Game Theory Application and Strategic Bidding in Electricity Supply Market

Transcription

1 World Journal of Engneerng and Technology, 2016, 4, ISSN Onlne: ISSN Prnt: Game Theory Applcaton and Strategc Bddng n Electrcty Supply Market Zhao Wang, Kwok Lun Lo Electronc and Electrcal Engneerng Department, Unversty of Strathclyde, Glasgow, UK How to cte ths paper: Wang, Z. and Lo, K.L. (2016) Game Theory Applcaton and Strategc Bddng n Electrcty Supply Market. World Journal of Engneerng and Technology, 4, Receved: July 14, 2016 Accepted: October 13, 2016 Publshed: October 20, 2016 Abstract Ths paper ntroduced the applcaton of game theory n electrcty power market. Moreover, the electrcty pool model and the mert order dspatch method was ntroduced. In pool mode, partcpants are tryng to maxmze ther beneft va competton wth each other. Hence the market can be regarded as a non-cooperatve game, especally, the electrcal supply competton. Players (generators) could use strategc bddng to occupy advantages n competton. The bddng strateges of generators n electrcty pool model were researched va buld a 3-generator competton model. Moreover, Nash Equlbrum dea was used to explore generator s optmal bddng strategy. The results show when players are n Nash Equlbrum; thestrategy s ther optmal bddng strategy. Keywords Non-Cooperatve Game Theory, Nash Equlbrum, Electrcty Pool Model 1. Introducton The establshng of electrcty pool come wth the electrcty ndustry deregulaton. Its orgnal am s to reduce electrcty prce to the fnal consumer va ntroducng competton. As competton ntroducng, n a deregulated electrcty power market, partcpants are focusng on ther own beneft. And the compettve envronment enablesmarket partcpants to seek to maxmze proft va prcng ther electrcty strategcally. Ths Paper focuses on the study of generators behavors n electrcty power supply market. An electrcty pool model (EWPP-England and Welsh Power Pool, supply sde only) s smulated to explore the compettve behavor of generators. In pool model, electrcty tradng s centralzed, and use mert order dspatch. Generatng companes make ther bd to Independent system operator (ISO), ISO ranks these bd from lowest prce to hghest prce and arrange the electrcty generaton accordng to the demand DOI: /wjet D010 October 20, 2016

2 sde offer or load forecast. In compettve pool model, generatng companes could use strategc bddng to seek maxmum proft. Game theory as a study of strategc decson makng was ntroduced to analyss the bddng behavors of generatng companes. To explore the bddng behavors of generatng companes n pool model, a 3 generator bddng game s modeled. In ths model, generator companes are regarded as player and these players are n an ncomplete nformaton envronment, n whch each player has full nformaton on tself but lacks other players nformaton. All these players are tryng to maxmze ther beneft. Hence ths game s a non-cooperatve game. Nash Equlbrum has shown excellent performance n the non-cooperatvegame. It wll be used n our model as a crtcal method n analyss optmal bddng problem. 2. Market Type and Game Theory Concepts 2.1. Electrcty Pool Mode Tradng process n an electrcty pool mode s centralzed, whch means generatng plants that partcpatng electrcty pools must make bds, be scheduled and be dspatched centrally. Bds of market partcpants refer to the prce of correspondng generaton volume, and ths prce does not have to reflect ts margnal cost. The aucton n pool mode s a unform aucton. The bddng n our electrcty pool model s supplysde only Strategc Bddng Global socal welfare quantzes the total beneft earned n transactons. It s usually used to measure the performance of the market. Here the global socal welfare s equal to the sum of proft of generator and the net consumer surplus. It reflects the wllngness of socety to pay for the electrcty. A globe welfare could acheve maxmze n a perfect competton market. Whle the real market s usually not a perfectly compettve market, t has a lower effcency than a perfectly compettve market and ts global welfare postonng n a lower level. A perfect electrcty power market has suffcent amount of power supplers and consumers. Therefore all these power supplers are a prce taker. In mcroeconomc theory pont of vew, the optmal bddng strategy for a suppler n a perfect compettve market s to bd at ts short-term margnal cost. Hence, ts producton should be adjusted to ensure ts margnal prce equal to the market prce. At ths tme, all market partcpants are n an equlbrum status. No one could beneft from strategc bddng. Because f the suppler ncreases ts prce, t wll lose ts market share and cannot sell any electrcty; on the contrary, f the suppler reduces ts prce, ts prce s lower than the margnal prce, n ths stuaton, t s not worth to contnue producng. However, strategc bddng enables a suppler to make a proft n an mperfect market. Generally, n an mperfect market, there exsts at least one suppler that has a certan large market share. The behavors of ths suppler to make a proft va strategc bddng are regard as exertons of market power [1]. 73

