Bidding Strategies for Generation Companies in a Day-ahead Market using Fuzzy Adaptive Particle Swarm Optimization

Transcription

1 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu Bddg Stateges fo Geeato Compaes a Day-ahead Maet usg Fuzzy Adaptve Patcle Swam Optmzato J. VIJAYA KUMAR *, D. M. VINOD KUMAR ad K EDUKONDALU Depatmet of Electcal Egeeg Natoal Isttute of Techology Waagal Waagal, Adhapadesh INDIA * veee@gmal.com Abstact: - Ths pape pesets a methodology based o Fuzzy Adaptve Patcle Swam Optmzato (FAPSO) fo the pepaato of optmal bddg stateges coespodg ut commtmet by Geeato compaes (Gecos) ode to ga maxmum pofts a day-ahead electcty maet. I a compettve electcty maet wth lmted umbe of supples, Gecos ae facg a olgopoly maet athe tha a pefect competto. Ude olgopoly maet evomet, each Geco may cease ts ow poft though a favoable bddg stategy. I FAPSO the eta weght s tued usg fuzzy IF/THEN ules. The fuzzy ule-based systems ae atual caddates to desg eta weght, because they povde a way to develop decso mechasm based o specfc atue of seach egos, tastos betwee the boudaes ad completely depedet o the poblem. The poposed method s tested wth a umecal example ad esults ae compaed wth Geetc Algothm (GA) ad dffeet vesos of PSO. The esults show that fuzzyg the eta weght mpove the seach behavo, soluto qualty ad educed computatoal tme compaed to GA ad dffeet vesos of PSO. Key-Wods: - Bddg Stategy, Electcty Maet, Fuzzy Ifeece, Maet Cleag Pce (MCP), Patcle Swam Optmzato (PSO). Itoducto A ecet chage egulatoy polces electcty dustes has ceated compettve evomets ad maets fo powe supples. Theefoe, ecoomcal opeato ad poft have become the pmay obectves of maet patcpats ad pepag a optmal bddg stategy has sgfcat mpact all aoud the wold have toduced competto may dusty sectos as electcty, gas ad telecommucatos. Ths pape focuses o maet systems based o sealed-bd auctos. I ths maet, patcpats submt the offes to sell ad to buy to the maet opeato, who detemes the Maet Cleag Pce (MCP). I ths evomet, patcpats buld the offes maxmzg the expected pofts. Ths pocess s ow as stategc bddg. []. Howeve, the electcty maets ae olgopolstc pactce, ad powe supples may see to cease the poft by bddg a pce hghe tha magal poducto cost. Kowg the ow costs, techcal costats ad the atcpato of val ad maet behavo, supples face the poblem of costuctg the best optmal bd. I geeal, thee ae thee basc appoaches to model the stategc bddg poblem vz. ) based o the estmato of maet cleag pce ) estmato of val s bddg behavo ad ) o game theoy. Davd [] developed a coceptual optmal bddg model fo the fst tme whch a Dyamc Pogammg (DP) based appoach has bee used. Goss ad Faly adopted a Lagaga elaxatobased appoach fo stategc bddg Eglad- Wales pool type electcty maet []. Jahu [4] used evolutoay game appoach to aalyzg bddg stateges by cosdeg elastc demad. Ebahm ad Galaa developed Nash equlbum based bddg stategy electcty maets [5]. Davd ad We [6] poposed to develop a oveall bddg stategy usg two dffeet bddg schemes fo a day-ahead maet usg Geetc Algothm (GA). The same methodology has bee exteded fo spg eseve maet coodated wth eegy maet by Davd ad We [7]. Ugedo developed a stochastc-optmzato appoach fo submttg the bloc bds sequetal eegy ad acllay sevces maets ad ucetaty demad ad val s bddg behavo s estmated by stochastc esdual demad cuves based o decso tees [8]. To costuct lea bd cuves the Nodpool maet stochastc pogammg model has bee used by Flete [9]. The oppoets bddg E-ISSN: 4-50X 6 Issue, Volume 7, July 0

