Markets for Reliability and Financial Options in Electricity: Theory to Support the Practice

Transcription

1 Markets for Relablty and Fnancal Optons n Electrcty: Theory to Support the Practce by Tm Mount Professor of Appled Economcs and Management Cornell Unversty 214 Warren Hall Ithaca, NY tdm2@cornell.edu Wllam Schulze Professor of Appled Economcs and Management Cornell Unversty 301 Warren Hall Ithaca, NY wds3@cornell.edu Rchard E. Schuler Professor of Economcs and of Cvl and Envronmental Engneerng Cornell Unversty 422 Hollster Hall Ithaca, NY res1@cornell.edu Abstract The underlyng structure of why and how consumers value relablty of electrc servce s explored, together wth the technologcal optons and cost characterstcs for the provson of relablty and the condtons under whch market mechansms can be used to match these values and costs effcently. Ths analyss shows that the level of relablty of electrcty provded through a network s a publc good wthn a neghborhood, and unless planned demand reductons by customers have the dentcal negatve value as an unexpected servce nterrupton, market mechansms wll not reveal the true value of relablty. A publc agency must determne that value and enforce the relablty crtera. Furthermore, n order to get an effcent level of demand response by customers n perods of system stress, they must see real tme energy prces plus they must be pad an amount equal to the supplers cost of addng relablty to the system, f that amount s not ncluded n real tme prces. An llustraton s provded of how VARs mght be scheduled and prced n contrbutng to system relablty, and a co-optmzaton procedure s requred to determne energy and reserves smultaneously, smlar to the method proposed by Chen, Thorp, Thomas, and Mount [1] for locatonal reserves. The optmzaton can be decomposed nto a two step process frst, both requred capacty and energy are selected based upon supplers offers over both dmensons through the mnmzaton of expected costs over the lst of contngences necessary to satsfy the relablty crtera. Ths frst step commts the reserves, but energy supples are allocated n real tme based upon the prevous offer prces but the actual realzed state of the electrc system. Ths procedure whch satsfes physcal realtes has a natural parallel n fnancal markets that have a forward opton market wth a strke prce, followed by real tme market clearng. Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

2 1. Introducton Electrcty supply s comprsed of at least three broad attrbutes that are valued by customers. However, n most nstances these characterstcs are bundled together wth the flow of energy and sold at a combned prce per mwh. From a customer s perspectve these consttuent parts are: (1) quantty of energy, (2) upon demand, (3) at a specfed, consstent qualty (e.g. voltage and frequency stablty, low harmonc content, VARs upon demand). When partally unbundled, the electrcty suppler may vary unt prces based upon the proportons of energy (1) and peak demand (2), snce that nfluences the relatve sze of nvestment, but regulatory bodes normally set standards for the qualty of servce as gauged by (3), wth some supplers chargng for kvarh usage, and supplers average the costs for provdng fewer outages than allowed by regulators n base prces. Unplanned outages can be thought of as a falure to satsfy category (2) servces, snce when the power s out, customers cannot satsfy ther desre to consume as much energy as they want (1) at the qualty they expect (3). So when thnkng about the relablty of electrc servce, t s comprsed of category (3) and some aspects of category (2) of the electrcty supply attrbutes that are valued by customers. Note that from a suppler s perspectve, ther response to these demand attrbutes may be through a dfferent set and combnaton of mechansms. As examples, provdng reserve margns (spare capacty) of both generaton and electrc lnes wll satsfy both the customer s desre to use as much electrcty as they want at the flck-of-a-swtch and to not have ther servce nterrupted (partcularly unexpectedly). Furthermore, the provson of VARs whle causng machnery to rotate, also can reduce the probablty of an unexpected outage, so there s not a drect oneto-one set of mappngs from the three demand attrbutes and the effcent supply responses. Nevertheless, for the purposes of ths analyss that focuses on potental customer actons, energy purchases wll consst of category (1) and