Multi-settlement Systems for Electricity Markets: Zonal Aggregation under Network Uncertainty and Market Power 1

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1 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes Mult-settlement Systems for Eletrty Markets: Zonal Aggregaton under Network Unertanty and Market Power 1 Ransh Kamat and Shmuel S. Oren Unversty of Calforna at Berkeley 4135 Etheverry Hall, Berkeley, CA, {Kamat Abstrat We analyze alternatve market desgns for a multsettlement system for eletrty n whh the resoluton of the transmsson network model s nreased as tme approahes real-tme, and unertanty about ongeston patterns s resolved. Varatons of suh systems are mplemented or have been proposed n Calforna and other parts of the U.S. We am to ompare welfare mplatons of suh market desgns aganst more entralzed sngle-settlement systems, suh as those mplemented n the Northeastern ontrol areas of the U.S. We model the mult-settlement system as a two-perod game and ompute subgame perfet Cournot-Nash equlbra for the varous market desgns. 1. Introduton Over the past deade, wholesale eletrty markets have gone through fundamental hanges n the U.S. and around the world. Eletrty ndustry restruturng began n Latn Ameran ountres n the early 1980s, and more famously, n the Unted Kngdom n In the late 1990s, several U.S. states or ontrol areas suh as Calforna, Pennsylvana-New Jersey-Maryland (PJM) Interhange, New York, and New England establshed markets for eletrty; and more reently, FERC Order 2000 prompted several proposal for the establshment of Regonal Transmsson Organzatons (RTOs). Two key ommon aspets of the transton toward ompettve eletrty markets n the U.S. and around the world are a ompettve generaton setor and open aess to the transmsson system. However, there s onsderable dversty among the mplementaton paths hosen by dfferent states and ountres. The dfferenes are refleted n varous aspets of market desgn and organzaton, suh as groupngs of funtons, ownershp struture, and the degree of deentralzaton n markets. The experene ganed from the frst wave of restruturng n plaes suh as the Unted Kngdom, Sandnava, Calforna, and PJM, have led to several reassessment and reforms of varous market desgn aspets n these ursdtons. Two maor themes n market desgn have emerged n the restruturng proess, and have been mplemented or urrently proposed for the varous markets n the U.S. The frst one reles on entralzed dspath of all resoures n the market, varatons of whh are mplemented n the PJM Interhange, New York, and New England. In ths desgn, an ndependent system operator runs real-tme as well as day-ahead markets wth entralzed dspath. Blateral trades are allowed n suh system and are harged a ongeston fee that equals to the loatonal pre dfferenes between the neton and wthdrawal ponts n the realtme market. Congeston harges an be hedged through some type of transmsson ongeston ontrats, whh are defned as fnanal nstruments that guarantee the holder the pre dfferental between loatons spefed n the ontrat. The seond desgn reles on a more deentralzed approah, at least n the day-ahead energy market. The verson, whh was orgnally mplemented n Calforna, had two separate enttes, a Power Exhange (PX), whh was one of many short-term forward markets, and an ndependent system operator (ISO) whh managed real-tme operatons. The verson mplemented n Texas reles on blateral 1 The work desrbed n ths paper was oordnated by the Consortum for Eletr Relablty Tehnology Solutons on Behalf of the Department of Energy. The work was also supported by the Unversty of Calforna Energy Insttute and by PSERC /02 $17.00 () 2002 IEEE 1