2 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu behavos ae epeseted as a dscete pobablty dstbuto fucto solved usg Mote Calo method by Davd ad We [0]. The detemstc appoach based optmal bddg poblem was solved by Hobbs [], but t s dffcult to obta the global soluto of b-level optmzato poblem because of o-covex obectve fuctos ad o-lea complemetay codtos to epeset maet cleag. These dffcultes ae avoded by epesetg the esdual demad fucto by Mxed Itege Lea Pogammg (MILP) model [] whch ut commtmet ad ucetates ae also tae to accout. The geeatos assocated to the compettos fms have bee explctly modeled as a alteatve MILP fomulato based o a bay expaso of the decso vaables (pce ad quatty bds) by Peea []. Jave developed a stochastc mxedtege quadatc pogammg model fo optmal bddg stateges of themal ad geec pogammg uts a day-ahead electcty maet [4]. Azadeh fomed optmal bddg poblem fo day-ahead maet as mult obectve poblem ad solved usg GA [5]. Ja ad Svastava [6] cosdeed s costat, fo sgle-sded ad double- sded bddg ad solved usg GA. Ahmet used PSO to deteme bd pces ad quattes ude the ules of a compettve powe maet [7]. Kaaasabhapathy ad Swaup [8] developed stategc bddg fo pumped-stoage hydoelectc plat usg evolutoay tstate PSO. Bapa developed leal ad bloced bd model bddg stategy a compettve electcty maet usg PSO ad FAPSO [9, 0]. Recetly the combato of PSO ad Smulated Aealg (SA) s used to pedct the bddg stategy of geeato compaes []. I geeal, stategc bddg s a optmzato poblem that ca be solved by vaous covetoal ad o-covetoal (heustc) methods. Depedg o the bddg models, obectve fucto ad costats may ot be dffeetable; that case covetoal methods caot be appled. Wheeas, heustc methods such as GA, Smulated Aealg (SA) ad Evolutoay Pogammg (EP), Patcle Swam Optmzato (PSO) etc., have ma lmtatos of the sestvty to the choce of paametes, such as the cossove ad mutato pobabltes GA, tempeatue SA, scalg facto EP ad eta weght, leag factos PSO. Theefoe, Fuzzy Adaptve Patcle Swam Optmzato (FAPSO) s poposed to ovecome the shotcomgs of PSO ad GA. I FAPSO the eta weght (w) s adusted usg fuzzy IF/THEN ules. The fuzzy ule-based systems ae atual caddates to desg eta weght, because they povde a way to develop decso mechasm based o specfc atue of seach egos, tastos betwee the boudaes ad completely depedet o the poblem. The ma cotbuto of ths pape s, the optmal bdg poblem s fomulated as a bloced bd model whch supples ad vals bddg coeffcets ae detemed wth the help of pobablty desty fucto (pdf) usg FAPSO stead of Mote Calo method [0]. The a optmal bd pce fo each bloc has to be detemed. Based o the bd pces, u the ut commtmet usg FAPSO. The esult shows that the poposed algothm ca geeate bette qualty soluto wth shote computato tme ad stable covegece chaactestcs compaed to GA ad dffeet vesos of PSO. The pape s ogazed as follows. Secto pesets the mathematcal fomulato of optmal bddg poblem. Secto cotas a bef ove vew of the poposed FAPSO method ad the applcato of FAPSO fo solvg the optmal bddg