the porton of (2) requred to respond to the customers normal pattern of usage; whereas relablty wll encompass category (3) and that part of (2) nvolved n mtgatng unplanned servce nterruptons. In that lght, the effcent set of prces, and consequently the desred structure of markets, are explored that serve the customers desres, whle beng suppled through the least cost combnaton of avalable technologcal responses. Further, the tme lags assocated both wth dfferent supply responses (e.g. dfferent generator ramp rates) and wth the ease of customer adustment, are compared and matched wth a vew toward devsng an effcent sequence of markets that mght be algned wth tradtonal fnancal paradgms. 2. Why Servces Have Been Bundled Allegedly, hgh costs of meterng and avodance of customer rrtaton are reasons gven for not mplementng wdespread tme-ofuse (TOU) prces. Real tme prcng (RTP) s smply an extenson of the TOU concept over a much fner tme-gran, and t s even rarer n practce. VARs are rarely blled separately, n part because up to a pont they can be generated wth no addtonal cost n conuncton wth the supply of energy, but above a gven proporton, further supply becomes qute expensve. And, customers rarely are asked what they are wllng to pay for relable servce; reserve margns are provded accordng to regulatory crtera and the costs are averaged nto the prce of supplyng energy. The excepton s the occasonal avalablty of nterruptble rates or payments for emergency demand response. But these prcng mechansms are dfferent than chargng for relablty: the customer has some warnng about when they wll be asked to reduce load, n some nstances the load reducton s stll voluntary when requested, and only a small proporton of customers are nvolved n these programs n the lmted areas where they are avalable. Why are prces not unbundled and varable wdely over space and tme? Over space, homogeneous prces wthn a partcular utlty s servce terrtory, for a gven customer class, has been a tradton promoted by nearly every regulatory body, presumably under the theory that ther legslatve mandate that prces be far and non-dscrmnatory means that they should be the same for all of a suppler s customers (never mnd that the cost of servce may vary wdely, geographcally). Here regulatory tradton, and a pecular sense of what s far, s a sgnfcant explanaton. Over tme, why has RTP not caught on snce the costs of generaton vary so wdely? One answer s to consder the lkely effect on a suppler s (utlty s) profts. Even wth Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

3 decreasng costs, proft relatonshps as a functon of prce can be shown to be concave n prces as depcted n Fgure 1, and f under real tme prces P 1 and P 0 n peak versus low-load days, the suppler were to earn profts π 1 and π 0, respectvely, then ther average proft would be π. If however, the suppler s allowed to charge the same average prce n both perods, wth a concave proft functon, the frm would charge P and earn π( P ) whch s greater than the result under real tme prcng. Ths result s analogous to the Fredman and Savage [1] analyss of choce under uncertanty, except here the varablty s assumed to be known. So one possble explanaton for averaged, bundled prces s that t has been advantageous to supplers. Fgure 1. Profts and Varyng Average Prces 3. Theoretcal Analyss of Optmal Supply of Relablty Consder electrcty customers whose value (utlty for ndvduals; profts for busnesses) s determned by the desred amount of electrcty they consume, q, ts relablty, r, and the amount of all other goods (productve nputs for busnesses), z, acqured. Also consder the possblty that customers can agree to reduce ther use of electrcty by an amount, r, upon request, n order to mantan system relablty, but that ths agreed upon reducton n consumpton also reduces the customer s value, so a more than offsettng compensaton s requred to nduce ths demand reducton behavor. By specfyng the problem ths way, the possblty that a decrease n relablty and an agreed upon demand reducton may not be the same can be explored, as well as crcumstances when they may be smlar snce both do result n less use of electrcty. What s dfferent about the two s the fact that servce nterruptons are frequently unantcpated; whereas, advanced notce s gven for demand reductons. Furthermore, snce there s a publc good aspect to electrcty relablty when servce s provded through a network (even f one customer