Application of Designing Economic Mechanisms to Power Market - Part 1 Generation Side Power Market Design

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1 TEKOMNIKA, Vol. 11, No. 4, Aprl 01, pp. 1961~1966 ISSN: Applcaton of Desgnng Economc Mechansms to Power Market - Part 1 Generaton Sde Power Market Desgn XIE Qngyang 1, ZHU Yonggang 1,, YING mng 1 1 School of Electrcal Engneerng, Wuhan Unversty, Wuhan 4007, Chna Hube Electrcal Power Company, Wuhan 40077, Hube Provnce, Chna Correspondng author, e-mal: MYng@whu.edu.cn Abstract The paper studes on the core phlosophy and algorthm of the desgnng economc mechansms theory, a new algorthm of desgnng ncentve compatble power market mechansms s proposed, a generaton sde power market mechansm model whch has features of nventve compatblty, nformatonally effcent and decentralzed decson s constructed. The power market based on the desgnng economc mechansms theory can lead to the Pareto Optmalty of the resource allocaton; meanwhle GENCOs are permtted to pursue profts maxmzaton. The paper s n two parts. Part 1 focuses on the process of constructng a generaton sde power market compettve mechansm model based on the desgnng economc mechansms theory. Part presents the characterstc analyss of the generaton sde power market compettve mechansm. Keywords: power market, desgnng economc mechansms, reflexve rectangle method, flagpoles method Copyrght 01 Unverstas Ahmad Dahlan. All rghts reserved. 1. Introducton The mechansm desgn of power market s the key ssue about the successful mplementaton of power market and the market effcency [1]. Thus, researchers always pay a close attenton to how to desgn a power market mechansm wth an effcent allocaton of resources. In recent decades, the asymmetrc nformaton game theory, the socal selecton theory and the mechansm desgn theory are appled wdely n economcs, socety and engneerng feld such as the electronc commerce, the aucton, the prcng of publc goods and the deregulaton of utltes [-9]. So, researchers begn to apply those theores to desgnng power market mechansms and realze that ncentve compatble mechansms are able to restran strategc game behavors of GENCOs (Generaton Companes) n essentally [10]. The desgnng economc mechansms theory used n ths paper s dfferent from other mechansm desgn theores, whch s able to acheve ncentve compatblty and nformatonally effcent smultaneously. By applyng the vew of the nformaton economcs, the desgnng economc mechansms theory researches on how to desgn a mechansm whch meets expectatons of desgners n a system condton as the same as a power market wth the freedom of choce, the voluntary exchange and the asymmetrc nformaton.. The Basc Theory and Algorthm of Desgnng Economc Mechansms The desgnng economc mechansms theory whch s presented by Professor eond Hurwcz who won the 007 Nobel Prze n economcs and Professor Stanley Reter researches on how to desgn an ncentve compatble, nformatonally effcent and decentralzed mechansm [11, 1]. The desgnng economc mechansms theory defnes that a mechansm conssts of three parts: M m a message space, gm (, ) the equlbrum relatons and hm ( ) the outcome functon that translates equlbrum relatons nto the mechansm outcome. A mechansm models communcaton through messages, verfcaton scenaro by agents, and the outcomes assocated wth equlbrum messages. It can be wrtten as ( M, g, h) (1) Receved December 8, 01; Revsed February 17, 01; Accepted March 1, 01

2 196 ISSN: The entre algorthm of the desgnng economc mechansms can be dvded nto three stages: dervng the goal functon, constructng the coverngs of agents equlbrum message and generatng the agents equlbrum message functons and outcome functons. The reflexve rectangles method and the flagpoles method are man algorthms n the process of desgnng. (1) Reflexve Rectangles Method An agent s n equlbrum f and only f hs equlbrum message functon g ( m, ) 0. The coverngs C v of agents equlbrum message functons are the set of ponts that makes every agent s g ( m, ) 0 n the parameter space. The reflexve rectangles method s an mportant approach to constructng coverngs C v of agents equlbrum message functon g ( m, ). Professor Hurwcz and hs colleagues have proved that coverngs C v structured through the reflexve rectangles method are parttons and dsjont [1, 14], the mechansm s able to meet nformatonally effcent s requrement because of ts low amount of nformaton. The coverngs correspondence s wrtten as V ( ), ts doman s the parameter space and ts range s the Cartesan product of. The correspondence V ( ) s gven by V( ) G(, ) 0 () In Equaton (), V ( ) s a self-belongng correspondence, t corresponds to a gven factorzaton of the parameter space, whch reflects the ntal dsperson of nformaton among the agents [11]. Also, V ( ) s compatble wth the goal functon n that all elements of V ( ) are n the same goal functon s contour set. () Flagpoles Method The functon H ( ) 0 s defned as a flagpole. When coverngs C v of the parameter space are parttons and the Jacoban matrx J whch s made up of the partal dervatve of each agent s equlbrum message functon G / and flagpoles functons partal dervatve H / s nonsngular, the flagpoles are called the system of dstnct representatves (SDR). Then, the outcome functon hm ( ) s to be generated from the SDR [15], and the entre desgnng process wll be accomplshed n the end. G1 / 1 G1 / G / 1 G / J H1 / 1 H1 / H / 1 H / (). The Compettve Mechansm Desgnng of Generaton Sde Power Market based on the Desgnng Economc Mechansms Theory The followng uses the compettve mechansm desgn of generaton sde power market as an example to descrbe how to desgn an ncentve compatble, nformatonally effcent and decentralzed power market by the desgnng economc mechansms theory..1. The Dervaton of Goal Functon In the generaton sde power market, we assume that each GENCO s equvalent to a generator unt. Accordng to the unt s equvalent generaton cost wth quadratc functon: C ( P) P P (4) TEKOMNIKA Vol. 11, No. 4, Aprl 01 :