poblem. Secto 4 epots the esults ad dscussos compaed wth GA ad dffeet vesos of PSO. Secto 5 summed up the fal outcome of the pape as Cocluso. Poblem Fomulato The followg otatos ae used ths pape: M: Numbe of uts; T: Schedulg Peod; I (t): th ut status at tme t (/0 fo o/off); P (t): Output powe of th ut at tme t; P max (t)/p m (t): Maxmum/mmum output powe of ut at tme t cosdeg amp Rate; D (t): Demad powe at tme t; MU /MD : Mmum up/dow tme of ut ; X o (t)/ X off (t): Duato of cotuously o/off of ut at tme t; c u : Stat-up cost of ut c d : Costat shut dow cost; h: Hot stat-up cost ($), cosdeed whe ut has bee shut dow fo a shot tme. τ : Coolg tme costat (h). T off : umbe of hous of a geeato shutdow. δ: Cold stat-up cost ($), cosdeed whe ut has bee shut dow fo a log tme; a, b, c: cost coeffcets; c, c: costats of the valve pot loadg effect; Cosde a system cosst of M+ Geeatos o supples, a te-coected etwo cotolled by a Idepedet System Opeato (ISO) ad a Powe E-ISSN: 4-50X 7 Issue, Volume 7, July 0

3 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu Exchage (PX), a aggegated cosume (load) whch does ot patcpate demad-sde bddg. Geeato-G, fo whch a optmal bddg stategy has to be developed, s havg M vals the maet. Each geeato bds fo evey oe hou tadg peod ude stepwse potocol ad ufom Maet Cleag Pce (MCP) system. Geeatos submt the bds tems of quatty (MW) ad pce ($) fo each hou 4-h hozo to compete a day-ahead maet. Geeato-G ad each val geeato ca bd maxmum I blocs of output fo each tadg peod. Fo lage themal geeatos, put-output chaactestcs ae ot always smooth due to sequetal opeg of mult-umbe of valves to obta eve-ceasg output of the ut []. Typcally, as each steam admsso valve a tube stats to ope, t poduces a pplg effect o the ut cuve. Ths pplg effect of valve pot loadg has bee modeled as a ecug ectfed susodal fucto, whch cofms the mpotace of pecse poducto cost fucto applcato stategc bddg. Cosdeg o-dffeetable, o-covex poducto cost fucto c p (t), the opeatg cost fucto c ( t ) fo the th bloc of geeato-g ca be wtte as p u d c ( t) = c ( t) + c ( t) c ( t) () + Whee c p ( t ) = a( p + c s( c ( p ( t )) m + b( p p ( t ))) ( t )) + c () u Toff c = h + δ exp τ The optmal bddg stategy of geeato-g ca be fomulated as poft maxmzato poblem tems of dspatched powe output p (t) ad Maet Cleag Pce M(t). The poduct of dspatched powe ad MCP gves the eveue obtaed. The cumulatve poft fo I blocs of the geeato ove tme peod T s expessed as: Maxmze F( M( t), p ( t)) = T I t= = ( M( t) p ( t) c ( t)) () Subect to ) System powe balace The geeated powe fom all the commtted uts must satsfy the load demad whch s defed as M D ( t ) = p ( t ) (4) = ) Geeato lmts m max p p ( t ) p, t T (5) ) Mmum up/dow tme Oce a ut s commtted/de-commtted, thee s a pedefed mmum tme afte t ca be decommtted/commtted aga. o ( I ( t + ) MUT X ( t), fi ( t) = (6) off I ( t + ) MD X ( t ), fi ( t ) = 0 4) Lmtatos o bd pce c ( t ) p ( t ) p (7) It s clea that, maet patcpats ca set MCP at the level that etus the maxmum poft to them f they ow bddg stategy of othe fms. But sealed bd aucto based electcty maet, fomato fo the ext bddg peod s cofdetal whch supples caot solve optmzato poblem fomed Eq. () dectly. Howeve, bddg fomato of pevous oud wll be dsclosed afte