Proactive Transmission Investment in Competitive Power Systems

Transcription

1 Appears n the Proeedngs of the PES General Meetng, June 18-22, Proatve Transmsson Investment n Compettve Power Systems Enzo E. Sauma, Student Member, IEEE and Shmuel S. Oren, Fellow, IEEE 1 Abstrat We formulate a three-perod model for studyng how the exerse of loal market power by generaton frms affets the equlbrum nvestment between the generaton and the transmsson setors. Usng a 3-bus network example, we ompare the transmsson nvestment desons made by a proatve network planner (who proatvely plans transmsson nvestments to ndue a more soally-effent equlbrum of generaton nvestments) wth both those made by an ntegrated-resoures planner (who jontly plans generaton and transmsson expansons) and those made by a reatve network planner (who plans transmsson nvestments only onsderng the urrently nstalled generaton apates). We show that, although a proatve network planner annot do better (n terms of soal welfare) than an ntegrated-resoures planner, t an reoup some of the lost welfare due to the separaton of generaton and transmsson plannng by proatvely expandng transmsson apaty. Conversely, a reatve network planner, who gnores the nterrelatonshp between the transmsson and the generaton nvestments, foregoes ths opportunty. Index Terms Cournot-Nash equlbrum; market power; mathematal programmng; mathematal program wth equlbrum onstrants; network expanson plannng; power system eonoms. D I. INTRODUCTION URING the past deade, many ountres nludng the US restrutured ther eletr power ndustres, whh essentally hanged from one domnated by vertally ntegrated monopoles (where the generaton and the transmsson setors were jontly planned and operated) to a deregulated ndustry (where generaton and transmsson are both planned and operated by dfferent enttes). The fat that generaton and transmsson expansons are planned by dfferent enttes reates onflts of nterests among these nsttutons, whh generally leads to soal losses. Sne the exstng US eletrty transmsson network was desgned to 1 The work reported n ths paper was supported by NSF Grant ECS1193, The Power System Engneerng Researh Center (PSERC) and by the Center for Eletr Relablty Tehnology Solutons (CERTS) through a grant from the Department of Energy. E. E. Sauma s wth the Department of Industral Engneerng and Operatons Researh, Unversty of Calforna at Berkeley, Berkeley, CA 9472 USA (emal: esauma@eor.berkeley.edu). S. S. Oren s wth the Department of Industral Engneerng and Operatons Researh, Unversty of Calforna at Berkeley, Berkeley, CA 9472 USA (emal: oren@eor.berkeley.edu). serve a vertally ntegrated ndustry that no longer exsts, one of the man hallenges of the deregulated system s to reate market rules that allow the upgrades needed to ensure the relablty of the system at the mnmum soal ost. Beause of the unque nature of eletrty, there are nherent operatonal and nvestment omplementartes and substtutabltes between the generaton and the transmsson setors. A vertally ntegrated monopolst an norporate the system-wde effets when makng operatng and nvestment desons. As a result of the unbundlng from the transmsson nfrastruture, however, ndvdual generaton frms wll make these desons to maxmze ther own proft, gnorng ther aton s external effet on other generaton frms and the transmsson system. Thus, whle these hanges are prerequste to a ompettve ndustry, they also reate a market haraterzed by ubqutous externaltes. A key queston s whether the transmsson management protools desgned to fore generaton frms to nternalze ther external dspathng effets also ounter the orrespondng nvestment externaltes. In ths paper, we formulate a three-perod model for studyng how the exerse of loal market power by generaton frms affets both the generatng frms nentves to nvest n new generaton apaty and the equlbrum nvestment between the generaton and the transmsson setors. The model struture s a mathematal program subjet to an equlbrum problem wth equlbrum onstrants (MEPEC), n whh the network planner solves a mathematal programmng problem subjet to the equlbrum of generaton apaty expanson (where eah frm solves a mathematal programmng problem wth equlbrum onstrants (MPEC)). Usng a 3-bus network, we show that a proatve network planner (.e., a network planner who plans transmsson nvestments n antpaton of generaton nvestments so that t s able to ndue a more soallyeffent Nash equlbrum of generaton apates) an reoup some of the welfare lost due to the unbundlng of the generaton and the transmsson nvestment desons by proatvely expandng transmsson apaty. Conversely, we show that a reatve network planner (.e., a network planner who plans transmsson nvestments only onsderng the urrently nstalled generaton apates and, n ths way, gnorng the nterrelatonshp between the transmsson and the generaton nvestments) foregoes ths opportunty. The onept of a proatve network planner was formerly