3 TEKOMNIKA ISSN: where P s the output of GENCO, C( P ) s the generaton cost under the output,,, are GENCO economc parameters related to the generaton cost. A compettve generaton sde power market model wth three GENCOs s to be establshed. For focusng on desgnng power market mechansm, the power system model s to be smplfed by gnorng transmsson losses, flows of power and some detaled techncal parameters. GENCO margnal cost MC s gven by dc MC P (5) dp We assume that the total output of three GENCOs s greater than the next perod loads P. The constrant (6) must be kept for the balance between outputs and the load. P1P P P (6) Accordng to the prncple of proft maxmzaton n economcs, the GENCO s n equlbrum and gets the maxmum profts when ts margnal cost MC s equal to margnal revenue MR. At the same tme, the resource allocaton of power market s Pareto Optmalty and the socal beneft acheves the maxmzaton. From the vew of the desgnng economc mechansm theory, nputs and outputs of the mechansm should be known. The next perod requrement of load P and the generaton cost functon s parameters,, of GENCO belong to nputs. Assumng that the settlement mode s the unform clearng prce, we regard GENCO s power P whch wns the bddng and the unform clearng prce of market p as outputs. Those nformaton parameters decde the feasble confguraton set, the avalable exchange set and the Pareto Optmalty s exchange set of the whole generaton sde power market. Consderng the equlbrum condton of MR MC, GENCO s output P s gven by P ( p )/( ) (7) Then, the Equaton (8) s to be derved by the market clearng condton (6) and the market equlbrum condton (7). P p 1,, (8) Defne 1 a1, 1 a, b1, b, c1, c, solvng the Equaton (8) leads to bc a c a b bc Pbc P1 ab ac bc (9) ac ab ac bc Pac P ab ac bc (10) ab 1 ab 1ac 1 bc 1 Pab 1 1 P ab ac bc (11) p abc abc abc Pabc ab ac bc (1) Applcaton of Desgnng Economc Mechansms to Power Market (Xe Qngyang)

4 1964 ISSN: In parameter space, we defne that the goal functon F( ) s GENCO 1 output P 1, and hence, the goal functon gven to the desgner s bc a c a b bc Pbc F( ) ab ac bc (1) In the Equaton (1), ( abc,, ), a ( a1, a), b ( b1, b), c ( c1, c)... The Constructon of Equlbrum Messages Coverngs The coverngs C v of the parameter space are constructed by the reflexve rectangles method. The equlbrum relaton of GENCO 1 s defned by G (, a) F(, a) F( ) 0 (14) 1 We obtan the GENCO 1 equlbrum functon (15) by solvng the Equaton (14). G (, a) a F a p 0 (15) 1 1 bc a c a b bc Pbc F ab ac bc where,, abc abc abc Pabc p ab ac bc Solvng the Equaton (15) for a and accordng to the reflexve rectangles method, the equlbrum functon of GENCO s gven by G (, b) b ( P F R) b p 0 (16) 1 Smlarly, the equlbrum functon of GENCO s gven by G (, c) c Rc p 0 (17) 1 R ( pc where, ) c1. Now, accordng to the reflexve rectangles method, coverngs C v of GENCO s equlbrum messages n the parameter space ( abc,, ) have been constructed completely. G1 (, a) 0 Cv G (, b) 0 G (, c) 0 (18).. Generatng Equlbrum Message Functons and Outcome Functons For usng the flagpoles method, we assume a 1 b 1 c 1 1, flagpole functons are defned by H1 a1 1 0, H b1 1 0 and H c The Jacoban matrx J lke the Equaton () can be dervng from the equaton set of coverngs (18) and flagpole functons. J F P F R R (19) TEKOMNIKA Vol. 11, No. 4, Aprl 01 :

