MARKETS FOR REACTIVE POWER AND RELIABILITY: A WHITE PAPER

Transcription

1 MARKETS FOR REACTE POWER AND RELABLTY: A WHTE PAPER Engneerng and Economc o Electrcty Reearch Group (E 3 RG) CORNELL UNERSTY E 3 RG contrbutng author: Robert Thoma, Drector Faculty and Reearch Aocate: Tmothy Mount, Rchard Schuler, Wllam Schulze, Ray Zmmerman Graduate Atant: Dan Shawhan, Davd Toomey Th project wa upport n part by the US Department o Energy through the Conortum or Electrc Relablty Technology Soluton (CERTS) and n part by the Natonal Scence Foundaton Power Sytem Engneerng Reearch Center (PSERC). Addtonally we would lke to thank Duane Chapman, Danel Tylavky, George Gro, Fernando Alvarado, Joe Eto, Shmuel Oren, Phl Overholt, and the army o pat and preent tudent who worked on part o th project over the year or ther upport and or helpul comment durng the coure o th work. All concluon, recommendaton, and remanng error are the ole reponblty o the author.

2 Executve Summary The FERC report on reactve power clearly and uccnctly lay out the ue and rae mportant queton about market power, contngent-clam veru real-tme market, the need or an optmal power low that ncorporate reactve power, etc. Unortunately, the economc/engneerng model o ar avalable n the lterature al to repreent the true economc optmum. Th optmum nvolve maxmzaton o the expected net benet o electrcty producton, tranportaton, and ue under the contrant o a ull alternatng-current (AC) power low where the expected net benet dened a the um o the probablty-weghted economc outcome or all contngence, ncludng lne and generator alure. Th the correct way, n term o economc, to determne optmal relablty, level o nvetment, and operaton parameter under alternatve contngence, a well a ecent and optmal producton and prce or real and reactve power. The purpoe o th paper to take a broad look at how market hould be organzed, not only or reactve power but or real power and relablty, nce thee market are undamentally nterdependent and eental or ecent and relable delvery o electrc power. To accomplh th end, the paper open wth peccaton o an economc/engneerng model o optmal nvetment and operaton that then mulated o that prncple and goal or optmal market degn can be etablhed. The paper then examne ue o market power through both mulaton and expermental economc. Fnally, a varety o poble market degn are preented and evaluated n lght o the concluon drawn rom the conceptual model, mulaton, and experment. The paper conclude wth pecc recommendaton. The concluon drawn rom the reearch are: ) Although network relablty ha long been dented a a publc good, voltage and requency have not been o dented. The modelng and mulaton preented here ung AC power low demontrate the publc-good nature o voltage and relablty o lne. Note that, except under pecal crcumtance, prvate ncentve or provon o publc good are nucent and ecent provon requre ome central authorty. ) Both real power and reactve power are techncally prvate good nce they are excludable and rval. Thu, unlke voltage and relablty, well-degned prvate market are theoretcally ecent the publc good needed to upport the ytem are optmally provded. 3) Smulaton o optmal operaton under derent contngence demontrate that nodal reactve-power prce are almot alway equal to zero optmal nvetment n reactve-power

3 ource (e.g., generator and reactve-power compenator) occur throughout the ytem. Nonzero reactve-power prce, whch optmally are ound only durng contngence, uch a when alure occur, reman relatvely low becaue o the low cot o nvetment n a reactvepower upply. 4) The average or expected revenue derved rom ale o reactve power at optmal real-tme prce durng rare contngence ucent to provde ncentve or optmal prvate nvetment n reactve-power capacty. However, th a hghly volatle and uncertan ource o revenue that depend on uch rare contngence actually occurrng. Thu, prvate nvetment n reactve capacty are nherently rky nvetment. Note that when reactve capacty n hort upply the wllngne-to-pay, or ocal value, o reactve power many order o magntude greater than nvetment baed on cot per unt durng contngence, o t optmal to make large nvetment n reactve-power capacty to prevent hortage even durng rare contngence. 5) However, both mulaton and economc experment how that opportunte or the exerce o market power by prvate uppler o reactve power n real-tme market are plentul n a network envronment n whch tranmon o reactve power lmted to hort dtance, a etablhed by Krcho law. Thu, even wth ucent reactve-power capacty, uppler are lkely to ubmt oer that wll produce potve real-tme reactve-power prce n noncontngency tate or whch optmal prce are zero. 6) Wherea vrtually all demand or real power come rom prvate buyer (loe n the tranmon network are mall, on the order o -3%), demand or reactve power come rom two ource: () demand rom prvate buyer to meet the need o motor, arc welder, and other equpment that requre a magnetc or electrc eld to operate and () the oten greater demand rom a central authorty, actng n the publc nteret, or reactve power a an nput to provon o a publc good voltage. We nclude n th category the oten large amount o reactve power conumed by tranmon lne that are operatng ar rom ther urge mpedance loadng. Thu, nce voltage eental or relablty, reactve power play a pecal role n the ecurty o the power ytem. 7) Optmal real-power prce how greater upde volatlty than optmal reactve-power prce, prncpally becaue nvetment n generaton o expenve that t cannot optmally cover all contngence. Optmal generaton nvetment doe conorm to the conventonal wdom o coverng the wort ngle contngency by meetng load ater the lo o the larget generator n the mulaton. However, peak prce durng ome contngence are much hgher or real power becaue optmal nvetment n capacty cannot ecently cover load wth the lo o multple generator. Note that optmal nvetment wll occur n a ree market only when prce are not capped nce the next-to-wort-cae cenaro or generator alure provde the ncentve or nvetment n the urvvng generator to provde optmal relablty through prce on the order o 0,000 per megawatt hour. 8) Optmal nvetment n lne n the mulaton ucent o that thermal lne contrant are never bndng, even durng contngence. Thu, a lole DC optmal power low were ued there would never be nodal prce derence that could be ued or, or example, tranmon ee. Ung a ull AC power low doe, however, how ubtantally derent nodal prce or 3

4 both real and reactve power, but only durng contngence. There can be no tranmon ee rom nodal prce derence or real and reactve power unle prce are computed rom a ull AC optmal power low. Thee prce are needed to provde both revenue and charge or reactve power conumed by lne (to mantan voltage) that wll generate optmal ncentve or lne nvetment. Baed on thee reearch concluon, we recommend the ollowng: ) The rt concluon preented that ome central authorty needed to provde the publc good o relablty and voltage (a well a requency) mple that electrc power doe not lend tel to the degree o decentralzed decon-makng that common n other market. Thu, there mut be ome nttuton that ha government-lke authorty to degn, plan, and manage the ytem. Th entty reerred to a the central authorty becaue current ndependent ytem operator do not have authorty or plannng and degn. ) For the central authorty to act n the publc nteret and be able to optmze the ytem, a well a provde neceary publc good, the central authorty mut poe a robut AC Optmal Power Flow (AC OPF) program that can reolve real- and reactve-power problem properly. The program hould nclude unt commtment, ancllary ervce, and contngence. A proper AC OPF needed to gve an accurate pcture o the ytem or operaton, a well a accurate prce normaton or real power, reactve power, and tranmon. Such prce are neceary a a ba or proper nvetment decon n generaton, reactve compenaton, and tranmon. A major reearch and development program hould be undertaken to provde th capablty. 3) The thrd concluon tate that reactve-power prce wll be motly zero wth approprate nvetment n reactve compenaton. When a real-tme market or a prvate commodty ha nancal tranacton on rare occaon and, becaue market are expenve to operate, natural economc orce wll retructure the market to avod tranacton cot. The commodty ued n thee market called a contngent clam, whch a clam or ervce that can be made only one or more peced event occur. Contngent-clam market, whch are approprate or reactve power, operate well n advance o the contngence that juty clam and are the normal replacement or real-tme market, whch rarely have tranacton. n a contngent-clam market, the central authorty eentally rent major reactve-power ource rom uppler that ubmt the lowet-prced oer and ntruct the uppler n how to operate thoe ource n real tme. For generator, the contngent-clam contract can provde xed compenaton or reducton n real-power output reactve-power need requre uch reducton. 4) Becaue the central authorty reponble or relablty and operaton need reactve power on demand o that t can deal wth contngence and thereby aure relablty (concluon 6) and becaue the ubtantal nvetment requred to meet that demand mut be aured n advance (concluon 4), the reactve-power market mut be run well n advance o any contngency to aure needed upply. Contngent-clam market are approprate or reactve power becaue they cloe well n advance o any clam made and, run ucently ar n advance, can provde a ure ource o revenue, encouragng nvetment. Rather than obtanng revenue through unpredctable rare contngence, ource that ubmt wnnng oer obtan teady revenue n the orm o rent to compenate them or provdng reactve power on demand. Note that, nce th 4

