An Economic Analysis of the Self Commitment of Thermal Units

Transcription

1 An Economc Analyss of the Self Commtment of Thermal Unts Smon Ede, Ray Zmmerman, Tmothy Mount, Robert Thomas, Wllam Schulze Cornell Unversty Abstract Gven the load profle of an electrcty market and the capabltes of the set of generators supplyng power to that market, t s lkely that at any ven pont n tme, avalable supply wll exceed demand. If only a subset of generators s reured, some method s reured to commt and de-commt generators. In the past, system operators have employed a centralzed method of unt commtment. Deregulaton of the electrcty ndustry throws doubt on the contnued sutablty of ths method due to farness ssues and avalablty of accurate cost data. Ths paper wll examne the performance of decentralzed unt commtment, where dspatch of generators s determned by offer curves submtted nto a spot market by power producers. Ths paper wll frst dscuss, the objectves of centralzed unt commtment. Doubt s cast upon the contnued effcency of centralzed dspatch n the presence of asymmetrc nformaton n deregulated markets. The second secton of ths artcle wll descrbe the propertes of an aucton mechansm that s beng appled n electrcty spot markets to determne dspatch. In the thrd part of the dscusson, we wll examne the mpact of uas-fxed costs, such as start-up costs, upon the offer stratees of generators n such auctons and ther mpact upon the cost effcency of dspatch. The paper wll conclude wth emprcal evdence gathered from a seres of economc experments conducted at Cornell Unversty's Laboratory for Expermental Economcs and Decson Research, usng a computer based smulaton of a real transmsson network.. Introducton In regulated or state monopoly power markets, a central system operator made the decson whch subset of generators should be operatng at any partcular pont n tme. That system operator had access to all relevant nformaton such as heat rate curves, mnmum up and down tmes, start-up costs and other such system and operatng constrants. Provded that the nformaton avalable to the system operator was accurate, t was possble to dspatch generators so as to mnmze systemoperatng costs, consstent wth generator and network constrants. Lberalzaton of energy markets worldwde has led not only to the prvatzaton of generaton and network assets but also of nformaton. Prevously, the nformaton would have been ether common knowledge or obtanable by mandate. If the effcency of dspatch depends on the accuracy of the nformaton avalable to the dspatcher, then effcency of centralzed dspatch n a deregulated market depends upon the wllngness of power producers to accurately reveal ther cost structures. 2. Centralzed Unt Commtment In the most conventonal form of economc dspatch, the problem facng the system operator was to mnmze total operatng costs such that total generaton was eual to total load. Ths s shown below n an example of a market n whch generatng unts may be turned on or off but there are no start-up costs or mnmum up or down tmes. Throughout ths paper, t shall be assumed that capacty s offered nto the market n blocks at a sngle prce per block. Where multple blocks are offered, the resultng offer curve would be a step functon. The am of the system operator s: ng () mn uc ( u, g subject to ng = (2) u = Qd where: = ) The followng model follows that developed by Marja Illc and Frank Galana n "Power Systems Restructurng: Enneerng and Economcs" Eds. Illc, Galana, Fnk, /00 $0.00 (c) 2000 IEEE

2 u = 0, = on-off state of generator. C ( ) = cost functon of generator = unts of power produced by generator. Q d = demand for load. = number of generators n generaton set. n g The followng lagranan can be formed: ng n g (3) L( u,, λ) = uc ( ) λ Qd u = = The frst order condtons of (3) solve to and reure: dc (4) = λ, d λ s the effect upon () of relaxng constrant (2) by one unt. As such ths s the marnal cost to the whole system of producng one more unt of power. At the optmum all generators wll produce such that ther marnal costs are eual to λ. Generaton s therefore a functon of λ..e. (5) = (λ) Ths can be substtuted nto (3) and the subseuent lagranan wll be: (6) ng n g L( u, λ) = uc ( ( λ)) λ Qd u ( λ) = = If (6) s mnmzed wth respect to u, t s possble to derve the "Swtchng Law": (7) u 0 = f f C ( ) λ C ( ) λ > 0 < 0 In other words, only those generators whose average cost s less than the system marnal cost wll be dspatched n any ven perod. Addng network and generator constrants can easly complcate ths smple model but ts basc relance