An Engineering Approach to Monitoring Market Power in Restructured Markets for Electricity

Transcription

1 An Engneerng Approach to Montorng Market Power n Restructured Markets for Electrcty C.E. Murllo-Sanchez, S.M. Ede, T.D. Mount, R.J. Thomas, and R.D. Zmmerman Cornell Unversty and PSERC Abstract The hgh average prces and hgh volatlty of prces n many restructured markets for electrcty have rased concerns about the abuse of market power by generators. At the same tme, nformaton about the true costs of generaton, that was readly avalable under regulaton, s no longer dsclosed by generators. Hence, t s becomng mpractcal to use a comparson of actual prces wth compettve prces as the bass for dentfyng the use of market power. In ths paper, an engneerng procedure s proposed for a gven pattern of dspatch to measure the potental for market power for all generators n a network. Ths procedure s equvalent to a set of factor demand equatons n a standard neoclasscal model of producton. An optmal dspatch, for gven sets of offers to sell and constrants on capacty, can be replcated exactly by resolvng the dspatch usng the optmal nodal prces as offers wth no constrants on capacty. Market power exsts when the degree of substtutablty for power generated at a partcular ste s low. Wthholdng capacty and/or rasng offers to sell at such a ste would be one of the possble ways to explot market power. Senstvty of the results for any gven pattern of dspatch can gve some ndcaton of how effectvely prces have been rased by a generator. Under compettve condtons, submttng hgher offers to sell at a ste wll result n a substantal reducton of the capacty dspatched, and the own-prce elastcty of demand for generaton at the ste s very large (negatve). As market power ncreases, the own-prce elastcty gets smaller and approaches zero. These effects can be aggregated easly to deal wth a specfed group of generators, whch could represent generators n a load pocket or ownershp by a parent company. Use of these procedures s llustrated by evaluatng the results of two experments desgned to test market power. These experments were conducted wth undergraduates and utlty executves usng POWERWEB, whch smulates a full AC network wth 30 buses, sx of whch are generators. The objectve of the experments was to determne whether two of the generators could dscover that they were n a load pocket and rase ther profts by explotng market power. The authors are: Postdoctoral Assocate, School of Electrcal and Computer Engneerng (ECE); Graduate Research Assstant, Department of Appled Economcs and Management (AEM); Professor, (AEM); Professor, (ECE); and Senor Research Assocate, (AEM) at Cornell Unversty. For correspondence, use tdm2@cornell.edu (Tm Mount) or Appled Economcs and Management, 214 Warren Hall, Cornell Unversty, Ithaca, NY Ths project was part of the research program of the Power Systems Engneerng Research Center (PSERC) sponsored by the Natonal Scence Foundaton. Addtonal support came from the Consortum for Electrc Relablty Technology Solutons (CERTS) program n the U.S. Department of Energy and a project on complex nteractve networks supported by the U.S. Department of Defence and the Electrc Power Research Insttute (EPRI).

2 2 1. Introducton The prospects for customers n electrcty markets are omnous f the events n Calforna snce the Summer, 2000 are at all ndcatve of the future for other regons. Although most customers n the U.S.A. are stll payng regulated rates for electrcty, customers n San Dego came to the end of the transton perod from regulaton and were expected to pay the actual market prces for electrcty. These market prces were much hgher than antcpated, and poltcal nterventon was mmedate. Prce caps n the market were lowered, and customers eventually receved rebates. James Hoecker, Charman of the Federal Energy Regulatory Commsson (FERC) s quoted as sayng, Never has ths Commsson had to address such a dramatc market meltdown as occurred n Calforna s electrcty market ths summer. Never have resdental customers been exposed to economc rsk and fnancal hardshp as they were n San Dego (FERC, 2000). FERC proposed a major modfcaton n the structure of the aucton n the Calforna market. Many of the problems n the Calfornan market have been recognzed by the Market Survellance Commttee (MSC) of the Calforna Independent System Operator (CAISO) (see Wolak, et al. [2000]) and n earler academc papers by Borensten and Bushnell [1997], Borensten et al. [1999a]) and Borensten et al. (2000). The MSC report ncludes the followng recommendaton: Place greater emphass... on the market-power mplcatons of proposed market rule changes, recognzng that relablty and market-power concerns are nextrcably lnked. (op. ct. p. 3). When hgh prces are observed n a market, the possblty that market power s the prmary cause s nevtably nvestgated by regulatory agences. (For example see Newbery [1995], Wolak and Patrck [1997] and Wolfram [1999] for dscussons of the market n the U.K., whch was ntally manpulated by two domnant supplers.) The opportuntes for explotng market power n electrcty markets go well beyond the standard concern of havng a few frms controllng large shares of producton capacty. In fact, Rudbech et al. (1998) and Bunn (1999) suggest that the characterstcs of an electrcty market make t necessary to have more frms than are needed n a typcal market to be compettve. Bunn proposes that frms should be lmted to no more than 12% of total producton capacty compared to the conventonal maxmum of 20% (op. ct. p. 20). Other ways to explot market power nclude 1) explotng network characterstcs usng generators at dfferent locatons (Hogan, 1997), 2) usng fnancal contracts when frms are vertcally ntegrated (Prrong, 2000), 3) usng physcal blateral contracts (Joskow and Trole, 2000), and 4) rasng the prce of natural gas (New York Tmes, 2001).

3 3 If frms are large enough n any regon, there are numerous ways to explot market power and rase prces above compettve levels. Many authors have ponted out the lmtatons of conventonal measures of concentraton, such as the Hrschman-Herfndahl Index (HHI). (For example, Borensten et al. (1999), p. 80, show how changes n the HHI can be nversely related to market power when large frms wthdraw capacty to rase prces, and at the same tme, lower the HHI). A better way to measure market power s to compare actual prces wth compettve prces. 1 Usng ths approach, Wolfram (1999) showed that the two large frms n the U.K. market dd not explot the full potental of ther market power. For the Calfornan market, Borensten et al. (2000) estmate that average market prces were about 15 percent above compettve levels from June 1998 to September (Spot prces n the wnter 2000/2001 have been ten tmes hgher.) The problem wth analyses of ths type s that they requre knowng the true costs of producton. Although nformaton on true producton costs was readly avalable under regulaton, generators are no longer requred to provde data on costs to regulators. Furthermore, treatng true costs as prvate nformaton s consstent wth the objectves of deregulaton. Compettve markets for other commodtes do not requre that cost nformaton s made publc. If a producer tres to rase prces above compettve levels, the penalty s to lose a lot of market share when a market s compettve. Deregulated markets for electrcty should work n exactly the same way, but ths wll not happen untl the underlyng causes of market power are understood more fully and then corrected. Hence, t s unfortunate that dentfyng marketng power s more dffcult now under deregulaton when the capablty to dentfy market power effectvely s needed most. In summary, the general mplcatons from the lterature are 1) the characterstcs of electrcty markets are atypcal, and standard measures of concentraton, such as the HHI, are poor ndcators of market power, 2) market power can be exploted by supplers n many dfferent ways that are often dependent on the current operatng condtons of the power grd, and 3) there s ample emprcal evdence showng that market power has been exploted successfully to rase prces n specfc stuatons n dfferent markets. However, the most effectve way of detectng the use of market power, by comparng actual prces to compettve prces, s lkely to become less vable n the future because publc data on the true costs of producton wll no longer be avalable. 1 The Lerner ndex s a conventonal measure to use, and t measures the percentage ncrease of actual prces above compettve prces.