5 market run ar n advance, the central authorty mut project the amount o reactve power capacty needed or prvate buyer and to mantan voltage. Thu, baed on the central authorty determnaton o how much reactve power wll be needed and where (projected nodal demand), th market mut be run locally to ecently acqure reactve-power ource. 5) Market power a erou problem or the upplyng o reactve power (concluon 5) n realtme market, more crtcal than n the cae o real power. The overall demand or reactve power come n great part rom the central authorty reponble or ytem operaton and provdng relablty to meet publc need. Compettve prce wll be aured n contngent-clam aucton only ome oered unt are potentally excluded. We recommend that contngent-clam aucton or reactve power be run ucently ar n advance to allow contructon to occur (three to ve year) o that extng uppler are placed n competton wth potental nvetor and new ource o reactve power, encouragng compettve prce. 6) Although real-tme market or real power are potentally eable and can provde table revenue or nvetment n generaton through orward market (a the Autralan example ugget), capped real-power prce pad to generator, a common n U.S. power market, wll not provde ucent ncentve or nvetment n generaton to aure optmal relablty. Thu, we upport meaure to upplement generaton nvetment prce to generator are capped. Although a number o approache are beng tred to encourage nvetment n generaton, t not yet clear any are ucceul or cot-eectve. 7) The central authorty reponble or relablty and operaton mut have legal authorty to mpoe the trngent penalte neceary to enorce contract purchaed n contngent-clam market. 8) To provde ncentve or conervaton o real- and reactve-power demand, large cutomer and marketer hould pay real-tme nodal prce or real and reactve power a derved rom the ytem AC OPF. Contngent clam market are approprate or the upply de o the reactve power market, but real tme nodal prce are approprate or ale to marketer nce they wll then have ncentve to ntall meterng and then ether pa on real-tme prce or ntall automated control on cutomer equpment n exchange or a lower xed rate. Th wll alo make dtrbuted energy reource and load repone much more economcally vable. 9) Nodal prce rom a DC power low can provde ncorrect prce gnal, ncludng ndcator or nvetment n lne. Proper ncentve requre that tranmon ee be equal to the nodal prce derence or real and reactve power derved rom a ull AC power low and be appled to tranmon o both real and reactve power. Tranmon mut alo pay or reactve power conumed by lne. Note, however, that tranmon ee typcally may be near zero wth optmal lne nvetment but tend to be potve durng contngence. A n the cae o reactvepower market, real-tme market may be napproprate. To aure ecency and relablty, the central authorty mut plan and manage tranmon. 5

6 . ntroducton Extng wholeale market or electrcty n the Unted State vary wdely n term o ther empha on hort-run operatonal eature and the exchange o energy. Some jurdcton alo employ a market-drven electon o uppler to mantan both ytem relablty and ervce qualty through electon o operatng reerve and regulaton. But none o the hort-term market determne the provon o Ar to upport ytem voltage. Gven the promnent role that AR hortage played n the equence o event that led to the Augut 4, 003 Northeat blackout, the U.S. Federal Energy Regulatory Common (FERC) ha expreed an nteret n determnng whether or not and how the ntroducton o Ar market mght enhance the ytem relablty and ecency. Th analy addree that ue, but n the much broader context o determnng an optmal bulk power upply ytem, both n term o uch a ytem operaton and o t nvetment or capacty n tranmon lne, generaton, and capactor. Th broad, ntegrated perpectve requred becaue o the complex nteracton between ndvdual apect o the electrcty upply ytem. By ung the economc objectve o maxmzng net benet to ocety (gan rom conumpton o electrcty that relably provded at table voltage mnu the cot o ecent provon), we not only determne optmal level o energy conumpton and ntalled capacty o aclte but alo etmate the ocally optmal level o relablty endogenouly by weghng t benet and cot. By adoptng the perpectve o a benevolent ocal planner, the analy dente the decon that can be decentralzed and determned ecently through market and the ervce that, becaue they have publc-good-lke attrbute, requre ome nterventon by a central authorty to properly provde that apect o the electrc power upply. n earler analye t ha been demontrated why the relablty (ee Jokow and Schmalenee, 983, and Klendorer and Fernando, 993) and qualty ncludng voltage, tablty, and requency (Toomey et al., 005) o electrcty that erved rom a wred network ha publcgood apect. n economc termnology, the market alure that are not becaue o the lack o compettve upply o thoe qualty-related component. Rather, the problem are becaue all cutomer n a neghborhood who are erved rom the ame wre receve an dentcal level o thoe qualty-o-ervce attrbute regardle o ndvdual pobly wdely derent valuaton o thoe ervce. Thu, the market alure n the demand de nce ndvdual cutomer have trong ncentve to undertate or overtate ther preerence or relablty. Regardle o what they clam they are wllng to pay, each o them receve an dentcal qualty o ervce. So a buyer perceve that ther actual bll wll be related to ther tated preerence, then they have an ncentve to undertate the value o relablty to them n antcpaton that other wll vote or and pay or t. O coure, a mlar ncentve ext or all other cutomer to ree rde and the net eect or th market lke the tragedy o the common wth too lttle relablty provded through the grd. Whle ndvdual cutomer can repond to th market-baed ytem by ntallng ther own emergency tandby generaton, that outcome the ecent, leat-cot oluton, the electrcty grd probably hould be abandoned. t not, ome regulatory authorty requred to etablh and enorce cot-eectve relablty, voltage, and requency or the grd, all o whch are publc good. The reaon that ome central authorty requred to operate the grd that publc good are nonexcludable and nonrval and cannot readly be uppled by decentralzed market. Prvate 6

7 good are excludable and rval and can be ecently uppled by market. Excludable mean that conumer can be kept rom enjoyng a good ether by eller or by a conumer who own a good and an ndvdual conumer chooe whether to buy the good and how much o t to buy. Rval mean that a good that conumed by one peron cannot be conumed by another. A mple example o a prvate good an apple. you buy one, no one ele can take that apple away rom you (legally anyway), o t an excludable good. Smlarly, you eat (conume) t, t gone and no one ele can enjoy eatng t, o t a rval good. A a reult o thee charactertc, prvate rm can produce and have approprate ncentve to upply uch prvate good to cutomer. n contrat, conder a publc good uch a a treet gn. A treet gn placed on a redental treet corner can be een by all who pa by. t not excludable (or t would loe t purpoe). Smlarly, a drver o a pang car who need normaton provded by the gn can obtan the normaton rom t wthout n any way dmnhng the ablty o a econd drver to obtan normaton rom the gn. The gn not rval. Thee properte make provon o publc good by prvate rm dcult or mpoble. For example, magne that a cty decded to deregulate treet gn. You, a an entrepreneur, decde to get nto the bune o provdng treet-gn ervce. Ater rentng pace or your gn rom the owner o a corner lot, you attempt to collect ee rom pang motort. magne akng a drver who jut took a good long look at your gn or the uage ee. Surely the drver wll ay Oh no, wan t lookng at the gn. jut wanted to take a good look at you. Th behavor called ree-rdng becaue uer can get the normaton, avod the ee, and hope that enough other ool wll contrbute to keep the gn n place. The reult o ree-rdng an underprovon o publc good, and t a problem created by the behavor o conumer o the ervce. Unlke purely prvate good, where the conumer chooe the amount to be conumed by h or her houehold, wth publc good, to nure adequate provon, ome central authorty or the acton o many determne the level o provon. Thu, ndvdual conumer decde how much real and reactve power to conume by turnng ar condtonng, lght, computer, and televon o or on. ndvdual ndutral cutomer alo control ue o motor, computer, and other power-conumng devce. So, real power and reactve power are prvate good even though addtonal amount are needed a nput to mantan ytem voltage and relablty (Hogan 99b). Prvate good are typcally ued n the producton o publc good. The metal pot, teel or alumnum gn, and pant needed to make a treet gn are all prvate good needed to make a publc treet gn. n act, reactve power, whch a prvate good neceary to produce the publc good o voltage and relablty, ometme mtakenly decrbed a a publc good becaue t needed n the producton o thee publc good. Note that when voltage, a publc good, drop n an area, an ndependent ytem operator (SO) or other centralzed operator mut decde whether to obtan reactve power to retore voltage, a publc good. Toomey et al. (005) provde an engneerng and economc model that ncorporate the true economc value o relablty and voltage along wth approprate engneerng contrant. The model allow or ortng out o the nature o the relevant commodte. The nature o thee commodte ha mplcaton or the type o market, any, that can ucceully provde relable hgh-qualty electrc power. The Northeat power outage o Augut 4, 003 provde a dramatc llutraton o the lack o attenton thee publc-good apect have receved n retructurng the electrc ndutry. The voltage o a ytem mut be mantaned near the degn level or cutomer equpment wll be damaged. Reactve power neceary both to mantan voltage and to upport the low o real 7