2 2 proposed by Craft n her dotoral thess [5]. However, Craft only studed the optmal network expanson n a 3-node network that presented very partular haratersts. Spefally, Craft s work assumes that only one lne s ongested (and only n one dreton), only one node has demand, there s only one generator at eah node, energy market s perfetly ompettve, and transmsson nvestments are not lumpy. These strong, and qute unrealst, assumptons make Craft s results hard to apply n a real transmsson system. The model presented n ths paper extends Craft s model n several ways. Whle some other authors have onsdered the effet of the exerse of loal market power on network plannng, none of them have modeled the nterrelatonshp between the transmsson and the generaton nvestment desons. In [4], [6], [7], and [9], the authors study how the exerse of market power an alter the transmsson nvestment nentves n a two- and/or three-node network n whh the entre system demand s onentrated n only one node. The man dea behnd these papers s that f an expensve generator wth loal market power s requested to produe power as result of network ongeston, then the generaton frm owng ths generator ould have no nentve to releve ongeston. Referene [2] presents an analyss of the relatonshp between transmsson apaty and generaton ompetton n the ontext of a two-node network n whh there s loal demand at eah node. In ths paper, the authors argue that relatvely small transmsson nvestment may yeld large payoffs n terms of nreased ompetton. Bushnell and Stoft [3] propose that transmsson nvestors are granted fnanal rghts (whh are tradable among market partpants) as reward for the transmsson apaty added to the network and suggest a transmsson rghts alloaton rule based on the onept of feasble dspath. They prove that, under ertan rumstanes, suh a rule an elmnate the nentves for a detrmental grd expanson. However, these ondtons are very strngent. Joskow and Trole [6] analyze the Bushnelland-Stoft s model when assumptons that better reflet the physal and eonom attrbutes of real transmsson networks are ntrodued. They show that a varety of potentally sgnfant performane problems then arse. Some other authors have proposed more radal hanges to the transmsson power system. Oren and Alvarado (see [1] and [8]), for example, propose a transmsson model n whh a for-proft ndependent transmsson ompany (ITC) owns and operates most of ts transmsson resoures and s responsble for operatons, mantenane, and nvestment of the whole transmsson system. Under ths model, the ITC has the approprate nentves to nvest n transmsson. However, ths approah requres the dvestture of all transmsson assets, whh does not seem to be vable n the US system. II. THE PROACTIVE TRANSMISSION INVESTMENT MODEL We propose a three-perod model for studyng how generaton frms loal market power affets both the frms nentves to nvest n new generaton apaty and the equlbrum nvestment between the generaton and the transmsson setors. A. Assumptons The model does not assume any partular network struture, so that t an be appled to any network topology. Moreover, the model allows demand at every node of the network. For smplty, we assume that all nodes are both demand nodes and generaton nodes and that there s exatly one frm ownng generaton faltes at eah node. We allow generaton frms to exerse loal market power. Furthermore, the model allows many lnes to be smultaneously ongested. Although ths fat makes the analyss omplex, ths s a very mportant feature of real network operatons. The model onssts of three perods, as dsplayed n Fg. 1. We assume that, at eah perod, all prevous-perods atons are observable to the players makng a deson. That s, we defne the proatve transmsson nvestment model as a omplete- and perfet-nformaton game 2 and the equlbrum as sub game perfet. Fg. 1. Three-perod model for proatve transmsson nvestment. The last perod (perod 3) represents the energy market operaton. That s, n ths perod, we ompute the equlbrum quanttes and pres of eletrty over gven generaton and transmsson apates. We model the energy market equlbrum n the topology of the transmsson network through the DC approxmaton of Krhhoff s laws. Spefally, flows on lnes an be alulated by usng the power transfer dstrbuton fator (PTDF) matrx, whose elements gve the proporton of flow on a partular lne resultng from an njeton of one unt of power at a partular node and a orrespondng wthdrawal at an arbtrary (but fxed) slak bus. Dfferent PTDF matres wth orrespondng probabltes haraterze unertanty regardng the realzed network topology n the energy market equlbrum (the generaton and transmsson apates are subjet to random flutuatons (ontngenes) that are realzed n perod 3 pror to the produton and redspath desons by the generators and the system operator). We wll assume that the probabltes of all redble ontngenes are publ knowledge. The energy market equlbrum s onsdered a subgame wth two stages. In the frst stage, Nature pks the state of the world (and, thus, settles the atual generaton and 2 A omplete- and perfet-nformaton game s defned as a game n whh players move sequentally and, at eah pont n the game, all prevous atons are observable to the player makng a deson.