4 4 The prmary objectve of ths paper s to explore the potental for usng an engneerng approach to measure the exstence of market power n the real-tme operatons of a power grd. An mportant feature of ths approach s that t requres only nformaton that typcally should be avalable to an Independent System Operaton (ISO), such as the actual offers submtted to supply power and the engneerng measures needed to determne nodal prces. Our approach to measurng market power assumes that an ISO solves an Optmal Power Flow (OPF) to determne the least cost pattern of dspatch based on the avalable offers n a unform prce aucton. The OPF s determned subject to physcal constrants on the power grd, such as thermal lmts on transmsson lnes, and operatng constrants, such as mantanng voltage levels. In the applcaton, a full AC representaton of power flows s used so that both real energy and reactve power are reflected n nodal prces, but at ths tme, the provson of other ancllary servces such as reserve generatng capacty s not ncorporated nto the analyss. Offers to sell power are specfed n blocks of capacty, mplyng that a generator submts a specfc capacty (e.g., 150 MW) and a prce (e.g. $30/MWh) for each block nto a unform prce aucton. Wth ths structure for offers, a block of capacty may 1) be fully dspatched (nodal prce > offer), 2) be partally dspatched (nodal prce = offer), or 3) not be dspatched (nodal prce < offer). An addtonal operatng constrant s that the frst block for each generator must be dspatched fully, or not at all, to represent the mnmum operatng level for generatng power. The nodal prces correspondng to an optmal pattern of dspatch can be computed for every generator (and every load). These prces ncorporate dfferent shadow prces for the operatng constrants that are bndng, as well as the offers of generators that are selected by the aucton (the last accepted offer s used to set the clearng prce). The procedures used to determne nodal prces have evolved from the semnal work of Schweppe et al.(1988). It s mportant to note that the nodal prces usng a full AC network n our analyss are not the same as the nodal prces usng a DC approxmaton (e.g., the procedure used to allocate transmsson shares among generators at a flowgate). The nonlnear relatonshps n an AC network, whch are essental for modelng voltage constrants, tend to ncrease the dfferences among nodal prces when transmsson constrants are bndng. Snce the potental for explotng market power also ncreases when transmsson lnes are constraned, t may be serously msleadng to use a DC network to measure the physcal potental for market power n a network.

5 5 Snce an OPF determnes the optmal pattern of dspatch and the assocated nodal prces, t s possble to replcate an optmal soluton by replacng offered prces by nodal prces, removng capacty constrants, and resolvng the OPF. In ths representaton, real energy generated at a ste can be treated as an nput factor nto a producton process used to meet a specfed level of output (.e., the pattern of loads). Snce the objectve of an OPF s to mnmze the total cost, the dervatves of total cost wth respect to the nodal prces for each generator gve factor demand equatons (by Shepard s Lemma). Elements of the correspondng Hessan matrx of second-order prce dervatves represent the complete set of own-prce and cross-prce effects among generators. These prce effects provde the nformaton needed to measure the physcal potental for market power mpled by the optmal pattern of dspatch determned by an OPF. The steps needed to derve the Hessan matrx of prce effects from an OPF are descrbed n Secton 2 of ths paper. Snce the prce effects, and the correspondng measures of market power, apply to the specfc patterns of dspatch, load and nodal prces n the OPF, t s desrable to determne how senstve the results are to changes of the nodal prces. One possble alternatve would be to replace the nodal prces wth compettve prces. Whle t s straghtforward to compute a new OPF, our underlyng assumpton s that the nformaton about true costs needed to determne the compettve prces s not avalable. Two addtonal OPF solutons are proposed n Secton 2 as alternatves for evaluatng senstvty when a load pocket has been dentfed. These solutons provde some gudance about how effectvely the market power n a load pocket has been exploted. Secton 3 descrbes the results of two experments on market power usng POWERWEB, whch smulates an AC network wth sx generators. Ths platform has been used extensvely to test the performance of dfferent structures for electrcty markets. In ths applcaton, the objectve of the experments s to determne whether two of the generators can dscover that they are n a load pocket and explot ths stuaton to rase prces. The results show that dfferent groups of undergraduates and a group of utlty executves can explot market power effectvely by the end of the experment. The experments n market power provde a convenent bass for testng the engneerng measures of market power proposed n Secton 2. The results are evaluated n Secton 4. They show that the engneerng measures are able to dentfy the two generators n the load pocket relatvely easly. Snce the true costs are known for ths applcaton, the engneerng measures can also be determned for the compettve OPF. These results show that the potental for market power can be dentfed for one compettve OPF but not for the other one, and reasons for ths dfference are gven. It s also possble

6 6 to determne whether the senstvty from expermental OPF analyses can dentfy how effectvely market power s exploted. The results about the level of explotaton are more dffcult to nterpret than the engneerng measures for the exstence of market power. Developng more nformatve ways to use the engneerng measures s the subject of ongong research. The conclusons and suggestons for further research are presented n Secton An Engneerng Measure of Market Power 2.1 The Economcs of Producton The dualty of producton, cost and proft functons has been developed by McFadden and others to form the bass of modern neoclasscal producton theory (Fuss and McFadden, 1978). Under specfc regularty condtons, representng the maxmum proft as a functon of the output and nput prces can be used to derve supply functons for outputs and demand functons for nputs. If outputs are fxed, as they are n our applcatons, representng the mnmum cost as a functon of the nput prces and the output levels can be used to derve demand functons for nputs. Chapter 7 n Chambers (1988) provdes a concse summary of the theory of a multproduct proft functon, and Chapter 2 n Chambers (1988) and Chapter 5 n Varan (1978) dscuss the theory of a cost functon for nputs. The cost functon for gven levels of output, y, n nputs, z, and n nput prces, w, can be defned as follows: 2 n (w, y) = Mn. ( w z ) w.r.t z C = s.t. F(z) y 1 where = [ z ] 1, z 2,, z n [ w, w,, ] z K are the nput levels, = 1 2 w n w K are the nput prces, F(z) s a producton functon. If the cost functon s dfferentable, prce effects can be derved from the followng condtons (Varan op. ct., Sectons ): ) C(w,y) s homogeneous of degree one n w, ) C(w,y)>0 for w 0 and y>0, ) * * C(w, y) C(w, y) for w w, 2 For the followng dscusson, t s assumed mplctly that output levels (loads) are held at fxed levels.