partcpates n demand reducton, but a neghbor doesn t, both wll be nterrupted dentcally f there s a system falure), the search for the optmal level of relablty must be modeled n the context of a centrally planned economy to allow for the optmal provson of servces wth publc-good-lke attrbutes, lke relablty. In ths context, the analyss demonstrates whch decsons mght be decentralzed, allowng markets to provde effcent outcomes, and whch requre some publc nterventon (by the planner) to reach optmal outcomes. The planner s problem s to maxmze socety s welfare, whch s enhanced by ncreased value to socety s customers, subect to physcal resource and technology constrants. Formally, the planner s task s to solve the problem n equaton (1). Each of the varables could be assgned a partcular tme desgnaton so that q 0 mght be s desred electrcty use n an off-peak perod and q 1 mght represent desred peak day usage, as an example., Max W U q, r, z r z c q, r 1 + λ ( ) + λ g 2 ( r ) + f r r + µ q r q 1 + r + µ Z z z 2 0 r 1 Where: = customers = frms W = Socety s welfare rankng U = s utlty q = electrcty consumpton = Agreed upon reducton tmes r probablty of selecton r = relablty z = all other goods (1) Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

4 In ths specfcaton, each suppler s thought to be able to produce greater supples of electrcty, q, and/or enhance t s relablty through r, ether by provdng reserves and/or VARS, as examples, but n so-dong the frm uses up resources (captal, labor and materals) so that less of the other goods can be produced, and z represents that offsettng reducton. Thus, each frm s cost of producng energy and relablty s represented by the reducton n z requred to free the necessary resources, assumng effcent assgnment of productve resources throughout the economy. In ths way, each electrcty suppler s use of resource s represented by ts cost constrant (multpled by Lagrangan λ ) and socety s aggregate resource constrant s represented by the maxmum possble producton of Z n the equaton multpled by Lagrangan µ, whch s allocated to the consumpton of z 2 or the producton of q and r through z. The other two constrants descrbe alternatve means of producng electrc servce relablty, r, n the equaton multpled by Lagrangan, λ 2, and n the equaton multpled by µ 1 whch equates the desred demand for electrcty, as adusted by the realzed relablty and agreed upon demand reductons, wth the avalable supply. As specfed, relablty s bounded by the unt nterval and represents the probablty the desred demand wll be realzed, f there s no call for demand reductons. The frst order condtons are summarzed n equatons (2) through (5) when the four constrants n (1) are bndng. Here the λ multplers are equal for all frms, so that as shown n equaton (2), the producton of energy should be allocated across all supplers so that ther margnal costs are equal. 1 u µ 1 r q c µ = = 2 u q z P( q) = MV( q ) = MC( q ) 1 (2) c λ2 = r µ g 2 r u u z r u z ~MC(r) through r = λ f + µ µ µ r 2 r 2 1 = λ + u 2 2 µ q µ µ where: MV( ) = margnal value MC( ) = margnal cost P( ) = prce (3) (4) (5) Further, the margnal cost of supply should equal the customers wllngness to forego consumpton of other goods n order to use more electrc energy (ther margnal valuaton), whch n turn should be equlbrated across all customers. Snce the equaltes n equaton (1) are across all customers and supplers, and n turn are equal to the rato of the Lagrangan multplers (analogous to the prce of electrc energy), ths welfare optmzng soluton s attrbutes show that smlar results would be acheved by decentralzng the energy supply and consumpton decsons by lettng a market solve the problem. Note, however, f these decsons were ndexed by tme, and dfferent margnal producton costs and/or margnal values of use emerged at dfferent tmes, then dfferent prces are requred for each tme perod. Equaton (3) requres that the servce relablty provded by supplers be allocated among them so that ther margnal costs of producton be equal. Equaton (4) factors n the customers contrbuton to servce relablty and emphaszes that agreed upon demand reductons should be thought of as an alternatve way of producng relablty, ust as supplers do so by provdng greater reserves. To have an effcent level of demand reducton, equaton (3) emphaszes that customers must receve a beneft equal to the sum of the foregone supply sde alternatve for provdng that relablty, plus the Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

