prices in electricity

4 . O c t o b e r 2005 SIAM N E W S movmg power to meet demand and ImPoswansmsslon charges thac would r~flect the supplyidemand balance In each area of the gnd (The ut~l~ues conunued,to Own the lines and were to be compensated for theu use ) CAISO was also to manage a real-hme market power, notes Sevenn Borensteln market for power, as well as for other anala professor of busmess adm~n~straoon and 9 lary services necessary for munmmng the publ~cpollcy at the Untvets~tyof Cahfordesign of current markets:' Meyn says By Sara Robinson stab~lityof the gnd nla at Berkeley, in a paper titled 'The Econormsts lntesvlewed for t h ~ sm c l e As In markets that had been establtshed tn Trouble wtth Electnctty Markets Underdlsagree with Cho and Meyn's conclusion In 1996, in the hope of reducing its hisstanding Callfornta's Restructuring DISother countnes, the wholesale pnce for of about the v ~ a b ~ l ~ t ydecentrahzed power torically high electricity prices, California aster" (lournal of Ecrnwmrc Perspecnves, power was to be deternuned by auctton All markets, potntlng to restructured markets In became the fir*t U.S. state to vote to open its W~nter 2002). the generators would submlt btds to supply the UK, Lat~nAmenca, and, to a lesser energy markets to competition. Following a speclfied amount of power at a ceaain extent, Australia as funcuon~ngbetter than electricity reform efforts in other countries. T h e California Debacle: pnce The Power Exchange would then the regulated government-owned monopothe state planned to unbundle the different How Things W e n t W r o n g the accept b~ds,stmlng w~th lowest, untll l ~ e s preceded them "Restructunng has that functions of the old regulated monopolies, In the late 1990s, desp~tethese chaldemand was sat~sfiedThe price of the last reduced electric~ty production costs and introducing competition for power generalenges, Cahforn~aand other p a w of the benefited consumers relatlve to the former Increment of power needed would then be tion and relail delivery. U S moved qu~ckly restructure the~r to marthe pnce paid to all successful b~dders In reg~me a number of countnes around the In California's venture, however, turned into kets Cahfornla's Power Exchange opened world, but th~s taken a number of has the case of an overabundance of available a disaster of immense proportions, and for tradlng in March 1998, two years after years," says Frank Wolak, a professor of power, wlih Inany generators compeung to became the poster child of an anti-powerthe vote that set the transltton ~nmotlon By econonucs at Stanford Univers~ty supply 11, the pnce would be low When resuucturing movement. Beginning in the "Every market 1s ~mperfect," adds Paul then, the state's three major electnc utll~t~es demand exceeded ava~lablesupply, howevsummer of 2000 and continuing through the had auctioned off most of the11 foss~l fuelJoskow, a professor of econormcs and maner, generatoe, no longer at nsk of be~ng summer of 2001, wholesale power prices agement at the Massachusetts Institute of fired power plants The new owners--enerunable to seil all the11power, would have an soared, forcing the federal government to gy companies based In Texas and the Technology, "and m many of these markets, lncentlve to bld hlgh subsidize power for low-income families in Southeast, lncludlng Duke, AESlW~ll~ams, the performance before [restructunngl was Dunng the first year, there were already San Diego and bankrupting one of the Dynegy, Muant, and Rehant-were expectawful" slgns that market pmlapants were testlng state's three maior utility companies. At the . . . ed to sell power back to the ut~littesm daysame time, mysterious shortages in availthen abll~tyto affect pnces On one July The ahead, hourly, and real-time markets To able generation capacity forced statewide afternoon In 1998, for example, the pnce reimburse the utlht~esfor then "stranded rollinp. blackouts. All in all. the enerzv cri. Economists and engineers agree that p a d to generators for provlhng reserve some of the umque ph;sical atGbutes of assetsv-~nvestments from whlch they sis may have cost the slate as much $45 power h ~ t$9999 per megawatt-hour of would no longer benefit-the billion in higher electricity costs, lost busicapaclty avalable, compared with the usual state le~lslamrefroze consumer ness due to blackouts. and a slowdown in pnce of about $10 At the same ume, market elecml'y rates through March economlc growth, according to the Publlc pnces for power also soared to record ,Cconomists and engineers agree that Pollcy Insutute of Callfomla 'Ought to be henheights In response, CAlSO asked the some of the unique physical attributes 2002at eficial to the utilities; the freeze Follow~ng Cal~forn~a's several other vote, Federal Energy