3 3 transmsson apates as well as the shape of the demand and ost funtons at eah node). In the seond stage, frms ompete n a Nash-Cournot fashon by seletng ther produton quanttes, whle takng nto onsderaton the smultaneous mport/export desons of the system operator whose objetve s to maxmze soal welfare whle satsfyng the transmsson onstrants. In the seond perod, eah generator nvests n new generaton apaty, whh lowers ts margnal ost of produton at any output level. For the sake of tratablty we assume that generators produton desons are not onstraned by physal apaty lmts. Instead we allow generators margnal ost urves to rse smoothly so that produton quanttes at any node wll be lmted only by eonom onsderatons and transmsson onstrants. In ths framework generaton expanson s modeled as strethng the supply funton so as to lower the margnal ost at any output level and thus nrease the amount of eonom produton at any gven pre. Suh expanson an be nterpreted as an nrease n generaton apaty n a way that preserves the proportonal heat urve or alternatvely assumng that any new generaton apaty nstalled wll replae old, neffent plants and, thereby, nrease the overall effeny of the portfolo of plants n produng a gven amount of eletrty. Ths ontnuous representaton of the supply funton and generaton expanson serves as a proxy to atual supply funtons that end wth a vertal segment at the physal apaty lmt. Sne typally generators are operated so as not to ht ther apaty lmts (due to hgh heat rates and expansve wear on the generators) our proxy should be expeted to produe realst results. The return from the generaton apaty nvestments made n perod 2 ours n perod 3, when suh nvestments enable the frms to produe eletrty at lower ost and sell more of t at a proft. In the frst perod, the system operator makes a sngle transmsson expanson deson n antpaton of the generaton expanson desons (perod 2) and the eletrty market equlbrum (perod 3). In ths perod, the proatve system operator s lmted to dede on the best loaton and the magntude for the next transmsson upgrade. We assume the transmsson expanson does not alter the orgnal PTDF matres, but only the thermal apaty of the lne. Ths would be the ase f, for the expanded lne, we replaed all the wres by new ones (wth new materals) whle usng the same exstng hgh-voltage towers. Sne the energy market equlbrum wll be a funton of the thermal apates of all onstraned lnes, the Nash equlbrum of generaton apates wll also be a funton of these apaty lmts. The proatve system operator, then, has multple ways of nfluenng ths Nash equlbrum. By atng as a Stakelberg leader and antpatng the equlbrum of generaton apates, ths system operator s able to nfluene generaton frms to make more soally optmal nvestments. We further assume that the generaton ost funtons are both nreasng and onvex n the amount of output produed and dereasng and onvex n generaton apaty. Furthermore, as we mentoned before, we assume that the margnal ost of produton at any output level s dereasng as generaton apaty nreases. Moreover, we assume that both the generaton apaty nvestment ost and the transmsson apaty nvestment ost are lnear n the extraapaty added. We also assume downward-slopng lnear demand funtons at eah node. To further smplfy thngs, we assume no wheelng fees. B. Notaton Sets: N: set of all nodes L: set of all exstng transmsson lnes C: set of all states of ontngenes Deson varables: q : quantty generated at node n state r : adjustment quantty nto/from node by the system operator n state g : expeted generaton apaty of falty at node after perod 2 f l : expeted thermal apaty lmt of lne l after perod 1 Parameters: g : expeted generaton apaty of falty at node before perod 2 f l : expeted thermal apaty lmt of lne l before perod 1 g : generaton apaty of falty at node n state, gven g. f l : thermal apaty lmt of lne l n state, gven f l. P ( ): nverse demand funton at node n state CP (q, g ): produton ost funton of generaton frm loated at node n state CIG (g,g ): ost of