带条件风险约束的发电商最优投标模型及计算

37920109()JournalofHunanUniversity(NaturalSciences)Vol.37,No.9Sep2010:16742974(2010)09004906*罗可1,赵志学1,2,童小娇1(1.,410076;2.,410205):采用条件风险(CVaR)作为风险度量指标,建立了双层优化的发电商投标模型,上层解决社会效益最大和风险最小问题,下层解决发电商利润最大问题,设计了启发式粒子群算法(PSO)求解该复杂的双层优化模型.在4节点2机系统和9节点3机系统进行了实验,说明该模型和算法具有较好的计算效果和时效性,通过实验数据比较显示CVaR比VaR更准确地度量了发电商的风险.:优化;粒子群优化算法;投标策略:TM743:ABasedonRiskConstraintoftheBiddingStrategyModelandComputationforGeneratingCompanyLUOKe1,ZHAOZhixue1,2,TONGXiaojiao1(1.ChangshaUnivofScienceandTechnology,CollegeofComputerandCommunicationEngineering,Changsha,Hunan410076,China;2.HunanUnivofCommerce,CollegeofComputerandElectronicEngineering,Changsha,Hunan410205,China)Abstract:TaketheConditionValueatRisk(CVaR)asameasureofriskindicators,atwotieroptimizationofelectricitymarketbiddingmodelwasbuilt.Theupperlevelobjectiveistosolvemaximizingsocialprofitsandriskproblem,thebileveloptimizationisthelargestpowergenerationcompanyprofitoptimization.Inthispaper,wedesignedheuristicparticleswarmoptimization(PSO)algorithmtosolvethecomplextwotieroptimization.TheIEEE4bussystemandIEEE9bussystemhavebeentested.NumericalexamplesofsomestandardtestedIEEEsystemsshowthatthenewmodelandalgorithmhavebettereffectofcomputationandpractical.ThecontrastanalysisshowthatCVaRcanmoreaccuratelymeasuretheriskofthepowersuppliersthanVaRKeywords:optimization;particleswarmoptimizationalgorithm;biddingstrategy,.[1],3:,;,,;,,.*:2009-11-02:(10871031,10926189);(2008FJ3015);(07A001):(1961-),,,,,Email:[e-mail]()2010,.,,.,.[2]Markowitz,,.,.2090ValueatRisk(VaR).AlexanderGBaptistaA[3]VaRVaR.RockafellarUryasev[4]2000VaR,(ConditionValueatRisk:CVaR).VaR,CVaR,;,CVaR,VaR.CVaR,[5-13].CVaR.[14-15],CVaR,3!!!,,PSO(ParticleSwarmOptimization,PSO),.IEEE.1CVaRx∀XRn,y∀Rmp(#),f(x,y).[4],RockafellarUryasevCVaR(x):VaR(x)=min∀R:(x,)∃,CVaR(x)=(1-)-1%f(x,y)∃(x)f(x,y)p(y)dy,y∀Rm.(1):,VaR(x).[4]F(x,)CVaR(x),:F(xi,)=+(1-)-1%y[f(x,y)-]+#p(y)dy.(2)[t]+=max{t,0};!(xi)=CVaRi(x)=mina∀RFi(xi,).(3)[4]F(x,).CVaR.(2),,!Fi,(4):!Fii(xi,)=+(Ni(1-))-1&Nik=1(Zi)k,(Zi)k∃0,-fi(xi,yk)++(Zi)k∃0,k=1,2,∋,N.(4)2n,,:Si(qi)=ai+biqi,i=1,2,∋,n.