2 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes tradng and prvate exhanges for day-ahead energy tradng and some of the emergng RTOs also rely on varous forms of deentralzed day-ahead markets. The key feature of ths sheme s that day-ahead energy tradng and settlements are based on a smplfed ommeral model of the transmsson network where nodes are grouped nto few zones and only few nterzonal transmsson onstrants (deemed ommerally sgnfant - CSC) are enfored (.e., pred) on day-ahead shedules submtted to the system operator. Congeston on CSCs an be hedged through fnanal or physal rghts on these onstraned nterfaes. Suh zonal aggregaton faltates lqudty of the day-ahead market but t allows shedulng of transatons that are physally mpossble to mplement due to relablty onstrants. A entrally oordnated real-tme physal market n whh operatonal desons are based on an aurate operatonal model of the transmsson grd orrets these nfeasbltes. The extent to whh fnanal settlements n the real-tme market reflet operatonal realtes s a hghly debated ssue that s not yet resolved n many of the emergng RTOs. The debate onerns the extent to whh the osts of orretng nfeasble shedules should be dretly assgned to the ausers as opposed to soalzng these osts through unform or load-share based uplft harges. The man goal of ths paper s to examne the extent to whh a mult-settlement system wth zonal aggregaton n the forward market faltates forward tradng as well as the welfare and dstrbutonal mplatons of havng suh zonal aggregaton n the presene of network unertanty. As a benhmark for omparson we use a sngle-settlement nodal model. 2 The remander of the paper s as follows. The next seton provdes a revew of the relevant lterature on spot market modelng, and modelng nteratons between spot and ontrat markets. Seton 3 presents our formulatons of the varous market desgns analyzed n ths study. In Seton 4, we analyze the mpat of network unertanty n a smple two-node example. Seton 5 provdes some onludng remarks and addresses future work. 2. Lterature Revew We revew lterature on eletrty market modelng wth transmsson onstrants, and models wth ontrats. Whle some eletrty market models have attempted to nlude transmsson onstrants, models wth two-settlement systems (or forward energy ontrats) usually treat the eletrty market as f t s delverable at a sngle loaton Eletrty Market Models Shweppe et al. [15] desrbe the theory of ompettve eletrty markets. Gven osts of all generators on the network, demand, and network topology, loatonal pres an be alulated usng an optmal power flow model, whh seeks to mnmze the total ost of generaton. In a deentralzed envronment, these pres an elt the optmal quanttes from ompettve agents. Dfferenes n loatonal pres are ust dfferenes n equlbrum margnal osts at varous loatons, and an be used to set transmsson harges for blateral ontrats (Hogan [11]). Studes modelng eletrty spot markets n the lterature, however, have foused on a non-ompettve vew of the spot market. Equlbra wth two onetural varatons, supply funton equlbra n models wthout transmsson onstrants (see Green and Newbery [9]; Bolle [3]), and Cournot-Nash equlbra n models wth transmsson onstrants have been examned. We wll fous on models wth transmsson onstrants. An mportant modelng hoe s the assumpton on whether agents wll game transmsson markets. Assumng that agents wll game the market, leads to non-onvex problems wth possbly multple equlbra (see Oren [13]; Cardell, Htt and Hogan [6] among others). 3 On the other hand, f the man purpose of the model s to onsder generator behavor n the energy market, assumng that agents at as pre takers n the transmsson market allows the models to be solved as omplementarty problems or varatonal nequaltes (see Hobbs [10]; Smeers and We [16]). In suh models, frst order ondtons for all the generators an be aggregated along wth those of transmsson owners, and the equlbrum an be solved as a omplementarty problem. Smeers and We [16] onsder a separated energy and transmsson market, where the system operator onduts a transmsson apaty auton, and power marketers purhase transmsson ontrats to support blateral transatons. They fnd that suh a market onverges to the optmal dspath for a large number of marketers. Borensten and Bushnell [4] use a grd searh algorthm to teratvely onverge to a Cournot model wth data on the Calforna market. Hobbs [10] uses lnearly 2 We gnore transmsson ontrats n ths study, and fous on a market wth a sngle zone. 3 See Luo, Pang and Ralph [12] for a omprehensve analyss of suh problems /02 $17.00 () 2002 IEEE 2