8 power on tranmon lne. t wa reported that at tme pror to the nal cacade to a blackout that the voltage level ell on certan ytem bue. Th a clear ndcaton to operator o a problem and need to be mmedately addreed. When the operator requeted that ome generator reduce ther output o real power and ncreae ther output o reactve power (or whch they would receve no compenaton under the market degn then n place), the generator procratnated becaue they were makng o much money ellng real power. However, whle the benet to the network o complyng wth the operator requet could have ealy compenated or the ndvdual generator ncome loe, no mechanm wa n place to traner adequate benet to the ndvdual generator. When load (.e., cutomer) cut o rom the ytem or the protecton o cutomer, t oten becaue the large load have caued the voltage to become depreed beyond an acceptable lmt. A load removed,, the producton o real power wll exceed demand and the ytem requency wll re to adjut to the mmatch. That, unle the generator are ramped back quckly, the exce producton o real power wll caue generator to pn ater a exce energy aborbed by the rotatng ma contaned n the turbne. A a conequence, the ytem requency wll re ater than the Automatc Generaton Control (AGC) ytem can adjut to. Szable devaton rom the degn requency or a generator can caue extremely expenve damage to thee machne, (e.g., damage to the turbne blade). n repone to devaton n requency and the reultng large power wng that occurred durng the cacade phae o the blackout, automatc protecton ytem trpped generator olne to avod uch damage and generator trppng olne contrbuted to the collape o the ret o the ytem. All o thee actor the decon by generator owner to argue wth operator about the need or them to upply reactve power to help mantan voltage, the automatc decon to cut o cutomer when voltage devate beyond lmt, and the automatc decon to hut down generator when requency devate too ar rom the degn peccaton llutrate the problem aocated wth the provon o publc good. Current ytem degn are conervatve and avor protectng equpment by removng t o t not damaged and avalable or ue ater the emergency ha paed. Th analy delve n ome detal nto the conttuent electrcal component that together provde relable, hgh-qualty ervce over a network. The three conttuent o ervce dered by buyer are the low o energy, t qualty (a much a they want at the lck o a wtch and at a peced voltage and requency), and t relablty (ew unannounced nterrupton o ervce a oppoed to nterruptble ervce where outage are preceded by a warnng that allow buyer to take acton). Some uer equpment uch a motor, welder, and nducton heater requre AR n addton to energy to operate eectvely, and that demand or AR a uncton o a prvate good and can be arranged through a market. n all electrcty ytem, thee demanded ervce are provded through combnaton o energy and AR upple rom generaton, by provdng redundant generaton (wth the rght combnaton o ramp rate) and tranmon aclte, and by ntallng capactor. But the demanded ervce and attrbute do not have a drect one-to-one correpondence wth the uppled ervce that aty them. So one role o the ytem operator and planner to mantan a balanced tranlaton between dered attrbute and the uppled conttuent component o ervce a real-tme aembly problem. The planner alo mut enure the avalablty o adequate exce capacty or each conttuent to mantan optmal level o relablty n the ace o lkely alure and contngence. 8

9 Thu, n addton to the theoretcal analy, a mple, tylzed model o an electrcal network preented to mulate the mplcaton o the analytc reult. Sentvty analye are perormed to demontrate the robutne o outcome. n addton, the reult o related experment n whch people attempt to prot by ellng both energy and AR to a mple electrcty network (the PowerWeb 30-bu model) provde nght nto the eectvene o market tructure. Fnally, the adequacy o market-related allocaton mechanm revewed n lght o the numercal and expermental reult. The next ecton decrbe an optmal economc model o voltage and real and reactve power n a network envronment wth the poblty o generator and lne alure. The mplcaton o th model or market degn are explored through mulaton o optmal economc perormance. Secton 3 provde example o market power arng rom reactve-power ue. Secton 4 preent recommendaton or ecent market degn.. Conceptual Ba or Evaluatng Market Structure or Reactve Power, oltage, and Relablty n th ecton we attempt to decrbe what ome o the charactertc o an deal electrc power ytem hould look lke n term o tructure and perormance. Th rt bet ytem obvouly not achevable n the hort run, but t erve to denty the approprate target, n term o market degn and operaton. We hereater how that a real world econd bet ytem, t ever to approach a rt bet, mut have market or reactve power (hereater degnated a Ar). However, we alo how n mulaton that thee market are lkely to have ome pecular charactertc. The goal o the deal ytem would be to maxmze the expected net benet over all the poble tate o the ytem. That, the deal ytem would maxmze the um o benet mnu cot n each tate o the ytem multpled by the probablty o that tate occurrng. We conder two type o alure that can produce derent tate o the ytem. Frt, generator can al; econd, lne between node can al. We take thee probablte a gven n th mple analy o potental reactve-power market, but obvouly they are uncton o expendture on mantanng the ytem.. The Network The mple network ued n our analy and hown n Fgure tructured to allow a clear graphcal preentaton o the reult o the mulaton. The patal conguraton o the network, partcularly the locaton o generaton, not optmzed and aumed to be contraned by other actor (e.g., locaton o uel upple). Thu, the numercal reult are llutratve o th partcular network and mght vary wth a derent patal conguraton. However, the qualtatve reult, uch a whch ervce are publc and whch are prvate, are general. Each bu n th equence o bue ha a load, and three generator are located at the rt bu. The bue repreent ubtaton, and t aumed that the dtance between any two equental bue ve mle. The bue are connected by two dentcal parallel lne; there alure n one lne, power can tll be delvered va the other. We treat th network a a true alternatng-current (AC) ytem wth Krcho law holdng or all power low. Correpondngly, the voltage and the phae angle o each bu are olved when determnng power low. The network n our mulaton contructed by optmzng the admttance o the power lne, the quantty o wtchable Ar compenaton devce ntalled at each bu, and the ze o each o the 9

10 generator. The ytem operated wth the controllable Ar compenaton optmally wtched n or out dependng on the ytem alure tate. Generaton 5 Mle 5 Mle 5 Mle Load 40 MW Load 0 MW Load 3 0 MW Load 4 60 MW Fgure The tuaton decrbed here may be thought o a a long land. There are generator at one end o the land and a tranmon network that delver power up the land to derent communte. There no way to mport power to the land and, hence, the land redent mut develop ther own entrely el-contaned electrc power ytem.. Buyer Charactertc n a gven tate, the net benet to buyer equal to ther maxmum wllngne-to-pay or real and reactve power mnu any damage rom devaton n voltage. Fgure how a typcal onehour aggregate demand curve or buyer at a ubtaton. Th amount o load mlar to average conumpton by 40,000 typcal U.S. home, though the hape o the curve baed on a mx o redental, commercal, and ndutral cutomer. n th gure and throughout th paper, we aume or mplcty that real and reactve power are jontly conumed by buyer n xed proporton, that each buyer power actor a contant 5% (o the MAr conumpton rate = 0.57 the megawatt (MW) conumpton rate or all cutomer at all tme). The demand curve ued here and hown n Fgure baed on a tudy done by Woo et al. (99) that decrbed n Woo and Pupp (99). Th dtrbuton bell-haped and the demand curve, obtaned a the cumulatve dtrbuton, ha the tepped appearance. Thu, whle demand extremely nelatc or typcal delvered prce o around 00 per megawatt-hour (MWh), t become much more elatc above 9,000 per MWh becaue at that rate many uer would preer to hut down when gven the opportunty. Other tude that upport th approxmate hort-run demand curve nclude Cave et al. (990) Doane et al. (988a, 988b) Goett et al (988). Hartman et al. (99), Moeltner and Layton (00), Sullvan et al. (996), and Wacker et al. (985). A cutomary n economc, the ndependent varable, prce, on the vertcal ax. 0

11 Quantty (MWh) Fgure. Buyer Demand or Real and Reactve Power The hourly demand curve how that the value to cutomer vatly greater than the typcal cot. one were to draw a horzontal lne n th gure at a typcal cutomer prce o 00, conumpton would be very cloe to the horzontal ntercept o 40 MW o real power and MAr o reactve power. However, the majorty o cutomer value electrcty o hghly that they would not elmnate t ue untl the prce reache 0,000 or more. The prce or combned real and reactve power at whch a buyer wll curtal ue called the maxmum wllngne-topay and the meaure o the benet o electrcty to that cutomer. A an example o the value o mantanng relablty, conder the derence between two cenaro. n the rt, the ytem collape completely, preventng all electrcty delvery. n the econd, the ytem tll able to erve the 50% o load that ha the hghet wllngne-to-pay. n the demand curve hown here, the value o ervng th 50% o load the area under the let hal o the demand curve. Th value greater than 0,000 0 = 00,000 per hour. However, the revenue obtaned rom preervng the ytem and ellng electrcty at a regulated rate o 00 (per MWh 0.57 megavolt hour (Mh)) only,000, whch two order o magntude le. Clearly, an nvetment o 00,000 (e.g., or tree trmmng) would prevent a complete lo o power or one hour and ntead allow the ytem to contnue ervng the 50% o load wth the hghet wllngne-to-pay, that nvetment hould be undertaken. However, a utlty revenue ncreae rom uch an nvetment would typcally be only,000, o a protmaxmzng or rate-mnmzng utlty would chooe not to make the nvetment n pte o t hgh value to ocety. For comparon, a prot-maxmzng dcrmnatng monopoly uppler chargng unregulated, real-tme rate to all o t cutomer would charge 00,000 or the added ale that the nvetment would enable, makng the nvetment worthwhle to uch a uppler. What the eparate value o reactve power n th example? Wth a xed power actor o 0.5, a one-mar reducton n upply o reactve power would orce a one-mar reducton n reactve-power demand and a 6.6-MW reducton n real-power demand, jontly valued at approxmately 0, = 66,000 per hour. Thu, a one-mar hortage o reactve power (aumng real power avalable) could caue a lo n benet o 66,000 per hour. n contrat,