nvestment n generaton apaty at node to brng expeted generaton apaty to g. CI l (f l, f l ): ost of nvestment n lne l to brng expeted transmsson apaty to f l. φ l, : power transfer dstrbuton fator on lne l wth respet to a unt njeton/wthdrawal at node, n state C. The Formulaton Frst, we formulate the thrd-perod problem. In the frst stage of perod 3, Nature determnes the state of the world. In the seond stage, for a gven state, the frm loated at node solves the followng proft-maxmzaton problem: Max s.t. q q π = P (q, + r N ) q Smultaneously wth the generators produton quantty desons, the system operator solves the followng welfare maxmzng redspath problem (for the gven state ): CP (q,g ) (1)

4 4 Max s.t. {r } q ΔW r = N f φ l l, N + r = N r r P (q f l + x ) dx, l L, N Gven that we assume no wheelng fees, the system operator an gan soal surplus, at no extra ost, by exportng some unts of eletrty from a heap-generaton node whle mportng them to other nodes untl the pres at the nodes are equal, or untl some transmsson onstrants are bndng. The prevously spefed model assumptons guarantee that both (1) and (2) are onave programmng problems, whh mples that frst order neessary ondtons (.e. KKT ondtons) are also suffent. Consequently, to solve the perod-3 problem (energy market equlbrum), we an just jontly solve the KKT ondtons of the problems defned n (1), for all N, and (2). In perod 2, eah rsk-neutral frm determnes how muh to nvest n new generaton apaty by maxmzng the expeted value of the nvestment subjet to the antpated atons n perod 3. Sne the nvestments n new generaton apaty redue the expeted margnal ost of produton, the return from the nvestments made n perod 2 ours n perod 3. Thus, n perod 2, the frm loated at node solves the followng optmzaton problem: Max s.t. g E [ π ] CIG (g,g KKT ondtons for perod 3 ) The problem defned n (3) s a Mathematal Program wth Equlbrum Constrants (MPEC) problem (see [1]). Thus, the perod-2 problem an be onverted to an Equlbrum Problem wth Equlbrum Constrants (EPEC), n whh eah frm faes (gven other frms ommtments and the system operator s mport/export desons) an MPEC problem. However, ths EPEC s onstraned n a non-onvex regon and, therefore, we annot smply wrte down the frst order neessary ondtons for eah frm and aggregate them nto a large problem to be solved dretly. In Seton IV, we solve ths problem for the partular ase-study network, usng sequental quadrat programmng algorthms. In the frst perod, the system operator makes a sngle transmsson expanson deson. In ths perod, the system operator s lmted to dede whh lne (among the already exstng lnes) t should upgrade, and what transmsson apaty t should onsder for that lne, n order to maxmzes the expeted soal welfare subjet to the equlbrum onstrants representng the antpated atons n perods 2 and 3. 3 Thus, n perod 1, the system operator solves the (2) (3) followng soal-welfare-maxmzng problem: q + r Max, E l f l P (q) dq CP (q, g ) N s.t. N { CIG (g,g )} CI l(fl,fl ) KKT ondtons of perod - 3 problem and all optmalty ondtons of perod - 2 III. ILLUSTRATIVE EXAMPLE problem We llustrate the omputatonal model desrbed above usng a stylzed verson of the 3-bus Cornell network, n whh the nodes are loated wthn three zones as dsplayed n Fg.2. There are sx generaton frms n the market (eah one ownng the generator at a sngle node). Nodes 1, 2, 13, 22, 23, and 27 are the generaton nodes. There are 39 transmsson lnes. 4 Fg bus Cornell network. The unertanty assoated wth the energy market operaton s lassfed nto seven ndependent ontngent states (see table I). Sx of them have small ndependent probabltes of ourrene (two nvolve demand unertanty, two nvolve network unertanty and the other two nvolve generaton unertanty). Table II shows the nodal nformaton n the normal state. (4) 3 No attempt s made to o-optmze the system operators transmsson expanson and redspath desons. 4 The eletr haratersts of the lnes are omtted due to spae onstrants and an be obtaned upon request from the authors.

