CHAPTER - 7. Firefly Algorithm based Strategic Bidding to Maximize Profit of IPPs in Competitive Electricity Market

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1 CHAPTER - 7 Frefly Algorthm sed Strtegc Bddng to Mxmze Proft of IPPs n Compettve Electrcty Mrket 7. Introducton The renovton of electrc power systems plys mjor role on economc nd relle operton of power system. The generton compnes nd tl end customers ppers to undergo mjor multple tsk of desgnng of proper opertng methodologes. A sgnfcnt mount of reserch work s n vogue n the pst pertnng to the mrket structure nd to the development of optml ddng strteges. The tools supportng the ddng process seem to wy from glol soluton n vew of the complexty nd szes of the prctcl prolems. Therefore n exhustve formulton of optml ddng strtegy forys contenton of the generton compnes nd the end consumers. An nnovtve pproch for defnng optml ddng strtegy for Independent Power Producers sngle sde cton s presented s stochstc optmzton prolem nd solved y Frefly lgorthm.fa. The Frefly Algorthm s Met heurstc, nture nspred, optmzton lgorthm whch s sed on the socl flshng ehvor of frefles nd hs een ntroduced for the ddng prolem to otn the glol optml soluton. It effectvely mxmzes the proft of power supplers. The numercl exmples wth Sx genertors power supplers test system nd IEEE 30 us system re consdered to revel the essentl fetures of the proposed method nd test results tulted. The smulton result shows tht ths pproch effectvely 07

2 mxmzes the Proft of Power supplers, converge much fster nd more relle when compred wth the exstng methods [3]. 7. Prolem formulton 7.. Mthemtcl Model Consder system consst of m power supplers prtcptng n pool-sed sngle-uyer electrcty mrket n whch the seled ucton wth unform Mrket Clerng Prce MCP s employed nd pctorlly represented n Fg, 7.. Assume tht ech suppler s requred to d lner supply functon to the pool. Fg. 7.. A Typcl Model of Electrcty Mrket for Sngle sde cton Fg. 7.. Mrket Equlrum Pont for MCP 08

3 The th suppler d wth lner supply curve s denoted y G P = + P where =,..m. The P s the ctve power, nd re non-negtve ddng coeffcents of the th suppler. The Independent System Opertor ISO receves d from ll mrket prtcpnts nd usng predcted ggregte lod from the smll users, the ISO determnes MCP tht ttempts to lnce the energy demnd nd Supply. The process s grphclly expressed n Fg. 7.. The ojectve of IPPs s to mxmze ther own proft. Suppose the power producers expressed y cost functon n equton 7. P = ep fp C + 7. The ojectve functon of power producer cn e defned s n equton 7. Mx : F, = RPC P 7. Mrket Clerng Prce R s represented y the equton 7.3 R Q + 0 = = m K+ m = 7.3 The ggregted lod demnd cn e formulted s n equton 7.4 Q R = Q KR 7.4 o Constrnts. Power lnce constrnts: m = P = Q R 7.5 p R = =,... m

4 0. Power generton lmt constrnts: mx mn p p p =,... m Development of ddng strtegy The GENCOs my not hve the posslty to know the exct nformton of ther compettor. Hence t s mndtory for GENCO to understnd the opponents unknown nformton. It s ssumed tht the prevous ddng coeffcents re vlle n pulc domn. The th GENCO cn therefore estmte the ddng prmeters usng prolty densty functon pdf otned through sttstcl nlyss of hstorcl ddng dt. Usully, pdf s used to represent the dstruton of rvls ddng prmeters whch cn e expressed s n equton 7.8 = exp x x pdf µ π 7.8 Where, - Stndrd devton µ - Men vlues The ddng coeffcents, re dependent of ech other. Hence one of the co-effcent s kept constnt nd the other s rtrrly chnced usngpdf. The pdf of rndom vrle s formulton whch cn e ntegrted so s to get the prolty tht the vrle choose vlue s specfed ntervl, + Π = exp, pdf µ µ µ ρ µ ρ ρ 7.9