upon symmetrc nformaton should be easly evdent. The central system operator needs power producers to accurately reveal C ( ) to determne u correctly. Any devaton could lead to an neffcent dspatch of generators. In the smplfed model, wth many compettors, there s lttle apparent ncentve to reveal naccurate cost curves. Wth rampng constrants, uas-fxed costs and network constrants, the stuaton s more complcated. It s mportant to ensure that the problem of unt commtment s solved eutably. Unt commtment algorthms can freuently produce more than one effcent dspatch schedule. Whch schedule would be approprate? Under some form of common ownershp, operatng rghts can be shared eutably through the system. Under decentralzed control t s less clear. As a result, spot markets have been used to resolve the nherent dffcultes n solvng the unt commtment problem. 3. Decentralzed Unt Commtment Suppose that the decson rule that determnes the dspatch schedule s changed so that unt commtment s determned by the nteracton of offer curves submtted nto a spot market, subject only to network constrants. Can an aucton lead to effcent dspatch n the same way as a central system operator wth perfect nformaton? Alternatvely, can generators nternalze ther constrants nto a sngle offer curve? Ths s self-commtment. McAfee and McMllan [] defne an aucton to be a market nsttuton wth an explct set of rules whch s used to determne the allocaton of a resource and ts prce dependng on the offers and bds of the partcpants n the market. If ths defnton of an aucton s appled then the role of the system operator s reduced to adjustng the spot market outcome, n an eutable manner, to satsfy network constrants. One possble aucton format for the deregulated electrcty market s a varaton on a frst prce sealed bd aucton. In ths aucton format, generators submt offer curves for ther capacty whch represent the mnmum prce at whch they would be wllng to operate that generatng capacty. The aucton determnes dspatch on an hourly or half-hourly bass. Generators know the result of the prevous aucton before they submt ther offer curves for the next aucton. Oren and Elmaghraby classfy ths as an "Hourly Supply Curve Vertcal Aucton" [2]. The system operator then ranks the offers from cheapest to most expensve and then dspatches the generators n order of cost, subject to network constrants, untl demand for load has been satsfed. All generatng unts are then pad a unform prce that represents the offer of the last unt of capacty to be dspatched. Ths s referred to as a "unform prce aucton" /00 $0.00 (c) 2000 IEEE 2

3 It has been demonstrated usng computer based economc experments that n ths knd of aucton where there are no network or generator constrants, offers wll approxmate marnal cost curves when the number of market partcpants s sx or greater [3], [4]. Ths can shown by developng the model above further. The spot market re-forms euaton (7) by substtutng O ( ) for C( ) nto (), where O ( ) s the offer curve submtted to the system operator by generator. Ths leads to the followng results: do (8) = λ and d (9) u 0 = f f O ( ) λ O ( ) λ > 0 < 0 Unless O = C, dspatch wll be dfferent. They wll be dfferent only when there s an ncentve to devate. In a world wthout network and generator constrants wth many compettors, a ratonal generator wll seek to maxmze profts. (0) max Π( ) where, () Π( ) = p C ( ) where, p Π = unform prce = proft functon Where the number of compettors s large and the prce converges to a sngle electrcty prce for buyers and sellers, p, t s possble to maxmze proft to ve: dc (2) = p, =,,n g d We know ntutvely that a generator would not wsh to operate f the return from dong so s negatve. Ths mples: C (3) p > If the generator apples ths rule to determne offers, t wll only be turned on f t meets the same average cost rule, developed n euatons ()-(7). Therefore, f competton prevals, dspatch s lkely n the absence of network constrants, to produce the cost effcent dspatch schedule. Network constrants can cause generators to submt offers n excess of ther cost curves not only n they are affected by the constrant but also by a cascadng effect through the rest of the system [5]. The remander of ths paper wll demonstrate the effect of uas-fxed costs such as start-up costs. 