ISO decde MCP ad eveyoe ca mae use of ths fomato to stategcally bd fo the ext oud of tasacto betwee supples ad cosumes. A mmedate poblem fo each supple s how to estmate the bddg coeffcets of vals. Let, fom the th supple s pot of vew, val s () bddg coeffcets ( ) obey a ot omal dstbuto wth the followg pobablty desty fucto (pdf): pdf ( a, b ) = ( a ) max Π σ σ ρ ( b ) a µ ρ ( a µ )( b µ ) σ σ σ exp ( ρ ) b µ + σ (8) Hee ρ s the coelato coeffcet betwee a ad (a) (b) b. µ, µ, σ ad σ ae the paamete of the ot dstbuto. The magal dstbutos of a ad b ae both omal wth mea values µ ad µ, ad stadad devatos σ ad σ (a) (b) (b) (a) espectvely. Usg pobablty desty fucto of Eq. (8) fo Geeato-G ad vals, the ot dstbuto betwee a ad b, the optmal bddg E-ISSN: 4-50X 8 Issue, Volume 7, July 0

4 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu poblem wth the obectve fucto of Eq. () ad costats Eq. (4)-(7) becomes a stochastc optmzato poblem ad FAPSO algothm s vey effcet to solve the stochastc optmzato poblem, peseted the followg secto. Poposed FAPSO Algothm PSO s smla to the othe evolutoay algothms that the system s talzed wth a populato of adom solutos. Each potetal soluto, call patcles, fles the D-dmesoal space wth a velocty whch s dyamcally adusted accodg to the flyg expeeces of ts ow ad ts colleagues []. The locato of the th patcle s epeseted as X = (x, x x D ). The best pevous posto of the th patcle s ecoded as P best. The dex of the best, P best amog all the patcles s epeseted by the symbol g. The locato P bestg s also called G best. The ate of velocty fo the th patcle s epeseted as V = (v, v v D ). The modfed velocty ad posto of each patcle ae calculated usg cuet velocty ad the dstace fom P best to G best as Eq. (9) ad (0). V + + a = w V ad ( G + a ad best X ( P ) best X ) (9) + + X = X + V (0) Whee, s the teato coute ad max s the maxmum teato umbe. The PSO seach pocess s a olea ad complcated pocess ad a lea deceasg Ieta Weght Appoach (IWA) PSO o lealy deceasg leag factos Velocty Updated Relaxed (VUR) PSO has a lea tasto of seach ablty fom global to local seach, whch does ot tuly eflect the actual seach pocess equed to fd the optmum [4]. Ths especally s tue fo dyamc optmzato poblems. Theefoe, fo bette pefomace, the eta weght should be olealy, dyamcally chaged to have bette dyamcs of balace betwee global ad local seach abltes. Theefoe, the FAPSO s poposed, to desg fuzzy adaptve eta weght (w) usg fuzzy IF/ THEN ules fo solvg the optmal bddg poblem. The fuzzy system cossts of fou pcple compoets: fuzzfcato, fuzzy ules, fuzzy easog ad defuzzfcato whch ae descbed as follows [5]. () Fuzzfcato: To obta a bette gavtatoal costat value ude the fuzzy evomet, two puts ae cosdeed, a) Nomalzed Ftess Value (NFV). b) Cuet eta weght (w) ad output s the coecto of the eta weght ( w). The tagula membeshp fuctos ae cosdeed fo the fuzzfcato of the put vaables ae peseted thee lgustc values, S (Small), M (Medum) ad L (Lage), whee as the output vaable ( w) s peseted thee fuzzy sets of lgustc values; NE (egatve), ZE (zeo) ad PE (postve) wth assocated tagula membeshp fuctos, as show Fgue. () Fuzzy ules: The Mamda-type fuzzy ules ae used to fomulate the codtoal statemets that compse fuzzy logc. Fo example: IF (NFV s S) AND (w s M) THEN chage eta weght ( w) s NE. The fuzzy ules ae desged to deteme the chage eta weght ( w). As thee lgustc vaables ae cosdeed fo the NFV, w ad w, total e ules ae desged as show Table. Each ule epesets a mappg fom the put space to the output space. () Fuzzy easog: The fuzzy cotol stategy s used to map the puts to the output. The AND opeato s typcally used to combe the membeshp values fo each fed ule to geeate the membeshp values fo the fuzzy sets of output vaables the cosequet pat of the ule. Sce thee may be othe ules fed the ule sets, fo some fuzzy sets of the output vaables thee may be dffeet membeshp values obtaed fom dffeet fed ules. Table Fuzzy ules fo the vaato of eta weght (w) To obta a bette eta weght ude the fuzzy evomet, the vaables selected as put to the fuzzy system ae the cuet best pefomace evaluato (NFV) ad cuet eta weght (w); wheeas the output vaable s the chage eta weght ( w). The NFV s defed as; NFV Rule No Atecedet Cosequet NFV w w S S ZE S M NE S L NE 4 M S PE 5 M M ZE 6 M L NE 7 L S PE 8 L M ZE 9 L L NE FV FV m = () max FV FV m E-ISSN: 4-50X 9 Issue, Volume 7, July 0

5 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu The Ftess Value (FV) calculated fom Eq. () at the fst teato may be used as FV m fo the ext teatos. Wheeas FV max s a vey lage value ad s geate tha ay acceptable feasble soluto. Typcal eta weght s 0.4 w.0. Both postve ad egatve coectos lmts ae equed fo the eta weght. Theefoe, a coecto age of -0. to +0. has bee chose fo the eta weght coecto. w t+ t = w + w () (v) Defuzzfcato: defuzzfcato of evey put ad output, the method of cetod (cete-of-sums) s used fo the membeshp fuctos show Fgue. Step5. The th dvdual s selected. Step6. The best local posto (P best ) s selected fo the th dvdual. Step7. Update the FAPSO paamete (w) usg fuzzy IF/THEN ules. Step8. Calculate the ext posto fo each dvdual based o the eta weght (w) of Eq. (9) ad the checed wth ts lmt. Step9. If all dvduals ae selected, go to the ext step, othewse =+ ad go to step5. Step0. If the cuet teato umbe eaches the pedetemed maxmum teato umbe, the seach pocedue s stopped, othewse go to step. Step.The last G best (.e. b ) s the soluto of the poblem Step. Calculate the optmal bd pces of each bloc ad u the ut commtmet fo dffeet loads. Step. Calculate poft of each supple usg Eq. (). The flowchat fo the poposed algothm show Fgue Fg. Membeshp fuctos of put vaables (a) Nomalzed Ftess Value (NFV) (b) Ieta weght (w) output vaable (c) chage eta weght ( w).fapso algothm fo bddg poblem I the optmal bddg poblem, each patcle s composed of the stategc vaable. Fo the cosdeed supple lea bd model usg pobablty desty fucto the posto of epesets the optmum value of b. Fo each geeated patcle, poft maxmzato obectve fucto of Eq. () s tae as a ftess fucto. P best epesets the best posto of the patcle ad the best posto eached by the swam G best the fal teato gves optmal value of stategc vaable. The computatoal steps fo seachg bddg coeffcets usg FAPSO algothm ae descbed below. Step. Read put data µ σ, ρ, b ad maxmum = stadad devato, ρ = coelato coeffcet of Eq. (8), b = cost coeffcet// Step.The tal populato ad tal velocty fo each patcle should be geeated adomly. Step. The obectve fucto s to be evaluated fo each dvdual usg Eq. (8). Step4. The dvdual that has the mmum obectve fucto should be selected as the global posto. teatos. // whee µ = mea, σ Fg. Flowchat fo the poposed FAPSO algothm E-ISSN: 4-50X 40 Issue, Volume 7, July 0