3 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes dereasng demand and onstant margnal ost funtons, whh result n lnear mxed omplementarty problems, to solve for suh Cournot equlbra. In a blateral market, Hobbs analyzes two types of markets, wth and wthout arbtrageurs. In the market wthout arbtrageurs, non-ost based dfferenes an arse beause the blateral nature of the transatons gves generators more degrees of freedom to dsrmnate between eletrty demand at varous nodes. Ths s equvalent to a separated market as n Smeers and We [16]. In the market wth arbtrageurs any non-ost dfferenes s subet to arbtrage by traders who buy and sell eletrty at nodal pres. Ths equlbrum s shown to be equvalent to a Cournot-Nash equlbrum n a POOLCO power market Contrat Markets Work n ths area has foused on the welfare enhanng propertes of forward markets. Theoretal studes have shown that for ertan onetural varatons, forward markets nrease eonom effeny through a prsoners' dlemma type of effet (see Allaz [1], and Allaz and Vla [2]) 4. The bas model n Allaz [1] s that produers meet n a two perod market where there s some unertanty n demand n the seond perod. In the frst perod, produers buy or sell ontrats and a group of speulators take opposte postons. In the seond perod, a non-ompettve market wth Cournot onetures s modeled. An arbtrage relaton between forward and spot pres dedes the forward pre. Allaz shows that generators have a strateg nentve to ontrat forward f other produers do not. Ths result an be understood usng the strateg substtutes and omplements termnology of Bulow, Geneakoplos and Klemperer [5]. In the spot market, produers onsder a partular produer's produton as a strateg substtute. 5 The avalablty of the forward market makes a partular produer more aggressve n the spot market. Ths produes a margnal negatve effet on other produers' produton, and mproves the proftablty of the partular produer under 4 Ths effet s not seen, for example, wth the Bertrand onetural varaton. 5 A produer onsders another produer's produton quantty as a strateg substtute f an nrease n the other produer s quantty has a negatve effet on ts own margnal proftablty. Ths s seen by negatvely slopng reaton funtons n Cournot markets. onsderaton. 6 Allaz shows, however, that f all produers have aess to the forward market, t leads to a prsoners' dlemma type of effet, redung profts of all produers. Soal welfare s hgher than n a snglesettlement ase wth produers behavng à la Cournot. Allaz ponts out that the results are very senstve to the knd of onetural varaton assumed, and shows that Cournot and market-sharng onetural varatons n the forward market lead to very dfferent results. Allaz and Vla [2] extend ths result to the ase where there s more than one tme perod where forward tradng takes plae. For a ase wth no unertanty, they establsh that f the number of perods when forward tradng takes plae tends to nfnty produers lose ther ablty to rase market pres above margnal ost and the outome tends to the ompettve soluton. von der Fehr and Harbord [17] and Powell [14] are early studes that nlude ontrats, and examne ther mpat on an mperfetly ompettve eletrty spot market, the U.K. pool. von der Fehr and Harbord [17] fous on pre ompetton n the spot market wth apaty onstrants and multple demand senaros. They fnd that ontrats tend to put a downward pressure on spot pres. Although, ths provdes dsnentve for generators to offer suh ontrats, there s a ountervalng fore n that sellng a large number of ontrats ommts a frm to be more aggressve n the spot market, and ensures that t s dspathed to ts full apaty n more demand senaros. They fnd asymmetr equlbra for varable demand senaros where suh a ommtment s useful. Powell [14] expltly models the effet of reonstrutng by Regonal Eletrty Companes (RECs) after the maturaton of the ntal portfolo of ontrats set up after deregulaton. He adds rsk averson on the part of RECs to the earler models. Generators at as pre setters n the ontrat market, but they ompete n a Cournot equlbrum n the spot market. The RECs set quanttes n the ontrat market. He shows that the degree of oordnaton has an mpat of the hedge over demanded by the RECs, and ponts to a 'free rder' problem whh leads to a lower hedge over hosen by the RECs. 3. Formulaton We analyze the problem wth the help of several llustratve examples on a smple two-node network. 6 Bulow, Geneakoplos and Klemperer [5] warn, however, that assumptons of lnearty on the demand often produes strateg substtutes, but that ths may no longer be true f the demand funton exhbts onstant elastty or s nonlnear /02 $17.00 () 2002 IEEE 3

