Competitive Generation Expansion Planning Using Imperialist Competitive Algorithm. *Corresponding author

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1 Compettve Generaton Expanson Plannng Usng Imperalst Compettve Algorthm HEDAYATFAR, B. 1 *, BARJANEH, A. 2 1 Electronc Engneerng Department, Islamc Azad Unversty, Saveh Branch, Saveh, Iran 2 Electronc Engneerng Department, Islamc Azad Unversty, Saveh Branch, Saveh, Iran *Correspondng author e-mal: Behrad.Hedayatfar@Gmal.Com Abstract: Deregulaton n the electrcty ndustry leads to new challenges n Generaton Expanson Plannng (GEP), due to the competton among the Generaton Companes (GENCOs) and opposng objectves of GENCOs and polcy makers. Ths paper presents the GEP problem n compettve envronment and apples the Imperalst Compettve Algorthm (ICA) to solve ths problem. The objectve of each GENCO s maxmzaton of ts proft whle the regulatory body s concerned wth market and system stablzaton trough provdng the approprate sgnals to nvestors to avod the over/under nvestment. Other objectves of the regulatory body are optmzaton of generaton capacty, mantanng system and natonal securty and maxmzaton of the socal welfare. In order to model the competton between the GENCOs and opposng objectves n ths problem, the GEP problem s modeled as a Cournot game wth Nash equlbrum. The GEP problem s solved teratvely by self-optmzng of each GENCO usng ICA and satsfyng the regulatory body n Cournot model. The proposed algorthm s tested on a smple case and the results are compared wth those drawn n prevous works. The obtaned results demonstrate the effectveness of the proposed ICA-based method. [HEDAYATFAR, B., BARJANEH, A. Compettve Generaton Expanson plannng Usng Imperalst Compettve Algorthm. LIFE SCI J 2013;10(8S): ] (ISSN: ).. 48 Keywords: Cournot games, Generaton Expanson Plannng (GEP), Imperalst Compettve Algorthm (ICA) 1. Introducton The fundamental dfferences between the today s power systems and those before the era of restructurng are mostly due to the soco-economcal aspects rather than techncal ssues. The fast changes n fnancal structure of power systems have led to wde varatons n techncal structure and varous progresses n these systems. One of the man dfferences s that tradtonally, n least cost Generaton Expanson Plannng (GEP) the problem was to dentfy the optmal tmng, locaton, sze and technology of new generaton whch mnmze the total constructon cost of the new unts and satsfy the load balance and securty constrants [1-2]. However, competton among the Generatng Companes (GENCOs) s the man goal of deregulaton and wth the ntroducton of competton several changes have been taken place n the electrc power ndustry [3-4]. In a compettve power system, expanson partcpants are proft maxmzng companes. New technologes n power generaton and nformaton technology also affect the GEP problem. Opposng crtera of market partcpants and regulatory body and conflcts among GENCOs are the man dfferences that make the compettve GEP a more complex problem to solve comparng to the classc GEP problem. It s dffcult to formulate these changed GEP envronments ncludng GENCOs and the regulatory body n a mathematcal form and solve the problem usng conventonal optmzaton technque [5-6]. GENCOs submt ther constructon offers to Independent System Operator (ISO) based on ther predcton of the future load share and dfferent sgnals such as prce predcted by ISO. ISO s concerned wth optmal generaton capacty (to prevent over/under capacty nvestments n the market), system securty, relablty and approprate fuel mx (there are always some regulatons on the total capacty of each fuel type. Here a Coumot model [7] s consdered n order to formulate the compettve GEP problem and gamng among ISO and GENCOs, the objectve of whch s to reach to the Nash equlbrum n an teratve framework n case of exstence of such equlbrum. Nash equlbrum s a set of players decsons n the game such that no player can obtan hgher proft by modfyng ts strategy n the case that other players stck to ther equlbrum strateges. Such equlbrum s hard to predct due the nature of the power markets wth so many partcpants each wth opposng crtera wth the others and ISO and also strateges that are hard to predct. The market may also have no equlbrum pont, due to nteger varables of GEP problem. It should be also noted that markets are dynamc and n constant moton. However, the decsons may reman near the equlbrum pont n the long run. In order to mantan 307

