Market for Energy 2 Conclusions 3-4 Real-Time Pricing and Settlement 12 p. 1 The Two-Settlement System 2 Setting the Real-time Price 3 Ex-Post Prices: The Trader’s Complaint 3-5 Why Have a Day-ahead Market? 9 p. 1 When Marginal-Cost Bidding Fails 2 Reliability and Unit Commitment 3 Efficiency and Unit Commitment 4 The Congestion Problem 3-6 Day-Ahead Market Designs 13 p. 1 Defining Day-Ahead Auctions 2 Four Designs 3 The Impact of Startup Insurance 4 Transmission Bids and Virtual Bids 3-7 Multi-Part Unit Commitment? 16 p. 1 How Big is the Unit Commitment Problem? 2 Market Design #1: A Pure Energy Auction 3 Market Design #3: A Unit Commitment Auction 3-8 A Market for Operating Reserves 11 p. 1 Bid-Based Pricing. 2 Opportunity-based pricing Part 4: Market Power 56 p. Part 5: The One-Line Network 63 p.

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  • Power System Economics (389p)Designing Markets for Electricity 2001

    Steven Stoft

    Excerpts from Part 3Part 1: Introduction 88 p.Part 2: Price Spikes, Reliability and Investment 110 p.Part 3: Market Architecture 78 p.3-1 Key Questions of Market Architecture 5 p.

    1 Spot Markets, Forward Markets and Settlements2 Controversies3 Simplified Locational Pricing

    3-2 The Pure Bilateral approach 5 p.1 No central market2 Central Coordination without Price3 A Pure Transmission Market

    3-3 Why Have a Spot Energy Exchange 7 p.1 A Pure Spot Market for Energy 2 Conclusions

    3-4 Real-Time Pricing and Settlement 12 p.1 The Two-Settlement System2 Setting the Real-time Price3 Ex-Post Prices: The Traders Complaint

    3-5 Why Have a Day-ahead Market? 9 p.1 When Marginal-Cost Bidding Fails2 Reliability and Unit Commitment3 Efficiency and Unit Commitment4 The Congestion Problem

    3-6 Day-Ahead Market Designs 13 p.1 Defining Day-Ahead Auctions2 Four Designs3 The Impact of Startup Insurance4 Transmission Bids and Virtual Bids

    3-7 Multi-Part Unit Commitment? 16 p.1 How Big is the Unit Commitment Problem?2 Market Design #1: A Pure Energy Auction3 Market Design #3: A Unit Commitment Auction

    3-8 A Market for Operating Reserves 11 p.1 Bid-Based Pricing.2 Opportunity-based pricing

    Part 4: Market Power 56 p.Part 5: The One-Line Network 63 p.

  • Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-1Questions of Market Architecture

    MARKET ARCHITECTURE CONCERNS THE KEY DESIGNELEMENTS. While Part 2 abstracts from all questions of market design tofocus on market structure, Part 3 considers alternative designs for the realtimemarket, the day-ahead forward markets and the relationship between the two.It also discusses several controversies, such as the degree of centralization, thathave often plagued the design process. Design elements are considered in justenough detail to allow comparisons between the main alternative approaches.

    While Part 3 moves forward from real-time it does not move past the day-ahead market, and it does not consider private bilateral markets that operatebeside the markets organized by the system operator (SO). It focuses only onthose markets that are typically part of an ISO design.

    Section 1: Spot Markets, Forward Markets and Settlements.Forward markets are financial markets while the realtime (spot) market is aphysical market. To the extent power sold in the day-ahead market is notprovided by the seller, the seller can buy replacement power in the spot market.This is the basis of the two-settlement system that underlies one standardmarket design in which the SO conducts both day-ahead and spot energymarkets.

    Section 2: Controversies. Three major controversies have beset thedesign of power markets. First is the conflict over how decentralized themarket should be. One view holds that both day-ahead and spot markets shouldbe bilateral energy markets, and the SO should have no dealings that involvethe price of energy but instead sell (or ration) only transmission.

    The second conflict arises only if the day-ahead market is to be run by thesystem operator (centralized). One view holds that such an auction marketshould utilize multi-part bids to solve the unit commitment problem in the

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    traditional way. Another view holds that bids should specify only an energyprice.

    The third conflict concerns the level of detail at which locational prices arecomputed. The nodal view typically argues for hundreds or thousands oflocations, while the zonal view typically calls for well under one hundred. Thiscontroversy is less fundamental and is not considered in Part 3.

    Section 3: Simplified Locational Pricing. All markets discussed inPart 3 produce energy prices that are locationally differentiated. The theory ofsuch prices is not presented until Part 5, so a summary of their properties isgiven in Section 3. These prices are competitive and thus independent of themarkets architecture. Because they are competitive they have the normalproperties of competitive prices; they minimize production cost for a givenlevel of consumption, and they maximize net benefit.

    3-1.1 SPOT MARKETS, FORWARD MARKETS AND SETTLEMENTSTrading for the power sold in any particular minute begins years in advance andcontinues until real time, the actual time at which the power flows out of agenerator and into a load. This is accomplished by a sequence of marketswhich often overlap. The earliest markets are typically forward markets thattrade non-standard long-term contracts. Futures contracts typically cover amonth of power during on-peak hours and are sold up to a year or two inadvance. Trading continues in less formal markets until about one day prior toreal time. Typically, just as this informal trading peters out, the system operatorholds its day-ahead (DA) market. This is often followed by an hour-ahead(HA) market and a realtime market also conducted by the system operator.

    All of these except the realtime market are financial markets in the sensethat suppliers need not own a generator to sell power. The realtime market isa physical market, as all trades correspond to actual power flows. While theterm spot market is often used to include the DA and HA markets, this bookwill use it to mean only the realtime market because it is the only physicalmarket. A customer in the DA market does not purchase electricity but rathera promise to deliver electricity. If the promise is not kept, the supplier must buythe power it failed to deliver in the spot market. It is possible to sell power inthe DA market without owning a generator and cover the sale with a spotmarket purchase. A clever speculator can make money on such purely financialtransactions, but he cannot trade only in the spot market.

    Financial markets need a way for traders to unwind their position. If asupplier sells, in a financial market, 1600 MWh to be delivered evenly over the

  • 4 PART 3: Market Architecture

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    sixteen peak hours of July 1, this should impose only a financial commitment.Typically such a sale includes a clause for liquidated damages; if the power isnot delivered, the supplier must pay the cost of replacement. This alwaysallows the supplier the option of buying replacement power, and, except in themost extraordinary conditions, this can be done in a subsequent market.

    The most formal arrangement for purchasing replacement power occurs inthe system operators markets. Any power that is sold in the DA market but notdelivered in real time is deemed to be purchased in real time at the spot priceof energy. This is called a two-settlement system and has a number of usefuleconomic properties. They are discussed in Chapter 3-4.

    3-1.2 CONTROVERSIESThree main controversies regarding architecture have beset the design of manypower markets.

    1 Central vs. bilateral markets2 Exchanges vs. pools3 Nodal vs. zonal pricing

    The first two controversies both concern the amount of centralization. Intheory all power trades could be handled by bilateral markets in which privatetraders trade directly with each other, or through a middleman (powermarketer), but not with an exchange or pool. This approach is particularlycumbersome for balancing the system in real time. Once it is admitted thatcentralization is needed, an attenuated form of the same controversy questionsthe extent to which the system operator should provide coordination. Shouldit collect large amounts of data on generators and compute an optimal dispatch,or should it let generators signal these parameters indirectly through the energyprices they bid?