5 5 TABLE I STATES OF CONTINGENCIES ASSOCIATED TO THE ENERGY MARKET OPERATION attempt to solve for an equlbrum, f at least one exsts, by teratve deleton of domnated strateges. We solve eah frm s proft-maxmzaton problem usng sequental quadrat programmng algorthms mplemented n MATLAB. For the PSO model, the optmal levels of generaton apaty under absene of transmsson nvestments are (g 1 *, g 2 *, g 3 *, g 4 *, g 5 *, g 6 * ) = (1.92, 13.72, 11.15, 95.94, 77.7, 87.69), n MW. Table III lsts the orrespondng generaton quanttes (q ), adjustment quanttes (r ) and nodal pres (P ) n the normal state. Fg. 3 llustrates these results for the Cornell network. In Fg. 3, thk lnes represent the transmsson lnes reahng ther thermal apates (n the ndated dreton) and rles orrespond to those nodes wth the hghest pres (above $48/MWh). TABLE III GENERATION QUANTITIES, ADJUSTMENT QUANTITIES, AND NODAL PRICES IN NORMAL STATE, IN THE PSO MODEL, UNDER ABSENCE OF TRANSMISSION INVESTMENTS TABLE II NODAL INFORMATION USED IN THE 3-BUS CORNELL NETWORK IN THE NORMAL STATE OF CONTINGENCY As shown n table II, we assume the same produton ost funton, CP ( ), for all generators. Note that CP ( ) s nreasng n q, but t s dereasng n g. Moreover, reall that we have assumed generators have unbounded apaty. Thus, the only mportant effet of nvestng n generaton apaty s lowerng the produton ost. We also assume that all generaton frms have the same nvestment ost funton, gven by CIG (g,g ) = 8 (g g ), n dollars. The beforeperod-2 expeted generaton apaty at node, g, s 6 MW (the same for all generaton nodes). The KKT ondtons for the perod-3 problem of the proatve system operator (PSO) model onsttute a Lnear Complementarty Problem (LCP). We solve t, for eah ontngent state by mnmzng the omplementarty ondtons subjet to the lnear equalty onstrants and the non-negatvty onstrants. 5 The perod-2 problem of the PSO model s an Equlbrum Problem wth Equlbrum Constrants (EPEC), n whh eah frm faes a Mathematal Program subjet to Equlbrum Constrants (MPEC). 6 We 5 Reall that any LCP an be wrtten as the problem of fndng a vetor x R n suh that x = q + M y, x T y =, x, and y, where M R n x n, q R n, and y R n. Thus, we an solve t by mnmzng x T y subjet to x = q + M y, x, and y. If the prevous problem has an optmal soluton where the objetve funton s zero, then that soluton also solves the orrespondng LCP. 6 See [1] for a defnton of both EPEC and MPEC.