2 a confdent level of securty mantanng a proper level of capacty reserve s necessary. System relablty s enforced n ths paper va consderng Loss of Load Expectaton (LOLE) constrant. In order to avod over and under capacty nvestment ISO decreases and ncreases the future prce va a proper functon suted based on the market structure and prevous experences. In order to avod the low values of LOLE (lower than a fxed value enforced by socal-economcal characterstcs of the power system and market) a constrant s consdered n selfoptmzaton of each GENCO. In ths paper each GENCO optmze ts strategy at each teraton usng Imperalst Compettve Algorthm (ICA) whch s an evolutonary computatonal method that has been used to solve dfferent optmzaton problems. Lke most of the heurstc methods, ICA does not need the gradent of the functon n ts optmzaton process and therefore, s sutable to solve the problem whch the objectve functon s not convex and dfferentable. ICA s a computer smulaton method conceptualzed from the humans socal evoluton. The am of each GENCO s maxmzaton of ts proft whle the ISO s concerned wth market and system stablzaton trough provdng the approprate sgnals to nvestors to avod the over/under nvestment and to mprove system securty. Other goals of the ISO are optmzaton of generaton capacty, mantanng system and natonal securty and maxmzaton of the socal welfare. In self-optmzaton of each GENCO, some constrants whch are mposed by the regulatory body should also be consdered. In the case of volaton of such constrant an approprate penalty s added to the value of the objectve functon to avod such soluton. The contrbutons of ths paper are lsted below: Employment of ICA optmzaton tool for solvng the complex problem of market-based GEP. Incluson of relablty n prce sgnal to nvestors to mprove the system securty. Modelng of the market-based GEP problem as a Cournot game wth Nash equlbrum. The rest of ths paper s organzed as follows. ICA algorthm s presented n secton II and proper references are gven. Secton III dscusses the proposed compettve GEP algorthm. The results of applcaton of proposed GEP algorthm on a smple case s presented and dscussed n detal n secton IV. The concludng remarks are drawn n Secton V. I. Imperalst Compettve Algorthm Evolutonary optmzaton methods, nspred by natural processes, have shown good performance n solvng complex optmzaton problems. All of these methods are smlar n on aspect that the move from one soluton to another s done usng rules based upon human reasonng, so the called ntellgent. Heurstc algorthms may search for a soluton only nsde a subspace of the total search regon. They are not lmted by the search space characterstcs lke exstence of dervatve of the objectve functon and contnuty. Several heurstc methods can be addressed such as: partcle swarm optmzaton, smulated annealng, Tabu search and genetc algorthms; each one wth some advantages and dsadvantages n dfferent areas of the problems. These algorthms are generally nspred by modelng the natural processes and other aspects of speces evoluton, especally human evoluton. But Imperalst Compettve Algorthm has been conceptualzed from soco-poltcal evoluton of human as a source of nspraton for developng a strong optmzaton strategy. ICA s a relatvely new evolutonary optmzaton algorthm. Imperalsm s the polcy of extendng the control of an mperalst beyond ts boundares. It may try to domnate other countres by drect rule or va controllng of markets for goods. ICA s a novel global search heurstc that uses mperalstc competton process as a source of nspraton [8]. Ths algorthm starts wth an ntal populaton (a number of randomly produced solutons). Each soluton n the populaton s called country. Consderng the value of objectve functon as the measure, some of the best countres n the populaton selected to be the mperalsts and the rest form the colones of these mperalsts. In ths algorthm the more powerful mperalst, have more colones. As the competton starts, mperalsts try to acheve more colones and the colones start to move toward ther mperalsts. So durng the competton the powerful mperalsts wll be mproved and the weak ones wll be collapsed. At the end of algorthm just one mperalst wll reman. In ths stage the poston of mperalst and ts colones wll be the same. The algorthm steps are summarzed as follows. More detals about ths algorthm can be found n [9-14]. 