5 real tme producton cost savng for not havng to supply that electrcty. Only f they receve these combned savngs wll customers be nduced to accept suffcent loss n the consumpton value of electrcty by droppng ther energy usage to optmal levels. Optmal system relablty requres both demand reducton ncentves and accurate real tme prcng! Equaton (5) specfes the optmal level of relablty for the system, and the formulaton emphaszes that the optmal level of relablty cannot be determned by a market; a regulatory mechansm s requred to determne the sum of each customer s margnal valuatons. If left solely to the market, each customer would equate ther ndvdual margnal benefts (not the sum) to the margnal cost, the prce would be too low, and too lttle relablty would be provded. Ths s a classc publc good problem, and whle t s frequently dffcult for a central authorty to nfer the sum of the valuatons to customers of mproved relablty, compettve markets wll not get t rght. Furthermore, even f supplers were to provde relablty n order to further ther own proftablty, they would merely equate the two terms on the rght-hand-sde of equaton (5), settng the margnal cost of provdng addtonal relablty to ts margnal beneft n terms of addtonal electrcty sales. But equaton (5) emphaszes that the cost of producng that addtonal electrcty because relablty has ncreased s a cost, ust as s the cost of supplyng reserves, that must be added together and weghed aganst the sum of the margnal value over all effected customers. Equaton (6) compares the prvate valuaton for demand reducton n equaton (4) wth the publc demand for relablty n equaton (5). Whle not the same, can the valuaton for λ 2 µ 1 MV ( r ) = + r µ µ r r r ( ) MV r = 2 2 MC( r) P( q ) λ µ µ µ (6a) q (6b) 2 2 demand reducton that s nferred by offerng the proper ncentves on the rght hand sde of equaton (6a) be used to nfer the prvate demand for relablty for use n equaton (6b)? If t could, then these margnal values could be summed to nfer the publc demand for relablty. But note, even f the queston n equaton (7) s true, and t probably s not Queston: s MV ( r ) MV ( r ) r r? (7) snce planned demand reductons and unplanned nterruptons may have qute dfferent valuatons, summng up the rght hand sde of equaton (6a) leads to a very dfferent cost than s represented by the rght hand sde of equaton (6b). Thus the margnal value of relablty must be determned through surveys or the poltcal process; marketderved nformaton wll not be adequate. 4. Example of Supplyng Relablty: VARs In establshng markets for electrcty thus far, the conceptual problem of how to prce VARs effcently n terms of ther contrbuton to mproved system relablty has been gnored. In the context of equaton (1), ths contrbuton of VARs can be thought of as descrbng g (r ) n detal, and of understandng ts cost characterstcs n terms of mprovng system relablty, r. The setup for ths example s an magnary town that can mport cheap hydropower (q h ) from a consderable dstance that costs c h per mwh to produce. However, the town has a constant power factor so that t needs X = γq mvar to support load (where Q s total load) whch must be suppled by local fossl fuel generators. Each of these dentcal fossl fuel generators has a cost of c f per mwh for the power that each produces (q f ). We assume that the unt cost of fossl power s much more expensve than hydro-power, so c f > c h. Each of these plants has a mnmum (q f mn ) and maxmum (q f max ) power settng. The reactve power produced by each generator (x f ) wthn ths range s descrbed as follows: α - βq f x f. Note that x f s measured n absolute value unts. If m fossl fuel generators are runnng out of n potentally avalable, then the total power avalable s Q = mq f + q h, and the total avalable reactve power s mx f X. Now consder the case where the probablty of each of the fossl fuel generator falng s (1 - ρ). If n generators are avalable, the probablty that m wll be runnng s then gven by: φ(m,n) = ρ m (1 - ρ) n-m (m!)/(n!(n-m)!) (8) Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