4. The Impact of Quas-Fxed Costs Oren and Elmaghraby [2] suggest that start-up and other such uas-fxed costs can dstort the effcency of dspatch by provdng neffcent generators an ncentve to undercut the offers of more effcent generators and sneak nto the dspatch schedule. The nter-temporal dependences caused by start-up costs provde an ncentve to accept losses or reduced profts n one perod n order to ncrease profts overall. In a smple two perod model, ths mght mply submttng an offer below cost, losng money, n order to avod the greater cost of payng for start-up costs n the next perod. Each and every generator must determne whether t should operate contnually or cycle on and off wth the peaks and troughs n demand. In an ntensely compettve market, the optmal strategy wll be one that leaves the generator at worst ndfferent between the cyclng and contnual operaton. In a repeated game, ths strategy can be determned by use of backward nducton. Ths can be generalzed as follows for a smple two perod game, where perod has low demand and perod 2 has hgh demand: Suppose: A = set of actons avalable to generator, a t A = acton avalable to generator n perod t t =,2 u (A,A j ) = payoff functon to generator, j Lookng forward, each generator wll estmate the set of possble outcomes n the hgh perods and then select the acton n the hgh perod whch wll maxmze the expected payoff n that perod. The pay-off functon to generator can, therefore, be re-characterzed as: (8) u I = u (a,a j,a 2 *,a j2 * ) Where, /00 $0.00 (c) 2000 IEEE 3

4 * a 2 * a j2 = payoff maxmzng acton n perod 2 for. = payoff maxmzng acton n perod 2 for j. Gven ths understandng of the necessary actons n the hgh perod t should be then possble to select the optmal acton n the low demand perod a * and a j *..e. (9) u * = u (a * (a 2 *,a j2 * ),a j * (a 2 *,a j2 * )) Where u * s the optmal payoff to generator ven that generator j adopts ts best strategy whch s smlarly determned. Ths can be shown through a smple two stage proft maxmzaton process, based agan on the hgh-low perod model of demand. Let us assume that the demand for electrcty can be broken nto two perods, low and hgh demand and that ths schedule repeats tself through tme. Let: k = tme perod [=low, 2=hgh] = generator p t = prce receved n perod t by generator t =uantty of electrcty sold be generator n perod t Π t = proft to generator n perod t c = marnal cost of producton for generator = start-up cost for generator S Usng the loc of backward nducton, generator, n perod wll form an expectaton of the payoffs avalable to t n perod 2. If mn c p S p2 2 c 2 (20) Π = [ ] + 2, >0 Maxmzaton of profts n perod 2 s nter-temporally dependent upon decsons made n perod. The frst term s the debt receved from ts operatons n perod. If the generator decded not to enter the aucton n perod one, then the frst term wll collapse to S. Ths wll be the start-up cost ncurred n perod two should the generator decde to enter the aucton. If the generator dd enter the aucton n the low perod but was not dspatched then the term wll also collapse to S. If the generator was dspatched n perod then the frst term wll be eual to the loss ncurred n perod. We assume that the generator would not wsh to enter the aucton n the low perod unless the proft or loss ncurred s less than or eual to the start-up cost ncurred n the next perod due to non-dspatch. Knowng ths, the generator can decde upon ts optmal low load perod strategy. The choce essentally bols down to whether the generator attempts to run n low perods even though t may ncur a loss n that perod (as ths would ncrease aggregate profts over both perods) Usng the above model agan, t s possble to develop a rule of thumb for an optmal strategy. We wll consder two separate stratees. Frstly we examne the optmal strategy of a generator whch s currently operatng. Secondly, we wll consder the strategy of an dle generator. A generator that s currently dspatched should fnd t optmal to reman operatng n low demand perods, f and only f t ncurs a loss less than or eual to that whch would ncurred n start-up costs n the hgh demand perod..e. mn dtc (2) d p S d TC mn Where: = 0 = total cost of generator = mnmum generaton reured to operate If the generator s to be turned on t must produce mn. Ths s the key threshold for the generator. strategy wll dffer for < mn and > mn. For > mn, generaton has been ensured and there s no need to further consder the mpact upon the next perod. Above mn, therefore, offers n a compettve market should revert to smple marnal cost prcng. The above euaton can be smplfed to: (22) TC( mn ) S p mn or (23) AC( mn ) p p =c, > mn, S mn, < mn It s mportant to note that the generator's optmal strategy returns to marnal cost prcng for all unts /00 $0.00 (c) 2000 IEEE 4