Regulation Comm~ss~on to electric'ty make the design of regions of the U S -notably parts of the was to be lifted sooner ~fthe utlllnstltute pnce caps of $250 per megawattpower markets a Northeast and Texasdec~dedto resuucities collected enough to Day off hour, whch 11did ture the11 power markets as well Wh~le their debts before that dak . The pnce caps d ~ dnot prevent other there have been no full-out d~sasters,these To operate new auctlon-based forms of corporate msch~ef,however In electricity make the design of effic~ent markets for power, and to manage the transmarkets, too, have been beset w~thvolaule n May 1999, E ~ o scheduled a shpment of power markets a challenge. (See "The wholesale pnces and other problems rmsslon gnd, the state had created two non2900 megawatts of powet over a llne whose Power Grid: Fertile Ground for Math The convent~onal explanat~onfor Caliprofit corporations the Cal~formaPower capaclty was only 15 megawatts In the conforn~a's power cr~sls1s that flaws in the Research." SlAM News, October 2003; Exchange, whlch would operate the maln gestlon and chaos that followed, prlces shot restructuring agreement, comblned w ~ t h http://www.siam.org/siamnewsllO-031 forward cornpetlove energy markets Into was up more than 70% slatewide ( E ~ o n poor federal overs~ght, made 1 poss~blefor 1 powergrid.htm.) whlch generators would sell electr~ctty, and later fined just $25,000 for the ~ncident) One constraint IS that power must be procompanies to antficially drive up pncqs. the C?hfornlp IqQi?p$depf SysterpQ~erator Desp~te gliuho, the wc functlonkl such k 1 duced as it Is needed because of the problbRestructured markets that are well designed (CAISO), which was to prov~detransmlswell for the most om through 1998 and operate more effiitively high cost of stodng it. Because slon services to all electricity suppl~ers, and well regulated w~ll See Electricity Markets on page 8 dcmand for power is difficult to prcd~ct. ciently than the old monopoly system, most economlsls ;a). althodgh moat expens agree some power plants are kept on reserve, that U.S ourkets, ,o far, have not reallzed ready to begln producuon on short notice. Even so. there is a lag time before adhtlon. tha promise. al power can be generated. Because of Sean hleyn, an electncd engineer, anJ capaclty constralnls in pouer lines and other ln-Koo Cho, an economist, both at the equipment. it can also oe a challenge to Cn~veoltyof llllno~s at Crbana-Chunddliier electricity where it is needed, when weighing in with an alternative paign, FOR GRADUATE FELLOWSHlP PROGRAM it is needed. A local imbalance of supply perspective on restructuring. In a recent and demand, moreover, is not an isolated paper, not yet published, the researchers event: It threatens the stability of the entire introduce a dynamic pricing model for regional grid, potentially disrupting all condecentralized power markets that incorposumers and suppliers. Compounding the rates some of the unique engineering conproblem, consumers are not exposed to realstraints, such as the slow ramp up of reserve time prices under the current systems, and power sources and inelastic supply and demand. From their model, the researchers thus have no incentive to decrease their power consumption when prices are high. conclude that restructured power markets (in their current form) are doomed to fail. In this environment, short-term prices for DEPARTMENT OF ENERGY "The difficulties that have appeared in electricity tend to bevery volatile, and there are many opportunities for the exercise of California and elsewhere are intrinsic to the ~ ~ @ c s 3 COMPUTATIONAL SCIENCE Math Model Explains High Prices in Electricity Markets trig - - - GRADUATE FELLOWSHIP The DOECSGF program supports students pursumg doctoral studies at US UNvCCSlUea 1" sucnufic and cnsnccnng Lsuphnes that rely upon lugh-perbrmance computation In thcherr thesls rescarch Benelits indude: Payment of turnon and reqwed fees A competittve yearly stipend Research practlfum nt s DOE laboratorj - YcrdY IcUow- c o s s f s ~ " ~ ~ 0% help 60m thc new, cxtemvc h.oubMoohng s m o a of lypeoningDmmrr with Sotcnf& WorWIaecondSczent& Word,ThudEdiNDn 8 a O c t o b e r 2005 SlAM NEWS co,zrtnuedfrom l~aagc 4 Electricity Markets cap on wholesale power prices across the West. Economists' Perspective 1999, with wholesale prices hovering on the Crisis around $35 per niegawatt-hour. California's power problems, Woldk sugCaliforttia's dentand for elect~icitypeaks gests in a paper titled "Lessons from the in the summer months, when air conditionCalifornia Electricity Crisis" (Elecrricify ers are in use. The state usually counters the Jourf~al, August 2003), stemmed primarily increased demand by importing hydropower front some critical miscalculations by