    Last, there is a controversy over how finely the system operator shouldcompute locational energy prices. A nodal pricing approach would definemore than a thousand distinct locations in California. When the market wasfirst designed the advocates of zonal pricing suggested that two zones wouldbe sufficient, though many more were added later around the edge. More weresubsequently required in the interior. This is the least fundamental of the threecontroversies and is not discussed in Part 3.

    Central vs. bilateral markets. The first two controversies concern therole of the system operator (SO). Some wish to minimize its role at almost anycost. Chapter 3-2 takes up the question of whether completely bilateral marketsare possible and concludes that the system operator must perform a centralizedallocation of transmission rights, but with the use of sufficient penalties and

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    curtailments the SO could be kept from making any trades. Of course, itsinfluence on the market would still be pervasive.

    Chapter 3-3 considers the possibility of a centralized spot market intransmission only. This would allow private bilateral markets to provide thespot energy market, but because this arrangement makes the realtime balancingof the system difficult and expensive, it is rejected in favor of an energy spotmarket (realtime balancing market) run by the SO.

    Chapter 3-5 considers the same question for the DA market, but in this casethe answer is less obvious as the time pressure is far less severe. Here theanswer hinges on the unit commitment problem and the need for coordination.Although a private bilateral market would cause much less inefficiency, thereappears to be a strong case for at least the minimal central coordination that canbe provided by a pure-energy market run by the system operator.

    Exchanges vs. Pools. Unit commitment is the process of deciding whichplants should operate. Integrated utilities have always done this using acentralized process that takes account of a great deal of information about allavailable generation. If this is done incorrectly the wrong set of plants may bestarted in advance which can lead to two problems: (1) inefficiency and (2)reduced reliability. As just noted, a bilateral market solves this problem poorly,so a centralized DA market is preferred. The second controversy concerns theextent of central coordination.

    There are two polar positions: let generators bid only energy prices (1-partbidding) or let generators bid all of their costs and limitations (multi-partbidding). One-part bidding allows the SO to select the amount of generationto commit in advance but gives it very little information about the generatorscosts and limitations. Consequently it can apply none of the usualoptimization procedures, but it can provide some coordination by purchasingthe correct quantity of power a day ahead. With multi-part bids, the SO canselect bids on the basis of the traditional optimization procedure.

    Typically, this controversy focuses on comparing the existence, efficiencyand reliability of the market equilibria for 1-part and multi-part auctions.Chapter 3-7 demonstrates that both types of markets have equilibria that existand that are likely to be very efficient and reliable. If there is a problem, it isthat markets have difficulty in arriving at the equilibrium of a 1-part auctionmarket when costs are non-convex as they are in power markets. Thisdifficulty arises from the extensive information requirements of 1-part bidding.In such an auction, competitive suppliers should not simply bid their marginalcosts but must estimate the market price in advance in order to determine howto bid. This is a far more difficult task than simply bidding ones own costs asrequired by normal competitive markets or by a multi-part bid auction.

    Unfortunately, not enough is known about how such markets perform inpractice so no conclusion can be drawn as to which is preferable, though itseems plausible that a two or three part auction could be designed to capture

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    most of the advantages of both extremes. Fortunately, the unit commitmentproblem is small enough that it may not matter much which design is adopted.(While this controversy is often lumped with the nodal pricing controversy,it has only a little to do with locational prices.)

    3-1.3 SIMPLIFIED LOCATIONAL PRICINGEnergy prices differ by location for the simple reason that energy is cheaper toproduce in some locations and transportation (transmission) is limited. Whena transmission line reaches its limit, it is said to be congested, and it is thiscongestion that keeps energy prices from equilibrating between differentlocations. For this reason locational pricing of energy is equivalent tocongestion pricing.

    The pricing of congestion is not explained until Part 5, but Part 2 makes useof some basic concepts of congestion pricing. These can be explained withoutdelving into the underlying economics. The interested reader will find all of thefollowing results explained in Chapters 5-3, 5-4 and 5-5.

    Locational prices of energy are just competitive prices, and these are unique.They are determined by supply and demand and have nothing to do with thearchitecture of the market, provided it is a competitive market. This means apurely bilateral market that is perfectly competitive will trade power at the samelocational prices as a perfectly competitive, centralized nodal-pricing market.Of course, a bilateral market is likely to be a little sloppier with its pricing andnot arrive precisely at the competitive equilibrium, but given enough time andsmall enough transaction costs it should arrive at the full set of nodal prices justas efficiently as a fully centralized market.

    Because there is a unique set of locational prices, there is also a unique setof congestion prices, which will also be called transmission prices. Again,these are determined be competition and supply and demand conditions andhave nothing to do with the market architecture, provided the market isperfectly competitive.

    If the competitive energy price at X is $20/MWh and the price at Y is$30/MWh, then the price of transmission from X to Y is $10/MWh.Transmission prices are always equal to the difference between thecorresponding locational prices. If this were not true, it would pay to buyenergy at one location and ship it to the other. In that case arbitrage wouldchange the energy prices until this simple relationship held. This relationshipcan be expressed as follows:

    PXY = PY PX,

    which is read, the price of transmission from X to Y equals the price of energyat Y minus the price of energy at X.

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    This relationship is all that is needed to understand Part 3, but it containsone surprise that deserves attention. Because transmission prices are not basedon a cost of transporting the power (we ignore the cost of losses which isminor) but are based instead on the scarcity of transmission (line limits),transmission costs can be negative. In fact, if the cost of transmission from Xto Y is positive, then the cost from Y to X is certain to be negative. This is adirect result of the above formula.

    This peculiarity can be understood by noting that when power flows fromY to X it exactly cancels (without a trace) an equal amount of power flowingfrom X to Y, thus making it possible to send that much more power from X toY. A second consequence of the above formula is that the cost of transmittingpower from X to Y does not depend on the path chosen

    All of the markets discussed in Part 3 are assumed to compute locationalprices and to operate competitively. Consequently, they will produce thelocational energy prices and transmission prices just described. In spite of theirubiquitous presence, the reader will not need to understand details of howlocational prices are computed and nor rely on either of the properties justdiscussed. They are presented merely to provide context.

  • 1 Although, it does recognize the need to enforce transmission constraints it proposes to dothis with arbitrary curtailments and without the use of any market mechanism..

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-2The Pure Bilateral Approach

    THE MIN-ISO APPROACH TO POWER MARKET DESIGN,POSTULATES THAT THE LESS COORDINATION THE BETTER THEMARKET.1 This philosophy underlies attempts to keep the system operator outof the energy market. In other markets this would be possible. For example theU.S. Department of Transportation does not buy or sell trucking services, it justprovides highways and charges for their use. This chapter examines theinefficiencies that would result from keeping the system operator out of thereal-time energy market.

    Section 1: No Central Coordination. Imagine an electricity market run asa system of highways. Every power injection by a generator could be measuredand charged to pay for the cost of the system. Any generator could sell powerto any customer and deliver that power by injecting it at the same time thecustomer used it. Unfortunately, there would be no way to prevent theft. Withtrading fully decentralized, no one would know who had paid and who had not.

    Section 2: Central Coordination without Price. The simplest actualproposal for a power market suggests that all trades be registered with thesystem operator who would accept only sets of trades that did not cause anyreliability problem. This proposal takes the first step towards the enforcementof reliability and the prevention of power theft, but it does not take the secondstep of specifying what happens when traders violate their schedules. In thissystem the operator knows nothing of prices, and imposes no penalties.