6 Fgure 2 compares the probabltes of m generators runnng when n=2 and n=3 for a value of (1 - ρ) =.4, admttedly a very large probablty of falure, but useful for examnng the propertes of the dstrbuton. Fgure Probablty of m generators runnng wth n=2 and n=3 and probablty of falure = n=2 n= If we treat φ(m,n) as contnuous n the optmzaton problem to be defned below, the followng approxmatons can be used: φ/ n = ((m-nρ)/(n-m))φ, and (9) φ/ m = ((nρ-m)/((1-ρ)m))φ. (10) From (9), the probablty of havng m generators runnng s ncreased by ncreasng n f m > nρ and decreased f m < nρ. Note that nρ s the expected number of runnng generators. In Fgure 2 above, wth two ntal generators, nρ = 2(.6) = 1.2. Thus, addng a thrd generator decreases the probabltes of m=0 and m=1 snce m<1.2 n these cases, and ncreases the probablty of m=2 and adds a postve probablty of m=3 snce m>1.2. From (10) the probablty ncreases n m for nρ>m and the converse, as s approxmately true for both the dstrbuton for n=2 and the dstrbuton for n=3 shown n Fgure 2. Thus, (9) and (10) determne how system relablty ( r through g(r ) n Secton 3) s mproved as the number of generators runnng, m, ncreases, and how n turn these probabltes change as the number of avalable generators, n, ncrease. If we set ths up as a statc problem, the decson on n corresponds to how many fossl generators to construct to acheve an optmal level of relablty and the sngle perod total cost for n plants s n tmes the captal recovery factor, CRF, tmes the nvestment cost, I. Thus, the total cost s n(crf)i. The fnal component necessary to set up the optmzaton problem for choce of the number of fossl power plants to construct, n, ther level of operaton, q f, and the amount of hydro power to mport, q h, s to defne the benefts of power delvered as Q B(Q) = E(q)dq, 0 where B(Q) s smlar to socety s welfare functon n equaton (1), and E(q) s the nverse demand equaton for power that determnes the market prce, E, as a functon of the quantty of power produced. Note that, wth downward slopng demand, E < 0, and consequently, B > 0 and B < 0. To solve the optmzaton problem we start by maxmzng the net benefts for each state of the world defned by m, the number of fossl generators n operaton. Thus we wsh to maxmze NB(m) = B(mq f + q h ) mc f q f - c h q h (11) subect to the constrant on reactve power, m(α - βq f ) - γ(mq f + q h ) 0 (12) (wth the assocated Lagrange multpler λ), the constrant on mnmum power settng, q f - q f mn 0 (13) (wth the Lagrange multpler ψ), the constrant on maxmum power settng, q f max - q f 0 (14) (wth the Lagrange multpler θ), and the constrant on hydro-power avalablty, q h max q h 0 (15) (wth the Lagrange multpler ω). For brevty we wll dscuss only the most nterestng cases. Frst consder the case wheren only constrants (12) and (13) are bndng. Note that as m vares, dfferent constrants wll become bndng. Ths case arses when costmnmzaton forces the mnmum power settng Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

7 on fossl fuel generators to supply needed reactve power and hydro-power can meet demand net of m q f mn, whch s necessarly produced at hgher cost to supply reactve power. In ths stuaton, the frst order condtons for q h and q f mply that (where we note that E = B whch s smlar to the market prce) E = c h + λγ, and E + ψ = c f + λβ + λγ. Thus, the economc nterpretaton of these condtons s that hydro power s prced at cost plus a charge λ for reactve power, and fossl power operates at a vertex soluton (at the mnmum power settng) for each generator so ψ>0 and cheaper hydro power sets the market prce. Here, f VARs are requred only for provdng short-run relablty on the wred network, the prce for that relablty should be λγ, and f only hydro frms are sellng energy, they should pay λ for the reactve power that the energy they sell requres. Note that the term λβ n the fossl generator optmzng condton represents the opportunty cost of producng less reactve power n order to produce greater mwhs. Now consder the case where hydropower s not able to meet demand so that (15) holds wth equalty. In ths stuaton, ω s postve and fossl generators wll optmally be run above the mnmum power settng. The mnmum power constrant no longer holds so ψ s equal to zero. Now the frst order condtons mply that E = c h + λγ + ω, and E = c f + λβ + λγ, so fossl generaton sets the market prce of electrcty and ω can be nterpreted as the excess unt proft earned by hydro gven that more expensve fossl generaton now sets the market prce. Agan, both hydro and fossl generaton pay for needed reactve power that s ncorporated nto the bundled prce of electrc power pad by customers, and the prce of relablty s λ ( γ + β). The market structure mpled by these condtons n ths