4 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes For the mult-settlement ases, we formulate the problem as a two perod game. In perod 2, we model a spot market (produton game) where generators use a Cournot onetural varaton. We assume that generators take transmsson pres as gven and do not try to game the transmsson system (Hobbs [10], and Smeers and We [16] make suh an assumpton). In all our examples, the spot market s organzed at a nodal level. 7 There s a probablty r that one of the transmsson lnks wll be bndng n the spot market. In perod 1, we model a forward market (forward game) n whh ths transmsson onstrant s gnored, and the nodes are aggregated nto a sngle zone over whh the pre s unform. Generators an enter nto ontrats n ths perod, whh are settled n perod 2. We analyze the followng ases (a detaled desrpton of eah ase follows): Case A. Optmal Dspath Case B. Sngle-settlement Centralzed Market. Case C. Sngle-settlement Separated Markets. Case D. Mult-settlement System for Eletrty (Zonal Forward Market). D1. Resdual Centralzed Spot Market. D2. Centralzed Spot Market and Transmsson Charge for Congeston Causaton. D3. Resdual Separated Spot Market D4. Separated Spot Market and Transmsson Charge for Congeston Causaton. In a mult-settlement system t beomes neessary to aurately desrbe the ommodty, or the ommodty pre n ase of fnanal ontrats, for whh forward transatons are beng entered nto. In the entralzed market desgns there s a sngle pre n the forward market as transmsson onstrants are gnored n ths market. In a resdual market, spot transatons are settled at nodal pres. Ths means that there wll be fewer forward pres than spot pres, and forward pres for dfferent nodes wll be equal. Ths wll lead to arbtrage possbltes f the dreton of ongeston an be easly predted. We onsder two sets of ases. For one set of ases (reported as D1a and D2a n the results), we assume that the ommodty pre beng traded s the demand-weghted average pre n the spot market. In the presene of speulators, the forward pre wll onverge to the demandweghted expeted spot pre (assumng rsk neutralty 7 Another nterpretaton s that ongeston at the ntra-zonal level s also onsdered and pred f there s a zonal forward market. and zero nterest rates), and ths fat s used to determne forward pres. In our examples, we fnd that ths model predts relatvely small aggregate postons n the forward market. 8 There seems to be ample empral evdene, however, that generators over a large porton of ther spot sales under forward ontrats. There s also evdene that fnanal dervatves markets n eletrty are generally llqud, and tradng n these markets has been muh less than n omparatve markets for other ommodtes. In an attempt to explan that realty we examne a seond set of ases (reported as D1b and D2b n the results). Spefally, we explore a physal market n whh the forward ontrat s pred assumng that all demand shows up n the forward market, and s aggregated to determne the forward pre. Ths ase an be seen as a purely physal market, beause n the presene of speulators who ould arbtrage between forward and spot markets, suh a system would not work. 9 Ths essentally relaxes the no arbtrage ondton, and provdes generators wth the opportunty to extrat a strateg premum n the forward market. In the ase of separated markets, there an be multple forward pres, one orrespondng to eah node n the network. In keepng wth the above framework, for ases D3a and D4a, we assume that speulators elmnate any dfferenes n forward and spot pres, and so there s one forward ontrat per node, whh s settled fnanally at the respetve nodal pre. Forward pres at all nodes wll onverge to respetve spot pres n these ases as well. For ases D3b and D4b, we assume that all demand shows up n the forward market, and ths s used to determne forward pres at the nodes (even though transmsson onstrants are gnored there an be multple pres n suh systems as s explaned below). We now desrbe the ases n more detal. Case A. Ths s the welfare-maxmzng 10 outome and wll be the soluton to: A p = MC( q ) for all nodes wth generaton, A p = p ( D ) for all demand nodes, p q 1 2, q β = D = p + β = f , λ f transmsson lne onstraned for all nodes and hub ( ) 8 Ths may hange, although to a small extent, wth the ntroduton of rsk-averson n the model. 9 Ths also assumes that demand behaves non-strategally. 10 We use the sum of onsumer and produer surpluses as a welfare measure /02 $17.00 () 2002 IEEE 4