5 greater than mn. Once dspatch has been acheved, there should be no further need to ncur losses. Ths can be generalzed to a game of T perods, n whch generators form expectatons as to when the next hgh demand, or proft makng perod, wll occur. Let: T = Expected number of perods untl the next hgh demand perod. Euaton (2) can now be amended to: T T dtc p S d t= 0 = 0 t= 0 Gven the nvarablty of costs between adjacent perods, (24) can be smplfed to: mn (24) d (25) where S p = AC( mn ), < mn T mn p s the average prce. Euaton (25) n tself does not really provde much nformaton. It shows, however, that n mult-perod games, generators who assess there to be a motve to reman dspatched, even n low demand perods, wll need to carefully balance ther offer stratees. One partcular case of (25) allows us to draw up a few rules of thumb. Suppose that n perod t=0, demand s at ts lowest and n order to be dspatched, generator must submt ts lowest possble offer. Euaton (23) provdes that offer. If we substtute that result nto euaton (25) we can derve an nterestng result for all T- perods. (26) AC( mn ) T S + mn t= T (27) p t = AC(T ) t = T p t S AC T Euaton (27) mples that f a mnmum offer s reured n one perod, then the average offer prce for all other perods leadng up to the next hgh demand perod should eual the average cost of runnng mn unts of capacty. For all unts of capacty greater than mn, the same strategy of marnal cost prcng apples. mn Ths establshes an mportant rule. If the expected average prce of electrcty n shoulder perods (.e. other than lowest demand perods) s less than average cost, then the generator should not attempt to reman dspatched n between hgh demand perods. Ths wll avod the worse case scenaro of ncurrng losses for remanng dspatched and also ncurrng start-up costs. The fnal element to consder n the offer strategy of generators s to decde what the approprate offer strategy should be n hgh demand perods. There are two basc scenaros to consder whch have alternatve answers. Frstly, f the generator was able to pursue a schedule of contnuous operaton, the costs of operatng are entrely fxed. Beng sunk costs, they should not enter consderaton for the marnal prcng decson. If, however, the generator has been cyclng on and off between hgh and low load perods, then the start-up cost s not a deadweght cost. It can be avoded by not operatng n the hgh demand perod. In ths case, loc predcts that the generator wll not wsh to be dspatched n the hgh demand perod unless t breaks even. Snce the hgh demand perod, s n essence the proft makng perod, f proft cannot be made n t, t should not operate at all. Ths s demonstrated below for the smple two perod low-hgh demand perod: (29) p TC ) S (30) (3) mn whch mples: p ( mn AC ( mn ) + S mn dc p =, > mn d, < mn Euaton (30) s the reverse of euaton (23). The generator wll de-commt tself unless t can be guaranteed to make a proft. It s possble to generalze (30) further. If A s the number of perods the generator expects to reman operatng, the prcng rule can be determned n the followng way: A A (32) pamn TC a ( mn ) S a= 0 a= 0 Whch can be solved as: /00 $0.00 (c) 2000 IEEE 5

6 (33) p AC ( mn ) + S A Agan, once the generator has ensured dspatch, t can revert to marnal cost prcng on addtonal unts dspatched above mn. Those generators that expect to be on for an ndefnte amount of tme,.e. where A s very large, wll only need to submt offers n excess of average cost. Ths s the same result as one would expect from a generator currently operatng where start-up costs are sunk costs. Only generators that expect to be dspatched perodcally are bound by (33) to offer capacty above cost. Usng backward nducton, the followng conclusons can be drawn. A generator wll not commt tself to operaton n the low perods of demand unless t be sure that t wll be able to break even over the complete cycle of demand. Those generators, therefore, whch do operate n low demand perods should need only to submt offers n hgh demand perods of c (for the capacty up to and ncludng mn ). All other generators wll choose to de-commt themselves n the low demand perods and follow (33) n hgh demand perods. In the real world t s dffcult to separate the effects of start-up costs from the nose from other factors. The Cornell Unversty Laboratory on Economcs and Decson Research (LEEDR) has, conseuently conducted a seres of economc experments usng an Internet based smulaton of an electrcty market, known as PowerWeb [6] to assess how power producers would react to the exstence of start-up costs. mn 5. Ratonale for Experments Davs and Holt dentfy two advantages