12 wtchable capactor can produce reactve power or a per-perod captal cot o approxmately 0.05 per MAr per hour (baed on a captal cot o 4,00 per MAr). A th llutrate, the paradox o extremely hgh value and low producton cot even more extreme or reactve power than or real power. alue-maxmzng buyer would purchae capactor to reduce reactve-power charge the charge or reactve power were not bundled wth charge or real power a prevouly decrbed. n our mulaton, we aume that buyer have a xed power actor but can purchae capactor to reduce ther reactve-power demand below that mpled n Fgure. We urther allow the ntallaton o nductor, whch conume Ar when wtched n. Whle hunt nductor compenaton omethng that not done routnely today, t needed here a an opton n degnng the optmal tranmon ytem. n ome ntance, large low o Ar are requred to aty power-low equaton or ele power delvery mut be curtaled. For a node to be able to ometme receve more Ar than cutomer and generator there can conume, nductor are needed to conume the extra Ar. The aumed per-perod captal cot o th type o nductor 0.06 per MAr per hour (C. W. Taylor, 994). The nal component n modelng electrcty buyer the potental damage caued by voltage devaton. The ollowng gure how aggregate damage or buyer wth the aggregate demand curve hown n the precedng gure. Th damage uncton a very rough approxmaton baed on a good gue and no more. The reaon, rom the perpectve o economc, to ncorporate uch a damage uncton rather than relyng on arbtrary nodal lmt on voltage that th allow u to how that voltage, n act, a publc good. Unortunately, conuon ext n th regard n part becaue o engneerng work done by Km (005) that argued or a market or voltage. We how that th noton ncorrect becaue ndvdual cutomer do not have the power to chooe the level o voltage they receve rom a node. So voltage not a prvate good. A hown n the ntroducton, n the cae o prvate good, buyer mut have the power to chooe whether to conume a good and at what level to conume t baed on prce alone. oltage at a node n a network, on the other hand, determned by the nteracton o all o the decon-maker n the ytem (ee the Appendx or a techncal demontraton) and mut be regulated by ome authorty (e.g., an SO) or exce damage wll reult. n contrat, cutomer can decde how much real and reactve power to conume. The damage hown wll naturally help to dene approprate voltage level at the node n the ytem a part o the maxmzaton o expected net benet over the deal ytem a a whole.

13 0000 Damage () oltage Fgure 3. Aggregate Equpment and Applance Damage rom Extreme oltage The equaton or net benet to cutomer rom electrcty ervce can be wrtten a cutomer net benet = wllngne-to-pay or real and reactve power cot o capactor voltage damage..3 Generator Charactertc Generator are aumed to have capablty curve a hown n Fgure 4 wth upper and lower lmt or real-power producton, G, and the capablty o producng reactve power, Q, alo wth upper and lower lmt. Th curve an approxmaton o the uual capablty curve derved rom a generator ratng and t eld and armature heatng lmt (re: C.W. Taylor). Whle t mportant to nclude the generator capablty relatonhp n the analy, the tylzed hape we ue doe not lmt the general concluon o the analy. The model aume that uel cot depend on real-power producton but not on reactve-power producton. However, a Fgure 4 how, a generator maxmum producton or conumpton o reactve power ncreae a t real-power producton reduced below the maxmum level. 3

14 .4 Theoretcal Reult Fgure 4. Generator Capablty Curve The rk aced n th ytem are alure o any, ome, or all o the three generator and alure o any, ome, or all o the x lne egment. Each poble tate o the ytem ha a known probablty. A tate n economc reer to a partcular combnaton o poble occurrence, uch a, or example, one generator down and all lne up wth hgh load; all generator up, one partcular lne down, and low load; or all generator and lne up. The Kuhn-Tucker condton hown n Appendx A mut be ated by truly ecent market and operaton and the Lagrange multpler n the problem, when dvded by the probablty o the relevant tate, can be nterpreted a real-tme optmal prce n that tate. We now provde an economc nterpretaton or the key optmzng condton and decrbe ther mplcaton or market degn. Equaton 9 n Appendx A can be nterpreted a a decrpton o optmal buyer behavor or purchae o real power and mple that Demand prce = nodal real-power prce power actor nodal reactve-power prce. Thu, deally, buyer hould pay the nodal prce or real power conumed plu the nodal prce or any reactve power conumed. Equaton 0 through n Appendx A decrbe optmal generator behavor and mply that, at a generaton node, Nodal prce o real power = margnal cot o producng real power nodal prce o reactve power any margnal lo n reactve power to produce real power. Thu, to provde the correct ncentve, generator hould receve nodal prce or both real and reactve power produced. Clearly, rom thee condton, real power and reactve power are prvate good or both buyer and generator nce nodal prce convey the correct ncentve. Equaton 3 through 3 optmze nodal voltage. The general cae hown n 3 and can be nterpreted a Margnal benet to tranmon o ncreaed voltage or all lne connectng a node margnal benet o ncreaed reactve-power producton by nductor and capactor rom ncreaed voltage = margnal damage rom hgher voltage net cot o margnal change n reactve power conumed to ncreae voltage. Snce, by denton, more than one lne connected to a node, benet o hgher voltage or tranmon low are ummed over multple lne, the key condton or a publc good. Alo, benet to tranmon at a node are ncreaed by hgher voltage at adjacent node. Thu, reerdng on the voltage rom neghborng node poble. Smlarly, hgher voltage at a node benet reactve-power producton rom capactor and nductor at the node. n addton, margnal damage rom voltage devaton accrue to all buyer connected to a ubtaton o thee are mplctly ummed n the damage uncton a well. Thu, voltage at a node a ocal decon that drectly aect benet and cot to many partcpant and mut be jontly determned n the publc nteret that, voltage a publc good. n contrat, the prvate-good 4

15 condton or real and reactve power only nvolve the repectve prce and benet and cot to the partcular buyer or eller. Equaton 4 n Appendx A optmze lne angle and alo take the orm o a publc-good condton that balance benet o ncreaed tranmon agant ncreaed cot or reactve power and the contrant on lne angle relectng tablty requrement, etc. Equaton 5 and 6 optmze nvetment n capactor and nductor, repectvely, at each node. Such nvetment may be undertaken, a approprate, by prvate nvetor, lne operator, and cutomer. Aumng that voltage cloe to one, the condton approxmately et the contngent-clam prce ummed over tate or reactve power at the node equal to the margnal cot o nvetment at the node. Or, ung real-tme prce (contngent-clam prce dvded by the tate probablty), the condton et the margnal cot o nvetment equal to the um acro tate o the probablty-weghted real-tme prce or potve or negatve reactve power at the node. Thu, optmal contngent-clam, or real-tme, prce provde the correct nvetment gnal or capactor and nductor. Equaton 7 plu equaton 0,, and and the mulaton reult hereater preented ugget that optmal nvetment n each o the three power plant determned by the expected prot that are obtaned olely rom the tate n whch the partcular generator the only one runnng (the other two have aled). Thu, the margnal cot o nvetment n generaton et equal to the ncreae n expected revenue obtaned n tate n whch that generator the only one runnng. The mulaton reult how ubtantal exce capacty, o optmal nvetment concerned only wth the very hgh prce and prot that occur n the tate where the ngle generator contran total capacty. Equaton 8 et the margnal cot o nvetng n lne capacty equal to the ncremental tranmon revenue or real and reactve power obtaned rom the capacty ncrement acro all lne egment net o the cot o reactve power conumed to mantan voltage. Note that the tranmon charge or real or reactve power acro a lne egment the nodal prce derence or real or reactve power, repectvely. We how n the mulaton that, wth optmal nvetment n lne, the thermal lne lmt never bnd and tranmon ee are near zero except n the cae o lne alure. Thu, tranmon revenue prmarly generated when lne alure occur n the mulated ytem. Note that a drect-current (DC) optmal power low were utlzed, tranmon ee would alway be zero wth the truly optmal level o nvetment n lne. Ung the optmal DC power low would reduce eemngly optmal nvetment n lne capacty untl thermal lmt became bndng. Note that the mulaton exclude lne loe whch are mall..5 Smulaton Reult Each generator aumed to have a 4% probablty o alure and the odd o alure or each lne egment are one out o two thouand. Gven thee probablte, ome tate are hghly unlkely, uch a two lne egment alng at the ame tme. To keep the analy manageable, thee hghly unlkely tate are not condered. n addton there are x poble network tate n the mulaton: the bae tate (no alure), alure o one o the generator, alure o two o the generator, alure o one o the lne egment between bue one and two, alure o one o the lne egment between bue two and three, and alure o one o the lne egment between bue three and our. 5