5 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes where, p, s the pre at node (we suppress the supersrpt for the state on energy pres and quanttes), q s the produton at node (t s assumed that eah frm has a sngle plant), D s demand at node, λ s the multpler assoated wth lnk 1 2 n state, {1, 2} an ndex set of states, β 1-2, s the power transfer dstrbuton fator or the amount of power that wll flow over ths lne when 1 unt of power s transferred from node to a referene node, and f1 2 s the apaty of ths lnk n state. Case B. In ths ase, we smulate a entralzed market outome wth generators behavng à la Cournot (see Hobbs [10]). In a entralzed market model, the system operator sets generaton and demand so as to maxmze gans from trade, and transmsson pres are set equal to the dfferene n nodal pres. We assume that generators take transmsson pres as gven. The equlbrum an be modeled as a two-stage game. In the seond stage of ths game, the system operator arbtrages any non-ost dfferenes n energy pres suh that n the resultng equlbrum, there s no spatal dsrmnaton n energy pres,.e. the pre dfferene between two nodes s exatly equal to the transmsson harge for transferrng energy between the two nodes. In the frst stage, generators antpate ths arbtrage and ompete n a Cournot-Nash manner. Eah generator wll solve the followng onstraned optmzaton problem n a entralzed market. Max Π = p q C( q ) q p = p + β 1 2, λ and hub ( ) q = D Though we model an equlbrum n quanttes, ths optmzaton problem s more easly modeled n pres, and the frst order neessary ondtons (FONCs) for ths problem an be obtaned after substtutng the onstrants nto the obetve funton, and makng p the deson varable. The two FONCs along wth the onstrants of the problem, and the flow onstrant, f bndng, wll determne the market outome n ths ase. Case C. In ths ase, the system operator onduts an auton for transmsson apaty and does not get nvolved n the energy market (see Smeers and We [16]). Generators behave à la Cournot n a blateral market, and then purhase transmsson serve from the system operator. For tratablty, we assume that generators reveal ther true wllngness to pay for transmsson apaty (ther opportunty ost). Ths outome an have spatal pre dsrmnaton as generators may set quanttes n suh a way that the pre dfferene between nodes s dfferent than the orrespondng transmsson harge. The system operator provdes transmsson serve to the network assumng t annot affet transmsson pres. Eah generator wll solve the followng optmzaton problem: MaxΠ = ( p ( s + s ) w ) s C( q ) + w q s ( θ ) : s = q k k where s s the amount of the blateral transaton between the generator at node and demand at node and θ s the multpler on the balane onstrant. The system operator, assumng that t annot affet transmsson pres, w n turn solves a lnear program of the followng form: Max R = w y y S ( λ ) : β 1 2, y f 1 2 where, w are transmsson pres and y s defned as transmsson serve from the hub to node n state. In order to determne the equlbrum the frst order ondtons of the generators and the system operator are aggregated. A market learng ondton s added whh equates the quantty of transmsson serves requested by generators to the quantty offered by the system operator at eah node n the network gven by: y = s q for all nodes Case D1. In ths ase, the system operator operates a forward market but gnores ongeston n ths market. Any transatons n ths market do not pay transmsson harges n the spot market. Resdual transatons made n the spot market are subet to nodal pres n the spot market. Ths an be nterpreted as a zonal prng sheme wth a sngle zone aross the nodes of the system. The system operator operates a entralzed spot market. Generators wll solve a 2 perod problem n ths ase. In the seond perod, generators wll maxmze profts gven ther forward ommtments: f MaxΠ = p f + p ( q f ) C( q ) p q = p q = + β 1 λ D 2, for all nodes and hub ( ) As n Case B, we an ollet frst order ondtons and solve for an equlbrum numerally f the forward /02 $17.00 () 2002 IEEE 5