6 6 Fg. 3. Results of the PSO model n the normal state, under absene of transmsson nvestment, for the 3-bus Cornell network. To solve the perod-1 problem of the PSO model, we teratvely solve perod-2 problems n whh a sngle lne has been expanded and, then, hoose the expanson produng the hghest expeted soal welfare. For smplty, we do not onsder transmsson nvestment osts (t an be thought that the per-unt transmsson nvestment ost s the same for eah lne upgrade so that we an get rd of these osts n the expanson deson). In ths sense, our results establsh an upper lmt n the amount of the lne nvestment ost. The four ongested lnes n the normal state, under absene of transmsson nvestment, are the obvous anddates for the sngle lne expanson. We tested the PSO deson by omparng the results of ndependently addng 1 MVA of apaty to eah one of these four lnes. The results are summarzed n table IV. TABLE IV ASSESSMENT OF SINGLE TRANSMISSION EXPANSIONS UNDER THE PSO MODEL In table IV, Avg. L orresponds to the average expeted Lerner ndex 7 among all generaton frms, P.S. s the 7 The Lerner Index s defned as the fratonal pre markup.e. (Pre Margnal ost) /Pre expeted produer surplus of the system, C.S. s the expeted onsumer surplus of the system, C.R. represents the expeted ongeston rents over the entre system, W s the expeted soal welfare of the system, and g* orresponds to the vetor of all Nash-equlbrum expeted generaton apates. From table IV, t s evdent that the best sngle transmsson lne expanson (n terms of expeted soal welfare) that a proatve system operator an hoose n ths ase s the expanson of lne Moreover, t s nterestng to observe that some expanson projets (as addng 1 MVA on lne 15-18) an derease soal welfare. Now, we are nterested n omparng the PSO deson wth the deson that would take a reatve system operator (RSO) under the same system ondtons. In the RSO model, the system operator plans the soal-welfare-maxmzng loaton and magntude for the next transmsson upgrade whle onsderng the urrently nstalled generaton apates. That s, the RSO does not take nto onsderaton the potental effet that ts desons ould have over the equlbrum of generaton apates. In evaluatng the outome of RSO nvestment poly we are onsderng the generators response to that nvestment and ts mplaton on the spot market equlbrum. We tested the RSO deson by omparng the results of ndependently addng 1 MVA of apaty to eah one of the same four lnes as before. The results are summarzed n table V, where we use the notaton x to represent the value of x as seen by the RSO. TABLE V ASSESSMENT OF SINGLE TRANSMISSION EXPANSIONS UNDER THE RSO MODEL From table V, t s lear that the soal-welfare-maxmzng transmsson expanson for the RSO s, n ths ase, to expand lne Thus, the true optmal levels of the RSO model soluton are: Avg. L =.561, P.S. = $ 3,15.7 /h, C.S. = $591.3 /h, C.R. = $ 39.9 /h, W = $ 3,646.9 /h, and g* = (1.62, 13.4, 1.93, 98.5, 78.56, 97.99), n MW. By omparng table IV and table V, t s evdent that the optmal deson of the PSO dffers from the optmal deson of ts reatve ounterpart. Fnally, t s nterestng to ompare the results obtaned wth the PSO model and those obtaned wth an hypothetal ntegrated-resoures planner (IRP). In the IRP model, we assume that the IRP jontly plans generaton and transmsson expansons, although the energy market operaton s stll deentralzed. We tested the IRP deson by omparng the results of ndependently addng 1 MVA of apaty to eah

7 7 one of the same four lnes as before. The results are summarzed n table VI. TABLE VI ASSESSMENT OF SINGLE TRANSMISSION EXPANSIONS UNDER THE IRP MODEL From table VI, t s lear that the soal-welfaremaxmzng transmsson expanson for the IRP s, n ths ase, to expand lne (the same as n the PSO model). By omparng table IV and table VI, we an observe that, although the IRP makes the same deson as the PSO, ths IRP s able to nrease the expeted soal welfare by hoosng generaton apates that are more soally effent than those hosen by the generaton frms n the PSO model. IV. CONCLUSIONS AND FUTURE WORK We proposed a three-perod model for studyng how the exerse of loal market power by generaton frms affets the equlbrum nvestment between the generaton and the transmsson setors. We showed that, although a PSO annot do better (n terms of expeted soal welfare) than an IRP, t an reoup some of the lost welfare by proatvely expandng transmsson apaty. Moreover, we llustrated that the optmal transmsson expanson made by a PSO an dffer