3 In theory, a perfectly compettve market could maxmze the global socal welfare. Thus t s a desrable market. Although the current market structure and the mecha- nsm are suffcently well desgned, perfectly competton stll can not be realzed.is s because the natural characterstc of electrcty power ndustry. For example, huge nvestment costs lmt the number of supplers, transmsson losses adverse long dstance transmsson and transmsson constrants restrct the path of power flow. These characterstcs enable a few generatng companes could olgopoly n a geographc regon and exert market power [2]. To exert market power enable to maxmze proft, a generator uses optmal bddng strateges. The optmal bddng strateges could acheve n three ways [3]. 1) Estmate the Market Clearng Prce (MCP): It s the most effcency way to make optmal bddng strateges f a generatng company could accurately estmate the MCP. The generatng company just need to set ther bddng prce a slghtly lower than the MCP. Whereas the estmaton of MCP cannot be exactly accurate, because the hstory date s not enough and loads forecast s not relable due to the fast developng of the electrcty ndustry. 2) Estmate other market partcpants bddng behavor. As the bds of market partcpants are prvate and generatng companes are not pad accordng to ther bddng prces, there s rare nformaton avalable to predct other players behavor. Currently avalable methods n ths knd of estmaton are fuzzy logc and probablty analyss. 3) Game Theory methods. Matrx game based method and olgopoly game method. The characterstc of the frst one s that t uses dscrete quanttes as bddng strateges, whle the second one based on some classc models, for example, Cournot model and Stackelberg model Game Theory Applcaton to Bddng Transactons A game can defne as a complete nformaton game (c-game) or ncomplete nformaton game (-game). The power transactons n a pool model s a typcal ncomplete game.every player has full nformaton of ts own payoffs whle t does not have full nformaton of other players [4]. Also, a game also can be regard as perfect nformaton game or mperfect nformaton games. If players have full nformaton of the early stage movement, ths game s a perfect game. Whle n an mperfect game, players do not have full nformaton on the early stage movements. An ncomplete nformaton game could transfer to a completed game wth mperfect nformaton. Nash Equlbrum dea could apply n the transformed game n order to solve the optmal bddng problem. The optmal bd of each play s ther bd n the state of Nash Equlbrum Mathematcal Expresson of Costs and Profts n Power Transactons The expresson of the cost of generator s: 74

4 C = a + bp+ cp (1) 2 The ntal state of partcpant f wth several generators and total load L f before 0 partcpatng transacton s P = L. The margnal cost s dervaton of ncremental cost agan generaton changes: f dc b 2cP dp = + (2) Players (partcpants) make bds as equaton 2 to ISO, ISO arrange the dspatch schedule usng mert order methods. The prce of the mnmum bd matchng load requred s the market spot prce π. The scheduled generaton for partcpant f s, t represented the sum of effcent output of all unts. Here P = P P o f actual the generaton level of generator. The proft of the player f s: P s Ω f = π Pf ( C) (3) To maxmze Ω, let the dervaton of equaton 3 = 0, The player should adjust ts f generaton to make ts margnal cost matches: dc d( Pf ) dp f d d = π = π + P π f = π + P π f (4) dp dp dp dp dp In the perfectly compettve market, the market has suffcent buyers and sellers, and none of these partcpants has an enough large market share. Thus none of them could affect the exstng spot prce. As shown n equaton 4, the optmal bd prce for a player n the perfectly compettve market s to bd at the gven spot prce π va adjustng ts producton to match ts margnal prce equal to π. Whle n an mperfect competton, partcpants could obtan more proft by strategc bddng. Hence the electrcty pool s modeled as anon-cooperatve game that enables ts players purchasng maxmum proft va competton. From Equaton (3), the proft of a player depends on the spot prce, scheduled generaton, and ts cost. Due to the spot prce and scheduled s not under the drect control of players, the drect way to maxmze proft s adjustng ts bds. So the strategy of a player s to adjust c to adjust ts bd, that s, a player s strateges are bd c tmes of ts margnal cost [5]. 3. Three Generators Bddng Game The dea of modelng a 3-generator bddng game s to explore players bddng behavors and optmal strateges n a game wth mult-players. These threegenerators are smulated to compete aganst each other n EWPP. Thedata of these generators selected from ESIS. They belong to top three market share generators. The selected three generators are shown n Table 1, whle Table 2 shows the data each generator, t represents the short-term margnal cost and generaton capacty of every generatng unt. In ths game, game players are these 3generators; ther strateges are the bds they made to ISO. These bds based on the margnal costs of each unt; they can bd m 75