6 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu 4 Results ad dscussos The effectveess of the poposed FAPSO has bee demostated cosdeg a umecal example based o poblem fomulated the pevous secto. The poblem s fomulated a dyamcally chagg evomet ad bddg stateges ae developed fo mult-houly tadg a day-ahead maet. I ths wo, the paametes used fo FAPSO, IWAPSO, VURPSO ad GA ae show Table. Smulatos ae caed o.66ghz, PIV Pocesso, GB RAM ad MATLAB 7.8 veso s used. c, c leag factos; w eta weght; mf mometum facto fo PSO; P e eltsm pobablty; P c cossove pobablty; P m mutato pobablty; l chomosome legth fo GA. Nomal pobablty dstbuto paametes of vals bloc bd pces Table ae tae such a mae that each bloc has a uque pdf. The paametes of all thee powe blocs of geeato-g ae show Table 4. At the stat of fst hou, blocs,, ad of geeato-g ae assumed to be ON, ON, ad OFF, espectvely. The bd pce fo each hou ad each bloc of geeato-g s obtaed usg FAPSO algothm. Table Paamete values used fo dffeet appoaches FAPSO IWAPSO VURPSO GA No. of patcles= 40; Max. teatos= 00; c=.5, c=.5; w= 0.4 to.0 No. of patcles= 40; Max. teatos= 00; c=.5,c =.5; w=.0 to 0.5 No. of patcles= 40; Max. teatos= 00; c, c vay fom 6.5 to.5; mf=0. Populat o sze = 40; Geeat os=00 ; P e =0.; P c =0.8; P m =0.0 0, l=6 Table 5 shows the optmal bd pce fo all geeatos fo each bloc, the aveage of all bd pces fo each bloc s ow as ISO (Idepedet System Opeato) MCP. Ru the ut commtmet fo all the geeatos based o ths MCP ad the uts ae commtted/de-commtted accodgly. Table 6 shows the dspatched ad o-dspatched powes of geeato-g ad vals dug each tadg peod. The followg obsevatos ca be made fom the esults show Table 6. of geeato-g s ot commtted the hous of egatve beeft (fom to 8 h) because of ts hgh poducto cost ad low system demad. Cold stat-up cost s accouted the poducto cost of bloc, whe t s commtted at 9 h, because t has bee shut dow fo a log tme (8 h). At the ed of h, bloc s decommtted due to low system demad, ad mmum dow tme costat s actve o h. s ecommtted at 4 h, ad hot stat-up cost s accouted the poducto cost of ths hou, because t has bee shut dow fo a shot tme (h). s aga decommtted fom 0 to 4 h due to low system demad. Fgue ad 4 shows houly ad cumulatve poft cuves of geeato-g, whee cumulatve poft s the aggegato of houly poft. At hou 8 ad, a shap cease houly poft, ad 48,8.080 s dectly elated to sudde se bd pce to.06 to.55 $/MWh, espectvely. Ths shap cease s followed by a sudde decease houly poft to $ ad 4, at hous 9 ad 4, espectvely because of the hgh stat-up cost of bloc, whch s commtted at these hous. I spte of magal dffeece bd pce at 7 ad 8 h, a huge cease poft fom $ to $ s obtaed by deceasg dspatched powe output of bloc of geeato-g fom 00 to 50 MW ad, theefoe, the poducto cost. The cumulatve poft of geeato-g ove 4-h peod usg FAPSO appoach s $94,78. Due to the adomess of the evolutoay algothms, the pefomace caot be udged by the esult of a sgle u. May tals wth dffeet talzatos should be made to each a vald cocluso about the pefomace of the algothms. A algothm s obust, f t ca guaatee a acceptable pefomace level ude dffeet codtos. I ths pape, 0 dffeet us have bee caed out. The best, wost, aveage values, total poft ad PD ove a peod foud by all the methods ae show Table 7. Fg. Houly poft of geeato-g E-ISSN: 4-50X 4 Issue, Volume 7, July 0