1.Generatng Intal Empres: The goal of optmzaton s to fnd an optmal soluton n terms of the varables of the problem. An array of optmzaton varable values s called country. The cost of a country s found by evaluatng the objectve functon for ths country. To start the optmzaton algorthm we generate the ntal populaton of sze N country. N mp of the most powerful countres are selected to form the empres. Other countres wll be the colones each of whch belongs to an empre. 2.Movng the Colones of an Empre toward the Imperalst: Imperalst countres start to mprove ther colones. Ths has been modeled by movng all 308

3 the colones n ths empre toward the mperalst. It means that a new country wll be generated based on the poston of each country n the empre and the dstance of ths country and mperalst. 3.Fndng the Total Power of an Empre: The total power of an empre s mostly affected by the power of ts mperalst. However, the power of ts colones of an empre has an effect, on the total power of empre. The mean value of the cost functon of other countres n the empre wll be added to the value of objectve functon for the mperalstc wth a small coeffcent to form the power of each empre. 4.Imperalstc Competton: each empre tres to take the control and ownershp of colones of other empres. Ths competton brngs about a decrease n the power of weaker empres and an ncrease n the power of more powerful ones slowly. The competton s modeled by choosng a number of weakest colones of the weakest empres and allow for the empres to compete for acqurng the chosen colones. 5.After a number of teratons only the most powerful empre wll reman and all the countres wll be controlled by ths mperalst whch s the optmum soluton of the problem. The ICA has been successfully appled to solve several problems [15-16]. The results of these studes demonstrate the effectveness of ICA over other heurstc methods. II. Generaton Expanson Plannng Formulaton n Compettve Envronment Tradtonally the objectve of the generaton expanson plannng ams at buldng an nvestment schedule that satsfes the demand and that mnmzes the present value of operaton and nvestment costs [17]. However, the nvestment decson process changed wth the development of competton n the power systems snce nvestment on new generaton capacty has become a commercal and rsky actvty. Ths s manly because nvestors are more nterested n short-term nvestment return and are less nterested n nvestng on generaton capacty that requres large captal nvestment and long recovery perods [18]. The generaton expanson plannng problem n compettve electrcty market envronment ncludes the nvestment decson-makng of ndvdual GENCOs whose objectves are the maxmzaton of ther own profts. In a fully compettve market, the decson-makng of each GENCO on capacty nvestment s hghly nfluenced by ts load-demand forecastng, market share, busness strateges. In compettve electrcty market all GENCOs should make decsons on ther future capacty nvestments wthout exchangng nformaton wth other GENCOs. However, n order to preserve natonal energy fuel mx strateges and avod over/under capacty nvestments n the market, there can be some regulatons on the total nvestments [19]. Generaton expanson plannng n compettve envronment s also nfluenced by load uncertantes, restructurng polcy and market management nstructons. On the other hand, nvestors should take nto account the possble behavour of the other compettors gven the nteractons exstng n ths decentralzed decson makng process. The formulaton of such a complcated decson makng process should pay attenton to a number of ssues such as the change n demand, market prces, varatons of regulatory polces and changes of fnancal and economc data [18]. The generaton expanson problem n a compettve envronment nvolves the