5 Table 1. Market share of 3 selected generators. Table 2. Generatng Unts Short term margnal cost and generaton capacty of each generator. tmes of ts margnal cost. To smplfy ths game, all unts of a generator use a same bd strategy. Hence the bds of each generator are smple bds rather than complex bds. To avod huge matrx, we smplfy the strateges. In our game, let m equal to 1, 1.5, 2 respectvely. That s to say, the strateges set of each player s (1, 1.5, 2) tmes of ts margnal cost. We use [Gen1, Gen2, Gen3] to present players strategy profle. For example, [MC, 76

6 2MC, 1.5MC] represent that the strategy of G1 s bddng at ts margnal cost, the strategy of G2 s bddng at 2 tmes of ts margnal cost and G3 s bddng at 1.5 tmes of ts margnal cost. The payoffs of players are the profts of generators. The calculaton of generators payoff based on the system margnal prce and the electrcty t generated. As we dscussed before, generators make bds to ISO (unform aucton), ISO schedule and arrange dspatch usng mert order method. Ths method ranks generators bds from lowest to hghest and selects the bd matchng electrcty supply and load demand as the margnal product of the system. The prce of ths bd s the system margnal prce (SMP). It s also known as market clearng prce (MCP). In ths game, we assume the load demand s 12,000 MW. Fgure 1 shows the Mert order dspatch n determnng SMP Payoff Matrx Mcrosoft Excel was used n smulatng mert order algorthm, calculate MCP and each player s payoff. Table 3 shows an example of how t works. Table 3 s used to calculate each player s payoff. The strategy profle s [MC, MC, MC], t means every generator are bds at ts margnal cost. Red font color was used to present G1 s unts, blue forg2 and green forg3 s unts. The bd of a unt s equal to the product to ts margnal prce and ts strategy. Then we sort these bds n ascendng Table 3. An Excel example of mert order method n determnng MCP. 77

7 Fgure 1. Mert order despatch n determnng SMP. order and compare the cumulatve avalablty wth the load demand, we could fnd the system margnal product and determne the system margnal prce. Also, all the output of unt plant whose bd lower than SMP wll be scheduled to dspatch. In ths strategy profle, the SMP s 19.9 /MWh. The payoff [Gen1, Gen2, Gen3] s [58.72, 38.52, 21.47]k /h. After fnshng smlar work of all strateges profle lke [MC, MC, MC] n Table 3, we got the payoff matrx of ths game. The payoff matrx shows n Table 4. The payoff matrx n Table 4 s a 3-d matrx Optmal Bddng Strategy and Nash Equlbrum To solve the optmal bddng problem, we ntroduce the concept of Nash equlbrum n our non-cooperatve 3-generator game. Nash equlbrum s an equlbrum state n a game that each player s playng the best response to others. It means that on one could beneft from changng ts own strategy whle the others reman ther strateges unchanged. So the strategy that each player used n Nash Equlbrum s ther optmal strategy. That s to say, n our game, f three generators are n Nash Equlbrum, none of them could gan a hgher proft from changng ts own bd whle the other two generators reman ther bds. GAMBIT 14 s a software to fnd Nash Equlbrum. We buld a three players game n GAMBIT and nput the payoff matrx we got prevously. Then use GAMBIT to fnd the Nash Equlbrum. As Table 5 shows, the column wth yellow background presents the Nash Equlbrum. It reflects the optmal strategy profle s [1MC, 2MC, 1MC], and the payoff for each generator at Nash Equlbrum s [112.19, 40.41, 47.02] k /h respectvely. Ths game s an ncomplete game at the begnnng because each generator only has ts own nformaton but lacks others nformaton. Moreover, ths game s an mperfect 78

8 Table 4. Payoff matrx of dfferent strateges profle ncludng the correspondng SMP. Table 5. Nash Equlbrum n the payoff matrx. game as three generators do not have full nformaton on other player s moves n early stages. However, as tme gong on, from the nteracton of generators, a generator could estmate other players strategy and correspond SMP accordng to hstory data. Fnally, the ncomplete game transform to a complete game wth mperfect nformaton. And we could use Nash Equlbrum to determne optmal bddng strategy. In our model, the optmal bddng strategy for each generator s bddng at 1 MC, 2 MC, 1 MC respectvely. As generator 3 s the smallest generator, n most tme, t s a prce taker, whch should better not bd hgh. G1 and G2 have a smlar market share. One bd hgh wll lose dspatch and ncrease the other s proft. As G2 s proft caused by hgh SMP exceed the loss due to ncreasng bd, G2 could bd hgh. At the same tme, G1 and G3 could beneft from G2 s hgh bddng. The market n our model s an example of mperfectly compettve market that shows a market partcpant wth a large per- 79