7 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu covegece. Hece t ca be used fo eal-tme applcatos. Fg.4 Cumulatve poft of geeato-g The Pecetage Devato (PD) s computed as follows. PD = ( Best Wost ) 00%. Best Table 7 shows that the PD s mmum fo the poposed FAPSO method compaed to GA ad dffeet vesos of PSO, fo a gve data ad t s clealy obseved that the optmal bddg stateges obtaed by FAPSO poducg hghe pofts compaed to GA ad dffeet vesos of PSO. I addto to that, FAPSO shows good cosstecy by eepg small vaato betwee the best ad wost soluto. I othe wods, the smulato esults show that, the FAPSO algothm coveges to global soluto has a shote c.p.u. tme ad small pecetage devato because, t ca easly follow the fequetly chagg demad each tadg peod though dyamcally chagg eta weght usg fuzzy IF/THEN ules. As a esult, the fal soluto lads at global optmum, whch avods pematue covegece ad pemts a faste covegece. 5 Cocluso I ths pape, the applcato of FAPSO was poposed to obta bddg stateges fo Gecos a day-ahead electcty maet wth a obectve of maxmzg total poft cosdeg ut commtmet ad valve pot effects the cost fucto. PSO s a effcet tool fo solvg complex optmzato poblems. The esults of the PSO ae geatly depedet o the eta weght ad the method ofte suffes fom the poblem of beg tapped local optma. To ovecome these dawbacs of PSO, the eta weght has bee dyamcally adusted FAPSO usg fuzzy IF/THEN ules. The umecal esults eveal the supeoty of the poposed FAPSO compaed to GA ad dffeet vesos of PSO wth espect to total poft ad covegece. The esult shows that, the poposed algothm poduces moe poft ad apd Refeeces: [] A. K. Davd, F. We, Stategc Bddg Compettve Electcty Maets: a Lteatue Suvey, Poc. IEEE Powe Eg. Soc. Summe Meetg, vol. 4, 000, pp [] A.K. Davd, Compettve bddg electcty supply, IEE Poc. Geeato Tasmsso Dstbuto. Vol. 40, 99pp [] G Goss, DJ Flay, Geeato Supply Bddg Pefectly Compettve Electcty Maets, Computatoal ad Mathematcal Ogazato Theoy Spge, vol. 6, pp. 8-98, 000. [4] Jahu Wag, Zh Zhou, Audu Botteud, A evolutoay game appoach to aalyzg bddg stateges electcty maets wth elastc demad, Eegy, vol. 6, pp , 0. [5] Ebahm Hasa, D Facsco, Galaa, Fast Computato of Pue Stategy Nash Equlbum Electcty Maets Cleaed by Met Ode, IEEE Tasactos o Powe Systems, vol. 5, pp. 7-78, 00. [6] A. K Davd, F. We. Stategc bddg fo electcty supply a day-ahead eegy maet. Electcal Powe Systems Reseach 00; 59: [7] A. K Davd, F. We, Optmally co-odate bddg stateges eegy ad acllay sevce maets, IEE Poc. Geeato Tasmsso Dstbuto, vol.49, 00, pp. 8. [8] A Ugedo, E Lobato, A Faco, L Rouco, J Fea dez-cao, J Chof, Stategc bddg sequetal electcty maets, IEE Poc. Geeato Tasmsso Dstbuto, vol. 5, 006, pp [9] S. E Flete, E Pettese, Costuctg bddg cuves fo a pce-tag etale the Nowega electcty maet, IEEE Tasactos o Powe Systems, vol. 0, pp , 005. [0] A. K Davd, F. We, Optmal bddg stateges ad modelg of mpefect fomato amog compettve geeatos, IEEE Tasactos o Powe Systems, vol. 6, pp. 5, 00. [] BF Hobbs, CB Metzle, JS Pag, Stategy gamg aalyss fo electc powe systems: a MPEC appoach, IEEE Tasactos o Powe Systems, vol. 5, pp , 000. E-ISSN: 4-50X 4 Issue, Volume 7, July 0