7 7 v) C(w,y) s a concave functon of w, * * * v) Z (w, y) = wc(w, y) = z are the optmal levels of nputs that mnmze cost (Shepard's Lemma), v) Z(w,y) s homogenous of degree zero n w, z 0, F(z) y s a strctly convex set, then Z(w,y) s sngle-valued, v) If { } * * v) If Z(w,y) s dfferentable, then M = Z(w, y) = C(w, y) s a symmetrc and negatve semdefnte Hessan matrx at {, y} w ww w *, and Mw * = 0. The frst four condtons defne the suffcent condtons for the exstence of a cost functon. The n n Hessan matrx M represents the own-prce and cross-prce effects for the n nputs (factors). If the elements of M are m, then the correspondng prce elastcty at { z * } j w s: * j, j = m j j w z * j * z = w j w z * j * Own Prce elastctes,, are non-negatve because (v) above mples M s negatve sem-defnte. Gven the homogenety condton n (v) above, = = j 1 j 0. After convertng M to the correspondng n matrx of prce elastctes, each row of elastctes sums to zero. For an electrcal grd, the pattern of loads on a network corresponds to outputs and the levels of generaton correspond to nputs. One of the complcatons for economsts when nterpretng standard engneerng expressons used n an Optmum Power Flow (OPF) s that P represents the quantty of real energy (MWh) and Q represents the quantty of reactve power (MVar). To avod ths confuson, u s used nstead of P for real energy njectons n the dervaton of M. If nodal prces are computed for the OPF, these prces are the system lambdas. Hence, the Hessan matrx of prce effects M has elements z w j u = λ j n the new notaton. However, the dervaton of M from an OPF s not straghtforward because the OPF s solved subject to a large number of non-lnear constrants that defne the operatng lmts of an AC network. The steps used to derve a tractable expresson for M are descrbed n Appendx A. For an ndvdual generator,, the margnal change of proft wth respect to the nodal prce s: d( λ u C ) = (u + λ m C m ) dλ (1) where λ s the nodal prce u s the real energy dspatched

8 8 C = C (u ) s the total cost of producton C s the correspondng short-run margnal cost u m = 0 s the own prce effect from the Hessan matrx M. λ Expresson (1) can be rewrtten n terms of the own-prce elastcty as follows: C λ d d Pr oft = Re venue 1+ 1 (2) λ λ Consequently, proft wll ncrease when the nodal prce ncreases f: C > 0 (3) λ In most stuatons, λ > C > 0, because λ s determned by the offers and not the true margnal costs, C and 0 < 1 < 1. Snce 0, the condton n (3) s equvalent to > 1 (1 C / λ ). If all λ generators submt honest offers equal to the margnal costs, then at least one generator wll have λ = C, mplyng that the condton s >, and thus, not nformatve. A more strngent crteron s to consder whether Revenue ncreases when λ ncreases. Usng ths more restrctve requrement, the potental for market power exsts f 1 < 0 for any value of C 0. Ths provdes a suffcent condton for generator that s not dependent on knowng the true costs and t corresponds to assumng the margnal cost s zero. The proposed condton for an ndvdual generator mples that addtonal profts can be made f the net-demand for power from that generator s nelastc. Ths s a standard result n mcroeconomcs, and t corresponds to an economc verson of a must-run unt. However, ths condton s too strngent as a test for market power because a small group of generators may also possess market power. In other words, even f competton exsts wthn the group, the group tself may be small enough n number to explot market power. In practce, such groups are lkely to be n sub-regons that have lmted transmsson capacty for mportng power or represent generators owned by one company. Consder the followng stuaton n whch the frst r<<n generators n a network may possess market power. For the th generator n the group, the margnal change n profts wth respect to proportonal ncreases of all nodal prces n the group s:

9 9 d [ j j λ j] r ( u λ C ) = u dλ + ( λ m C m ) d j= 1 dλ = u λ + λ C = + Re venue 1 1 λ ( λ C ) r j= 1 r λ m j= 1 j j dλ λ dλ j λ The same argument below (3) can be used to make (4) ndependent of nformaton about costs. The resultng condton can be stated: Revenue (and proft) for generator n the group wll ncrease f: r > 1 j = 1 j (5) The potental for market power exsts for a group of r generators f r r [ 1 + ] Re venue > 0 (6) = 1 j= 1 j It s clear that ths condton (6) holds f all of the generators n the summaton n (6) meet condton (5), but ths s not a necessary condton, partcularly f one company owns more than one of the generators n the group. The correct sze of the group, r, s dffcult to defne precsely because expresson (6) s lkely to hold f r s large enough, and t holds wth certanty for r = n. Hence, r must be relatvely small and represent stuatons n whch tact colluson among generators s lkely to be successful. For example, r = 5 s a reasonable value to start wth for a network, and ths value s stll smaller than the mnmum number of 8 generators proposed by Bunn (1999) for a compettve market. In practce, an ISO would know enough about the characterstcs of a network to dentfy lkely load pockets n advance, but the potental for explotng market power by ownng generators at dfferent locatons on a network s also mportant (Hogan (1997)). Observng repeated hgh nodal prces, compared to the average prces pad, s an obvous crteron for dentfyng generators n a load packet. Knowledge of ownershp patterns s the other way to determne potentally nterestng groups of generators. The effectveness of the proposed condtons (5) and (6) s demonstrated n Secton 4 usng the results of the two experments. These experments, whch are descrbed n Secton 3, focus on the potental for market power n a load pocket. (4)

10 10 3. Testng Market Power Usng POWERWEB 3.1 The Desgn of Experment I Two sets of experments were conducted to examne whether two generators nsde a load pocket could dentfy and explot the reduced ntensty of competton caused by a transmsson constrant. Each experment employed a sx generator, 30-node alternatng current (AC) network smulated by POWERWEB (a descrpton s provded n the Appendx B). In each experment, the network was dvded nto two regons (A and B) joned by transmsson lnks wth fnte thermal capactes. Each regon had a separate demand that could be satsfed by any of the sx generators operatng subject to the transmsson constrants. Fgure 3-1 shows a schematc representaton of the network for the frst set of experments. 240 MW generatng capacty Area A 116 MW demand 20 MW transmsson capacty Area B 120 MW generatng capacty 5 84 MW demand 6 Fgure 3-1: Transmsson Network Block Dagram Area B s the load pocket. Served by only two generators wth only lmted competton from the other four generators, prces n ths regon are expected to be hgher than compettve levels. In addton to the lmt on mports nto Area B, the two generators nsde the load pocket are mperfect substtutes. There are actually two transmsson lnes nto the load pocket. If ether of the generators nsde the load pocket generates less, the net demand at the end of one transmsson lne s ncreased. Ths causes ncreases n the flow of energy towards the node where the demand has ncreased, ncludng flows from outsde of the load pocket. In order to prevent the lne from beng overloaded when t s already at full capacty, some capacty outsde the load pocket must be backed down, representng an addtonal cost to the system. Generators n the load pocket can rase ther offers untl the margnal cost of ther energy equals the margnal cost of backng down generaton outsde the load pocket. The transmsson constrant, therefore, has both a drect effect that lmts flows of real energy

11 11 nto the regon and an ndrect effect caused by voltage support that affects nodal prces for all generators. Table 3-1 shows the cost parameters and block szes for the sx generators n the frst experment. Each generator was dvded nto three blocks of capacty wth dfferent margnal costs. Generators 1 through 4 were located outsde the load pocket n Area A. Generators 5 and 6 were located nsde the load pocket n Area B. Note that n ths experment, the sx generators are dentcal n cost and sze. However, the confguraton of ths network mples that generator 6 s n a more favorable locaton than generator 5. Generator 6 wll be backed down at a slower rate than generator 5 n response to makng hgher offers. Generator Table 3-1: Generator Costs and Capactes for Experment I Block 1 Block 2 Block 3 MW $/MW MW $/MW MW $/MW Insde Load Pocket Insde Load Pocket Gven the costs n Table 3-1, the compettve market soluton corresponds to generators submttng offers equal to the true margnal costs. The compettve soluton s shown n Table 3-2. Usng the Last Accepted Offer (LAO) to determne the market clearng prce, the second blocks of generators 1 and 3, whch are partally dspatched, set the market prce at $40/MWh. The hgher nodal prces pad to the other generators reflect network constrants and losses. However, the transmsson constrants from regon A to regon B are not bndng because only 12 MW of real energy s transmtted on lnes that have a maxmum capacty of 20 MW. Table 3-2: The Compettve Market Soluton for Experment I Generator MW Dspatched Nodal Prces $/MWh* LAO FRO Insde Load Pocket Insde Load Pocket * LAO Last Accepted Offer FRO Frst Accepted Offer