16 The mulaton urther nclude peak and nonpeak demand. Peak demand a hown n Fgure 50% hgher than nonpeak demand. Each level o demand occur hal o the tme. Gven, then, the two demand level and x poble network tate, there are twelve derent tate or the ytem. For maxmzng net benet acro all o the tate, we olve the mulaton to nd the optmal ytem contructon, whch llutrated by the ollowng table, and determne how the ytem wll optmally be run n each tate, whch decrbed by the dagram n Fgure 5 through 0. Table. Optmal Sytem Contructon Sze o Each Generator (MW o capacty) 85.8 Sze o the Lne (Per-unt admttance) 4.5 Capactor at Bu (MAr o capacty) 0.6 Capactor at Bu (MAr o capacty) 45.3 Capactor at Bu 3 (MAr o capacty) 4.6 Capactor at Bu 4 (MAr o capacty) 8.4 nductor at Bu (MAr o capacty) 0.0 nductor at Bu (MAr o capacty) 0.0 nductor at Bu 3 (MAr o capacty) 0.0 nductor at Bu 4 (MAr o capacty) 9.6 6

17 Load Lot (a a porton o bae load) [Nonpeak] Bu Bu Bu 3 Bu 4 gen down gen down Lne down Lne down Lne 3 down Load Lot (a a porton o bae load) [Peak] Bu Bu Bu 3 Bu 4 gen down gen down Lne down Lne down Lne 3 down Fgure 5 n the peak tate, enough generaton optmally contructed o that the alure o one generator reult n no drop n load. nteretngly, th content wth tandard ytem degn practce. When two generator al, however, gncant load mut be dropped becaue a ngle generator not capable o producng the entre peak demand. When there are lne alure, the load at bue two, three, and our drop becaue tranmon become more cotly. t become more cotly not jut n the lne where the alure occur but n the other lne a well, a wll be explaned hortly. Becaue tranmon then more cotly, t optmal to tranmt le, yeldng the load reducton hown here. The loe n thee load are greater when the alure 7

18 occur n an earler lne. Th becaue tranmon larger earler n the lne and gettng more tranmon over the ngle lne that reman ater a alure reult n hgher cot that then make le tranmon optmal. n nonpeak tate, there lo o load only when two generator al and the lo much maller than n the correpondng peak tate. 0 Angle D. between Bue (degree) [Nonpeak] Bae gen down gen down Lne down Lne down Lne 3 down 0 and and 3 3 and 4 Angle D. between Bue (degree) [Peak] Bae gen down gen down Lne down Lne down Lne 3 down 0 and and 3 3 and 4 Fgure 6 Real-power low between two bue drven prmarly by the derence n the phae angle between the two bue and by the ze o the lne. When there are no lne alure, the angle derence get maller movng down the lne a the amount o power tranmtted declne. When a lne egment al, the angle derence over that lne egment mut be conderably hgher to 8

19 retore low nce the ze o the lne between thoe bue now halved. Th ncreaed angle derence over the aled lne egment can reult n dculte or tranmon over the other two lne egment, a we wll explan. For the tablty o the ytem, the total angle derence or the entre length o the lne n the model lmted to 30 degree. retorng tranmon over a aled lne egment ue an angle derence o 8 degree, or example, that leave only degree or tranmon over the other our egment, reultng n tranmon dculte. Thee dculte are a undamental caue or load drop at bue located pror to a lne alure (along wth load at bue ater t) when that alure occur n the peak tate. n the dagram hown n Fgure 6, note that, n peak lnealure tate, the angle derence n the nonaled lne do drop below ther bae-tate level. n the nonpeak tate, wth lower low, maller angle derence can be ued or tranmon. There not, n act, an ntance n the nonpeak tate n whch the total angle derence reache 30 degree, whch explan why load never drop n nonpeak lne-alure tate. Note alo that, n tate n whch two generator al, the angle derence all drop mply becaue le real power tranmtted. 9

20 oltage [Nonpeak] Bu Bu Bu 3 Bu 4 Bae gen down gen down Lne down Lne down Lne 3 down oltage [Peak] Bu Bu Bu 3 Bu 4 Bae gen down gen down Lne down Lne down Lne 3 down Fgure 7 The thrd actor n real-power low voltage. Hgher voltage at ether end o a lne egment ncreae the avalable low through that egment. Hence, when there are dculte wth tranmon, t wll generally be optmal to ncreae the voltage even though th wll reult n ome voltage damage. Becaue o the damage that occur rom ncreang avalable tranmon n th way, th method o ncreang low capacty cotly. Note that, when there are no dculte wth tranmon, the voltage at all the bue reman eentally at one, yeldng zero damage. When there ha been a lne alure and there peak demand, there are dculte wth tranmon over all lne a prevouly explaned and optmal voltage at all bue greater to help low n all lne. Gven th cotly tranmon, the choce between maller loe o load wth greater damage or larger loe o load wth le damage. The optmal decon or th mulaton are llutrated n Fgure 7. 0

21 Note the mulaton nclude buldng optmal lne. And, n act, buldng a larger lne can elmnate tranmon dculte even wth egment alure, whch would then prevent voltage damage. However, there are cot aocated wth buldng larger lne and the probablty o acng the hgh voltage low. Optmal lne ze determned baed on the cot o t contructon, the probablty o lne alure, and the outcome o lot load or voltage damage when alure occur. The optmal lne allow all real power to be delvered durng nonpeak demand and when there are no lne alure, nearly all real power to be delvered when there are alure wth peak demand, and ome voltage damage n the peak-load lne-alure tate. A hown n Fgure 8, hgh prce or real power optmally occur n certan alure tate becaue hgh prce are requred to get buyer to reduce conumpton. When larger reducton n load are neceary, optmal prce are hgher tll to convnce buyer to make larger reducton. n the peak bae tate, the peak one-generator-alure tate, and all but one o the nonpeak tate, the prce that buyer pay mply the margnal cot o producton and bac delvery. For cutomer wth real-tme meterng, real-tme prce can provde or optmal curtalment o conumpton, a thee cutomer have an ncentve to turn o electrcty ue that are not worth ther expene n tme o hgh prce. For cutomer wthout real-tme meter, real-tme prce are not an opton, but relablty-derentated ervce could be ued to mplement a contngent-clam market uch that buyer would pay an expected prce or the real power that they ue. Thoe who chooe to pay a hgher prce that relect the hgh prce o certan alure tate would be able to contnue conumng n thoe tate. Thoe who chooe to pay a low prce would be hut o n thoe tate.

22 MW Prce (log cale) [Nonpeak] 0,000, Bae gen down gen down Lne down Lne down Lne 3 down 0 Bu Bu Bu 3 Bu 4 MW Prce (log cale) [Peak] 0,000, Bae gen down gen down Lne down Lne down Lne 3 down 0 Bu Bu Bu 3 Bu 4 Fgure 8 Reactve power requred by buyer or real-power conumpton and requred by lne n order to aty Krcho law or tranmon. The capactor ntalled at the bue provde reactve power when they are wtched n. Sometme tranmon requrement or reactve power can reult n too much reactve power at a bu. nductor at uch a bu can be wtched n to conume thoe extra Ar. At the rt bu, reactve power can be both produced and conumed by the generator. A a reult, n th mulaton, there eentally no need to ntall ether capactor or nductor at that bu. Fgure 9 how the Ar that are produced/conumed by capactor/nductor. Negatve value ndcate Ar conumpton. Note that the quantte o capactor and nductor that are ntalled are jut adequate to provde the maxmum hown n the dagram.

23 Capac/nduc Producton (pu-mar) [Nonpeak] Bu Bu Bu 3 Bu 4 Bae gen down gen down Lne down Lne down Lne 3 down Capac/nduc Producton (pu-mar) [Peak] Bu Bu Bu 3 Bu 4 Bae gen down gen down Lne down Lne down Lne 3 down Fgure 9 n the peak two-generator-alure tate, Ar producton all rom t bae-tate level becaue there le demand by both conumer and the lne. When a lne egment al, extra Ar are requred by the lne egment that reman, and there addtonal Ar producton to meet th requrement. To aty Krcho law whle meetng th requrement, addtonal Ar are requred to low away rom the alure a well, through the other lne. Th reult n large quantte o reactve power at the end bue n thee tate. At bu, the generator can conume the extra Ar themelve, but at bu 4 nductor are requred to conume the extra Ar. 3

24 A hown n the ollowng gure, mot o the tme the prce o reactve power zero. At the rt bu, Ar can be reely produced and conumed by the generator up to ther capablty curve, whch are ucent or all tate. At the econd and thrd bue, large quantte o capactor are ntalled to meet requrement n peak lne-alure tate, and thoe quantte are more than ucent or all other tate. At the ourth bu, there a mall, potve prce or Ar n the peak bae tate. Th tate requre more reactve-power producton at th bu than any other tate doe. n the lne-alure tate, Ar are lowng away rom the alure to th bu. Alo, nductor are needed at bu 4 n only two tate, makng prce or Ar negatve only n thoe tate. MAr Prce [Nonpeak] Bu Bu Bu 3 Bu 4 Bae gen down gen down Lne down Lne down Lne 3 down MAr Prce [Peak] Bu Bu Bu 3 Bu 4 Bae gen down gen down Lne down Lne down Lne 3 down Fgure 0 4