maxmzaton of the profts of each ndvdual GENCO. Therefore the objectve functon s as the followng. A. Objectve Functon In ths paper the generaton expanson plannng problem for th GENCO n a compettve envronment s formulated. The objectve functon of the optmzaton problem s as follows: max Proft (Pr C ) P (1) Where, Proft s the proft of the th GENCO that s amed to be maxmzed. Pr s the prce of one MW electrc power at the plannng horzon; C s the total cost of generaton of one MW electrc power for the th GENCO. Fnally P s the quantty of power generated by the th GENCO. The prce of electrc power (Pr) s defned as follows: N Gen Pr const P (2) 1 Where, Const s the constant value determned by the ISO or regulaton authortes. α s the demand coeffcent and N Gen s the number of GENCOs n the market who wants to partcpate n generaton expanson plannng problem. B. Constrants There are several constrants for ths problem that make t more complcated and make t harder to fnd the soluton. However n order for result to be applcable these constrants should be consdered n the optmzaton problem. The constrants consdered n ths paper nclude relablty, total capacty n each stage, nstallaton ablty and generaton mx. The numercal constrants nclude state constrants and path constrants. The soluton should satsfy all these constrants. 309

4 Reserve Margn The selected unts to be nstalled n the power system based on the best soluton along wth the exstng unts must satsfy the mnmum and maxmum reserve margn. N Gen 1 N Gen 1 P P (1 Res ) 0 P P (1 Res ) 0 Mn (3) Where, P 0 s the total power produced by the exstng generators n MW at the exstng year (year zero). Res Mn and Res are s the mnmum and maxmum reserve rate crteron, respectvely that are consdered 20% and 40%. Relablty Relablty s a state lmt whch s the most complcated one of the numercal constrants. The relablty ndex appled n ths paper s Loss of Load Expectaton that s called LOLE. For an acceptable soluton obtaned by the proposed method, ts retreved system LOLE should be smaller than a specfed and pre-defned value. Ths constrant can be formulated as the followng: LOLP (4) Where, s the pre-defned value that s consdered to be n ths paper. Upper Constructon Lmt Generally based on ISO polces each GENCO has a maxmum generaton lmt. Each ndvdual GENCO should generate power less than or equal to ts maxmum generaton constrant and t s expressed by (5). P P (5) Where, P s the maxmum generaton constrant of th GENCO. Fuel Mx Rato Constrant There are dfferent types of generatng unts such as Coal, Lquefed Natural Gas (LNG), Ol, and Nuclear n the generaton expanson plannng problem. To provde natonal securty, ISO mposes some mnmum rate fxed for each fuel type. P FMR Mn 1,2,..., N (6) Gen P Where, FMR Mn s the mnmum fuel mx rato of th type of generatng unts. III. Smulaton Results and Dscussons In ths secton we present the test system and the results obtaned from the proposed method. The proposed algorthm based on ICA for the generaton expanson plannng problem was mplemented usng MATLAB R2011a. A. Test System The data s adopted and modfed from [20]. The generaton system ncludes a mx of several technologes and n the expanson process ntal stage the system maxmum load s 4500 MW. The LOLE and the reserve margn for the nstalled system are also known. Table 1. Techncal and Economc Data of Exstng Plants Name Fuel Type No. of Unts Unt Capacty (MW) F.O.R. (%) Operatng Cost ($/MWh) Fxed O&M Cost ($/KW- Month) Ol # Ol # Ol # LNG G/T # LNG C/C # LNG C/C # LNG C/C # Coal # Coal # Coal # Nuclear #1 1 1, Nuclear #2 1 1, The data of the exstng plants nstalled n the network are presented n Table I. The test system ncludes fve dfferent GENCOs wth each GENCO havng the maxmum constructon lmt of 5, 4, 3, 3 and 3 wth capactes of 200, 450, 500, 1000 and 700 MW respectvely for each unt [21]. The margnal 310