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Section 3: A Pure Transmission Market. The next step is to selltransmission rights. This improves on the previous system by removing thearbitrariness from the distribution of transmission rights and reduces thetransaction costs by centralizing the transmission market. It does not solve theproblem of balancing the real-time market. This could be accomplished withpenalties and curtailments. These would induce the development of privatesystem operators. Because system operation is a natural monopoly it would benecessary to limit their size. Although this could produce a workable powermarket it would have much higher transactions costs than necessary.

    3-2.1 NO CENTRAL COORDINATIONMost markets do not need any central coordination. To understand why apower market does, imagine one without coordination. As with highways, anysupplier could use the wires and would be charged for their usage. The gridowner would meter each suppliers output and impose a per MWh or a annualpeak-MW charge sufficient to pay for the cost of the wires.

    Without any central coordination a supplier could sign a contract with acustomer for 100 MW all day on April 1 at $40/MWh. The generator wouldthen inject 100 MW and the load would take 100 MW and pay the generator.There would need to be thousands of such contracts, but this would be nodifferent from other markets.

    The most fundamental problem with this design is that loads would stealpower. Why have a contract? Just turn on the lights. The grid operator doesnot care because it gets paid for every watt transmittedit could measure eitherall injections or all withdrawals of power. Other generators and customers carebecause their power is being stolen, but they have no way to prove this.Because electricity cannot be directed by a supplier to its intended destination,there is no way to prevent theft. Power from every generator flows to everyload.

    A second problem, which would only occur if the first could be solved, isthat certain transmission lines would be overused. There are only twoapproaches to protecting lines: (1) load and generation can be disconnected toreduce flow on overloaded lines, and (2) overloaded lines can be taken out ofservices. The system is already programmed to take lines out of serviceinstantly and automatically when they reach their limits. While this protectslines, it also destabilizes the system which then requires extraordinary centralcoordination to restore its balance. Centrally controlled circuit breakers couldbe installed on all loads and generators, and these could be used to prevent

  • Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-3Why Have A Spot Energy Exchange?

    FORWARD MARKETS SELL PROMISES OF POWER, THE SPOTMARKET SELLS ELECTRICITY. But the system operator need not beallowed to trade electricity and instead could sell transmission to bilateraltraders of electricity. Although there is nothing inherently wrong with thisprocess, it is slower than centralized energy trading. When balancing thepower system, time is of the essence. In fact the price mechanism is orders ofmagnitude too slow to do the complete job. So to get the maximum benefitfrom markets, the fastest market must be used for balancing, and that is acentralized locational energy market.

    Section 1: A Pure Spot-Market For Energy. Every deviation from balanceis handled by a sequence of procedures the first of which take place in less thana tenth of a second. Because great speed is required, the initial process, to theextent it is not automatic must be centrally directed. Current pricingmechanisms are not much use in time frames under ten minutes. But at somepoint, the job of equating supply and demand can be handed over to a marketmechanism. This is the real-time or balancing market.

    System balance for a control area is determined by a combination of netinflow and system frequency. Even if every bilateral trade using a particularcontrol area is in perfect balance, the system operator will be directed to eitherincrease or decrease generation if the system frequency is off, which it almostalways is. Consequently the operator must have some control over energy.

    Section 2: Conclusions about the Real-Time Market. The essence of theproblem of system balancing is speed. Once the most time-critical part ofbalancing has been handled their comes a point where price can do the job. But

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    in order to maximize the usefulness of the market, the fastest market should beused, and that is a centralized energy market. A transmission market can onlysell transmission when two equal but opposite energy trades have been found.Thus a transmission market is just an energy market with restrictions, and it isinherently more expensive when great speed is needed.

    Of course by spending more on market infrastructure any market can bemade faster. The usual proposal is to impose penalties on bilateral trades thatget out of balance. This appears to keep them in balance cheaply, or even at aprofit. (To stay in balance they must adjust very quickly, so this is method ofspeeding up the market.) But penalties simply hide the costs, which must beborn by those with bilateral contracts. It is wiser to use a locational energymarket as the real-time market and leave bilateral trading to forward marketsthat can proceed at a more leisurely pace.

    3-3.1 A PURE SPOT-MARKET FOR ENERGYThe previous chapter considered three approaches to energy trading that mighthave eliminated the need for a centralized real-time energy market, but all wereneedlessly expensive. The real-time market needs fully centralizedcoordination because electrical energy is not stored and so supply must equaldemand second by second. In fact, this requirement is so severe that even acentralized energy market requires several types of reserves. Regulationoperates most quickly because it is automatically controlled. Next comes 10-minute spinning reserves, 10-minute non-spinning reserves and finally 30-minute non-spinning reserves. Each of these requires many generators to beunder the direct control of the system operator.

    The balancing market overlaps with the 10-minute reserve markets, which,by providing a safety net for emergencies, allow the more sluggish and lessreliable mechanism of a market-clearing price to be utilized in this time frame.Sluggish as this process is by engineering standards, real-time electricity pricesare probably the most nimble and effective prices to be found anywhere. Ona daily basis they balance supply and demand to within a few percent as thesechange at rates of up to 20% per hour. Rarely do any other markets see pricechanges of this speed and then only during panics. More typically prices adjust1000 times more slowly.

    Those who demand that the real-time energy market be taken out of thehands of the SO to be replaced by a transmission market and uncoordinatedbilateral energy trades base their demands on ideology and not a study of thecapabilities of present-day markets. The main substantive objections to energy

  • Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-4Real-Time Pricing and Settlement

    CUSTOMERS AND GENERATORS SHOULD RESPOND TO THE SPOTPRICE AS IF THEY HAD BOUGHT AND SOLD ALL THEIR POWER IN THESPOT MARKET. Typically, however, they buy and sell almost all of theirpower in forward markets. Fortunately, the correct settlement system insulatesthe real-time markets and preserves their incentives.

    Contracts for differences (CFDs) insulate forward contracts from the real-time (spot) price even though loads and generators trade all of the power intheir spot market after having already traded it in the forward markets. Froma traders point of view, the main problem with spot markets is timing oftransmission costs. These are not posted in advance but are determined alongwith the price of energy in the spot market. This is often called ex-post pricing.

    Although determining the real-time price is simple in theory (just set priceso supply equals demand), it is complex in practice. Most real time marketshave a large number of rules, and there is little consistency in these rulesbetween systems. Their purposes vary. Some are designed to limit marketpower, some to protect the system from sudden shifts in supply and demandthat might result from or cause price instability. Others are the result ofsoftware anomalies or various superstitions, but this chapter will ignore suchcomplexities and stick to basics.

    Section 1: The Two-Settlement System. If the system operator runs a day-ahead (DA) and a real-time (RT) market, generators should be paid for powersold in the DA market at the DA price regardless of whether or not theyproduce the power. In addition, any real-time deviation from the quantity solda day ahead should be paid for at the real-time price. This system allows an

  • CHAPTER 3-4 Real-Time Pricing and Settlement 23

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    almost complete separation between the markets. Even if a generator sellsessentially all of its power in the day-ahead market, it will still have the correctincentive to deviate from that contract in response to realtime prices. In realtime the generator has the same incentives as if it were selling all of its powerin real time. Loads are treated analogously with the same effect.

    If bilateral traders use contracts for differences (CFDs), and if the spot pricedoes not vary with location, bilateral trades will be unaffected by the spot priceeven though the generators and loads sell all of their power in the spot market,provided they generate according to their contract. In spite of this, CFDs leavethem with the proper incentive to deviate in ways that benefit the deviatingparty and leave the other parties unaffected.