25 Even when reactve-power prce are zero or the vat majorty o the tme, the prce charged provde ncentve and revenue to pay or the ntal ntallaton o both capactor and nductor becaue o the relatvely hgh prce generated by partcular alure tate. Thoe who ntalled capactor and nductor ought to receve that revenue. Furthermore, the prce o Ar are not regulated and there are not enough capactor or nductor to aty prvate demand plu the ytem operator demand to upport relablty and voltage, prce or Ar (potve, negatve, or both) are hgh. Th would encourage addtonal ntallaton, perhap even by buyer themelve. Addtonal ntallaton would contnue, arguably untl the optmal quantty wa ntalled, whch would drop prce to optmal level. Other mportant reult nclude the large amount o reerve provded n the optmal ytem a ubtantal extra generaton contructed to enure relablty on the olated land ued a the example ytem and the manner n whch tranmon and voltage nteract n alure tate..6 Prot A prevouly noted, unregulated prce or Ar can provde ncentve and revenue or ntallaton o capactor and nductor. Both the mulaton and a theoretcal analy o the model ugget that optmal prce or the ytem are revenue-neutral. That, they provde jut enough revenue to cover ntallaton cot wthout provdng exce prot. Th true not jut or ntallng capactor and nductor but alo or generator contructon. t hown, then, that allowng prce to re, ometme dramatcally, n contngency tate provde trong ncentve or ntallaton o captal mprovement that wll be ued n thoe tate and, n act, the revenue rom thoe prce neceary to get the optmal quantty o captal mprovement ntalled. Moreover, havng that quantty o captal nveted provde more than enough captal or all o the other tate. 5

26 Table. Annual Expected Cot and Revenue or Generator, Capactor, and nductor Generator (mllon o dollar) Capactor (thouand o dollar) Revenue rom MW ale 56 Revenue 0 Revenue rom MAr ale 0 Annualzed ntallaton cot 0 Producton cot 34 Exce Prot 0 Annualzed contructon cot 3 Exce Prot 0 nductor (thouand o dollar) Bu-4 revenue 5 Annualzed ntallaton cot 5 Prot 0 Wth lne contructon, optmal condton generate exce prot due to ncreang margnal cot n contructng the lne. Table 3. Annual Expected Cot and Revenue or Lne (hundred o thouand o dollar) Lne net revenue 8 Annualzed contructon cot 4 Prot 4 3. Network Contrant and Market Power The objectve o th ecton are () to llutrate ome unuual market tuaton that appear to be anomale but are n act content wth the unque contrant aocated wth low on tranmon lne governed by Krcho law and () to explan why the bac charactertc o a market or reactve power are almot certan to lead to peculatve behavor by generator. A bac problem or degnng an electrcty market that the phycal contrant o upplyng real power over an AC network may everely lmt the number o uppler that are able to produce energy and ancllary ervce at certan locaton at certan tme. n extreme cae, a ngle 6

27 relablty-mut-run (RMR) unt may be the only ource o reactve power, whch eental or mantanng voltage prole wthn peced lmt on part o the network. When only a ew uppler compete n a market, the extence o market power nevtable and the uppler can, allowed, ncreae ther prot by peculatng. When th type o peculaton occur, prce oered nto the market wll be hgher than true producton cot and ome producton capacty may be wthheld. The market not ncentve compatble becaue uppler can benet by ubmttng oer that are ubtantally hgher than honet oer that are equal to ther true margnal cot. The complexte that are nherent n an AC network mply that a vable electrcty market cannot be degned by blndly applyng market nttuton that work well or other good. Mot apparent anomale n electrcty market have uraced durng the coure o our reearch on varou apect o deregulatng the electrc power ndutry; they were ound, not concocted. Thee unexpected tuaton are qute derent rom the more predctable eect o tranportaton n a market or the conventonal type o commodty condered n economc textbook. There already a large body o reearch nvolvng market power and the mplcaton o congeton or electrc power market. Raent and Smth (988) perormed tude applyng expermental economc to radal network; Hogan (99a, 003) tuded AC power low ung trangular network. However, ew tude deal wth the ntrcace o an AC network. Our example o anomale typcally nvolve larger, more realtc network baed on EEE tet model, and, a a reult, we have evaluated a et o market condton that rcher than the one examned by other reearcher. When a realtc network model o an electrcal grd underle the market-clearng mechanm, the optmzaton, called an AC Optmal Power Flow (AC OPF), a ormdable mathematcal problem to olve. A a reult, a mpled lnear model o the grd very oten ued n practce or determnng market prce. Not that ome orm o AC analy ued by engneer to determne low and voltage, but the actual prce are determned by a DC power low. Th mpled optmzaton mplemented by, or example, addng ad hoc retrcton (called proxy lmt) on real power lne low that put contrant on dpatch to approxmate the true condton governed by Krcho law. n general, th type o approxmaton work reaonably well under normal operatng condton, but t generally al when the network treed or hghly congeted. The naccuracy o the approxmaton ued to determne market-clearng prce can ncreae opportunte or gamng by uppler addng an extra layer o necency to the market. To avod th addtonal ource o necency and ocu on the eect o the grd alone, n th ecton the market-clearng mechanm baed on a ull AC OPF that ncorporate all o the credble contngence and nonlnearte mpled by Krcho law. 3. The Eect o Reactve-Power Need on the Market or Real Power Whle many propoal ext or how to deal wth reactve-power ue, to date none o the deregulated market ha ntroduced a comprehenve plan or ung a market to manage reactve power. Nobody dpute the mportance o reactve power, but t ha been dcult to arrve at a conenu about the bet tructure o a reactve-power market. The network requre reactve power mply becaue t energzed, n order to mantan an adequate voltage prole (wthout whch electrcty uele to conumer), and to gve extra degree o reedom to the ytem 7

28 operator o that the network can be controlled n an ecent manner. Havng thee extra degree o reedom allow the ytem operator to congure the ytem to acheve the bet ue o extng tranmon capacty. Total cot, ytem loe, nodal prce derental acro congeted lne, and operatonal voltage lmt are all aeed n the dpatch produced by an AC OPF. The greater the number o controllable reactve njecton nto the network, the more reedom the ytem operator ha to optmze dpatch and lower cot. However, the mot mportant ource o reactve power on the network are the generatng unt, whch, by vrtue o the untcommtment decon, can produce reactve power only a mnmum block o real power dpatched at the ame tme. Four example o ncreang complexty are dcued n th ecton to llutrate how the producton o reactve power by generator nteract wth the market or real power. The mplet example llutrate the mplcaton o havng a generator become a relablty mut run (RMR) unt at hgh load when the unt eental or voltage upport. The nal example llutrate how the nodal prce o real power can be ubtantally hgher than the hghet oer prce ubmtted nto a market when producton rom one generator caue other unt to be re-dpatched to mantan an acceptable voltage prole on the network.. Relablty-Mut-Run Unt The ytem dcued n th example aroe durng the degn o an experment ung the PowerWeb [See Zmmerman, et. al., 999) platorm to tet the perormance o derent market or real energy. The underlyng topology o the network baed on the EEE 30-bu ytem. Th network wa ued to conduct an experment to compare the economc perormance o derent clearng mechanm n determnng nodal prce. The market wa dvded nto hghload and low-load perod, and t turned out that, n the hgh-load perod, generator 4 at bu 7 (ee Fgure 3) wa a mut-run unt becaue voltage lmt were reached at bu 30. The ndvdual n control o generator 4 quckly learned to oer the ntal block o real power at the hghet prce allowed (.e., the reervaton prce). Snce the rt block rom a generator cannot be partally dpatched due to the phycal lmt o the generator, the block mut be wholly accepted or rejected. Although generator 4 wa able to ell the ntal ve MW o power at the reervaton prce, that prce dd not et the overall market-clearng prce or real power becaue the unt wa contraned to a mnmum level o dpatch (.e., t wa dpatched out o mert order). The mportant mplcaton or market power that the ndvdual controllng generator 4 dd not have to know that th wa an RMR unt. The repone o the market to hgher oer prce at hgh load provded enough normaton or the ndvdual to recognze that generator 4 had market power and to explot th advantage to earn hgher prot.. Ar-Related Flexblty o Dpatch Th econd example uraced whle tetng a unt-commtment algorthm. Th algorthm baed on Lagrangan relaxaton but permt the ncluon o nonlnear AC OPF contrant. A realtc 68-hour load prole wa ued to tet the algorthm, and the peced generatng capacty wa a mxture o bae, houlder, and peakng unt, the derence beng n producton cot, tart-up cot, and mnmum hut-down and tart-up tme. Peakng unt would typcally have the hghet generaton cot, medum tart-up cot, and the hortet mnmum tart-up and hut-down tme. Thu, t wa expected that the algorthm would turn peakng unt on only durng daytme load peak. 8