5 Where ρ s the correlton co-effcent etween nd.the men µ, µ nd stndrd devton, re the prmeters of the jont dstruton. The mrgnl dstruton of, re norml wth men vlues µ, µ nd stndrd devtons, respectvely. Bsed on hstorcl ddng dt these dstrutons cn e determned. The prolty densty functon equton 7.9 represents the jont dstrutons etween nd, the tsk of optmlly coordntng the ddng strteges for suppler wth ojectve functon 7. nd constrnts 7.5 to 7.7, ecomes stochstc optmzton prolem. The Frefly lgorthm s ppled to solve the ove stochstc optmzton prolem. 7.3 Implementton of Frefly lgorthm to solve Bddng prolem Wth vew to sell electrcty t optml prces nd to mxmze proft, the power producers nd consumers need exclusve ddng strteges tht must consder constrnts such s Power lnce, Genertor lmts nd Lod consumpton lmts of mrket prtcpnts. The Frefly Algorthm cn drectly solve optml ddng prolem Mxmze proft ecuse of ts mxmzton chrcterstcs nd the flow chrt of the method s shown n Fg The Frefly Algorthm ncludes four essentl prmeters, Populton sze n, Attrctveness β, rndomzton prmeter α nd Asorpton coeffcent γ.the fesle prmeters otned y tertve processes re s follows. α = , β = 0..0, γ = 0. 0 nd n = Therefore, the followng prmeters of the proposed FA re consdered to solve the optml ddng prolem of sx ndependent power producers nd two lrge consumers. Where n = 30, β =0.0, = 0.5, α γ = nd the mxmum numer of tertons = Owng to the rndom nture of the FA, ther performnce cnnot e judged y the result of sngle run. Mny trls wth ndependent populton ntlztons re

6 necesstted to e mde to otn useful concluson of the performnce of the pproch. Strt Red system dt, Genertor dt Cost coeffcents, Genertor lmts, Aggregted lod nd Prce Elstcty Intlze the FA prmeters: Populton sze n. Attrctveness β, rndomzton prmeter α, Asorpton coeffcent γ nd numer of tertons Crete the ntl rndom populton of ddng co effcent Usng ddng coeffcents clculte Mrket Clerng Prce R m Q0 + = R = m K + = From MCP clculte ftness of ech populton usng the equton Mxmze: F, = RP C P Apply FA prmeters to otn the optml soluton Mx proft No Whether optml soluton s reched Yes Prnt the profts of power supplers Stop Fg.7.3. Flow chrt for Proft Mxmzton of IPPs y Proposed method

7 The supremcy of the proposed FA, s rought out through the test results nd vldted those reported n the recently pulshed methods such s PSO, GA nd Conventonl method for solvng the ddng prolem. The scenros re progrmmed n MATLAB 9.0 nd smulton crred on computer wth Pentum IV, Intel Dul core. GHz, GB RAM. 7.4 Cse study nd Results The GENCOs uld optml ddng strteges to mxmze the proft of power supplers nd mplements the modelng. The smulton s crred out on two cses of test system. The frst system conssts of Sx power supplers s Cse- I nd second test system of IEEE 30 us s Cse-. Test cse: Sx power supplers Test System The proposed Frefly pproch s ppled to test system gven n [] whch conssts of sx power supplers. The cost coeffcents of power generton nd mxmum/ mnmum lmts of sx power supplers re mentoned n ppendx A.9 Tle A.9.. Tle 7. Smulton Results for Sx Power supplers GENCOs Bddng Strtegy $/MW Bddng PowerMW Proft Totl proft $ Mrket clerng prce $/h 4.0 Computtonl tme sec.98 $ 3