9 centage market share could affect the market prce to exert market power. If the market s compettve, more generators wth smlar market share could partcpate n the competton, and there wll be more choce for ISO. As a result, f one partcular market partcpant ncreases ts bd, ISO could select another generator. Hence, n a compettve market, bd hgh s unwse, and the competton wll push down the prces and ncrease partcpants effcency. Our model bases on the competton on bddng prces and the bd are smple. Whle n real competton n EWPP, generators not only compete on prces but also compete on outputet al. Also, n areal envronment, bds are complex bds. Moreover, generators submt complex unts for every unt. These bds reflect the unt s technque parameters, output level for nstance, and cost characterstc, such as margnal cost, start-up cost, no load cost. 4. Conclusons The behavor of partcpants n electrcty power market s modeled as anoncooperatve game because, n the market, each partcpant s competng aganst each other to maxmze ts own proft. When a generator has a larger market share, ts bddng could affect the market prce. Ths bddng behavor defnes as an exercse of market power. Though the market desgners are tryng to realze perfect competton n the electrcal market, and no matter how they mprove the market mechansm, sometmes market partcpants could exert market power. It s determned by the nherent characterstc of electrcty power market that some generator s nevtable to monopoly n a geographcal regon. It s the weakness of pool market. Generators could take advantages of the weakness to ncrease proft va lmtng supply and bddng as hgh as possble. To mtgate market power, some strateges have been used, such as ncrease addtonal capacty and back-up, establsh nformaton dssemnaton mechansm, allowng nsttutons wth small generators enter the market [6]. In addton, to deal wth congeston, transmsson lne should be managed to expand. In some partcular condton, set a temporary prce cap s necessary. In a word, no matter what methods used to mtgate market power, the basc dea s to guarantee adequate supply. Moreover, we modeled a 3-generator bddng game to smulate the competton n EWPP. In ths game, these generators compete aganst each other to maxmze ts own proft. Hence t s a non-cooperatve game. Mert order method s used to schedule generaton dspatch. Large generators could affect the SMP va dfferent bddng strateges. If two generators have smlar market share, one bd hgh wll lose generaton whle the other would be scheduled to generate more. If the proft from the ncreased SMP could not compensate the loss from beng less dspatched, the best choce for the generator s not to make a hgher bd. Whle n a real market wth many generators, ISO have more choce, a partcular generator s hgh bd could not sgnfcantly ncrease the SMP, hence the generator tends to bd low. In our model, Nash Equlbrum s used to solve the optmal bddng problem. Be- 80

10 cause n Nash Equlbrum, every player s playng ther best response to the others, hence no one could beneft from ts own strategy whle others reman ther strategy unchanged. So the Nash Equlbrum strategy s the optmal bddng strategy. However, n real electrcty power market, the optmal long-term strategy does not exst. The man reason support ths dea s that the real electrcty market s expandng very quckly, and the avalable nformaton s lmted, the orgnal ncomplete nformaton game could not transfer to a completed game wth mperfectly nformaton and Nash Equlbrum could not apply. Thus t can be seen how mportant of the nformaton system, t allows all generators n a fully compettve market have the opportunty to analyss ther opponents strategy and adjust ther own strategy accordngly. Acknowledgements I would lke to express my sncerely grattude to my supervsor Professor K.L. Lo, Head of Power System Research Group, Insttute of Energy and Envronment of the Unversty of Strathclyde, for hs valuable gudance and great help throughout my entre work. Thanks are also expressed to my colleagues, especally Xnwen N and Zhongle Shao, of Power System Research Group at Unversty of Strathclyde for the nterestng dscussons that doubtless enrched methods worked n ths paper. References [1] Gross, G., Fnlay, D.J. and Deltas, G. (1999) Strategc Bddng n Electrcty Generaton Supply Markets. IEEE Power Engneerng Socety 1999 Wnter Meetng, [2] Newbery, D. and Green, R. (1992) Market Power and Power Market. Journal of Poltcal Economcs. [3] Melczarsk, W., Mchalk, G. and Wdjaja, M. (1999) Bddng Strateges n Electrcty Markets. Proceedngs of the 21st 1999 IEEE Internatonal Conference on Power Industry Computer Applcatons, PICA, [4] Ferrero, R.W., Rvera, J.F. and Shahdehpour, A. (1998) Applcaton of Games wth Incomplete Informaton for Prce Electrcty n Deregulated Power Pools. IEEE Trabs. on Power Systems, 13. [5] Ferrero, R.W., Shahdehpour, S.M. and Ramesh, V.C. Transactons Analyss n Deregulated Power Systems Usng Game Theory. IEEE Trans. on Power Systems. [6] Sparrow, F.T., Yu, Z. and Lusan, D. (1999) Market Gamng and Market Power Mtgaton Strateges. Proceedngs of the 1999 IEEE PES Wnter Meetng, New York. 81

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