12 12 Snce the aggregate margnal cost curve for all generators s a step functon, generators can rase the compettve prce above the LAO, wthout alterng the effcent pattern of dspatch, untl the next most expensve block s reached. Ths latter stuaton corresponds to settng the market prce to the Frst Rejected Offer (FRO) of $50/MWh for generator 6. The dfference between the LAO and FRO prces represents the potental range of compettve prces. In the experments, the expectaton s that prces outsde the load pocket wll be n ths range, and that prces n the load pocket wll be hgher than the FRO. Note that the dfference among LAO prces and among FRO prces are small because flows on the network are relatvely unconstraned. Total system demand s 200 MW and t s completely nelastc 3. The load pocket has a demand of 84 MW and each of the generators n the load pocket has a capacty of 60 MW. If the transmsson lne s constraned, whch t wll be f the prce nsde the load pocket s above the prce outsde the load pocket, then only 20 MW of capacty can be mported nto the load pocket. Ths leaves a resdual of 64 MW of load that must be dvded between 120 MW of generatng capacty. Snce the requred generaton of 64 MW n the load pocket s greater than the 60MW capacty of a sngle generator, both generators n the load pocket are essental. If one generator rases ts offer to the maxmum allowed prce (the reservaton prce of $80/MWh) and the other generator submts offers below the reservaton prce, then the latter generator wll be fully dspatched at 60 MW. 4 MW wll be suppled by the generator submttng offers at the reservaton prce, and ths wll set the margnal prce n the load pocket. Addtonal capacty cannot be mported from outsde the load pocket even f the offers there are much lower. The actual stuaton s slghtly more complcated because generators have a mnmum capacty requrement correspondng to the frst block of 12MW. Snce both generators are essental n the load pocket, each generator must operate at least the frst block of capacty even f the offer s at the reservaton prce. von der Fehr and Harbord (1993) pont out that one of the generators n ths type of stuaton can ncrease ts profts by submttng lower offers. By sellng more capacty at a hgh prce (set by the other generator) profts are ncreased. Ths poston can be mantaned by offerng capacty at a prce low enough to ensure that the other generator s payoff s reduced f t tres to undercut the low offers. 3 At present most deregulated markets model demand to be perfectly nelastc. Only a small percentage of the load s prce senstve and so the assumpton of perfect nelastcty n the experments s not unreasonable.

13 The Results for Experment I Ths experment was conducted for fve dfferent groups of undergraduates and one group of utlty executves. For each sesson, the same aucton was repeated 75 tmes. Indvdual partcpants knew only 1) the costs and capactes of ther own generators, 2) the total system demand, and 3) that there were fve other compettors n the market. They knew nothng about the network or the potental load pocket. Fgure 3-2 shows a comparson of the average prces nsde and outsde the load pocket for all of the undergraduate sessons. Prces n the load pocket, by the end of the experment, were much hgher than those outsde of the load pocket. The lne at $50/MWh represents the maxmum compettve prce (FRO) f all generators had submtted offers at the true margnal costs. Snce the correspondng mnmum compettve prce (LAO) s $40/MW, prces between $40/MWh and $50/MWh can be consdered compettve Prce, $/MW Tradng Perod Gen 5 Gen 6 Other Generators Compettve Fgure 3-2: Average Prces n Undergraduate Sessons: Experment I The average prce outsde the load pocket s rarely above the compettve range. The fact that prces are close to the upper boundary of compettve prces would suggest that wth only four partcpants the market s not lkely to be perfectly compettve. Ths s supported by prevous

14 14 expermental examnatons of LAO multple unt auctons by Bernard et al. (1998) who show that at least sx partcpants wth a fxed nelastc load are needed to be effcent. Insde the load pocket, prces are on average slghtly hgher than the upper boundary of compettve prces untl the last twenty rounds of the experment. Durng the last twenty rounds average prces n the load pocket jump, wth generator 6 (as expected) beng the prce leader. The lower prce for generator 5 reflects locatonal dfferences n nodal prces due to voltage support. Ths prce dfference s much larger than the dfferences shown n Table 3-2 because of the effects of transmsson constrants on voltage. Fgure 3.3 shows the same comparson of prces from the experment wth utlty executves. Note that the same general result s acheved wth prces outsde the load pocket approxmately compettve whle prces nsdes the load pocket are substantally hgher (wth generator 6 leadng n prce). The man dfferences between the executves and the undergraduates are the speed wth whch the executves dentfed the degree of market power they possessed, the hgher prces acheved nsde the load pocket, and the use of sgnalng by generator 6. Droppng the offers from the reservaton prce to margnal cost n some perods s an attempt to get generator 5 to rase ts offers. In duopoly experments, Bernard et al. (1998) found that the two dentcal partcpants generally reached some tact agreement to share the responsblty for rasng the market prce. However, n ths case, there are locatonal dfferences between generators 5 and 6. The behavor of generator 5 s more lke the strategy proposed by von der Fehr and Harbord (1993). A more complete analyss of these results s gven n Ede et al. (2000). There were notceable dfferences n how well ndvdual sessons wth the undergraduates exploted market power. Usng the average prce pad to generators over the last 10 perods of each sesson as a crteron, the utlty executves were pad prces of $63/MWh and $76/MWh for generators 5 and 6, respectvely. One of the undergraduate sessons receved even hgher prces. In contrast, two of these sessons receved prces that were not sgnfcantly hgher than the compettve FRO of $50/MWh. Fndng the load pocket requred some bold exploratory behavor. For example, generator 5 exhbts such behavor n the early perods n Fgure 3.3. Generator 6 realzes that somethng s gong on because sometmes hgh prces are pad, but these hgh prces for generators 5 and 6 do not have much effect on the prces pad to generators 1-4. If generators 1-4 follow the same behavor as generator 5, they smply lose market share and may be shut down. Learnng n actual

15 Prce, $/MW Tradng Perod Gen 5 Gen 6 Other Generators Compettve Fgure 3-3: Average Prces n Utlty Executve Sesson: Experment I markets s accelerated by observng prces n other markets. Once traders see what s possble (e.g., gettng prce spkes), t does not take long for them to fgure out how to duplcate the prce behavor f ther own market s vulnerable to explotaton (.e., market power exsts). 3.3 The Desgn of Experment II Once the load pocket has been dscovered n Experment I, t s relatvely easy for generators n the load pocket to explot market power. Snce both generators 5 and 6 eventually fnd out that ther servces are essental to meet demand, they can ncrease ther profts by rasng ther offers. The only competton between them wll be to determne how much of ther capacty s dspatched to meet the net-load of 64 MW. A second set of experments was conducted to examne a case n whch cost dfferences result n a bndng transmsson constrant whch creates a load pocket for generators 5 and 6. The market was agan parttoned nto two areas (A and B) n Fgure 3-1 wth area B beng the load pocket. Demand throughout the system s completely nelastc, but the demand nsde the load pocket was reduced from 84MW to 49MW. If one generator was completely shut down, demand could be entrely satsfed by the other generator. Ths would ensure that nether generator nsde the load