example where VARs are requred as a constant proporton of energy suggests that fossl generators can sell both energy at a prce of E - λγ and reactve power at a prce of λ. Thus, the market prce receved for power by generators s adusted downward to allow purchase of needed reactve power. Ths charge provdes the revenues necessary to purchase reactve power from fossl generators. To provde approprate ncentves n each state m, the proft of the hydro generator should be (E - λγ)q h - c h q h, and the proft for each fossl generator should be (E - λγ)q f +λ(α - βq f ) -q f c f where both E and λ are state dependant. In summary, the optmal state dependant market structure requres that all generators be pad (Eλγ) for each unt of power they produce and that fossl generators be pad λ for each unt of reactve power that they produce. Thus, we requre two smultaneous related markets, one for power and another for reactve power. The fnal ssue s the determnaton of the optmal number of generators, n, for the system, that s the captal nvestment requred to provde adequate reserves. Assumng constant statc load, and that the market structure follows that outlned above so that the optmal level of net benefts can be obtaned for each state of the world, NB(m)*, we wsh to choose n to maxmze n 0 φ(m,n)nb(m)*dm - n(crf)i. Where NB(m) s the welfare functon n equaton (1), and relablty s mproved by ( ) r g m. havng more generators avalable, ( ) Thus, n s optmally chosen to satsfy n φ( n,n)nb(n)*+ ( φ/ n) NB(m)*dm=(CRF)(I) (16) 0 and an addtonal n th generator should be added to the system as long as the sum of the expected net benefts wth n generators plus the sum of the change n the expected benefts over all possble states of the system wth respect to generator falure exceeds the annual captal cost of the nvestment. Note that, n general, addng a generator wll reduce the probablty of states where only a few generators are runnng and Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

8 ncrease the probablty of states where more generators are runnng. Note, that the optmzng condton for n ncludes net benefts. These ncorporate the consumer surplus (welfare benefts) that wll not be captured n the profts of ndvdual generators usng the market structure specfed n ths secton. Ether a governmental agency must make ths optmzng decson about the desred level of relablty, n, or ndvdual supplers must be able to capture ths consumer surplus. Thus, optmal prvate decsons on nvestment n generaton mples that electrcty must be sold by a dscrmnatng monopolst who s free to capture the surplus, a dffcult stuaton poltcally. 5. The Dynamc Process of Supplyng Relablty Although Secton 4 lays out a mechansm to determne an optmal number of generators that should be avalable to maxmze socety s net benefts (welfare) by provdng adequate VARs, snce VARs are assumed to be requred n fxed proporton to the energy requred (mwh), these mpled generaton reserves are also avalable to meet load under a range of possble falure condtons. What s of nterest s that the analytc development n Secton 4 follows actual operatonal procedures n reverse. The analytcs of Secton 4 have us select the optmal level of VARs, gven each state of the world (number of generators avalable, m), and then computes the optmal number of generators to make avalable, n, from the expectaton over all states of the world, m. Of course operatonally, the sequence s reversed and through a plannng process (years ahead), the optmal number of generators are bult, n; then a week or day ahead, adequate capacty s contracted for, turned on and ramped-up (agan lke narrowng a selecton of n); and then n real tme when the state of the world s revealed, an optmal dspatch s made over the avalable mx of generaton, m. If the plannng has been accurate, that generaton should be adequate to meet load, despte contngences (falures) wth a probablty of falng n only one day n one thousand (the current relablty standard specfed by NERC). Furthermore, the process descrbed here s smlar n sequence to the one mplct n the paper by Chen, Thorp, Thomas and Mount, 2003[2]. There, n solvng for optmal locatonal reserves, the frst step s to defne the maxmum and mnmum calls for generaton from each unt over the range of contngences (falures and unantcpated demand), that must be satsfed n order to meet pre-specfed relablty standards. Here agan, the mplct assumpton s that an over-archng authorty