from the Pac~fic Northwest. In the summer California's utilities, combined with exof 2000, howelrer. hydropower was less abundant than usual because of a drought. tremely poor oversight by regulators. In the At the same tlme, prices of natural gas and resulting environment, even a company with a small market share could drive up prices nitrogen oxide pollution permtts were unusually high, driving up the operating by withholding supply. Starting in the sumcosts of gas-powered generators. mer of 2000, that ability was enhanced by In an already precarious situation, these the diminished competition from hydroevents combined to create a perfect storm, power plants-outside the state. Several groups of economists (that with wholesale power prices soaring to levinclude Borenstein, Joskow, and Wolak) els nearly 500% higher than those of the previous summer. Consumers throughout perfonxed studies compartng the actual prices in California's markets with those most of the state were shielded from the predicted by models under the same supply1 price fluctuations, but the utiltttes were payIng as much as $750 per megawatt-hour, ten demand conditions. The actual market times the average wholesale rate that was prices were significantly higher than the implicit in the fixed retail rate for conmodels' predictions. At the same time, data sumers. indicates that the number of power plants Only the San Diego Gas and Electric offline for maintenance or emergency Company, which had already recovered its repairs was substanttally higher than norstranded-assets costs and was thus exempt mal. These factors, taken together, are evifrom the rate freeze, was able to ratse retail dence that companies were indeed exercisprices. In July, San Diego customers began ing market power during the crisis. Joskow receiving elecuic bills two to three times says. higher than those of previous summers. In resoonse to the ensuine howls r of protest, the state stepped In and ret~nposed the retatl caps Still, the federal government had to use emergency funds to help some restdents pay bills . . the11Inflated ut~llty As winter approached, demand for electricity lessened, but the power shortages and htgh prices continued unabated. On November 1. 2000. FERC issued a preliminary order concluding that the inflated power prices were "unjust and unreasonable:' and thus in violation of the 1935 Federal Power Act that FERC is mandated to uphold. The organizatton suggested several "remedies" for the situation, includ~ng replacement of the $250 per megawatt-hour price cap with a "soft cap" of $150 per megawatt-hour; bids exceeding the cap would be permitted Point Process Theory Selected Topics only if generators could show that and Applications in Convex Geometry their costs justified the bids. (FERC Marked Point and Piecewise Deterministic MARIA MOSZYNSK4 Wmow Unrrvmiv, WanauPuInnd also asked the state to raise retail rates Processes Thls bool.e~anirl31n.l,.n Illrc lull.rr .l. r.or8.r\ and make it easier for the utilities to M I N JACOBSEN U n ~ ~ e ~ ~ b u l l b p e n lDen,oork io~m, SeumclO tnatartsconcernro!nltlE cl devn sllhce, 1 s enter Into long-term contracts.) The e ~ncheoo, n-mercur eia~aplcs, 5~.IsIra!Ions,a td This text examines tile basic theoryol marked point markel sutveillance committee, chairprocesses,developing randomlyover tlme, and sl~ows erercbszs Cwr%c beg a, wln the then0 olrtr,ns~c volulnes lor convex bodies, aiongwiU~ Hadwi~er llte ed by Wolak, responded with a report hw lhts theoly may be used totreat piecewise detero n m~nisl~cslochaslie processes in contisuous lole.'ll~e clmrracrlnalion theorems,wllose prwls are baied o saying that the suggested remedies beaulilulgeomelnc ideas such as tile rounding theobook addressesappticat~oas Iheov,anat~ing olthe would not help and, in fact, were likethe Next. rems a~td Stcincr loru~uta. the book provides a various ~liodets inapplied statslics and probability, and ly to make things worse. The commitstlwey on cunanlreand surfacearea lnieasures and includes exanlpiesand exercises in sunnal analysis. extensionsolthe class olmnvex bodies. I add~lion. n the tee t~oted the soft price cap would that branching processes,ruin probabli~ties, sports (soclmponallt class ofstarbodiesandselectors for convex rlrk (arbitragerod cer). lina~lcca~~dmatlayen~ertt function like no cap at all, because and sWr bodlcs are examined,includingapresenlalio~i porllotlo trading slrategies).and queaelngtheoty. affiliate transactions could be used to oftwo famous problems o geornelrlctomograpl~~ f the ZWj/APPROX, 365 ~Q./HAROtOVtR/S59.9S inflate a generator's costs. justifying Shephardprobtealan~ie Busentann-Peffiproblem. Ul ISBN W1764215-3 higher bids. zoor/2r6 vr, 30 11tur./rontovtyrs~.9s SN 0.81764396.1 IB Nonetheless, FERC ~mplemented Probability and Its the soft cap. In January 2001, prices Applications Neural Networks and Sea soared to new highs, averaging $290 Differential Geometry of Curves and Time Series per megawatt-hour, and chronic shortSurfaces A Concise Guide Reconstruction and Extreme-Event ages of avatlable power forced stateVICTOR A. TOPONOGOII1baid~l111riWI~ofMoIl1~olta Analysis wide rolling blackouts, desp~te CaliNomiibmk, R w o fornia's relatively low power consumpllon in January. In response, then Governor Gray Davis declared a state of emergency. important idcaofRiemmnian~mmel&~b&utl~or The situation worsened through intmducesthe redderbcu~es, progrwesto then Tltis book is devoled lo tile appltation 01 ~nellral February and March, and by midnrlaccs,andEnalh.ton~oreconlplexlopicrin thcwnclud- kletworks tothecol~crete prohlcnlafhandling the tifne April, unr slate ulitity-Pacific Gab insscdon. Oirealtltcrbilng featuresoflhispresenla srrter olsea drla, i.e., rigabcant wave hcigillrrttd reu tion is the brge numberofnontrniala n d originulproblems. tcvcts. Beginningwlh en explallation 01 "coral Inelworks and Electtic Company-had declared sotnemlll usefull~inlsa~~d soiutions.wliichintroducea lundamenlals lor lxginners, the autltars lollow~v,th a bankruptcy (even as another indemotimted student into the realivortdolgeomet~ renew or general statements and rigorous hcts, and pendent subsidiary of PG&E's parent conctudewiU~appli~lionrandalgorith~~~s lor particular 2005/APPROK. 200 PL. 40 ILLUS./IO~COYtR/S59,9I company, PG&E Corporation, profittrlN 0-8ln43M.l dala sets llaving well-definedparanleters. ed enormously dunng the crisis from 2005/AQPROX. PP, 64 ILLUI./HAROresented bywell-known speclalists i the held, is an n oulgrowfh 01the E~ghfh lnternatio~~al Conference on llltegral Mellhods 10 sclence and engneertilg. Co~~tributors a wlde~ariehollopicrfrom Ihe cover theoretrat developmental bauidaly lntegrat methods lo the application 01inlegratio11-based aualytr and lnumeriwl lecl~niques inciude ilttegral equations, that l~nileand boundalyelements,conservation taws,l~*rid approuclns,andoltlcryrocedurer. ?OOS/AQ~ROx. PL, 51 ILtUS./NAROCOYlR/S8995 328 IB Odllb4377-X SN Birkhauser Boston . Basel. Berlin @ " PrOmOtlOn#Y1 1504 October 2005 SIAM NEWS. 9 ket power by participants. The static models used by economists to describe elect~icity markets do not capture ramp-up constraints. he says. Following the IMA workshop, he and Cho set out to devise a dynamic model that would capture these key physical constraints and yet be simple enough to yield an economic analysis. This spring, Meyn and Cho finally arrived at a model that, Meyn believes, captures the essential features of power markets, albeit in simplified form. They have summarized their results in a working paper titled "Optimization and the Price of Anarchy in a Dynam~cNewsboy Model." The researchers model normalized demand as a driftless Brownian motion that 1s completely unresponsive to price. The average demand is met through a long-term conuacc with the primary source, while shortterm fluctuations are accommodated by multiple ancillary power sources. All power sources are rate-constrained in their ramp up, with the ancillary power sources ramping up faster than the primary one. Any excess power produced can be dumped at any .time without cost, a simplifying assumption that is not hue in reality. Ancillary power prices are also assumed to have constant marginal costs as high as, or higher than, that of the primary source-a grossly simplifying assumption, the researchers note, because real costs are nonlinear. There is a high social cost of not meeting demand and incuning a blackout. , Starting from the premise that society benefits from the consumption of electricity, the researchers first solve for a policy that maximizes the total social value: the sum of the profits of the generators and the social value for the consumers. (For readers versed in control theory: This required solving a multidimensional singular control problem.) This policy represents what a centralized controller of a power market would ideally try to achieve. The theoretical goal for decentralized markets, however, is to optimize through the actions of individuals, without a central controller. Toward this end, the researchers show the existence of an equilibrium price functional for which both consumers and generators arrive at the same policy decisions in a decentralized market. They prove that this equilibrium is unique, and that it coincides with the centralized social optimum. Cho and Meyn go on to show that even when their statistical assumptions on demand are relaxed, an equilibrium price functional, if it exists, must be of the form obtained for the model with Brownian demand. Remarkably, the prices