6 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes postons are gven. In our examples, we assume that the ongeston pattern s easly predted, and therefore we an solve the equlbrum ondtons for ths ase analytally (after droppng the omplmentary slakness ondtons). Ths yelds pres and quanttes n terms of the forward postons, f, of the two generators. In order to alulate an equlbrum of the multsettlement system, we employ the noton of a sub-game perfet Nash equlbrum (SPNE) (see Fudenberg and Trole [8]). Ths says that n perod 1, generators wll orretly antpate the reatons of all the agents movng n perod two. The generators wll therefore solve an expeted proft maxmzaton problem n perod 1 (we assume that generators are rsk-neutral), subet to equlbrum onstrants n the forward market, f any, and usng the funtons derved for the spot market varables. 11 For the ase wth speulators, t s assumed that the forward market pre wll be the demand-weghted average pre n the spot market. Ths reates nonlnearty n the frst order ondtons and the soluton has to be obtaned numerally va a grd searh. Case D2. In ths ase, we assume that all transatons that are dspathed n the spot market are harged the spot transmsson harge (see Chao et al. [7]). Ths means that any forward transatons made n the zonal market, and not reversed n the spot market, wll be subet to a spot transmsson harge. Ths provdes nentves for generators to avod what s alled a DEC game n markets where suh aggregaton s done n the forward market, e.g. the now defunt Calforna PX market. Generators n suh markets have an nentve to over-shedule n the day-ahead market and then get pad for ongeston relef n the real tme market, n essene, get pad for not produng. In a entralzed market, t beomes neessary to dede on a hub whh establshes the spot transmsson harge. Keepng n lne wth our earler assumpton for the settlement pre for a forward ontrat, we use the demand-weghted average pre as the hub pre. Generators solve the followng optmzaton problem n the spot market: f MaxΠ = p f + p ( q f ) C( q ) f ( p p ) p q = p q = + β 1 λ D 2, hub for all nodes and hub ( ) 11 In general, the generator's problem wll be non-onvex due to the omplmentary slakness ondtons mposed n the spot market equlbrum. As mentoned earler, f ongeston patterns are easly predted these an be dropped. where, p hub s the hub pre. As the hub pre ntrodues nonlnearty n the equlbrum ondtons, we annot solve for the quanttes and pres n terms of the forward postons analytally. Instead, we ondut a grd searh to determne the optmal forward postons by numerally trang the reaton funtons n the forward market for both subases. For the subase wth speulators, the hub pre also serves as the settlement pre for forward ontrats. Case D3. Ths ase s smlar to ase D1 wth the hange that the spot market s separated (as n Case C). Generators wll have blateral forward ommtments n ths ase and wll solve the followng optmzaton problem n perod 2 (the spot market): f f k f MaxΠ = p ( s ) + ( p ( s + s ) w )( s s ) s ( θ ) : s C( q ) + wq = q k k The grd owners problem remans the same. Agan, pres and quanttes n eah state an be alulated n terms of the forward postons and the generators wll solve an expeted proft maxmzaton problem n perod 1 antpatng the spot market equlbra. Case D4. Ths ase s smlar to D2 above wth the hange that the spot market s separated (as n Case C). The dfferene s that blateral forward transatons an be harged the spot transmsson harge based on the delvery node. Generators wll solve the followng optmzaton problem n the spot market: f f k f Max Π = p ( s ) + ( p ( s + s ) w )( s s ) s ( θ ) : s = q C( q ) + w q k ( w k + w ) s The grd owner's problem remans the same. Agan, pres and quanttes n eah state an be alulated n terms of the forward postons, and the generators wll solve an expeted proft maxmzaton problem n perod A Numeral Example Consder the example n Fgure 1 wth a sngle generator at eah node of a smple two-node network. We assume there are two states of the world, one n whh the network does not have any transmsson onstrants, and the other where the apaty of the lne onng node 1 and 2 s K MW. The generator at node 1 f /02 $17.00 () 2002 IEEE 6