    Section 2: Ex-Post Prices: The Traders Complaint. Spot prices thatdiffer by location impose transmission costs on traders. These cannot beavoided by the use of CFDs, and they make trade risky. Time-of-usetransmission charges could be posted in advance as an approximation ofcongestion charges, but their inaccuracy would cause an inefficient dispatch.A reservation system would be required to avoid the most seriousinefficiencies.

    A market in transmission rights would be preferable to reservations sold atregulated prices. Such markets exist, but are limited and illiquid. Technicaland practical difficulties have prevented the development of more robustmarkets, but these problems are receiving considerable attention. Transmissionrights can be financial or physical, and financial rights can be used effectivelyas a reservation to assure complete protection from realtime transmissioncharges.

    Section 3: Setting the Real-Time Price. The real-time price should be setto clear the market. As not all response to price changes is reflected by supplyand demand bids, if price is set strictly on the basis of these bids, it willovershoot. This problem will grow as real-time pricing becomes moreprevalent, which will make it necessary for the system operator to improve itsunderstanding of the dynamic affects of price changes.

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    3-4.1 THE TWO-SETTLEMENT SYSTEMIf a supplier sells most or all of its power in the forward markets, the realtimeprice would appear to have little effect on that producers behavior. In aproperly implemented two-settlement system the opposite is true. The supplierwill behave as if it were selling its entire output in the realtime market and willstill behave, when selling in the forward market, as if that were its final sale.In this way, if the markets are competitive, suppliers (and also consumers) willbehave optimally in both markets.

    Separation from Forward TransactionsSay a supplier sells Q1 to the system operator (SO) in the day-ahead market fora price of P1. If this amount of power is delivered to the real-time market, thesettlement in the day-ahead (DA) market will hold without modification. Butwhat if none is delivered, or more than Q1 is delivered? In either case the DAsettlement should still hold, but there should be an additional settlement in thereal-time market. If no power is delivered to the real-time market, the supplieris treated as if it had delivered the amount promised in the DA market, Q1, andpurchased that amount in the real-time market instead of generating it.Consequently the supplier is still paid P1 for Q1, but is also charged P0, the real-time price, for the purchase of Q1. In general, if a supplier sells Q1 in the DAmarket and then delivers Q0 to the real-time market, it will be paid:

    Supplier paid: Q1P1 + (Q0 Q1)P0This is called a two-settlement system. If a customer contracts for Q1 andthen takes only Q0 in real time, it is charged exactly the amount that the supplieris paid.

    Result 3-4.1 A Two-Settlement System Preserves Real-Time IncentivesWhen the real-time market is settled by pricing deviations from forwardcontracts at the real-time price, supplier and customers both have the sameperformance incentives in real time as if they traded all of their power in thereal-time market.

    The incentive of this settlement rule can be revealed by rearranging theterms as follows:

    Supplier paid: Q1(P1 P0) + Q0 P0When real-time arrives, Q1 has been determined in the day-ahead (DA) market.Assuming the market is competitive, the generator has no control over eitherprice, and by real time the first term will be taken as given. The first term willbe viewed as a sunk cost or an assured revenue. This leaves the second term

  • 6 Part 2 focused on the consequences of the far more serious demand-side flaws incontemporary power markets. Part 3 ignores these and focuses on problems with generationcosts that are very small but unavoidable.

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-5Why Have a Day-ahead Market?

    POWER MARKETS ARE DIFFICULT TO COORDINATE BECAUSE THEYDO NOT SATISFY THE ASSUMPTIONS OF A CLASSICALLYCOMPETITIVE MARKET. Under classical assumptions, suppliers need toknow only their own costs, and no central coordinator is needed. For a powermarket to perform efficiently, either it must be centrally coordinated orsuppliers must know a great deal about the market equilibrium price inadvance. The root of the problem is generation costs that fail to satisfy a keyeconomic assumption used to prove the efficiency of competitive markets.6

    Because the proof of efficiency fails, uncoordinated power markets areoften believed to have no equilibrium or only a very inefficient one. In factthey have equilibria that are extremely efficient but difficult to discover. Thischapter argues that at least a small amount of central coordination is well worthwhile and should take the form of a centralized day-ahead market. Thequestion of whether this market should perform a full centralized unitcommitment is discussed in Chapter 3-7.

    In a classic competitive market, suppliers can offer to supply (in a bilateralmarket) or to bid (in an auction market) according to their marginal cost curve.When all do so, the market discovers a perfectly efficient competitiveequilibrium. But with non-convex costs of generation, it becomes necessaryfor generators to bid in a more complex manner.

  • CHAPTER 3-5 Why Have a Day-Ahead Market? 35

    7 Day-ahead bilateral markets could allow very complex contracts but do not because itwould make contracting too expensive.

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    One market design allows suppliers to continue bidding their marginal costsbut include other costs and limitations in their multi-part bids. This has theadvantage of allowing suppliers to base their bids on easily obtainedinformation: their own costs. Another approach can take the form of adecentralized bilateral market or a centralized market with one-part energy bids.In both cases, suppliers must account for all of their costs and limitations intheir energy price bid so they do not bid their true marginal costs.7 With thisapproach, suppliers must utilized considerable information about the externalmarket.

    This chapter argues that the second approach, with its formidableinformation requirements, causes coordination problems that are more severein bilateral markets than in a centralized one-part-bid energy auction. Itconcludes that the coordination problems in a bilateral market will besubstantial enough that this approach should not be adopted for the day-aheadmarket.

    If bilateral markets promised some important advantage, their reduction ofefficiency and reliability might be justified. But bilateral markets have highertransaction costs and are less transparent than a public auction. They are alsoimpossible to use for settling futures contracts. Finally, adopting a centralizedday-ahead market does not preclude the operation of a bilateral day-aheadmarket.

    Section 1: When Marginal-Cost Bidding Fails. A cost function is non-convex if costs increase less than proportionally with output. Startup costs,no-load costs, and several other components of generation costs contribute tomaking them non-convex. Consequently generation costs fail to satisfy theconditions necessary to guarantee a competitive equilibrium. This does notnecessarily prevent the market from being very efficient, but will causecompetitive suppliers to bid above marginal cost if they cannot bid their startupand no-load costs directly. The amount they should bid above marginal costsdepends on the outcome of the market which can only be estimated at the timeof bidding.

    Section 2: Reliability and Unit Commitment. In a bilateral market,generators must commit (start running) without knowing which other

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    generators have decided to commit. Because starting up is costly, they will notstart unless they expect to cover this cost, an outcome which depends on howmany other generators have started and will compete against them the next day.The uncertainties of this problem cause a random level of commitment in abilateral market, and this decreases reliability.

    Section 3: Efficiency and Unit Commitment. The randomness in the levelof commitment, causes inefficiency. Although this randomness is caused byinformation problems, a similar phenomenon can occur because of the lack ofa market clearing price. While this second phenomenon has received moreattention, it is probably of less practical importance.

    Section 4: The Congestion Problem. Transmission bottlenecks(congestion) cause prices to differ by location and make the price more difficultto estimate in advance. The congestion problem significantly exacerbates theinformation problem of bilateral and one-part bid markets, because these needto know the market price in advance. In bilateral markets, this leads to asignificant increase in randomness and inefficiency. A centralized one-part bidauction provides much of the coordination needed to take account ofcongestion efficiently.

    3-5.1 WHEN MARGINAL-COST BIDDING FAILSThe normal description of a competitive market, found in earlier chapters,requires bids that reflect marginal costs. In spite of all suppliers bidding theirmarginal costs, they were able to recover their fixed costs through infra-marginal (scarcity) rents. This situation obtains in markets that satisfy theassumptions needed to prove the existence of a competitive equilibrium. Theseassumptions are well approximated by many markets, but certain aspects ofpower markets fail to satisfy these classic assumptions.