29 FGURE The network ued wa the EEE 8-bu tet ytem that characterzed by a hgh generator-to-bu rato wth 54 generator and 8 bue. The ytem very lexble n term o the ablty o the ytem operator to dpatch reactve power when mot generator are onlne. Th, however, wa not the cae or the commtment chedule choen by the algorthm or nghttme when the load low; many generator were hut down and the ytem had much le lexblty or reactve dpatch. n partcular, ome o the optmum oluton ound by the unt-commtment algorthm had peakng unt commtted at nght. Thee unt were dpatched agant ther lower operatng lmt nce ther real power expenve, but ther reactve capablty wa ued wthout retrant. n Fgure, the unt at bue 90 and 9 are peakng unt and the unt at bu 89 a bg bae-load unt that alway dpatched at t maxmum operatng lmt. The unt at bu 9 uually dpatched tartng wth the houlderload level but olne at nght. Furthermore, the path ha conderably more loe than the more drect parallel path At nghttme, the optmum unt commtment dpatche the peakng unt at bue 90 and 9 to better manage loe along the path and help channel more o the real power beng njected at bu 89 to the 89-9 lne and then to the ret o the network. Th pattern o optmal dpatch unexpected and challenge tradtonal bele about tandard unt-commtment procedure. th network were to be ued n a deregulated market ettng, the two peakng unt would have exactly the ame type o market power dcued n the rt example, whch would nevtably lead to peculatve behavor by controller o thee unt. 3. Cacadng Market Power n a compettve market ung the lat (mot expenve) accepted oer (LAO) to et the clearng prce, the prce-etter can rae the clearng prce only a hgh a the prce o the rt rejected oer (FRO), and t the competton between the rt rejected and the lat accepted oer that promote honet margnal-cot oer. However, when there congeton and there are only a ew generator nde a load pocket, thoe generator have market power and can rae the clearng prce by tact colluon on the porton o the load nde the pocket that cannot be erved by ource outde the pocket. Under certan topologcal conguraton, t poble that the ablty to et hgher prce n the load pocket cacade uptream along the path o the congeted tranmon lne ervng the load pocket and t may be poble or other generator to unlaterally rae ther prce and prot thank to th cacadng eect. 9

30 Conder the moded veron o the EEE 30-bu ytem hown n Fgure 3. n th cae, area olated by congeton. When the generator ubmt compettve (margnal-cot) oer, the reultng nodal prce, quantte dpatched, and earnng are hown n the boxe next to each generator n the gure. Snce there congeton, however, generator and only compete wth one another n a duopoly or a porton o ther local load and they may be able to obtan hgher prce n area through tact colluon. For example, doublng the oer prce o generator and ncreae ther earnng ubtantally, a can be een n Fgure 4. The local market power o thee unt n area cacade to generator 4 on one o the major tranmon lne upplyng area even though generator 4 outde o the load pocket. Generator 4 can unlaterally ncreae revenue by rang t oer prce, a hown n Fgure 5. n addton, nce generator 4 can et a hgh prce or t own output, the topology o the network ha reduced the eectve number o compettor outde the load pocket rom our to three. Fgure 3. Cacadng Market Power: Margnal Cot Oer 30

31 Fgure 4. Cacadng Market Power: Duopoly n Area Fgure 5. Cacadng Market Power: Generator 4 Exert t Market Power 4. Complex nteracton among Contrant n the prevou example, the topology o the network wa reponble or creatng the noncompettve tuaton outde the load pocket. The cae we revew now llutrate an even 3

32 more complex tuaton n whch the nterplay between congeton, reactve dpatch, and voltage lmt conjugaton and create a rather anomalou tuaton. The ytem ued another modcaton o the EEE 30-bu network and hown n Fgure 6. Th tme, t area that olated by congeton. Generator 6 ha decded to wthdraw all but the rt block o power rom the market. The tranmon lne jonng bue 4 and maxmally loaded, and becaue t ntrumental n the traner o power rom area to area, mot o t reactve-power capacty needed to traner real power. n other word, th lne need to be Ar-compenated to a unty power actor on both end and th mpoe mportant contrant on how much reactve power hould be produced by generator and 6 and, to a leer extent, by generator. The hgh load on bue 6 and 7 put a tran on the voltage prole at bu 7 and oon the reactve dpatch o generator 6 mut repond to two conlctng requrement: ncreae producton o reactve power to allevate voltage problem at bu 7 or decreae t to compenate the near end o lne 4- o that more o t tranmon capablty can be ued. t not poble to aty both objectve multaneouly becaue the lne connectng bu 7 to bu 3 goe through bu, and the voltage o bu ted drectly to how well lne 4- compenated. Fgure 6. Contrant nteracton Example The mplcaton or nodal prcng are huge. The hadow prce on the thermal MA lmt or lne 4- are 5.78 per MA hour (MAh) at the let end and 75.3 per MAh at the rght end. The nodal prce or real power exceed 0 per MWh at bue through 0 a hown n Table 4 even though the hghet-prced oer only 50 per MWh. Furthermore, the optmum dpatch o real power hghly entve to change n load n area becaue ncreang the load by only one MW at bu 7 requre htng everal MW rom generator, whch ha low 3

33 producton cot, to generator 4, whch ha hgh producton cot. Th ht o dpatch explan why the nodal prce o real power are o much hgher than the oer prce. Nodal prce or both real and reactve power are preented n Table 4 or all o the bue. Even though the prce o reactve power are relatvely hgh at bue 5 through 0, the prce correpondng to the bue or nearby generator (3 and 3) reman zero. Th llutrate two undamental charactertc o the producton o reactve power by generator. Frt, unlke the margnal cot o ncreang producton o real power, the cot o producng more reactve power zero untl output reache the lmt o the capablty curve. When th contrant reached, t neceary to cut back on producton o real power to produce more reactve power. The cot o producng th addtonal reactve power the opportunty cot (lot prot) o ellng le real power. The econd charactertc that the need or reactve power hghly localzed. The margnal cot o upplyng reactve power to the load at bu 7 tll hgh (5 per MAh) even though the margnal cot o producng more reactve power rom the nearet generator at bu 3 zero. TABLE 4 33

34 3. Potental Problem or mplementng a Market or Reactve Power The our example o network condton preented n the prevou ecton decrbe the complex charactertc aocated wth provdng reactve power on a network and the urprng eect thoe charactertc can have on nodal prce or real power and the optmum commtment o unt to meet load. The hghly localzed nature o the demand or reactve power, llutrated n Table 4 by the ubtantal derence n nodal Ar prce at bue that are relatvely cloe together, ugget that uppler o reactve power are lkely to have market power n the type o aucton typcally ued or real power. Hence, there are two problem related to market power that hould be nvetgated beore tryng to mplement the type o real-tme market propoed by FERC Frt the potental eect o peculatve behavor n a Ar market on nodal Ar prce. Second the ndrect eect o peculatve behavor n a Ar market on the uppler level o market power n the market or real power. The optmum degn o a network derved n Secton provde addtonal nght nto the lkely charactertc o a market or reactve power. Ecent nodal prce or reactve power are zero mot o the tme (ee Fgure 0). Nodal prce are not zero only when contngence occur due to the alure o tranmon lne. When the ytem ntact, the tatc reactve power needed or tranmon uppled manly by capactor/nductor becaue th type o equpment relatvely nexpenve to ntall. t only when a contngency occur and the ytem treed that there a demand or dynamc reactve power, whch typcally provded by generator. The overall mplcaton that payng the ecent nodal prce or reactve power would provde a hghly volatle ource o revenue or rm upplyng dynamc reactve power. They would get pad only n emergence. Unlke producton cot or real power, producton cot or reactve power are zero a long a the dpatch wthn the lmt et by the capablty curve (ee Fgure 4). Th why the nodal Ar prce hown n Table 4 are zero or all x generator. The nodal Ar prce or a generator, on the other hand, can be extremely hgh once the Ar lmt on the capablty curve reached. Whenever th occur, there ucent demand or reactve power at that locaton to make t ecent to reduce the output o real power rom the generator. The nodal Ar prce or the generator determned by the opportunty cot o re-dpatchng other unt on the network to replace the reducton n real power rom the generator. A the ourth example n the prevou ecton llutrate, th opportunty cot can be very hgh and alo can reult n ubtantally hgher nodal prce or real power. We conducted a ere o experment a a plot tet o the perormance o a market or real and reactve power ung a veron o the EEE 30-bu network hown n Fgure 6. Market partcpant or thee experment (tet,, and 3) were tudent enrolled or all 005 n AEM 655/ECE55: Power Sytem Engneerng and Economc and were mater and doctoral tudent rom the Department o Appled Economc and Management and the School o Electrcal and Computer Engneerng at Cornell Unverty. Tet and 3 were conducted wth two eparate group o x tudent each who repreented the x generator on the network. Tet wa conducted wth one group o x tudent. All three tet were conducted n Cornell Laboratory or Expermental Economc and Decon Reearch. To provde realtc nancal ncentve, all partcpant were compenated wth alent monetary reward correpondng to a percentage o the prot they earned n each tet (Segel and Goldten, 959). The hared charactertc o the three tet can be ummarzed a ollow. 34