16 16 pocket was essental to the operaton of the system. Explotng the load pocket n Experment II requres tact colluson between generators 5 and 6. The transmsson lne was constraned because the margnal costs for the two generators nsde the load pocket were hgher than the margnal costs of the generators outsde the load pocket. Wth margnal cost offers, energy would flow to the maxmum extent nto the load pocket from outsde, and power flow along the transmsson lne would be at ts maxmum of 20MW. Ths stuaton s typcal for many urban load centers that mport nexpensve power from remote baseload generators. Table 3-3 shows the new cost and capacty parameters of each generator n the experment. The changes from Experment I are bold. Table 3-3: Generator Costs and Capactes for Experment II Generator Block 1 Block 2 Block 3 MW $/MW MW $/MW MW $/MW Insde Load Pocket Insde Load Pocket The compettve soluton for Experment II s summarzed n Table 3-4. Each of the generators nsde the load pocket sell at close to the mnmum generatng lmts, and the transmsson lnes are used to the maxmum of 20 MW. There are, n effect, two separate markets, and dfferent blocks set the prces nsde and outsde the load pocket. The ranges of compettve LAO and FRO prces are $40/MWh to $50/MWh outsde the load pocket, and $54.27MWh to $55.73/MWh nsde the load pocket. Table 3-4: The Compettve Market Soluton for Experment II Generator MW Dspatched Nodal Prces $/MWh LAO FRO Insde Load Pocket Insde Load Pocket * LAO Last Accepted Offer FRO Frst Accepted Offer

17 17 Havng two markets n the compettve soluton changes the nature of the ndrect market power assocated wth the transmsson constrant. In the prevous experment, changes n the dspatch levels of generators 5 and 6 n the compettve soluton affected the flow of energy throughout the system, and altered the dspatch of some generators outsde the load pocket. In ths experment, the effects of changes nsde the load pocket on generators outsde the load pocket are small. Takng nto account constrants on the transmsson network, f ether generator 5 or 6 submts offers for both blocks 1 and 2 above $55/MWh, the market can adopt the characterstcs of Bertrand prce competton, wth the other generator possessng suffcent capacty to undercut the offer and be the only generator dspatched n the load pocket. In Experment I, ths was the way to dscover that block 1 was essental. Consequently, rasng prces n the load pocket n Experment II requres tact colluson between generators 5 and The Results of Experment II Ths experment was conducted for sx dfferent groups of undergraduates, and the aucton was repeated 75 tmes n each sesson. Once agan the students were not told about the network or the load pocket. Fgure 3-4 compares the average prces outsde the load pocket across all of the undergraduate sessons aganst the average prces receved by generators 5 and 6, nsde the load pocket. All four generators outsde the load pocket sell most of ther second block of capacty. Competton for load would be wth the thrd blocks of other generators whch are prced at $50/MWh, and the range for compettve prces s $40-$50/MWh. It s evdent n Fgure 3-4 that the average prce outsde the load pocket converged on the upper boundary. Insde the load pocket, only a small proporton of one of the generator's second block s needed to meet the net load of (49-20) = 29 MW, leavng a large balance of unused capacty (2 x 24 5 = 43 MW) prced at $55/MWh. Ths would be, therefore, the prce at whch competton for load occurred. Gven that t takes a number of rounds for the subjects n the experment to understand the workngs of the aucton and the extent of market power, t s unlkely that the experment was long enough for the generators to explot market power fully. The results n Fgure 3-4 show that both of the generators nsde the load pocket were able to gradually rase ther prces throughout the experment. It s clear that prces ended up hgher than compettve levels, and t s lkely that they would have gone even hgher f the experment had contnued. Addtonal analyses of these results are presented n Ede et al. (2000).

18 18 There were dfferences among the sx sessons n the fnal levels of prces reached n the load pocket. Usng the average prce pad for the last 10 perods as a crteron, the prces for generator 5 ranged from $61/MWh to $72/MWh, and from $55/MWh to $71/MWh for generator 6. (In Experment II, generator 5 had the most favorable locaton n the load pocket for explotng market power, and the dfferences n prces between generators 5 and 6 reflect the spatal effects of nodal prcng usng an AC network). The man dfference from Experment I was that dscoverng market power n Experment II dd not requre bold behavor because the load pocket already exsted n the compettve soluton. Snce nether generator 5 nor 6 are essental, as they were n Experment I, the explotaton of market power n Experment II evolved gradually throughout the experment Prce, $/MW Tradng Perod Gen 5 Av. Gen 6 Av. Average Prce (OLP) Expected Prce (OLP) Fgure 3-4: Average Prces n Undergraduate Sessons: Experment II

19 19 4. Applcatons of the Engneerng Measures 4.1 The General Approach The two experments dscussed n the prevous secton showed that two generators n a load pocket could explot market power effectvely and rase prces above compettve levels. The four remanng generators were able to rase prces to the hgh end of the compettve range ($50/MWh) but not hgher. In the frst experment, there were no major bndng constrants on transmsson n the compettve soluton, and as a result, there s no load pocket n ths stuaton. The load pocket had to be created by havng generators 5 or 6 submt hgh offers that cause mports to ncrease untl transmsson constrants are bndng. Once ths has been accomplshed, however, both generators n the load pocket were essental to meet load. For these two generators, the prce for the frst block of capacty could always be rased to the maxmum allowed n the aucton by submttng all offers at the reservaton prce ($80/MWh). In the second experment, the compettve soluton exhbted a load pocket because the true costs of generaton were hgher for the two generators n the pocket than they were for the other four generators. Economc effcency requred that power should be mported from outsde the load pocket to the maxmum amount possble. Consequently, all transmsson lnes nto the load pocket were run at full capacty n the compettve soluton. Nether generator n the load pocket was essental, but they represented a duopoly for supplyng the remanng power needed to meet load. Consequently, they were able to rase prces through tact colluson (e.g. Nash barganng). The two experments represent completely dfferent stuatons n the compettve cases, and t should be possble to dentfy market power n Experment II but not n Experment I. Usng the procedures descrbed n Secton 2 and Appendx A, the correspondng matrces of prce elastctes are computed for the two compettve solutons to llustrate the dfferences. For each experment, an addtonal OPF was run to represent the sesson that was most successful n explotng market power (usng the hghest prces receved n the last 10 tradng perods as the crteron). The correspondng matrces of prce elastctes are computed to compare wth the compettve cases. For ths comparson, the compettve soluton can be vewed as a case n whch generators were unable to explot market power. Usng the matrces of prce elastctes, t s relatvely easy to dentfy the cases n whch the physcal potental for market power exsts. However, t s more dffcult to determne how effectvely market power has been exploted. Havng dentfed the two generators wth market power, the frst