    Without these assumptions, economics cannot prove a market has acompetitive equilibrium. This is a less devastating critique of a market thanis often supposed. The concept of a competitive equilibrium is quite narrow,and a market does not cease to function without one. Instead it produces someother type of equilibrium which may involve some market power or somerandomness. These flaws may reduce its efficiency very little. Economists,aware of this fact, depend on it when arguing that their results apply to the realworld, which never quite conforms to their assumptions.

  • Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-6Day-Ahead Market Designs

    THERE ARE MANY POSSIBLE DESIGNS FOR A CENTRAL DAY-AHEADMARKET, BUT ALL CAN BE DESCRIBED AS AUCTIONS. The mostobvious design just prices energy like the real-time market. A differentapproach turns the system operator (SO) into a transportation service providerwho knows nothing about the price of energy but instead sells point-to-pointtransmission services to energy traders.

    Either of these approaches presents generators with a difficult question.Some generators must engage in a costly startup (commitment) process in orderto produce at all. Consequently, when offering to sell power a day in advance,a generator needs to know if it will sell enough power at a price high enoughto make commitment worthwhile. Some day-ahead (DA) auctions requirecomplex bids that describe the generators startup costs and other costs andconstraints and solve this problem for the generators. If the SO determines thata unit should commit, it insures all its cost will be covered provided the unitdoes commit and produces according to the accepted bid. Such insurancepayments are called side payments, and their effect on long-run investmentdecisions is considered in Section 3-7.3.

    The three approaches just named, energy, transmission and unitcommitment can also be combined into a single auction that allows all threeforms of bid; this is how PJMs day-ahead market works. Generators can offercomplex bids and receive startup-cost insurance if they are selected to run.Anyone can offer to buy or sell energy with simple energy bids, and traders canrequest to buy transmission from point X to point Y without mentioning a pricefor energy. PJM considers all of these bids simultaneously and clears the

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    market at a set of locational energy prices together with startup-cost insurance.The differences in energy prices from location to location determine the pricesfor transmission.

    Section 1: Defining Day-Ahead Auctions. All day-ahead marketsorganized by system operators are auctions. Market participants submit bids,and the auctioneer (the SO) arranges trades according to a simple principle:maximize the net benefit as defined by the bids. If a customer offers to pay $40and manages to buy for $30, the net benefit is $10. The calculation forsuppliers is similar. The auction accepts the set of bids that maximize the sumof these net benefits and sets prices so that all trades are voluntary. The fourday-ahead markets discussed here follow these simple principles and differ onlyin the type of bids they allow. Some allow bids for energy, some fortransmission, and some allow complex bids that specify many costs andlimitations for each generator.

    Section 2: Four Day-Ahead Market Designs. Each auction is specifiedby three sets of conditions: bidding, determining which bids are accepted, anddetermining the payments associated with the accepted bids. Market 1, a pureenergy market, determines nodal prices. Market 2, trades only transmission andinvolves no prices for energy. Market 3 adds unit commitment to Market 1.Market 4 combines the features of the other three and is modeled on the currentPJM market.

    Section 3: Overview of the Day-Ahead Design Controversy. Forwardmarkets are bilateral and realtime markets are centralized. The day-aheadmarket can be designed either way and this causes a great deal of controversy.The nodal pricing approach specifies an energy market with potentiallydifferent prices at every node (bus), and, almost always, specifies that theauction should solve the unit commitment problem as well. This requires agreat increase in complexity of bids. The bilateral approach specifies thatenergy trades take place between two private parties and not between theexchange and individual private parties. To trade energy, the private partiesrequire the use of the transmission system, so the system operator is asked tosell transmission.

    Market 2, takes a purely bilateral approach, while market 3, takes the fullnodal pricing approach. Market 1, the simplest market, implements nodalpricing, but not unit commitment. Market 4, the most complex, implements allthe features from both the bilateral approach and the nodal pricing approach.

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    3-6.1 DEFINING DAY-AHEAD AUCTIONSThis chapter concerns day-ahead markets run by system operators. These takethe form of either exchanges or pools and are operated as auctions in which theprocess of selecting the winning bids is often complicated by transmission andgeneration constraints. Consequently, the selection process often requires theuse of enormously complex calculations and sophisticated mathematics.Unfortunately, the outlines of the mathematics are often presented as a way ofexplaining the auction. This is unnecessary, often confusing, and generally lessprecise than an approach that focuses on the intent of the calculation instead ofon the mechanics of the calculation.

    A Simplified Description of Auctions A bid acceptance procedure is often presented as a linear programming

    problem represented by several large sets of inequalities, a dozen sets ofvariables, and an objective function. This representation is generally anapproximation to the actual program and does not account for such power-system procedures as contingency analysis. For the purpose of defining themarket and understanding its behavior, it is more useful and accurate simply tospecify that production cost is to be minimized subject to transmission andgeneration constraints. This is the problem that the accepted bids must solve;linear (or nonlinear) programming is one possible technique for finding thesolution. Ideally, before the market is implemented, the actual calculationtechnique should be tested to see if it is accurate enough to produce areasonably efficient market. This is, however, no excuse for presenting theauction economics as a linear programming problem.

    Avoiding the details of the computation makes it easier to focus on moreimportant economic considerations such as restrictions on the form of bids, howthe winning bids are paid or charged, and penalties for non-performance. Thefollowing section presents such fundamental information for four types of day-ahead markets and follows certain conventions to facilitate the comparison ofthese markets.

    Determining Quantities

    Auctions must determine the quantities sold and purchased and the price.Although the two are closely related they are separate problems, and the sameset of bids can yield the same quantities but different prices under differentauction rules. From an economic perspective, it is quantities that determineefficiency, and prices are important mainly to help induce the right trades.

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    In all four auctions described here, quantities of accepted bids are selectedto maximize total net benefit. This assumes the bids reflect the bidders truecosts and benefits. Although they may not, assuming that they do generallyencourages truthful bidding.

    Total net benefit is the sum of customer and supplier net benefit, but it isalso the benefit to customers minus the cost to suppliers. This simplificationhelps explain the role of price as well as the economists attitude towards price,as an example will make clear. If a customer bids 100 MWh at up to$5,000/MWh, and the bid is accepted, the benefit to the customer is $500,000.If the market price is $50/MWh, the customers cost is $5,000 and net benefitis $495,000. Similarly, if a generator bids 100 MW at $20/MWh, its cost ispresumed to be $2000. If the market price is again $50/MWh, its net benefitwill be 100x($50$20), or $3000. Writing this calculation more generallyreveals that the price played no role in determining total net benefit.

    Total Net Benefit = Qx(VP) + Qx(PC) = Qx(VC),

    where Q is the quantity traded, V the customers value, C the suppliersproduction cost, and P is the market price. Thus the problem of maximizingnet benefit can be solved independently of any price determination.

    In an unconstrained system, net benefit can be maximized by turning thedemand bids into a demand curve and the supply bids into a supply curve andfinding the point of intersection. This gives both the market price and acomplete list of the accepted supply and demand bids. Unfortunatelytransmission constraints and constraints on generator output (e.g. ramp-ratelimits) can make this selection of bids infeasible. In this case it is necessary totry other selections until a set of bids is found that maximizes net benefit andis feasible. This arduous process is handled by advanced mathematics andquick computers, but all that matters is finding the set of bids that maximizesnet benefit, and they can almost always be found.