7 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes s assumed to be low ost, and would run at output levels that the transmsson lne would not be able to sustan n the state of the world where ths apaty lmt s bndng (see Table 1 for data). 2 + d 2 q 2 K + θ 1 + d 1q 1 p 2 = a 2 - b 2 q 2 p 1 = a 1 - b 1 q 1 Fgure 1. A Smple two-node network Table 1. Parameter Values for two-node example Parameter Value a 1, a b 1, b 2 2 1, 2 10 d 1 1 d 2 4 K 3 θ Large r 0.05 We use the sngle-settlement entralzed dspath results as our benhmark (see the Appendx for results). Ths market desgn has welfare levels that are lower than the optmal dspath n the amount of 7.8 perent and 5.1 perent, n the unonstraned and onstraned states, respetvely. A general observaton s that for ths level of ongeston, mult-settlement systems ontnue to be welfare enhanng, refletng the lterature on ontrat markets wthout transmsson onstrants. For the 'no arbtrage' ases, onsumers beneft beause of the hgher spot produton to the detrment of at least one produer, as n prevous lterature. The 'market learng' ases have even hgher welfare nreases due to larger overage n forward ontrats; however, onsumer surplus s lower as ompared to the other ases beause of the market learng assumpton used to set the forward pre. Produers are able to extrat as muh as 26.7 perent of onsumer surplus n ase D1b (resdual market wth entralzed dspath) as ompared to ase D1a (unonstraned state). In the 'no arbtrage' ases, spot pres average around $62 per MWh (ths s about the level they aheve n the unonstraned state; In the onstraned state, spot pre at node 1 s around $56 per MWh, whle at node 2 t s $69 per MWh). On the other hand, forward pres n the market learng ase are around $71 per MWh, wth expeted spot pres n ths ase averagng $57 per MWh (spot pres are lower n the 'market learng' ase due to hgher ontrat overage). Whle ths dfferene seems qute large, and almost unsustanable n a repeated market, pre dfferentals of a few dollars have been observed n the frst year of the day-ahead and real-tme Calforna markets. As mentoned above, a strkng result s that n the 'no arbtrage' ases, havng one forward perod yelds on average less than 15 perent ontrat overage. The 'market learng' ases, on the other hand, have ontrat overage of around 68 perent. Ths ponts to the fat that n the presene of market power, the strateg nentves that generators have to ontrat n short-term forward markets play a bg role n the outome of these markets, perhaps domnatng the rsk-sharng aspets of these markets. The addton of the spot transmsson harge has the desred result of redung net flow on the transmsson lne n the forward market. In the 'market learng' ase, frm 1 has a smaller forward poston, whle frm 2 has a larger forward poston redung net flow on the lne. One other sgnfant result s that n ase D3a, the generator at node 2 s long n the forward market at node 1. Ths means that t prefers to be less aggressve as ompared to the sngle-settlement ase at ths node. Ths also has a onsderable mpat on the grd owner's revenue, whh drops substantally between the resdual and spot transmsson harge ases. Long forward postons may mean that the grd owner may run a deft n a resdual market. 5. Conludng Remarks In ths paper, we model and analyze several eletrty market desgns urrently adopted or proposed n the U.S., n the presene of network unertanty and market power. We ompare the two maor approahes n market desgn that have emerged n the restruturng proess, the entralzed dspath paradgm, and the mult-settlement system paradgm wth aggregaton of nodes n the forward market. We fnd that n the presene of market power, welfare mpats of zonal aggregaton are hghly senstve to the probablty that a network ontngeny redues the transmsson apaty of an mportant lne n the /02 $17.00 () 2002 IEEE 7