20 20 senstvty run s to solve an OPF wth all offers for these two generators set at the reservaton prce. Ths result shows whether or not the two generators are essental (.e. do not lose market share), and f they are essental, one can conclude that the market power s not a local phenomenon for the specfc condtons n the orgnal OPF. It would also be possble to submt offers at the reservaton level for just one generator n the load pocket at a tme, and to compute the OPF to determne whether that ndvdual generator s essental. Consder the followng stuaton n whch 1) a load pocket has been dentfed, and 2) t s more than just a local phenomenon at the observed OPF. It s possble to compare the observed nodal prces wth the correspondng prces when offers n the load pocket are at the maxmum. If the two sets of nodal prces are close together, one could argue that market power has been exploted effectvely. One possble measure of explotaton would be the percentage of the maxmum revenue (.e., wth offers at the reservaton prce) actually pad to the generators n the load pocket. Ths measure would, however, be very senstve to the level of the reservaton prce (prce cap) n a market. A better procedure mght be to adopt a specfed hgh prce as a standard for the proposed measure of explotaton. Clearly, the deal measure of market power s to compare the observed nodal prces wth the compettve prces, but ths deal s unattanable under deregulaton. An alternatve s to measure the opportunty cost for power mported nto the load pocket. For the second senstvty run offers for the two generators n the load pocket are set at zero, but the capactes offered are constraned to the optmum levels n the orgnal OPF plus epslon. The small ncrease of generaton n the load pocket wll relax the transmsson constrants, and as a result, the nodal prces for the two generators n the load pocket wll correspond to the cost of mported power. Even f these nodal prces are consdered to be crude substtutes for the true compettve prces, they would stll be useful for evaluatng the potental benefts of expandng transmsson capacty nto the load pocket. For our purposes, when the nodal prces for the case wth zero offers are much lower than the correspondng prces n the observed OPF, the cause may be market power. Combnng the results for the observed OPF and the two senstvty runs, wth the hgh offer ($80/MWh) and the low offer ($0/MWh), respectvely, t s possble to calculate the followng measure of Relatve Market Power (RMP): Observed prce Low prce RMP = 100. Hgh prce Low prce

21 21 Hgh values of RMP close to the maxmum of 100 ndcate that market power has been exploted successfully. Although the RMP works qute well for our examples, t s stll not an deal measure. Developng better measures of the explotaton of market power s one of the ongong objectves of our current research. It should be noted, however, that the man lmtaton of the RMP s the nablty to dscover the true costs. Ths s a defcency on the supply sde. From the perspectve of customers, the prces pad are more mportant than measurng profts. Hence, the RMP, or, as an alternatve, the rato [observed prce/low prce], provdes a reasonably good measure of how well the power system s workng for customers n a load pocket. 4.2 Identfyng the Exstence of Market Power For both experments, the sx generators can be grouped nto three regons based on the layout of the network shown n Appendx B. (The 2x2 blocks of prce elastctes for generators n the same regon are bold n Tables 4.1 and 4.2). Hence, t wll be useful to dentfy the dfferences wthn regons from the dfferences across regons. In general, one would expect the degree of substtutablty between two generators to be nversely related to how far apart they are on the network. The elastctes for the Compettve soluton n Experment I (Table 4.1) represent a stuaton wth no major bndng constrants on transmsson (.e. no load pockets). The own-prce elastctes are all large (>12 n absolute terms), showng that ndvdual generators are hghly compettve. Generators 1-4 are relatvely close substtutes ((.e. have large postve cross-prce elastctes), and so are generators 3-6. In contrast, generators 1 and 2 have small complementary relatonshps wth generators 5 and 6.

22 22 Table 4.1 Matrces of Prce Elastctes for Generators: Experment I Compettve Soluton Dspatch (MW) Prce ($/MWh) Actual Experment Dspatch (MW) Prce ($/MWh) The elastctes for the Compettve Soluton n Experment II represent a case n whch generators 5 and 6 are n a load pocket. However, all of the own-prce elastctes are stll very large n absolute terms (>10) and ndvdual generators do not appear to have market power. The pattern of cross-prce elastctes s more complcated than t was n Experment 1. The most notable features are the relatvely large negatve and postve cross-prce elastctes that occur between generators 5 and 6 n the load pocket and the other four generators. The load pocket s not cut off from the rest of the network (.e. wth cross-prce elastctes close to zero) as one mght expect. The reason s that the transmsson constrants make t harder for the network to mantan voltage constrants. Changes of generaton wthn the load pocket can stll have mportant effects outsde the load pocket, even though the amount of power mported nto the load pocket stays the same.

23 23 Table 4.2 Matrces of Prce Elastctes for Generators: Experment II Compettve Soluton Dspatch (MW) Prce ($/MWh) Actual Experment Dspatch (MW) Prce ($/MWh) The key feature of the load pocket for the Compettve Soluton n Experment II s that the own-prce and cross-prce elastctes for generators 5 and 6 are roughly the same sze (but wth opposte sgns). The results n Table 4.3 summarze the net elastcty for each generator wth the other generator n the same regon Table 4.3 Net Elastctes for Each Generator Experment I Experment II Generators Compettve Actual Compettve Actual 1 wth wth wth wth wth wth

24 24 (e.g., for generators 1 wth 2 for the Compettve Soluton n Experment I, the net elastcty s ( = -9.5)). For the unconstraned compettve case (Compettve Soluton n Experment I), all net elastctes are <-2.8, and fall outsde the range proposed n condton (5) (see Secton 2) to dentfy the exstence of market power (.e. net elastcty >-1). For the other three cases, all of the net elastctes for generators 1-4 fall well outsde the range. In contrast, fve of the sx net elastctes for generators 5 and 6 are wthn the range, and two of them are actually postve. The one excepton for generators 6 wth 5 for the Compettve Soluton n Experment II (-1.4) s stll close to 1, and the combned crteron for generators 5 and 6, shown n condton (6), mples that market power does exst (55.0 x 17.6 ( ) x 12.0 ( ) = > 0). For the two Actual Experments, the results for both generators 5 and 6 gve strong support for the exstence of market power because the net elastctes are well above 1. The overall concluson s that the measures proposed n Secton 2 dentfy the exstence of market power correctly. The results n Table 4.3 show that market power exsts for generators 5 and 6 n all cases except the Compettve Soluton n Experment 1. In contrast, generators 1 and 2 do not have market power n any of the four cases, and smlarly, generators 3 and 4 do not have market power. However, the combned group of generators 1-4 must have market power when generators 5 and 6 have market power because the rows of elastctes sum to zero (see Secton 2). The mplcaton s that the two generators nsde the load pocket wll fnd t much easer to rases prces than the four generators outsde the load pocket. However, n a complcated network facng dfferent types of uncertanty, there s no guarantee that four generators wll be compettve even though they dd behave compettvely n our experments (one possble reason s that load was not stochastc n the experments). 4.3 Measurng the Explotaton of Market Power The results n Secton 4.2 show that generators 5 and 6 have market power n the Actual Experments. These are the cases that an ISO would observe. Hence, the next queston s whether or not generators 5 and 6 are usng ther market power effectvely to rase prces. Seeng prces for generators 5 and 6 substantally hgher than the prces pad to other generators may rase suspcons, but, ths stuaton s nether suffcent nor necessary for explotng market power. The two addtonal senstvty runs proposed n Secton 4.1 dentfy a hgh offer case (offers for generators 5 and 6 set to the reservaton prce of $80/MWh) and a low offer case (offers for generators