5 costs are assumed, based on the nvestment cost, operaton mantenance cost and salvage cost of the unts. The GENCOs based on the above, calculate ther total costs and select ther bddng prce and submt t to the ISO. The margnal costs of the fve GENCOs are assumed as 4, 5, 4.5, 3.75 and 4.25, respectvely based on [21]. The market constant s assumed as 9 and demand coeffcent as 0.001; the market prce equaton s P = x (sum of MW suppled by all GENCOs). B. Numercal Results There s a case study as dscussed n the prevous secton. All constrants are taken nto account. The maxmum constructon number of unts lmt s 5, 4, 3, 3, and 3 for each GENCO wth ndvdual capactes of 200, 450, 500, 1000, and 700 MW respectvely. Each GENCO use dfferent fuel such as Ol, Coal LNG, Nuclear #1, and Nuclear #2. The ISO has forecasted the total demand as 7000 MW and the mnmum and maxmum reserve rate as 20% to 40% respectvely. The fuel mx rato s set to be 20% for each fuel type. For the mnmum reserve rate the total capacty requred wll be 8400 MW and for the maxmum reserve rate, the total capacty requred wll be 9800 MW. The exstng capactes are 5450 MW. Hence, the mnmum and maxmum capacty requred wll be 2950 and 4350 MW respectvely [21]. The total maxmum capacty avalable wth each GENCO s 1000, 1800, 1500, 3000, and 2100 MW respectvely. The total capactes produced by each GENCO at the equlbrum pont were calculated by the ICA as an optmzaton tool. Table 2. The Equlbrum Ponts Obtaned by the Proposed Method Based on ICA Equlbrum Player 1 (P 1 ) Player 2 (P 2 ) Player 3 (P 3 ) Player 4 (P 4 ) Player 5 (P 5 ) Fnal Soluton P 1 Proft 1 P 2 Proft 2 P 3 Proft 3 P 4 Proft 4 P 5 Proft The ICA method s used to fnd the optmal soluton of each GENCO. The soluton methodology s maxmzaton the proft of each ndvdual GENCO. Ths process s performed for each ndvdual GENCO. After that ths procedure s performed untl the results do not change n two consecutve teratons. For ths problem, there are multple equlbrum ponts avalable. The ICA has the capablty of fndng the multple equlbrum ponts durng dfferent smulaton runs. For the best soluton the proposed algorthm, 16 dfferent equlbrum ponts have been acheved. These equlbrum ponts along wth ther correspondng capactes and profts are presented n the Table II. 311

6 Player 1 Player 2 Player 3 Player 4 Player 5 Fgure 1. Fg. 1 Varaton n Players Capacty for Each Player at each Iteraton Fg. 1 shows the varaton n players capacty for each player at each teraton based on Table II. There s no varaton n proft for the 5 GENCOs from teraton 15 to teraton 16 and equlbrum pont s reached. A tolerance value s set so that f the dfference between two teratons, for all GENCOs s less than the tolerance the procedure wll termnate, otherwse t wll contnue. The results obtaned by the proposed method are compared wth those obtaned by the PSO algorthm reported n [21] n Table III. As ths table depcts the proposed method based on the ICA s more capable of fndng the optmal soluton of generaton expanson plannng rather than PSO. The total beneft of the all GENCOs by the PSO method s whle the proposed method mproved the best soluton and enhanced the total benefts for more than 10% and rased t to Results demonstrate the effectveness of the proposed method. The proposed method based on ICA can guarantee the optmal soluton whle handle all constrants of the problem effcently. Table 3. Comparson of the Results Obtaned by the Proposed Method Based on ICA and PSO Beneft PSO [21] ICA P Proft P Proft Player Player Player `Player Player Total Beneft IV. Conclusons Ths paper has addressed the compettve GEP ssues. A Cournot game wth Nash equlbrum has been used to model the competton between the GENCOs and gamng between the ISO and market partcpants n GEP problem. The GEP problem has been solved n an teratve framework by selfoptmzng of each GENCO usng ICA and satsfyng the regulatory body n Cournot model. The results of case studes show that the proposed framework can solve the compettve GEP problem. They also show that dfferent constrants of market can be modeled n the objectve functon of each GENCO or prce sgnal of the ISO. Other sgnals such as ncentve capacty sgnal can be also modeled and used n the selfoptmzaton of each GENCO. References 1. Introducton to the WASP N model, User s manual. Internatonal Atomc Energy Agency, Venna, Austra: Nov Wang, X. and McDonald, I. R., Modern Power Sysfem Plunnng, London:McCraw Hll. 1994, pp Lo Le La (Edtor), Power sysem ReJtructudng and Dereguuton: nudng, 312

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