5 TEKOMNIKA ISSN: The Jacoban matrx (19) s nonsngular, whch means the flagpoles decded by the soluton of the equaton set (18) and flagpole functons exst n the parameter space ( abc,, ). Substtutng a b c nto the equaton set (18) leads to: a p F (0) b pp F R (1) c pr () Defne the message space M as a pont set ( a1, a, b1, b, c1, c) whch belongs to flagpoles n parameter space ( abc,, ). The basc elements of message space M are m ( m1, m, m), where m1 a, m b, m c. Substtutng m ( m1, m, m) nto the Equaton (0), (1) and (), we obtan m1 m m P F () m1m m P R (4) m1m m P p (5) GENCO s equlbrum message functon g ( m, ) s obtaned from substtutng the Equaton (), (4) and (5) nto the Equaton (18). g ( m, a) a ( m m m P ) a ( m m m P ) (6) g ( m, b) b ( m m m P ) b ( m m m P ) (7) g ( m, c) c ( m m m P ) c ( m m m P ) (8) Outcome functons h ( m ) of the generaton sde power market are gven by flagpoles n parameter space. m1m m P h1 ( m) F (9) h ( m) m1m m P R (0) m1m m P h ( ) m p (1) 1 ( ) h m, ( ) h m and ( ) h m correspond to 1 P the output of GENCO 1, P the output of GENCO and p the unform clearng prce. The output of GENCO s to be solved by Applcaton of Desgnng Economc Mechansms to Power Market (Xe Qngyang)

6 1966 ISSN: P P P1 P () Gven by the Equaton (), the fnal mechansm s made up of message space M, equlbrum message functons g ( m, ) and outcome functons hm ( ). [ M, g ( m, ), h( m)] () Now, we have constructed the compettve generaton sde power market mechansm whch follows the prncple of proft maxmzaton. Meanwhle, the mechansm wth ncentve compatblty and nforamtonally effcent s able to acheve the maxmum socal beneft. 4. Concluson The paper studes on the desgnng economc mechansms theory s core algorthms such as the reflexve rectangles method and the flagpoles method are also researched. A new approach based on the desgnng economc mechansms theory to desgnng an ncentve compatble power market mechansm s proposed. The paper constructs the compettve mechansm model of generaton sde power market by usng the reflexve rectangles method and the flagpoles method. The power market desgned by the desgnng economc mechansms theory has key features of the ncentve compatblty, the nformatonally effcent and the decentralzed decson. Thus, t s able to realze the Pareto Optmalty and the socal beneft acheves the maxmzaton when GENCOs also acheve proft maxmzaton. References [1] Chen HY, Wang X, Wang XF. Aucton Theory and Its Applcaton n Electrcty Market Part One Aucton Desgn and Its Expermental Research. Automaton of Electrc Power System. 00; 7(): 17-. [] Yu FP, Zhang SD, Zhou X. Incentve Mechansm Algorthm for PP Fle System n Campus Networks. Telkomnka. 01; 10(6): [] Sen S, Roy P, Chakrabart A. Generator Contrbuton Based Congeston Management Usng Multobjectve Genetc Algorthm. Telkomnka. 011; 9(1): 1-8. [4] Narahar Y, Nkesh KS. A Bayesan Incentve Compatble Mechansm for Decentralzed Supply Chan Formaton. The 9th IEEE Internatonal Conference on E-Commerce [5] Altman A, Tennenholtz M. Quantfyng Incentve Compatblty of Rankng Systems. The Twenty-Frst Natonal Conference on Artfcal Intellgence. 006: [6] Chandrashekar TS, Narahar Y, Rosa CH, Kulkarn D, Tew JD, Dayama P. Aucton Based Mechansms for Electronc Procurement. 006; 4(): [7] Garg D, Narahar Y. Desgn of Incentve Compatble Mechansms for Stackelberg Problems. Network and Internet Economcs. Sprnger. 005: [8] Gautam R, Hemachandra N, Narahar Y, Hastagr P. Optmal Auctons for Multunt Procurement Wth Volume Dscount Bdders. IEEE Conference on Electronc Commerce. 007: 1 8. [9] Mlgrom P. Puttng Aucton Theory to Work. New York: Cambrdge Unversty Press [10] Slva C, Wollenberg BF, Zhang CZ. Applcaton of mechansm desgn to electrc power markets. IEEE Trans on Power Systems. 001; 16(1): 1-8. [11] Hurwcz, Reter S. Desgnng Economc Mechansms. Cambrdge: Cambrdge Unversty Press [1] Tan GQ. Economc Mechansm Theory: Informaton Effcency and Incentve Mechansm Desgn. Chna Economcs Quarterly. 00; (): [1] Hurwcz. Optmalty and Informatonal Effcency n Resource Allocaton Processes. In: Arrow KJ, Karln S and Suppes P, Edtors. Mathematcal Methods n the Socal Scences. Stanford: Stanford Unversty Press; [14] Hurwcz. The Desgn of Mechansms for Resource Allocaton. The Amercan Economc Revew. 197; 6(): 1-0. [15] Hurwcz. Mechansm Desgn wthout Games. In: Sertel MR, Koray S, Edtors. Advances n Economc Desgn. Berln: Sprnger-Verlag; 00: TEKOMNIKA Vol. 11, No. 4, Aprl 01 :