to laboratory methods [7]. Frstly, the experments and results are replcable and so t s possble to verfy the fndngs ndependently. Most nformaton n the electrcty market s prvate and very propretary, conseuently t s dffcult to gather suffcent nformaton to verfy conclusons. Secondly, laboratory condtons can be set to control for extraneous crcumstances whch would be dffcult to avod and hard to mtgate n the real world. Ths can allow the researcher to elmnate the "nose" and concentrate upon the theory or polcy whch needs to be examned. A cause of concern s the selecton of subjects for the experments and ther smlarty to the real world decson makers. Experments conducted at LEEDR have shown that n these electrcal power experments that a student pool of subjects performed n a smlar manner to traned electrcty ndustry professonals [5]. There s the added ualtatve advantage to usng an "nexperenced" subjects that, should those subjects confrm the valdty of the theory. then t s more than lkely that experenced decson makers wll even more easly make the same decsons. Indeed, the dfference n behavor, n experments to test for market power, between the students and the professonals was the speed wth whch the subjects fgured out that they had the ablty to rase prces above marnal costs. In realty that the laboratory experments smplfy what s a complcated market. Conducted properly, however, they can allow for an assessment of the comparatve statcs of our theory of behavor. 6. The Experments In the research conducted, student subjects were recruted to partcpate n computerzed experments under controlled condtons at LEEDR. Students were pad at the end of the experments, based on ther performance n relaton to the other subjects. Students recruted for ths experment were busness and economcs students at Cornell Unversty. The majorty of students were sophomore through senors who had taken or were currently enrolled n ntermedate mcroeconomcs and/or a senor level class n prce analyss. One addtonal group was recruted from graduate economcs students at Cornell. Few of the students have prevously partcpated n an economc experment and were not allowed to partcpate more than once. Students were told that the experments would last about two hours and were asked to reman untl all the subject experments had been completed. Groups of sx subject generators were used n the experments n order to mnmze any potental for generators to exact market power. Each subject was assgned to one generator, the cost parameters of whch were selected to mmc three typcal level of costs for electrcal power generaton: baseload, md-level and peakng. The cost structure s shown n the tables and /00 $0.00 (c) 2000 IEEE 6

7 Varable Costs Block Block 2 Block 3 Generator MW Cost MW Cost MW Cost Ths was ntended to renforce the rules of the game and ensure that subjects began wth an eual understandng of the aucton process. Table. Generator Varable Costs Generator Type Start-Up Cost Peakng 50 2 Peakng 50 3 Baseload Md-Level 50 5 Md-Level 50 6 Baseload 500 Table 2 Start-Up Costs A vertcal hourly unform prce aucton was employed n whch generators submtted an offer prce for each of ts three blocks of capacty n each tradng perod. Generators dscovered the results of that aucton before submttng offers for the next aucton. Demand n the market was held to be perfectly nelastc. It vared from approxmately 200MW n hgh demand perods to 00MW n low demand perods. (The smulated network was allowed to experence transmsson losses but to an extent whch only marnally affected locatonal prces.) Fgure, whch s shown below, shows the network through whch the generators are lnked to the demand for load. It s a thrty bus system. For the purposes of these experments, the network was unconstraned by transmsson constrants but subject to transmsson losses. Subjects were nformed through an nstructon sheet and a bref presentaton by the experment leader of the rules of the game ncludng the reservaton prce for the experment, the number of other generators and for how many rounds the experment would last. They were nformed that the level of demand alternated between hgh and low demand perods. They were nformed of ther own cost structures but not those of ther compettors and that these costs would not vary durng the experment. Subjects were also not aware of the capactes of ther compettors. Subjects were also ven a bref tutoral to show how start-up costs appled and how to calculate profts ven start-up and varable costs. Fgure. System Dagram Throughout the experment, offers remaned prvate. The fnal prce n each tradng perod was reported to subjects after each aucton perod. Subjects were nformed of how much capacty n each of ther three blocks were sold. Subjects dd not know how much other generators sold. The number of generators meant that t would be mpossble for any one generator to guess whch generators has sold capacty and how much. An aucton was held for each of the tradng perods. The last accepted offer verson of the unform prce aucton was appled for each of the 50 tradng perods. 