    Determining the Market PriceIn an unconstrained auction, the market price is given by the intersection of thesupply and demand curves. The price determined by supply and demand is thehighest of all accepted supply bids or the lowest price of an accepted demandbid. It depends on whether the intersection of the two curves occurs at the endof a supply bid, and in the middle of a demand bid, or vice versa. When thedemand curve is vertical, the intersection is always in the middle of a supplybid, and the price is set to the supply bid price.

    Whichever curve is vertical at the point of intersection has an ambiguousmarginal cost or value (See Chapter 1-5). If the demand curve has a horizontalsegment at $200 that intersects a vertical part of the supply curve that changesfrom $180 to $220, then the marginal cost of supply is undefined but is inbetween the left-hand marginal cost of $180 and the right-hand marginal cost

  • 48 PART 3: Market Architecture

    12 The net benefit should be in $/h.. A kW, rather than a MW, is used to indicate that onlya marginal change is being made. Technically one should use calculus, but this is of nopractical significance.

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Figure 3-6.1Either marginal costor marginal value isambiguous.

    of $220. Consequently it causes no problem to say that the market price equalsboth the marginal cost of supply and the marginal value of demand. [fig]

    Consider how net benefit changes when an extra kW is added to the totalsupply of power at zero cost. This will shift the supply curve to the right andwill have one of two consequences. Assuming that both curves are stepfunctions, it will either increase the amount consumed by 1 kW, or not increaseit at all. If consumption is increased, the benefit of that consumption will be themarket price, and the cost of supply (the added kWh) will be zero. The netbenefit per kW is the market price. If consumption is not increased, somesupply with a cost equal to the market price will be displaced by the new zero-cost kWh. This leaves benefit unchanged and reduces cost, so again the netbenefit per kW is the market price. If the supply and demand curves weresmooth, the result would have been the same except there would have been acontribution from both increasing benefit and decreasing cost. Similarly thereduction in net benefit from extracting a kW from the system is also given bythe market price. Thus, no matter how you compute it, the marginal value ofpower to the system sets the market price.

    Contrary to popular belief, auctions are not designed to determine who sellsand who buys by comparing bids to the price determined by marginal-cost.Marginal cost pricing is not a goal, it is a byproduct. Auctions determine whichset of trades is the most valuable possible (feasible) set of trades, and selectsthis set. Once they have been selected, the market price at each location is setto the marginal value or marginal cost of supply to the system at that location.12

    The market price, MP, determined in this way has two properties. First, atevery location, the MP falls on the dividing line between bids that are acceptedand those that are not. If some bids are partially accepted then MP is equal totheir price. Second, given the first property, the difference between the total

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    amount paid by customers and the amount paid to suppliers is as small aspossible. No other price would have these two properties.

    Conventions and Notation for Describing AuctionsThe use of supply- and demand-curve bids is common in DA auctions.

    Typically these curves are represented by either piece-wise linear functions(connect the dots with straight lines) or step functions. Typically these allowthe bidder to specify about ten sloped lines or horizontal steps, but all thatmatters is that bidders can submit a fairly accurate approximation to their actualsupply and demand curves. This will be assumed, and the details will beignored.

    An auction market has three distinct sets of rules: one set for bidding, asecond for bid acceptance and rejection, and a third for settlement. Thedescription of each of the four DA markets is broken into these threecategories.

    3-6.2 THE FOUR DAY-AHEAD MARKETSFour subsequent pages give summaries of the economics of four types of day-ahead markets. Each is a locational market and these locations may be eithersingle buses or zones containing several buses. If zones are used, thetransmission constraints will represent the market less accurately, and so a moreconservative representation of constraints may be required. This affects onlythe details of the constraint specification and not the specification of themarkets.

    Market 1: Pure Energy

    The bids in a pure energy market are sometimes called one-part bids because,for a given quantity of energy offered, the only a single price is specified. Insome respects this is the simplest DA market. Participants do not search fortrading partners and do not have to consider many prices in many locations.Each trader simply trades with the exchange at the traders location. The SOsjob is simple because it ignores the unit commitment problem. The onedifficulty, discussed in Chapter 3-7, is that suppliers cannot always bid theirmarginal cost.

    Market 2: TransmissionThe transmission auction is equally simple for the system operator but requiresa complex pre-market step for market participants. Buyers and sellers mustfind each other and make provisional energy trades that depend on whether or

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    not they successfully buy transmission, or power traders must be brought intothe picture to arrange such trades and must bid for transmission. In either casethe SO sells only transmission.

    Market 3: Energy with Unit CommitmentSolving the unit commitment problem requires a great deal of information, sothe bids in this auction are quite complex. This is more of a burden for thesystem operators than for the generators who are familiar with the requireddata. The system operator must perform a complex calculation, but thenecessary software is available. The outcome is locational energy prices thatare sometimes too low to induce the needed generator to start up.Consequently suppliers are given side-payments also calculated by the SOsprogram.

    Market 4: Commitment, Pure Energy and Transmission

    The market is modeled on PJMs current market and includes all of the typesof bids allowed in the previous three markets. This is the most complex marketfrom the SOs point of view, but, like market 3, it can be quite simple forsuppliers if they simply bid competitively. This requires only that they bid theircosts.

    Notation used in auction market descriptionsPS(Q), and PD(Q) Supply offer curve and demand bid curveQD Quantity demanded ( used in place of PD(Q) )QA Quantity accepted (supply or demand)MPX, MPXY Locational market price in DA auction for energy or transmission.MP0, Q0 Price and quantity of a specific participant in the real-time market.X, Y Two different locations.Cstart Startup cost.Cost Variable production cost. Sum of area under all PS(Q), 0 ! Q ! QABenefit Consumer benefit. Sum of area under all PD(Q), 0 ! Q ! QA{ } a set of prices or quantities

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    Market #1: A Pure, Day-Ahead Spot Market for EnergyBidding Rules:

    Format (supply): Non-decreasing PS(Q)Format (demand): Non-increasing PD(Q) or QD

    Different supply and demand bids allowed for each hour.Bid Acceptance Rules:

    Format (for both): {MPX} and {QA} for each hour.Acceptance Problem: Maximize total NB = (Benefit Cost).

    MPX = Net Benefit, NB, of a costless kWh injected at X.Restrictions (supply): MPX >= PS(QA)Restrictions (demand): MPX

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    Market 2: A Pure, Bilateral Market for TransmissionBidding Rules:

    Format: {PT, Qmax > 0, from X to Y} for each hour.Bid Acceptance Rules:

    Format: {MPXY}, {QA

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    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Market 3: A Full Nodal-Pricing MarketBidding Rules:

    Supply Format: Non-decreasing PS(Q) / Cstart / ramp-rate limit / etc.Only one supply bid is allowed per day.

    Demand Format: Non-increasing PD(Q) or QD, one bid per hour.Bid Acceptance Rules:

    Format (supply): Commitment: Yes / NoFormat (for both): {MPX} and {QA} for each hour.Acceptance Problem: Maximize total NB = (Benefit Cost).

    MPX = Net Benefit, NB, of a costless kWh injected at X.MPX is computed with the selected units committed.

    Constraints: Transmission security, ramp-rate limits, etc.Settlement Rules:

    Supply: Pay: R = QA x MP + (Q0 QA ) x MP0Supply: Provide: Startup insurance if: Commitment = YesDemand: Charge: QA x MP + (Q0 QA ) x MP0 + uplift

    Comments:Startup insurance is provided to generators who are scheduled to startup by PJM in

    the DA market and who do startup and follow PJMs dispatch. Following dispatchamounts to starting up when directed to and keeping output, Q, within 10% of the valuethat would make PS(Q) equal the real-time price. Startup insurance pays for thedifference between as-bid costs and market revenues, R. As-bid costs include at leastenergy costs, startup costs and no-load costs.