specfes the relablty standard, r (e.g. solves equaton (5)). Subect to offered prces from each generator for energy and reserves, the optmzaton crtera s to mnmze the expected cost of meetng loads subect to the requrement that all load must be served under the specfed contngences and the maxmum quanttes of reserves and energy offered by each suppler. Ths optmzaton sets the reserve commtments and market clearng prces at each node, as well as an expected energy prce at each locaton. However, n real tme the state of the world (contngency, f any) wll be revealed, and so n real tme, t s optmal to select the energy dspatch and prces under the contngency that has been realzed. So ether under the VAR analyss for provdng relablty n Secton 4, or n arrangng for optmal locatonal reserves as n Chen, et. al [2], a mult-stage market s suggested where n the frst stage the optmal amount of generaton capacty s determned that guarantees meetng the relablty crtera at the lowest expected cost. Commtments are made for avalablty n ths frst stage and the prces for avalablty are set. Then n real tme, gven the state of the world, energy s dspatched at least cost and market prces for energy are set, based upon offers for energy n the frst stage! Ths s an essental part of co-optmzaton: supplers must submt ther maxmum avalablty and ther offer prces for supplyng that avalablty and energy smultaneously. In ths way compettve pressures are ncreased on supplers to provde offers consstent wth cost for both avalablty and energy, snce ther selecton for ether reserves and/or energy supply wll be based upon both offers! In an earler analyss that focuses solely on the provson of reserves (e.g. 10 mnute spn), Chao and Wlson [3] conclude that a two step clearng process s requred to derve ncentve compatble offers wheren actual energy prces are determned n the real tme spot market and reserve prces and selecton are set a perod ahead. Because Chao and Wlson [3] presume that many other non-reserve-offerng generators also offer nto the real-tme energy market (e.g. through day-ahead energy offers) Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

9 and the energy prce offers by potental reserve provders are added to the other offers n selectng who wll actually be called upon to generate n real tme, the real-tme energy market s assumed to be compettve. Gven that condton, Chao and Wlson [3] demonstrate that t s ncentve compatble to select generators for ten mnute reserve avalablty solely on the bass of ther reserve capacty prce offers, snce whether or not they wll actually be selected to run n real tme hnges on how ther energy offers stack up wth those of other supplers n real tme. Ths process dffers from that of Chen, et. al. [2], who seek to derve a smultaneous least cost dspatch of both reserves and all energy through locatonal co-optmzaton. Achevng the potental effcences of locatonally-specfc reserve assgnments requres that all generaton wth adequate rampng capablty that ndcates avalablty for energy supply also be avalable for reserve selecton. Under a co-optmzaton selecton procedure, t s mmateral f the generator s asked for offers for reserves and for energy or for total avalablty and for energy, snce the sum of reserves and generaton quanttes cannot exceed the total unt avalablty. If a two-stage sequence of auctons emerges, what s commtted n the frst stage (and what s requred physcally gven ramp rates and requred lead tmes to confgure the system) s the total avalablty of each unt. Then n real tme, t s effcent to mnmze the cost of delverng energy, condtonal on the energy prces offered and the capacty commtted n the frst stage. So the suggested sequencng s consstent wth Chao and Wlson [3]; what dffers s the bass for and nature of commtments made a perod ahead under co-optmzaton. Furthermore, under cooptmzaton there s no assumpton that energy markets wll be compettve. In fact, a maor obectve of market experments to be conducted on ths assgnment procedure s to assess the compettveness of two part offers. 