corresponding to this unique equilibrium are, on average, so high that a consumer would incur a negative Electricih/ Markets contrnuedfmm page 8 lic utility commissions will not implement retail pricing plans that charge customers according to the hourly wholesale price." An Engineering Perspective Without disputing that the issues cited by the econornists were in play in the Cal~forniapower crisis. Meyn says he cannot wholly agree with their conclusions. "Why should high prices imply the exercise of market power?" he asks. Such concluslons, Meyn says, are based on intuition obtarned from observing gross manipulation by Enron and others,and on decades of analysis of statlc models. For Meyn, the fundamental expianation for the problems in California and elsewhere lies in the engineering constraints on power markets. In March 2004, at a workshop on power networks at the Institute for Mathemat~csand its Applications at the University of Minnesola, Meyn questioned whether a lack of long-term contracts and market manipulation could completely explain the collapse of California's market. He hypothesized that the mmp-up constraints for power plants, combined with inelastic demand, might make any decentralized approach inherently inefficient. even in the absence of the exercise of mar- ' k. ., IMA INSTITUTE FORMATHEMATICS AND ITS APPLICATIONS Membership opportunities i n connection with the 2006-2007 thematic program on benefit from participating in the market. Prices will be volatile even without manlpulation, Meyn says, because the unpredictabihty of demand and the slow response of supply mean there will always be times when demand approaches the available supply and prices soar. In the model, generators are assumed to be price-takers, meaning that a single generator's actions cannot affect the price. When generators do have market power, however, the basic problem becomes more pronounced, Meyn says. If there is a real-time demand response to high prices, the problem disappears for the most part because demand would approach supply only rarely. Meyn points out. Still, if power reserve levels fall suddenly due to an outage or storm, prices could again explode. Steven Shreve, an applied mathematician at Carnegie Mellon University, considers the paper "a significant step fonvard:'both for its mathematical contributions and for the issue it raises. The next step for mathematicians, he says, will be to understand all the simplifying assumptions in the model to see if any of them are not justified. "Is this a problem we have to worry about, or is there something in the real market that is different than the model?" he asks. Snra Robin$o!t is a fmelarrce writer based in Lox A,tgeles, California. xcellent opporiunity for ackground in andlor an Call for Nominations for SIAM Prizes SIAM invites nominations for the following prizes, to be awarded in 2006: Richard C. DiPrifna Prize. Awarded to a young scientist who has done outstanding research in applied mathematics. Nominations must bc received in the SIAM office by October 15,2005. Julian Cole Lectureship. Awarded for an outstanding contribution to the mathematical characte~izationand solution of a challenging problem in the physicallbiological sciences or in engineering, or for the development of mathematical methods for the solution of such problems. Nominations must be received in the SIAM office by October 15, 2005. ersed in the thematic SLAMActiviry Croup on Analysis of Differential Equations Prize. with a broad range of fields ~esidcnt active participan and ections Visiting Professors are expected to be rc not assigncd formal duties. [;or lnorc ~nfonnation ~lpplicationmaterials see and \nnv.in~a.umn,edu/docslmembership.htn~l phone 612-624-6066. or The University of Minnesota 1s committed to thc policy ha1 all persons shall have equal access to its programs, facdtties, and employment w~thout regard to I c e , color, creed, religion, national ongin, sex, age, marital stahis, disability, publrc assistance sfatu, veteran status, or scxuai orientation. Awarded to the author(s) of the most outstanding paper, as determined by the prize committee, on a topic in parual differential ~ q ~ ~ n t i o pubnr lished in English in a peer-reviewed journal. Nominations must be received in the SlAM office by December 31, 2005. SIAMAcriviry Croup on Linear Algebra Prize. Awarded to the . @$The I t~ an ISF funded /nst&~te www.ima.umn.edu UNIVERSITYMINNESOTA OF J% author(s) of the most outstanding paper, as delemined by the prize committee, on a topic in applicable linear algebra published in English in a peer-rcviewedjournal. Nominations should be received in the SlAM office by January 15, 2006. Updated prize information can be foorul on the SIAM Web bite at hlrp.// www.siaa.org/prizes/.