7. Results Author's Note: At tme of wrtng, the majorty of experments were stll n progress. Ths secton reflects only the results of one group of graduate students. The results from the experments appear to valdate the conclusons of the theory proposed n ths paper. Table 3 shows for each generator the low perod offer strategy derved from the theory outlned above. 2 A copy of the set of nstructons and tutoral used n the experments are avalable upon reuest from the authors /00 $0.00 (c) 2000 IEEE 7

8 Block Block 2 Block 3 Cost Cost Cost Table 3. Optmal s Table 9 shows the comparson between optmal offers and those actually observed n the experments. The actual offer s calculated through a regresson of the followng format: (28) = Constant + β Hgh b b Hgh s a dummy varable that takes the value of one n hgh demand perods and zero n low demand perods. Regressons were conducted on each of the generator blocks, b=,2,3. Of nterest s the constant that should reflect the offer prce for the generator n the low demand perod. Table 9 shows the low demand perod offers for each of the generators =,..,6 for each of the blocks of capacty for whch offers were submtted. Table 4 shows that n general, offers n the low perod were marnal cost and lower. Of most nterest s the competton between generators,2 and 4,5. If generators,2 submt ther frst block at lowest possble offer and generators 4,5 prced ther frst block at marnal cost, then generators,2 could have been dspatched and unt commtment would have produced a cost neffcent outcome. As predcted n the theory outlned above, generators 4,5 were able to antcpate ths and both submtted at the optmal lowest possble offer. The end result was that generators,2 generally cycled on and off between hgh and low perods. The baseload generators could be dsplaced n the low load perods only by an rratonally low bd and so faced few ncentves to submt offers below marnal costs. In these experments the baseload generators tended to offer at marnal cost. Nevertheless, profts were reduced by ths falure to cut offers. Generator 6 n partcular faled to dspatch as much capacty as t should have done. As a note, the experment dd permt the generators to submt negatve offers. Subjects were nformed that any offer less than the reservaton prce was acceptable. The marnal cost curves of each generator were suffcent to guarantee at least break-even at marnal cost should the generator submt the last accepted offer n the hgh perod. In ths scenaro the optmal offer to submt would be marnal cost. Table 5, below, shows a comparson between optmal hgh perod offer and actual observed offers. Observed offers were calculated usng euaton (28). Block Block 2 Block 3 Optmal Optmal Optmal Table 4. Low Demand Perod Comparson Block Block 2 Block 3 Optmal Optmal Optmal Table 5. Hgh Demand Perod Comparson The results from the hgh perod are more mxed than for the low demand perods. Both baseload generators 3,6 offered sgnfcantly above cost on ther second block. Ths can probably be explaned by the fact that they were not the system marnal unts. Those generators who had the potental for possessng the system marnal unt n ther second blocks, generators,2,4,5, offered at marnal cost. As would be expected, where the ncentves to compete exst, behavor follows the predctons of the theory n ths paper. A sde effect of the offer stratees under self commtment s an ncrease n the prce volatlty. Where dscountng n low demand perod offers occurs, the dfferental between prces n the two perods has ncreased. The aucton process appears to be cost effcent. The results from the aucton tradng perods are compared to the outcome f all generators submtted marnal cost offers on ther capacty blocks. Fgure 2 below shows the cost effcency of dspatch over the experments for the experments run. There are 20 data ponts, each representng a par of hgh and low tradng perods. Of nterest are the latter perods, after a perod of /00 $0.00 (c) 2000 IEEE 8