6. Concludng Observatons The precedng analyss suggests that the effcent provson of electrc energy and servce relablty could requre a sequence of markets over tme where the spacng s dctated both by the mprovements n accuracy of nformaton about actual demand (weather) and supply (equpment falure) condtons as the actual nstantaneous transacton tme approaches. All other commodty markets offer the opportunty for physcal hedges aganst these uncertantes through storage and nventores, but that opton s not wdely avalable, physcally for electrcty. And so, the sequence of market nformaton could be tmed to match the sequence and lead tme requred for physcal responses by supplers, customers and the electrc grd operators. Important consderatons are the rampng rates of dfferent types of generaton avalable, the costs customers bear n rapdly adustng to dfferent market condtons as affected by the amount of advanced warnng they receve, and the tme requred for the system operator to update ther dspatch plan. Startng wth the real tme market when the state of the world and all contngences are known, f precedng markets have been properly desgned, suffcent unts should be ramped-up so that all that s requred to balance supply and demand quanttes s to make margnal calls for ncremental energy supply and/or ncremental demand reductons. The real tme market s a pure energy market, wth some lattude for varaton provded by unts on regulaton. Movng further back n tme, n the precedng perod all short term reserves wll have been arranged n antcpaton of contngences, plus commtments for suffcent energy to meet antcpated load. Alternatvely, avalablty payments could be made for the sum of each unt s reserves plus ts expected energy sales, but the payment for energy sales could be deferred untl the real tme realzaton of energy actually requred. Movng back n tme, to nsure adequate nstalled capacty, markets could agan be conducted for avalablty, but once agan those selectons should be made based upon the mnmzaton of expected costs of both avalablty and energy payments, where those expectatons are computed over a range of contngences and possble loads that together satsfy the system s relablty crtera. What s proposed, therefore, s a sequence of co-optmzatons, movng up to the real-tme clearng. In each perod except the real tme, each suppler provdes offer schedules wth prces for both avalablty and energy where the avalablty s selected by a co-optmzaton calculaton based upon both offer and demand schedules, where the avalablty quantty offered must equal or exceed the maxmum quantty of Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)

10 energy offered. What s pad n ths perod s the market clearng prces for avalablty. What s requred of the successful offerer s that ther total avalablty quantty offered n subsequent auctons must be the same or greater than n the prevous ones, and ther energy and avalablty prce offers can be no hgher than the successful clearng prces n the precedng auctons; otherwse the payments they receved n the prevous aucton wll be forfeted. Unts not selected n earler auctons would be free to revse ther offer schedules wthout lmt. 3. Chao, H. and Wlson, R., Mult- Dmensonal Procurement Auctons for Power Reserves: Robust Incentve- Compatble Scorng and Settlement Rules, EPRI and Stanford Unv., March 29, These markets would functon, therefore, lke a sequence of optons markets where generators would be selected based upon the least cost combnaton of offer and strke prces a two part prcng scheme. And to demonstrate the physcal vablty of earler successful offers, once selected, supplers would be requred to offer nto all subsequent markets quanttes and prces no less favorable than receved n earler successful auctons, up untl the fnal dspatch n real tme. Thus a sequence of markets nvolvng both capacty-avalablty and energy offers, whose selecton s cooptmzed n each perod to provde the lowest expected combned cost of electrcty, whle servng the physcal needs of supplers, customers and operators of the system, would also have natural parallels n the fnancal communty and could be represented as a sequence of bndng optons markets wth maxmum strke prces. There s ample room for further expermentaton to explore whether real physcal commtments must underle each of these markets n a sequence, or whether pure fnancal exchanges are suffcent, up untl the real tme physcal exchange of electrcty. References 1. Fredman, M. and Savage, L.J., The Utlty Analyss of Choces Involvng Rsk, Journal of Poltcal Economy, 1948, p Chen, J., Thorp, J., Thomas, R. and Mount, T., Locatonal Prcng and Schedulng for an Integrated Energy- Reserve Market, paper presented, at Thrty-Sxth Hawa Internatonal Conference on Systems Scence, Jan. 6-9, Proceedngs of the 36th Hawa Internatonal Conference on System Scences (HICSS 03)