25 25 5 and 6 set to $0/MWh). The nodal prces and optmal levels of dspatch for generators 5 and 6 n the two dfferent cases are shown n Table 4.4 for Experment I and Table 4.5 for Experment II. For Experment I, the total dspatch for generators 5 and 6 s lower n the Actual Experment (65.6MW) than t s for the Compettve Soluton (72.0MW), because ths s how the load pocket was created. The total dspatch n the Hgh Offer case s stll (65.5MW), mplyng that market power s persstent and not just a local phenomenon (the correspondng matrx of elastctes for the Hgh Offer case also confrm these conclusons). Table 4.4 Senstvty Analyss for Generators 5 and 6: Experment I Generator Compettve Actual Hgh Offer 1 Low Offer 2 RMP Prce % ($/MWh) % Dspatch (MW) Total Offers for Generators 5 and 6 set at $80/MWh 2 Offers for Generators 5 and 6 set at $0/MWh 3 Fxed to sum to 110% of the observed dspatch Table 4.5 Senstvty Analyss for Generators 5 and 6: Experment II Generator Compettve Actual Hgh Offer 1 Low Offer 2 RMP Prce % ($/MWh) % Dspatch (MW) Total Offers for Generators 5 and 6 set at $80/MWh 2 Offers for Generators 5 and 6 set at $0/MWh 3 Fxed to sum to 110% of the observed dspatch For Experment II, the total dspatch from generators 5 and 6 n the Compettve Soluton, the Actual Experment and the Hgh Offer cases are all close to 29.5MW. Once agan market power s not

26 26 a local phenomenon. Snce observed prces are lower than the maxmum levels, the full potental for market power has not been exploted as effectvely as t was n Experment I. The RMP s proposed n Secton 4.1 as a measure of explotaton and t measures the percentage of the dfference between the reservaton prce and the zero offer prce that s actually observed. The values of RMP for Experments I and II are shown n Tables 4.4 and 4.5 for generators 5 and 6. These results show that the partcpants n Experment I were more successful n explotng market power than the partcpants n Experment II. Ths concluson agrees wth the dscusson n Secton 3. Explotng monopoly power requred tact colluson n Experment II, and the results n Fgure 3.4 show that prces for generators 5 and 6 are stll trendng upwards after 75 rounds of the aucton. The stuaton for Experment I s dfferent because both generators 5 and 6 are essental to meet load. Ths fact can be determned drectly by notng that the total dspatch for generators 5 and 6 n the Actual Experment and the Hgh Offer case s greater than the total capacty of 60MW owned by each generator. 5. Conclusons The prmary objectve of ths paper s to show how the nformaton contaned n an Optmal Power Flow (OPF) for a power system can be converted nto useful ndcators of market power. The basc concept s that generators can be vewed as nputs nto a producton process to meet a pattern of loads (outputs) on a network. The optmal nodal prces, usng a last accepted offer aucton, correspond to nput prces. The OPF soluton corresponds to mnmzng total cost subject to operatng constrants. The frst order dervatves of mnmum cost wth respect to nodal prces gve the demand for generaton at dfferent nodes. The second order dervatves gve the complete matrx of prce effects for all generators. The prce effects are used to determne prce elastctes at the soluton values of the OPF. These elastctes are then combned to calculate a suffcent condton for the exstence of market power that does not depend on knowng the true costs of producton (see Secton 2). The basc measure s that a weghted sum of the own-prce and cross-prce elastctes for a group of generators should be greater than -1. Secton 3 descrbes two dfferent experments of market power usng POWERWEB to smulate an AC network wth sx generators. Students and utlty executves act as generators n a unform prce aucton to sell power. These experments show that two of the generators are able to dscover that they

27 27 possess market power and use ths knowledge to rase prces above compettve levels. In Secton 4, the proposed measures of market power are appled to the expermental results to demonstrate that the measures can dentfy the exstence of market power correctly. An addtonal objectve of Secton 4 s to measure how well market power has been exploted. A measure of Relatve Market Power s proposed whch does dstngush correctly between the two experments. However, ths measure of explotaton s dependent on usng the margnal cost of mportng addtonal power as a proxy for knowng the true producton costs. Our overall concluson s that measurng the exstence of market power n a network usng the nformaton n an OPF s a potentally valuable tool for an ISO to learn more about the economc characterstcs of a power system. However, more research s needed to determne f better measures of explotaton can be developed. The mplcatons of wthholdng capacty from an aucton s a specfc area that should be nvestgated further. In a real aucton, an ISO has more nformaton than the optmal dspatch and nodal prces from an OPF. Actual offers can be compared to nodal prces, and n many cases, nodal prces may be substantally hgher than the offers. For example, Eastern Electrcty was one of the companes n the UK market that benefted from the hgh prces set by the domnant duopoly, by acqurng capacty and sellng as much as possble (see Bower and Bunn (1999)). The ISO also has nformaton about the total capacty offered nto the aucton. Assumng that all generators must dsclose ther rated generatng capactes to an ISO, t would be possble to dentfy cases n whch capacty nsde a load pocket wth hgh nodal prces s wthheld from the aucton. In the two experments dscussed n ths paper, wthholdng capacty from the aucton dd not occur. However, other experments have shown that ths type of behavor s mportant for generatng prce spkes n a unform prce aucton when load s stochastc. Our current research plan ncludes nvestgatng the mplcatons of load uncertanty on measurements of market power.

28 28 6. Bblography Borensten, Severn, and James Bushnell (1997). "An Emprcal Analyss of the Potental for Market Power n Calforna s Electrcty Industry," Unversty of Calforna Energy Insttute, Berkeley. Borensten, Severn, James Bushnell and Chrstopher Knttel (1999). Market Power n Electrcty Markets: Beyond Concentraton Measures, The Energy Journal 20(4): Borensten, Severn, James Bushnell, and Frank Wolak (2000). "Dagnosng Market Power In Calforna's Deregulated Wholesale Electrcty Market. Unversty of Calforna Energy Insttute Power Workng Paper 064, July. Bower, John, and Derek Bunn (1999). "A Model-Based Comparson of Pool and Blateral Market Mechansms for Electrcty Tradng." London Busness School Energy Markets Group. Bunn, Derek W. (1999). Electrcty Markets are Dfferent, Strategc Prce Rsk n Wholesale Power Markets, London Busness School. Chambers, Robert G. (1988). Appled Producton Analyss: A Dual Approach, Cambrdge: Cambrdge Unversty Press. Ede, Smon, Tmothy D. Mount, Wllam Schulze, Rchard Schuler, Robert Thomas, and Ray Zmmerman (2000). "Expermental Tests of Deregulated Markets for Electrc Power: Market Power and Self Commtment," Report to the U.S. Department of Energy. Federal Energy Regulatory Commsson (2000). Commsson Proposes to Reshape Calforna s Serously Flawed Electrcty Markets wth Sweepng Changes, News Release, November, Washngton, D.C. Fuss, Melvyn and Danel McFadden (eds.) (1978). Producton Economcs: A Dual Approach to Theory and Applcatons, Vol. 1, Amsterdam: North-Holland Publshng Company. Hogan, Wllam W. (1997). A Market Power Model wth Strategc Interacton n Electrcty Networks, Center for Busness and Government, John F. Kennedy School of Government, Harvard Unversty, Cambrdge MA. Joskow, Paul L. and Jean Trole (2000). Transmsson Rghts and Market Power on Electrc Power Networks, Rand Journal of Economcs 31(3): Autumn. Newbery, Davd (1995). "Power Markets and Market Power," Energy Journal 16(3): Oppel, Rchard A. Jr. and Lowell Bergman (2001). "Deal for Use of Gas Ppelne Strs Dspute on Competton," The New York Tmes March 26, Prrong, Crag (2000). Manpulaton of Power Markets, John M. Oln School of Busness, Washngton Unversty, St. Lous. Rudkevch, Aleksandr, Max Duckworth and Rchard Rosen (1998). Modelng Electrcty Prcng n a Deregulated Generaton Industry: The Potental for Olgopoly Prcng n a Poolco, The Energy Journal, 19(3):