    Most generators that startup do not receive insurance payments as they make enoughshort-run profits. The total cost of this insurance is less than 1% of the cost of wholesalepower. Uplift includes the cost of startup insurance and several other charges.


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    Market 4: PJMs Day-Ahead Market*Bidding Rules:

    Format (supply): Non-decreasing PS(Q) / Cstart / ramp-rate limit / etc.Only one supply bid is allowed per day.

    Format (demand): Non-increasing PD(Q) or QD.Format (transmission): {PT, Qmax > 0, from X to Y} for each hour.Formats (virtual): Buy Q at up to PE. Sell Q at PE or higher.

    Bid Acceptance Rules:Format (supply): Commitment: Yes / NoFormat (both): {MPX} and {QA} for each hour.Acceptance Problem: Maximize total NB = (Benefit Cost)

    MPX = Net Benefit, NB, of a costless kWh injected at X.Constraints: Transmission security, ramp-rate limits, etc.

    Settlement Rules:Supply: Pay: R = QA x MP + (Q0 QA ) x MP0Supply: Provide: Startup insurance if: Commitment = YesDemand: Charge: QA x MP + (Q0 QA ) x MP0 + uplift

    Comments: * This description is still simplified as it leaves out PJMs daily capacity market,

    various other markets, and near-markets for ancillary services and all of theaccompanying uplift charges. However this formulation captures the centralcharacteristics of a flexible market containing the described Pool which uses complexbids.

    The acceptance problem solved by PJM differs from the one in Market 4 in that onlycost-savings from generation counts towards net benefit. In other words, a demand bidcan not set the price, only a supply bid can.

    Ramp-rate limit is meant as a proxy for this and various other constraints on theoperation of generators, such as minimum down time. Startup cost, Cstart, is also meant asa proxy for other costs that are not captured in the supply function PS(Q), such as no-loadcost.


  • 14 Quite possibly, these systems still rely on much of the data that is no longer collected butwhich operators are well aware of; this would include ramp rates.

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-7Multi-Part Unit Commitment?

    BY ALLOWING ONLY 1-PART ENERGY BIDS, A DAY-AHEADAUCTION CAN FORCE SUPPLIERS TO SOLVE MUCH OF THE UNITCOMMITMENT PROBLEM INDIVIDUALLY. The extreme alternative is toallow multi-part bids so generators can specify, start-up costs, no-load costs,ramp-rate limits and many other costs and parameters, then have a systemoperator make the traditional calculation. Traditionally, utilities have used agreat deal of information about each generator and in recent years haveperformed sophisticated calculations to decide which units to commit. Somepower markets, such as those in California, Alberta and Australia, abandonthis approach with little apparent degradation of the dispatch.14

    Chapter 3-5 considered whether the unit-commitment problem should besolved with the aid of a centralized auction market or a decentralized bilateralmarket and concluded that the auction market is preferable. Chapter 3-6described four auction designs two of which will be analyzed in this chapter. Market design #1, a pure energy market allows generators only 1-part bidsthat specify a price of energy which depends on their level of output, andmarket design #3, a unit-commitment (UC) market allows generators tospecify a long list of parameters describing their costs and physical limits.

    Utilities use huge quantities of data, sophisticated software, and advancedmathematics to determine which units to commit in advance and how long tokeep them committed. In a pure-energy auction, all of this is replaced by a

  • CHAPTER 3-7 Multi-Part Unit Commitment 59

    15 This chapter ignores the transmission congestion problem in order to focus on the classicunit-commitment problem which assumes a unified market.

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    simple rule that says, use the cheapest power first.15 That this works at all istestimony to the coordinating powers of a market, but there are a number ofunanswered questions. This chapter investigates how a market performs thiscoordination and what problems it may encounter.

    Section 1: How Big is the Unit Commitment Problem? Startup costs areone of the more significant costs contributing to the unit commitment problem.Typically, these amount to less than 1% of retail costs. More than half of theseare covered by normal marginal cost pricing. If the inefficiency caused by theremaining startup costs were as high as 50%, the total loss from poor unit-commitment would be less than 1/4% of total electricity costs. Quite plausibly,actual inefficiencies caused by even the pure-energy auction may be an orderof magnitude smaller.

    Fixed cost must be covered by marginal cost pricing and they are muchgreater than startup costs. As they are taken out of infra-marginal rents beforefixed costs, startup costs usually are covered by energy revenues except in thecase of generators that provide only reserves.

    Section 2: Market Design #1, A Pure Energy Auction. Sometimes anefficient dispatch and marginal-cost pricing do not cover startup costs.Example 2 considers this situation from four perspectives. Case Ademonstrates that there is no competitive equilibrium in the classic sense.Case B demonstrates that an auction without startup-cost bids or side paymentscan have an efficient competitive Nash equilibrium in spite of lacking a classiccompetitive equilibrium. Case C considers a 1-part, pure-energy auction. Thisproduces an inefficient but competitive equilibrium. Case D includes thepossibility of de-commitment, i.e. failing to generate the power sold in the day-ahead market. This possibility leads to greater over-commitment in the day-ahead market and then de-commits to the point of an efficient dispatch.

    Section 3: Design #3, a Unit-Commitment Market. A unit-commitmentmarket insures generators dispatched in the day-ahead market against failingto cover their startup costs. If all generators bid honestly, and the dispatch isalways efficient, these insurance payments will interfere with long-runefficiency by providing inappropriately large investment incentives togenerators with especially large startup costs. Because insurance payments are

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    UnitsStartup costs are measured in $ per MWof capacity started. For a unit that isstarted once per day, the cost flow ismost conveniently measured in $/MWday. For comparability, energy and fixed costswill also be converted to $/MWday inmany of the examples.

    small, the inefficiency should be small. By allowing more detailed bids, theunit-commitment auction solves the coordination problems of the pure-energyauction, and this should lead to a slight increase in dispatch efficiency.


    If generators cannot bid certain cost components and physical limits, they willfind ways to include these cost in prices they can bid, and they will find waysto compensate for their limitations. These adjustments will typically beimperfect, but if the problem is fairly small to begin with, the adjustmentsusually will be more than adequate. In spite of this optimistic view, there areno guarantees, and it makes sense to investigate the performance of marketswith known imperfections. It also makes sense to avoid rigid restrictions suchas a restriction to 1-part bids. Because markets are good at taking advantageof whatever flexibility is available, adding a second part to the bid maysignificantly improve the outcome. By the same token, adding 20 parts to thebid is almost surely overkill.

    3-7.1 HOW BIG IS THE UNIT COMMITMENT PROBLEM?Both a pure energy auction (Chapter 3-6, design 1) and a UC auction

    (Chapter 3-6, design 3) work best when generators can simply bid theirmarginal cost curves and the resulting market prices automatically cover theirstartup costs. In this case the only significant inefficiency should result fromthe system operators errors in predicting the next days load and new forcedoutages of transmission and generation.

    When marginal-cost bids do not cover startup costs, both markets can runinto problems. Fortunately total startup costs are a small fraction of totalgeneration cost, and the majority are probably covered by marginal-cost bids.These two points are investigated in turn. No-load costs are another source ofdifficulty and may be slightly larger than startup costs, but they are not largeenough to change these conclusions qualitatively.

    The Magnitude of StartupCostsStartup costs typically range from $20to $40/MW and not every generatorstarts every day. Typically,generators that serve base-load, startless frequently, and very few startmore often. Hydro generators have

  • 22 Australia often defines spin as the five-minute increase in output.23 This value can be improved by the generator owner, and markets may lead to suchimprovements.