from the one made by a RSO. In that ase, the PSO wll make more soally effent expanson desons than ts reatve ounterpart beause a PSO takes nto onsderaton not only the welfare ganed dretly by addng transmsson apaty (on whh a RSO bases ts deson), but also the way n whh ts nvestment alters the Nash equlbra of expeted generaton apates. There are several ways n whh the model proposed here an be extended. One nterestng extenson s the analyss of two sequental transmsson nvestment desons. That s, one we appled our model and deded the best transmsson expanson, to determne the next best sngle transmsson upgrade. We expet that the sequental nvestment desons by the PSO dverge from those made by a RSO. Another attratve extenson s the analyss of our model when buldng lnes at new loatons (rather than upgradng exstng lnes) s allowed. In ths ase, an expanson an hange the eletr propertes of the network (and, thus, the used PTDF matres), whh represents a more realst senaro. Other valuable extenson s the study of the model when allowng frms to own generators loated at more than a sngle node. We expet that suh a possblty enhanes generaton frms market power and, n ths way, vares the equlbrum nvestment between the generaton and the transmsson setors. Ths fat wll potentally reate addtonal soal benefts aheved by a system operator that ats proatvely. V. REFERENCES [1] F. Alvarado and S. Oren, Transmsson System Operaton and Interonneton, Natonal Transmsson Grd Study - Issue Papers, U.S. Department of Energy, pp. A1-A35, May, 22. [2] S. Borensten, J. Bushnell and S. Stoft, The Compettve Effets of Transmsson Capaty n a Deregulated Eletrty Industry, RAND Journal of Eonoms, vol.31 (2), pp , Summer 2. [3] J. Bushnell and S. Stoft, Eletr Grd Investment Under a Contrat Network Regme, Journal of Regulatory Eonoms, vol.1 (1), pp , July [4] J. Cardell, C. Htt and W. Hogan, Market Power and Strateg Interaton n Eletrty Networks, Resoure and Energy Eonoms, vol.19, pp , [5] A. Craft, Market Struture and Capaty Expanson n an Unbundled Eletr Power Industry, Ph.D. dssertaton, Department of Engneerng-Eonom Systems and Operaton Researh, Stanford Unversty, Stanford, [6] P. Joskow and J. Trole, Transmsson Rghts and Market Power on Eletr Power Networks, RAND Journal of Eonoms, vol.31 (3), pp , Autumn 2. [7] S. Oren, Eonom Ineffeny of Passve Transmsson Rghts n Congested Eletrty Systems wth Compettve Generaton, The Energy Journal, vol.18, pp , [8] S. Oren, G. Gross and F. Alvarado, Alternatve Busness Models for Transmsson Investment and Operaton, Natonal Transmsson Grd Study-Issue Papers, US Department of Energy, pp. C1-C36, May, 22 [9] S. Stoft, Fnanal Transmsson Rghts Meet Cournot: How TCCs Curb Market Power, The Energy Journal, vol.2 (1), pp. 1-23, [1] J. Yao, S. Oren, and I. Adler, Computng Cournot Equlbra n Two Settlement Eletrty Markets wth Transmsson Constrants, n Pro th Hawa Internatonal Conferene on Systems Senes, p.251b. VI. ACKNOWLEDGMENT The authors gratefully aknowledge the ontrbuton of R. Thomas for faltatng the 3-bus Cornell network data used n our ase study. VII. BIOGRAPHIES Enzo E. Sauma s an Assstant Professor n the department of Industral Engneerng at Pontfa Unversdad Catola de Chle (PUC) n Chle. He holds a Ph.D. and M.S. n Industral Engneerng and Operatons Researh from the Unversty of Calforna, Berkeley as well as B.S. and M.S. degrees n Eletral Engneerng from Pontfa Unversdad Catola de Chle. He was the repent of a Chlean Government Fellowshp durng 21, 22, 23 and 24. Hs researh fouses on market based approahes for transmsson nvestment n restrutured eletrty systems. Shmuel S. Oren (IEEE Fellow) s Professor of the Industral Engneerng and Operatons Researh department at the Unversty of Calforna, Berkeley. He s the Berkeley ste dretor of PSERC a multunversty Power System Engneerng Researh Center sponsored by the Natonal Sene Foundaton and ndustry members. He has publshed numerous artles on aspets of eletrty market desgn and has been a onsultant to varous prvate and government organzatons nludng the Brazlan Eletrty Regulatory Ageny (ANEEL), The Alberta Energy Utlty Board, the Polsh system operator (PSE) and to the Publ Utlty Commsson of Texas (PUCT), were he s urrently a Senor Advser to the Market Oversght Dvson. He holds B.S. and M.S. degrees n Mehanal Engneerng from the Tehnon n Israel and also M.S. and Ph.D. degrees n

8 Engneerng Eonom Systems n 1972 from Stanford Unversty. He s a Fellow of the IEEE and of INFORMS. 8