8 The fuel cost functon of ech genertor s expressed s qudrtc equton. The prmeters ssocted wth the lod chrcterstcs re consdered from the sme reference where n the ggregted lodq 0 s equl to 450 MW nd the prce elstcty K equls to 0. Tle 7. Comprson of MCP nd Generted power of Proposed wth Conventonl method GENCOs FA Proposed Conventonl Method [] MCP PMW MCP PMW The smulton results of power supplers re presented n Tle 7.. It ncludes ddng strtegy, ddng power, MCP nd proft of power supplers. The comprtve studes wth conventonl method [] re dsplyed n Tle 7. to nlyze the MCP nd ddng power of power supplers. It cn e seen tht the proposed method provde mxmzed profts whch s etter thn the conventonl method. Besdes, t converges much fster nd more relle thn the other vlle methods. Test cse: IEEE 30-us system The IEEE 30 us system conssts of Sx Power supplers who supply electrcty to n ggregte lod. The genertor dt tken from reference [] s shown n ppendx A.0 Tle A.0.. The fuel cost functon of ech genertor s vlle s qudrtc equton. The prmeters ssocted wth the lod chrcterstcs re consdered from the sme reference where n the ggregted lodq 0 s equl to 500 MW nd prce elstctykequls to 0. 4

9 Tle 7.3 Smulton Results of Sx Power supplers for IEEE 30 us system GENCOs Bddng Strtegy $/MW Bddng Power MW Revenue $ Fuel Cost $ Proft Totl Proft $ 063. Mrket clerng prce $/MWh 7.65 $ The smulton results of Sx power supplers for IEEE 30 us system s presented n Tle 7.3. It ncludes ddng strtegy, ddng power, MCP, revenue, fuel cost nd proft of the sx power supplers. The totl proft of sx power suppler s equls to 063. $ nd computtonl tme.98 sec. It s due to fct tht the Frefly lgorthm plys vtl role n serch of the glol optml soluton. Tle 7.4 Comprson of Bddng Strteges of Sx Power supplers for IEEE 30 us system GENCOs FA Proposed PSO [7] GA [4] Trdtonl GSS method [04]

10 GENCOs Tle 7.5 Comprson of Bddng Power nd Proft of Sx Power supplers for IEEE 30 us system FA Proposed PSO [7] GA [4] Trdtonl GSS method [04] PMW Proft$ PMW Proft$ PMW Proft$ PMW Proft$ Tle 7.6 Comprson of MCP, Totl proft nd Computtonl tme of Sx Power supplers for IEEE 30 us system FA Proposed PSO [7] GA [4] Trdtonl GSS method [04] MCP $/hr Totl Profts $ Computtonl tme sec Tle 7.7 Performnce Comprson of Proposed method wth Exstng methods for IEEE 30 us system Totl proft $ Methods Best Averge Worst FA Proposed PSO [7] GA [4]

11 The comprtve studes wth Prtcle Swrm Optmzton [7], Genetc Algorthm [4] nd Trdtonl GSS method [04] re mde to nlyze the ddng coeffcents of power supplers nd dsplyed n Tle 7.4. The Tle 7.5 elortes the Bddng power nd Proft of dfferent methods. The comprson of mrket clerng prce MCP, totl profts nd computtonl tme of power supplers for dfferent methods re presented n Tle 7.6. The performnce of totl profts of power supplers re compred wth proposed nd exstng methods n Tle 7.7. It s evdent from Tle 7.6 the totl proft of the proposed method s mproved wth less computtonl tme thn the other vlle methods. 7.5 Summry The Frefly lgorthm hs een ppled to solve ddng strtegy n order to mprove the proft of GENCOs Power supplers n n open electrcty mrket. The numercl exmples wth Sx genertors power supplers Test system nd IEEE 30 us system hve een consdered to llustrte the essentl fetures of the proposed method. The Frefly lgorthm hs een used to determne the optml ddng strtegy n dfferent mrket rule, dfferent fxed lod, dfferent cpcty of uyers nd sellers. The results hve een projected to rng out the promsng nture of technque for solvng complcted power system optmzton prolem under deregulted envronment. 7