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    Chapter 3-8A Market for Operating Reserves

    A MARKET FOR OPERATING RESERVES PAYS GENERATORS TOBEHAVE DIFFERENTLY FORM HOW THE ENERGY MARKET SAYSTHEY SHOULD. If they are cheap and would produce at full output, themarket might tell them to produce less. If they are too expensive to produce atall, it may tell them to start spinning, and this may require them to produceat a substantial level. The purpose is to increase reliability.

    Spinning reserve (spin) is the most expensive type of reserve because agenerator must be operating (spinning) to provide it. Spin is typically definedas the increase in output that a generator can provide in ten minutes.22 Steamunits can typically ramp up (increase output) at a rate of 1% per minute whichallows them to provide spin equal to 10% of their capacity.23 Spin can also beprovided by load that can reliably back down by a certain amount in tenminutes.

    The next lower qualities of operating reserves are ten-minute non-spinningreserves, typically provided by combustion turbines, and 30-minute non-spinning reserves. This chapter will consider only spinning reserve because itis the most critical and illustrates many important design problems.

    Spin can range from free to expensive. Incidental spin is provided bygenerators that are not fully loaded simply because they are marginal and theirentire output is not required, but more often because they are in the process of

  • CHAPTER 3-8 A Market for Operating Reserves 75

    24 The root of this problem was a market separation ideology, although several peculiarrules played a role as did FERC.

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    ramping down. Sometimes generators are given credit for spin when they areramping up at full speed to keep up with the morning ramp. While these maymeet the letter of the definition, they do not meet its spirit because they couldnot help to meet an contingency such as another generator dropping off line.Typically the spinning reserve requirement of a system is roughly equal to thelargest loss of power that could occur due to a single line or generator failure,a single contingency.

    Providing spin from generators that would not otherwise run is costly forseveral reasons. Most importantly, generators usually have a minimumgeneration limit below which they cannot operate and remain stable. If thislimit requires a generator to produce at least 60 MW, and its marginal cost is$10/MWh above the market price, and it can provide 30 MW of spin, this spincosts $20/MWh. In addition there would be a no-load cost due to powerusage by the generator that is unrelated to its output. Startup costs should alsobe included.

    Providing spin from infra-marginal generators, ones with marginal costsbelow the market price, is also expensive. If a cheap generator has been backeddown slightly from full output, its marginal cost may be only $20/MWh whilethe competitive price is $30/MWh. In this case, backing it down one MW willsave $20 of production cost but will require that an extra MW be produced at$30/MWh. The MW of spin provided costs $10/MWh. Sometimes it isnecessary to provide spin in this manner because too little is available frommarginal and extra-marginal generators. This is typically the case when themarket price reaches $100/MWh.

    The three operating reserve markets are tightly coupled to each other andto the energy market. California demonstrated the folly of pretendingdifferently and managed to pay $9,999/MWh hour for a class of reserves lowerthan 30-minute non-spin at times when the highest quality reserves were sellingfor under $50/MWh.24 This chapter will not consider the problem of how themarkets should be coupled, although the most straightforward answer indicatesthey should be cleared simultaneously using a single set of bids that can beapplied to any of the markets.

    Section 1: Scoring by Expected Cost. One approach to conducting amarket for spin is to have suppliers submit two-part bids, a capacity price, R,

  • 76 PART 3: Market Architecture

    25 This approach was developed by Robert Wilson for the California ISO, and is explainedalong with the problems of expected-cost bidding in (Chao and Wilson, 2001).

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    and an energy price, P. An obvious way to evaluate such bids is to score themby their expected cost R+hP, where h is the fraction of the time that energy isexpected to be required from a supplier of spin. This gives the expected costof using spin from this supplier. Unfortunately there is no single correct h,because the amount of energy used depends on the suppliers energy price.Evaluating the bids by using the wrong h leads to gaming, which, dependingon the structure of the auction, can be either extreme or moderate. Althougha reasonably efficient auction based on expected-cost scoring seems possible,this has not yet been demonstrated.

    Section 2: Scoring based on Capacity Price Only. An alternative scoring approach calls for the same two-part bids (R, P), but

    evaluates them simply by picking those with the lowest capacity price, R.25

    Remarkably, this works perfectly provided the bidders are exceptionally wellinformed and only extra-marginal spin is needed. Sometimes spin is mostcheaply provided by infra-marginal capacity, e.g. by backing down a cheapsteam unit. For this scoring approach to work in such cases, the price of energyfrom spin must not be used to set the price of spot-market energy. Separatingthese two prices is, however, inefficient.

    Extreme information requirements present a more serious problem withcapacity-only scoring. Bidders must know how the probability of being calledon for energy will depend on energy-price, but this depends on who wins theauction and what they bid. In such a volatile market, this is extremely difficultto know, and without such knowledge, bidding will necessarily be inefficient.

    Section 3: Opportunity-Cost Pricing. Auctions in which suppliers offera capacity and an energy bid, require that they guess what their opportunity costwill be in the real-time market. For instance if they believe the spot marketprice will be $50/MWh , and their marginal cost is $49/MWh , they may offerspin capacity for $1/MWh. If the market price turns out to be $80 and they arenot called on to provide energy, they will have missed a significant opportunity.Of course with a low spot price they would have won their gamble. Theproblem is not with the averages, but with the randomness such guesswork willintroduce into the bidding process. As a remedy to this problem, suppliers canbe paid their opportunity cost, whatever that turns out to be. Unfortunately, this

  • CHAPTER 3-8 A Market for Operating Reserves 77

    Stoft, Power System Economics 2001 DRAFT: July 13, 2001

    raises some of the same gaming issues as two-part bid evaluation. Theseremain to be investigated.

    3-8.1 SCORING BY EXPECTED COSTThe expected cost of spinning reserve depends on the cost of the reservecapacity (C), the cost of the energy they provide (MC) if they are called on, andthe chance they will be called (h). Providing 10 MW of spinning reservecapacity for two hours might cost $20, which comes to $1/MWh, so both C andMC are measured in $/MWh. The probability h has no units and can bespecified as a percent or a fraction.

    Because the expected cost of spin is C + hMC, it seems natural to allowtwo-part bidding and score the bids using this expected cost formula. If h hasa single value known to the system operator, this is a reasonable scoringprocedure. But if the system operator is mistaken about h and the bidders knowh, the procedure is susceptible to a classic form of gaming. Say h is the correctprobability but the SO believes it is H, and the bidder bids R for C and P forMC. The accounting works as follows:

    Table 3-9.1 Accounting for and Expected-Cost AuctionBidders true expected costs: C + hMCBidders bid: R, PBidders score (S): R + HPBidders expected payoff: R + hPBidders expected profit: R + hP (C + hMC )

    The lowest score wins. Say the bidder wants to achieve a score of S. Itmust choose R = S HP, where it is free to choose any energy price, P. Withthis choice, profit will be:

    profit = (S HP ) + hP (C + hMC ), or

    profit = S (C + hMC ) + (h H ) P.

    S (C + hMC ) is unaffected by the bidders choice of P, so profit is controlledby the term (h H) P. For any given score, S, the bidder can achieve any profitlevel by choosing the correct P ! The choice of P will determine the bidderschoice for R, as described, but together P and R will produce any desired levelof profit and any desired score. This depends on the bidder knowing h, and thesystem operator choosing . If H < h, then the bidder should bid anH hextremely high price for energy and a low cost for capacity. If H > h, the