8 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu [] S Toe, J. M Aoyo, A. J Coeo, J Coteas, Pce mae self-schedulg a pool-based electcty maet: a mxed-tege LP appoach, IEEE Tasactos o Powe Systems, vol. 7, pp.07 04, 00. [] M.V Peea, S Gavlle, M Fampa, R Dx, L. A Baoso, Stategc bddg ude ucetaty: a bay expaso appoach, IEEE Tasactos o Powe Systems, vol. 0, pp.80 88, 005. [4] F Jave Heeda, Macos J Rde, Csta Cocheo, Optmal Bddg Stateges fo themal ad geec pogammg uts the day-ahead electcty maet, IEEE Tasactos o Powe Systems vol. 5, pp , 00. [5] A Azadeh, S. F Ghade, B Pouvalha Nohaada, M Shahalshah, A ew GA appoach fo optmal bddg stategy vewpot of poft maxmzato of a geeato compay, Expet Systems wth Applcatos, 0 I pess. [6] A. K Ja, S. C Svastava, Stategc Bddg ad s Assessmet Usg Geetc Algothm Electcty Maets, Iteatoal Joual of Emegg Electc Powe Systems, vol. 0, pp.-0, 009. [7] Ahmet D Yuceya, Joge Valezuela, Gey Doze, Stategc bddg electcty maet usg PSO, Electcal Powe System Reseach, vol. 79, pp. 5-45, 009. [8] P Kaaasabhapathy, K Shat Swaup, Bddg Stategy fo of Pumped-Stoage plat pool-based electcty maet, Eegy coveso ad Maagemet, vol. 5, pp , 00. [9] P Bapa, S. K Pua, S. N Sgh, Swam tellgece-based stategc bddg compettve electcty maets, IET Geeato Tasmsso Dstbuto, vol., pp , 008. [0] P Bapa, S. N Sgh, Fuzzy Adaptve Patcle Swam Optmzato fo Bddg Stategy Ufom Pce Spot Maet, IEEE Tasactos o Powe Systems, vol., pp. 5 59, 008. [] S Soleyma, Bddg Stateges of geeato compaes usg PSO combed wth SA method the pay as bd maet, Electcal Powe ad Eegy systems, vol., pp. 7-78, 0. [] A. J Wood; B. F Wollebeg, Powe Geeato Opeato ad Cotol. New Yo: Wely, 996. [] J Keedy, R Ebehat, Patcle Swam Optmzato, Poc. IEEE It. Cof. Neual Netwos. vol. 4, 995, pp [4] Y Sh, R C Ebehat, A modfed patcle swam optmze, I Poc. IEEE. Cog. Evolutoay Computato, 998, pp [5] Y Sh, RC Ebehat, Fuzzy adaptve patcle swam optmzato, I Poc. IEEE. It. Cof. Evolutoay Computato, 00, pp Rval (=) Rval (=) Rval (=) Rval 4(=4) Q (MW) Table Data of vals bddg paametes (=) (=) (=) µ σ Q (MW) µ σ Q (MW) µ σ E-ISSN: 4-50X 4 Issue, Volume 7, July 0

9 J. Vaya Kuma, D. M. Vod Kuma, K. Eduodalu a ($/MW /h) b c ($/h) Table 4 Data of geeato-g powe blocs c c q max q m ($/h) (ad/mw) (MW) (MW) MUT (h) MDT (h) Table 5 Optmal bd pces ( $/MWh) of geeatos fo each bloc Rval Rval Rval Rval 4 Geeato-G MCP (ISO) h ($) δ ($) τ (h) c d ($) Table 6 Dspatched powe output of geeato-g ad vals Load (MW) Hou Geeato-G Rval- Rval- Rval- Rval ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND 00 ND ND ND 00 ND ND ND ND 00 ND ND ND 00 ND ND ND ND 00 ND ND ND 00 ND ND ND ND 00 ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND 00 ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND 00 ND ND ND ND ND ND 00 ND ND ND 00 ND ND ND ND 00 ND ND ND 00 ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND ND Table 7 Pefomace compaso of dffeet appoaches FAPSO IWAPSO VURPSO GA Best($) Total poft ($) Wost($) Ave.($) PD (%) Aveage c.p.u. tme (sec) E-ISSN: 4-50X 44 Issue, Volume 7, July 0