9 expermentaton and acclmatzaton to the market, effcences reach nearly 00%. The vertcal hourly supply curve aucton s able to produce a cost effcent outcome. Generators were successful n nternalzng the mpact of start-up costs upon optmal dspatch. Effcency Tradng Perod Fgure 2. Aucton Effcences 8. Conclusons Theory and expermental evdence show that n the absence of network constrants, a spot market employng the last accepted offer verson of a unform prce aucton can produce a cost effcent dspatch of generators. The role of the ndependent system operator can be reduced to facltator of transactons and supervsor of system securty and relablty. Ths s, of course, a vastly smplfed verson of the real world market. The experments, however, help us to determne the relatonshp between self-commtment and the offer stratees of generators, holdng other factors such as networks and exstence of market power constant. The last accepted offer aucton s a reasonably smple aucton mechansm to admnster and ts robustness to the exstence of start-up costs s reassurng. Further research wll be needed to determne whether other aucton mechansms can mprove upon the effcences shown above. Ths concluson reles on the ablty of generators to realze that the problem at hand s not unt commtment but rather unt de-commtment. If generators are able to establsh accurately whether they ought to be runnng or not then dspatch should be effcent. Start-up costs and the ablty of generators to offer below cost, force generators to assess ths ueston. Gven the nverse relatonshp between varable costs and start-up costs and the optmal stratees outlned n the prevous sectons, those generators wth hgh start-up costs should be able to mantan contnuous dspatch. Those generators wth hgh varable but low start-up costs wll fnd themselves cyclng on and off. Ths produces the same result as the stuaton where a central system operator decdes dspatch based on accurate cost nformaton. LEEDR now plans to extend the scope of the experments to examne the mpact of start-up costs n the presence of network constrants. The results of ths wll be the subject of a future paper. 2. References [] R. Preston and J. McMllan, "Auctons and Bddng", Journal of Economc Lterature, 5, 987, pp [2] W. Elmaghraby and S. Oren, "The Effcency of Mult-Unt Electrcty Auctons", PSERC, 97-5, 997. [2] R.E. Bohn, M.C. Caramans and F.C. Schweppe, "Optmal Prcng n Electrcal Networks Over Space and Tme", Rand Journal of Economcs, 5(3), 984, pp [3] R. Zmmerman, R. Thomas, D. Gan, C. Murllo- Sanchez, "An Internet-Based Platform for Testng Generaton Schedulng Auctons", Proceedngs of the Hawa Internatonal Conference on System Scences, 997. [4] J. Bernard, R. Ether, T. Mount, W. Schulze, R. Zmmerman, D. Gan, C. Murllo Sanchez, R. Thomas, R. Schuler, "Markets for Electrc Power: Expermental Results For Alternatve Aucton Insttutons", Proceedngs of the Hawa Internatonal Conference on System Scences, 998. [5] R Ether, R Zmmerman, J.C. Bernard, R.J. Thomas, W. Schulze, "Energy Auctons and Market Power: An Expermental Examnaton", Proceedngs of the Hawa Internatonal Conference on System Scences, /00 $0.00 (c) 2000 IEEE 9

10 [6] J. Bernard, T. Mount, W. Schulze, R. Zmmerman, R. Thomas, R. Schuler, "Alternatve Aucton Insttutons for Purchasng Electrc Power: An Expermental Examnaton", Bulk Power System Dynamc and Control IV - Restructurng, Santorn, Greece, 998. [7] D.D. Holt and C.A. Holt, Expermental Economcs, Prnceton Unversty Press, 993. [8] W. Vckrey, "Counterspeculaton, Auctons and Compettve Sealed Tenders", Journal of Fnance, 6, 96, pp [9] W. Vckrey, "Auctons, Markets and Optmal Allocaton" n Bddng and Auctonng for Procurement and Allocaton, Ed. Ahmud, New York Unversty Press, 976. [0] C.A. Holt, "Compettve Bddng for Contracts under Alternatve Aucton Procedures", Journal of Poltcal Economy, 88(3), 980. [] P.R. Mlgrom and R.J. Weber, "A Theory of Auctons and Compettve Bddng", Econometrca, 50(5), pp [2] A. Dxt and B. Nalebuff, Thnkng Stratecally: The Compettve Edge n Busness, Poltcs, and Everyday Lfe, Norton, 993. [3] M. Illc, F. Galana, L. Fnk, Power Systems Restructurng: Enneerng and Economcs, Kluwer, 998. [4] R. Wlson, "The Aucton of Shares", Quarterly Journal of Economcs, 93(4), pp , 979. [5] N. von der Fehr and D Harbord, "Spot Market Competton n the UK Electrcty Industry", The Economc Journal, 03, pp , 993. [6] R.H. Patrck and F.A. Wolak, "The Impact of Market Rules and Market Structure on the Prce Determnaton Process n the England and Wales Electrcty Market", POWER Workng Paper, PWP-047, Unversty of Calforna at Berkeley, /00 $0.00 (c) 2000 IEEE 0