35 n all tet an AC OPF determned nodal prce and dpatch to mnmze the cot o meetng load n a unorm-prce aucton (lat accepted oer) ung the POWERWEB otware platorm (ee Zmmerman et al., 999). n all tet each generator controlled three generatng unt (low-, medum-, and hghcot). n all tet the ndependent ytem operator (SO) wa the ole buyer o electrcty and the pattern o load wa exogenou and vared rom one tradng perod to the next. Nodal prce had to be at leat a hgh a correpondng oer prce, but oer prce and the prce pad were retrcted to level below the peced prce cap. Each tet wa conducted or a total o 60 tradng perod 30 perod or Treatment A and 30 perod or Treatment B. n the ollowng decrpton o the three tet, the term energy and Ar are ued throughout to repreent real and reactve power, repectvely. Tet : Pay real tme nodal prce or energy and a contract prce o 5 per MAr or Ar Th tet correpond to typcal arrangement that are currently ued to procure Ar n the tranton rom a regulated to a deregulated market. t content wth FERC prelmnary recommendaton that or the preent, whle pot prce aucton market are beng urther tuded, we recommend payng real tme prce or actual reactve power producton baed on the provder own opportunty cot or baed on admntratvely determned prce announced n advance, n order to encourage uppler to produce reactve power where t needed. 3 n th tet, the SO execute contract wth uppler to provde Ar at a predetermned prce whenever needed. The maxmum amount o Ar (potve and negatve) that can be provded by each generatng unt are known by the SO (.e., the SO and the uppler agree on a pecc capablty curve or each unt and that curve lmt producton o Ar rom a unt even ome o the capacty or energy wthheld rom the aucton). Snce the prce and maxmum quantte o Ar or each unt are determned n a contract, the uppler decon are lmted to pecyng the prce and quantty oer or energy only. The maxmum allowed prce oer (and the prce pad) 00 per MWh or energy. 4 Note that th experment alo approxmate the outcome o a contngent clam market or reactve power. Tet : Pay real tme nodal prce or energy and nodal prce or Ar Th tet correpond to FERC current propoal to ntroduce a new market or ellng Ar n the tranton to deregulaton. n th market, the SO determne optmal pattern o dpatch or energy and Ar by mnmzng the cot o meetng load ung the prce/quantty oer or energy and prce oer or Ar a the cot. The maxmum Ar capablte (potve and negatve) that can be produced by each generatng unt are known by the SO (.e., uppler cannot wthhold Ar capacty and the SO and the uppler agree on a pecc capablty curve Th alo the approach ued to procure reactve power n the Unted Kngdom and n nda. 3 bd. p. 5[[[no reerence pror or the bd; not ure what th reer to]]] 4 Th content wth FERC uggeton to cap the uppler bd [c] whle allowng all accepted uppler to receve a market-clearng prce n the pot market that relect the hghet accepted bd. (p.5)[[[what work doe th reer to?]]] 35

36 or each unt, whch lmt producton o Ar rom a unt even ome o the capacty or energy wthheld rom the aucton). n th market, partcpant are pad nodal prce or energy and or Ar or the dpatched quantte. The maxmum allowed prce oer (and the prce pad) are 00 per MWh or energy and 50 per MAr or Ar. Tet 3: Pay real tme nodal prce or energy and nodal prce or Ar n a market wth: ) nterruptble load, and ) dpatchable ource o Ar. The aucton or energy and Ar the ame here a t or tet. The bac ratonale or th tet that regulator were concerned about the ablty o rm to explot a market or Ar n tet. A a reult, they have decded to make the market more reponve to hgh oer prce by () havng 30 MW o nterruptble load dtrbuted around the network (ued the prce o energy reache 75 per MWh) and, a an alternatve, () havng 30 MAr o dpatchable ource o Ar dtrbuted around the network (and pad 5 per MAr dpatched). Th tet conducted to ee whch approach the mot eectve way to mtgate market power n the Ar market. Note that perod through 30 tet nterruptble load and perod 3 through 60 tet dtrbuted ource o Ar. Wthn-Tet Treatment Tet and contan two treatment, each latng or 30 tradng perod. The rt treatment ue normal capablty curve, whch repreent operatng condton n whch there ample capablty to upply Ar. n the econd treatment, the total Ar capablty o the generatng unt reduced to two-thrd o the amount avalable n the rt treatment. Th ha the eect o htng the capablty curve nward and creatng a potental hortage o Ar producton. Thee retrcted capablte repreent operatng condton when the ytem treed due to contngence and there a need or dynamc Ar. n tet 3, the retrcted capablty curve are ued or all tradng perod and the rt treatment correpond to nterruptble load and the econd to dpatchable ource o Ar. 3.3 Reult rom the Plot Tet o a Market or Energy and Ar Tet can be thought o a the bae cae becaue the nodal Ar prce relect the true opportunty cot o procurng reactve power. 5 Fgure 7 demontrate that the nodal Ar prce or the x generator are cloe to zero mot o the tme (relectng the true margnal cot o producton when a generator not on the capablty curve) and are occaonally very hgh (relectng the opportunty cot o beng on the capablty curve). 6 Not urprngly, the econd treatment, n whch there le Ar capablty avalable n the ytem, produce hgher Ar prce when load hgh and the network more congeted. 5 Generator ubmt prce/quantty oer or energy and are requred to upply Ar when needed. They are pad the nodal prce or energy and a xed prce or Ar through a contract wth the SO. Note that, whle reactve power beng bought at a xed contract prce o 5 per MAr, the nodal prce reported here are the true opportunty cot o upplyng Ar. 6 Compettve Ar prce baed on true margnal cot are only greater than zero on the capablty curve. 36

37 Perod 30: Normal Capablty Curve Perod 3 60: Retrcted Capablty Curve Fgure 7. Nodal Ar Prce or Sx Generator n Tet n tet, the uppler were allowed to ubmt eparate oer prce or Ar and or energy. The maxmum oer allowed wa et at 50 per MAr, and uppler were not allowed to ubmt Ar quantty oer. From Fgure 8, we ee that nodal prce pad to generator were ubtantally hgher than they were n tet. The act that the nodal Ar prce were greater than zero mot o the tme, and thereore dd not relect the true cot o producng Ar, how that uppler were able to exerce market power eectvely. Furthermore, the derence n Ar prce pad to ndvdual generator alo ncreaed ubtantally. 7 Thee reult hghlght the concern raed earler that a market or Ar would be uceptble to the exerce o locatonal market power by generator due to the act that Ar do not travel long dtance economcally. 8 7 n tet, generator 6 made large prot by oerng Ar to the market at prce that were around 5 to 5 n all tradng perod. Ung th trategy, generator 6 wa tll dpatched or Ar mot o the tme and receved a hgh market prce. n contrat, generator 3 oered Ar or all three generatng unt at very low prce (almot all were below 3, wth ome a low a 0.). Th trategy wa not ucceul becaue the reultng Ar prce pad to th generator were alo low. 8 Allowng generator to ubmt prce and quantty oer or Ar could potentally lower avalable Ar capablty and create even greater opportunte or explotng market power. 37

38 Perod 30: Normal Capablty Curve Perod 3 60: Retrcted Capablty Curve (Gap n the equence correpond to tradng perod n whch the otware dd not nd a oluton.) Fgure 8. Nodal Ar Prce or Sx Generator n Tet Wth concern about the exerce o locaton-baed market power by generator realzed n tet, the jutcaton or evaluatng way to mtgate market power n tet 3 obvou. n tet 3, two approache were ued to make the market more reponve to hgh oer prce or Ar: () havng 30 MW o nterruptble load dtrbuted around the network and () havng an addtonal 30 MAr o dpatchable Ar capablty. The rt approach ha the potental to mtgate market power n the market or both energy and Ar becaue load are peced wth contant power actor (.e., purchae o energy and Ar by load are trctly proportonal). Wth the econd approach, gvng the SO more lexblty or meetng Ar need make t le lkely that expenve ource o Ar wll be dpatched. From Fgure 9 and 0, we ee that nterruptble load (perod 30) led to a general downward trend n nodal Ar prce or all x generator. Ung dpatchable ource o Ar (perod 3 60), nodal Ar prce remaned low or group, but or group there were a number o hghprce pke due to mportaton o expenve Ar rom other regon (th eature wa added to PowerWeb to try to enure that eable oluton could be ound when uppler wthheld a large amount o capacty rom the market). Although nodal Ar prce were tll greater than zero mot o the tme or all generator and there tll wa no ncentve to ubmt honet oer or Ar, both approache to mtgaton n tet 3 dd reduce the ablty o generator to explot market power. Average nodal Ar prce were lower than they were n tet, and they exhbted maller locaton-baed derence and alo were le erratc, partcularly or group. Thee reult ugget that ncorporatng ether nterruptble load or dpatchable ource o Ar may be an eectve way to lmt market power n a Ar market. 38

39 Perod 30: nterruptble Load Perod 3 60: Dtrbuted Source o Ar Fgure 9. Nodal Ar Prce or Sx Generator n Tet 3, Group Perod 30: nterruptble Load Perod 3 60: Dtrbuted Source o Ar Fgure 0: Nodal Ar Prce or Sx Generator n Tet 3, Group Average Ar prce pad to generator n the three tet are ummarzed n Table 5. n addton, average compettve prce are preented that are baed on ubmttng the margnal-cot oer or both energy and Ar. t mportant to note that, whle the contract prce or Ar n tet ha the lowet average cot or the SO compared to the other two tet, true nodal Ar prce 39