8 Proeedngs of the 35th Hawa Internatonal Conferene on System Senes network. Usng a duopoly model over a smple twonode network, we show that for small probabltes of ongeston, mult-settlement systems are found to be welfare enhanng, mrrorng results n a large body of lterature that model eletrty as f t s delverable at a sngle loaton. These results seem to be drven by the nentves for generators to be more aggressve n the spot market to the detrment of ts ompettors. When both generators undertake suh ommtments a prsoner's dlemma type of effet lowers ther proftablty, benefts onsumers and leads to hgher overall welfare levels. Of ourse, are should be taken when nterpretng results from a smple model suh as ours. However, examples of severe gamng n the Calforna market suggests that zonal aggregaton should be suh that ongeston s rare nsde eah zone. In our analyss, we fnd that the standard assumpton of 'no arbtrage' aross forward and spot markets leads to very lttle ontrat overage even n the no ongeston ase. Ths seems to be at odds wth empral evdene that there s substantal ontrat overage n eletrty markets. In provdng an alternatve vew of the market, we explore the mplatons of relaxng the 'no arbtrage' assumptons, and for a set of mult-settlement ases, assume that all of the demand shows up n the forward market and s aggregated to determne the forward pre usng a 'market learng' ondton. Ths essentally gves the generators an extra degree of freedom to extrat surplus from onsumers. Ths also re-establshes the nentves for generators to take short postons n the forward market, and we fnd hgher levels of ontrat overage n these ases. 6. Referenes [1] Allaz, B. (1992). "Olgopoly, Unertanty and Strateg Forward Transatons," Internatonal Journal of Industral Organzaton, Vol. 10, pp [2] Allaz, B. and J.-L. Vla (1993). "Cournot Competton, Forward Markets and Effeny, Journal of Eonom Theory, Vol. 59, pp [3] Bolle, F. (1992). "Supply Funton Equlbra and the Danger of Tat Colluson: the Case of Spot Markets for Eletrty," Energy Eonoms, Vol. 14, No. 2, pp [4] Borensten, S. and J. Bushnell (1999). "An Empral Analyss of the Potental for Market Power n Calforna's Eletrty Industry," Journal of Industral Eonoms, Vol. 47, No. 3, pp [5] Bulow, J., J. Geneakoplos and P. Klemperer (1985). "Multmarket Olgopoly: Strateg Substtutes and Complements," Journal of Poltal Eonomy, Vol. 93, pp [6] Cardell, J., C. Htt and W. W. Hogan (1997) "Market Power and Strateg Interaton n Eletrty Networks," Resoure and Energy Eonoms, Vol. 19, pp [7] Chao, H.-P., S. Pek, S. S. Oren and R. B. Wlson (2000). "Herarhal Effent Transmsson Prng," EPRI, Stanford Unversty and Unversty of Calforna at Berkeley. [8] Fudenberg, D. and J. Trole (1991). Game Theory. The MIT Press, Cambrdge, MA. [9] Green, R. J. and Newbery, D. M. (1992). "Competton n the Brtsh Eletrty Spot Market," Journal of Poltal Eonomy, Vol. 100, No. 5, pp [10] Hobbs, B. F. (2001). "Lnear Complementarty Models of Nash-Cournot Competton n Blateral and POOLCO Power Markets," IEEE Transatons on Power Systems, Vol. 16, No. 2, pp [11] Hogan, W. W. (1992). "Contrat Networks for Eletr Power Transmsson," Journal of Regulatory Eonoms, Vol. 4, pp [12] Luo, Z., Pang, J.-S., and D. Ralph (1996). Mathematal Programmng wth Equlbrum Constrants, Cambrdge Unversty Press, Cambrdge, UK. [13] Oren, S. S. (1997). "Eonom Ineffeny of Passve Transmsson Rghts n Congested Eletrty Systems wth Compettve Generaton," The Energy Journal, Vol. 18, pp [14] Powell, A. (1993) "Tradng Forward n an Imperfet Market: The Case of Eletrty n Brtan," The Eonom Journal, Vol. 103, pp [15] Shweppe, F. C., M. C. Caramans, R. D. Tabors and R. E. Bohn (1988). Spot Prng of Eletrty, Kluwer, Boston, [16] Smeers, Y. and We, J.-Y. (1997a). "Spatal Olgopolst Eletrty Models wth Cournot Generators and Opportunty Cost Transmsson Pres," CORE, Unversté Catholque de Louvan, Louvan-la-Neuve, Belgum. [17] von der Fehr, N.-H. M. and D. Harbord (1992). "Long-term Contrats and Imperfetly Compettve Spot Markets: A Study of the U.K. Eletrty Industry," Memorandum No. 14 (August 1992), Department of Eonoms, Unversty of Oslo, Oslo, Sweden /02 $17.00 () 2002 IEEE 8

Cournot equilibria in two-settlement electricity markets with system contingencies. Jian Yao, Shmuel S. Oren* and Ilan Adler

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