29 29 Schweppe, Fred C., Mchael C. Caramans, Rchard D. Tabors and Roger E. Bohn (1988). Spot Prcng of Electrcty, Boston, MA: Kluwer Academc Publshers. Varan, Hall R. (1978). Mcroeconomc Analyss, New York: W.W. Norton & Company. von der Fehr, Nls-Henrk Mørch and Davd Harbord (1993). "Spot Market Competton n the UK Electrcty Industry," The Economc Journal 103(418): Weber, James D. and Thomas J. Overbye (2000). "An Indvdual Welfare Maxmzaton Algorthm for Electrcty Markets," submtted for publcaton n IEEE Transactons on Power Systems February Wolak, Frank A. and Robert H. Patrck (1997). The Impact of Market Rules and Market Structure on the Prce Determnaton Process n the England and Wales Electrcty Market, Unversty of Calforna Energy Insttute PWP 047. Wolak, Frank A., Robert Nordhaus, and Carl Shapro (2000). An Analyss of the June 2000 Prce Spkes n the Calforna ISO s Energy and Ancllary Servces Market, Market Survellance Commttee, Calforna Independent System Operator, Sacramento. Wolfram, Catherne D. (1999). Measurng Duopoly Power n the Brtsh Electrcty Spot Market. Amercan Economc Revew 89:4:

30 30 Appendx A. Dervng the Hessan Matrx of Prce Effects Ths appendx shows how to compute the senstvty of dspatch to nodal prces startng from the soluton to a general nonlnear optmal power flow problem. Ths s defned as the mathematcal program mn f ( x ) subject to gx ( ) = 0. For convenence, x s assumed to have the followng structure: u x = y where u are the real power njectons that turn out to be free (.e., not aganst a mnmum or maxmum operatng lmt), and y s everythng else. Ths ncludes real power njectons that are fxed due to beng aganst a physcal lmt at optmalty, as well as all reactve njectons, bus voltage magntudes, bus voltage angles and any other control varables or state varables. Smlarly, g has the structure g ( x) gx ( ) = 1 g ( x) 2 wth g 1 beng the load flow equatons descrbng the real power msmatch exactly at the buses where the u varables apply,.e. k k k k k k g ( x) = G V V cos( θ θ ) + B V V sn( θ θ ) u 1 k B where B s the set of ndexes of buses that are connected to the th bus by means of an electrcal branch, V j and _ j stand for the voltage magntude and voltage angle at the jth bus, and G k, B k are the real and magnary part of the bus nodal admttance matrx element related to the nterconnecton of the th and kth buses. The vector g 2 (x) s made of all other constrants n the problem, namely, real k B power msmatch at all other buses, reactve msmatch at all buses, lne and transformer thermal lmts, voltage lmts, generaton lmts and any other bndng constrant n the formulaton. The Lagrangan for ths problem s T Lx (, λ) = f( x) + λ gx ( ) where the vector of Lagrange multplers λ s parttoned as λ = ( λ1, λ2 ), n a manner commensurate wth g = ( g1, g2). The frst order optmalty condtons are:

31 31 + gx ( ) f ( x) λ = 0 x gx ( ) = 0 T Close to a soluton, values of ( x, λ ) that are also solutons for a perturbed problem must satsfy λ1 g(x) + x g(x) = T λ λ 1 = 0 and ndeed, any ( x, λ) must satsfy the frst order expanson of the above, whch, for the case when the cost functons are lnear, takes the form: I gx ( λ g x) x+ 0 + ( ) ( ) 0 0 x gx ( ) x = 0 x Several smplfcatons are possble; frst, notce that g 1 = I. u Also, g2 = 0 u λ = 0 λ2 T 2 1 because the other actve msmatches, reactve msmatches or lne lmts are not n terms of the free actve njectons. Fnally, note that n the weghted Hessan sum λ 2 H g (x) = H H H only the H 22 term s nonzero, snce the u varables enter g affnely. Thus, the above equatons smplfy to H 22 T T g1 g2 y = λ1 λ 2 (1) y y g u = 1 y y (2) g2 y = 0 (3) y

32 32 From (1) T T g g y = H22 λ1 + λ 2 (4) y y Ths can be substtuted nto (3), whch can then be solved for λ 2 : λ = T 22 g y H g y 1 g2 y H g y T Ths can be substtuted nto (4) and the result substtuted n (2), to gve the followng expresson for the senstvty of dspatch to prce: g u = y λ T T 1 T 1 g 2 g 2 1 g 1 2 g g1 H λ 22 H 22 H 22 H 22 λ1 = M 1 y y y y 1 y where M s the symmetrc matrx of prce effects dscussed n Secton 2. Gven a soluton to an optmal power flow problem, t s possble to compute the senstvty matrx drectly wth ths formula for small to medum-szed systems. For larger systems, the sparsty of H 22 must be exploted. Appendx B The POWERWEB Platform POWERWEB s desgned to be a flexble Internet-based platform for performng economc experments. To date the experments mplemented usng ths platform have focused on examnng the behavor of electrcty markets usng realstc modelng of the physcal transmsson network and real human decson-makers. Its Internet-based archtecture elmnates the need for partcpants to be physcally present n a specally equpped laboratory. The POWERWEB server handles applcaton logc, data processng and computaton. Users submt offers to sell power through a standard web browser. In the electrcty markets currently mplemented n POWERWEB, each partcpant n a sesson plays the role of an owner of a generatng plant offerng to sell power through an ndependent system operator (ISO). An example offer submsson page s shown n Fgure A-1.

33 33 Fgure B-1: Offer Submsson Page from PowerWeb For most experments, POWERWEB selects the successful offers from competng generators through a unform prce last accepted offer aucton. It produces, va an optmal power flow smulaton, the market clearng prces and the generaton schedules whch optmally meet demand (whle respectng all of the physcal constrants of the power system). The page shown n Fgure B-2 dsplays the results of a sngle aucton, and the sellng prces correspond to nodal prcng. For the example shown n Fgure B-2, generator 6 sells the frst two blocks of capacty at the same prce of $4.03/MWh, havng submtted offers of $15/MWh and $40/MWh, respectvely. Fgure B-2: Aucton Results Page from POWERWEB

34 34 Fgure B-3 s a dagram of a 30 bus, 6 generator power system whose (some 200) physcal characterstcs and constrants are modeled by POWERWEB s smart market. An mportant feature of POWERWEB s that a full AC network s smulated. Ths s essental for studyng market power, because the ablty of a generator to support voltage at a partcular locaton s often a bndng constrant when transmsson lnes are fully loaded. The current network n POWERWEB was derved from a smplfed representaton of the New England Power Pool. However, the lve constrants and other features are modfed to create the approprate condtons for an experment. Fgure B-3: The Underlyng Network for the Aucton