(5)(xi,x-i)=((ai,bi),(a-i,b-i)),ai,bi,a-i,b-i,qi.:Ci(qi)=Aiqi+0.5Biq2i,Ai,Bi.(6):∀i(xi,x-i)=#i(x)qi(x)-[Aiqi(x)+0.5Biqi(x)2].(7):#i,qii,,ISO.i,.ISO.:max(q,d):W(x,q,d)=B(d)-C(x,q).s.t:g(q,d)=0;h(q,d)(0.(8):B(d)=&jj=1(pjdj-0.5∃jd2j);C(x,q)=&ii=1(aiqi+0.5btq2i).(9)d=(d1,d2,∋,dj)(),q=(q1,q2,∋,ql),B(d),C(x,q).h(q,d),KKT:L(x,q,d,#,%)=-W(x,q,d)+#Tg(q,d)+509:%Th(q,d).(10)(10)q,d#.,i:maxWi(xi))E∀i(xi,y),s.t&(xi)∃Vi.(11)(11)&(xi)∃Vif(x,y),(4)(10),:maxWi(xi))E∀i(xi,y),s.tmin!Fi(xi,)=+(Ni(1-))-1&Nik=1(Zi)k∃Vi,-fi(xi,yk)++(Zi)k∃0,(Zi)k∃0,k=1,2,∋,N.(12)3PSOKennedyEberhart1995.n,mtPjtVjt,:Pjt=(pj1,t,pj2,t,∋,pji,t,∋,pjn,t);Vjt=(vj1,t,vj2,t,∋,vji,t,∋,vjn,t):j=1,2,∋,m,;i=1,2,∋,n,;t.t+1,j:V[t+1]=wV[t]+C1#Rand()[PBest-P[t]]+C2#Rand()[GBest-P[t]].(13)j:P[t+1]=P[t]+V(t).(14)C1,C2,Rand()[0,1].ISO,.CVaR,PSO,.PSO,,NXi,ISO.[14]3∋,,k,kf(#i,qi),CVaR.,,.:S=E{#iqi(ai,bi)-[Aiqi(ai,bi)+0.5Biqi(ai,bi)2]}-c1(ai-aimax)-c2(bi-bimax)-c3(&(xi)-Vi).(15):r,c1,c2c3.:Step1,2(Swarm[ai,bi]),N,Tmax,eps,(13)C1C21.4962..Step2[a-i,b-i],kyk.Step3kykxti(t)ISOkf(xti,yk)(#ti,qti).kf(xti,yk)CVaR,&(xi)t.Step4(15),.(Pbest),Pbest,Pbest(Gbest).Step5(13)(14).Step6!!!Tmax(t∃Tmax)eps(xji(t+1)-xji(t)ximax(eqs,j),,t∗t+1,Step3,.441IEEE4busVIEEE4bus,.142,1,2;3,4.1ISO.,,2,51()2010C=19,=95%,[13],A2[0.5*3,10*3],B2[0.5*0.02500,10*0.02500],q,d.,V=25,a2=5.1598;b2=0.4001;q1,q2,d1,d2=(0.4624,4.5988,2.3262,2.7350)MW;R=6.9998/(MW#h),18.1298.图14节点2发电机结构图Fig.14node2generatorstructurechart1Tab.1TechnicalandeconomicparameterstableAiBiqminqmaxP∃11.000.06250103100.0723.000.0250104100.12,312Vai,bi#iMax∀.3,V,a2,b2,,q,f,.V,,.21VTab.2The1stgenerationcompany+sresultforagivendifferentVVa1b1q1#1Max∀VaRCVaR-55.19620.08243.50925.485315.3551-6.1251-4.9981-106.86740.09533.72137.222022.7213-13.5218-9.9872-157.43650.13933.79287.964825.9667-18.2341-14.9972-207.44560.15463.81988.036126.4207-21.4192-16.0324-3007.45720.19223.82058.191527.0190-21.4203-16.1032f(x,y),VaR,CVaR,,-VaR,-CVaR.,,-VaR-CVaR,.,-CVaR-VaR,CVaR,,-CVaR-VaR,-VaR.32VTab.3The2stgenerationcompany+sresultforagivendifferentVVa2b2q2#2Max∀VaRCVaR-54.09560.18783.03324.66524.9360-4.0326-3.9981-104.78670.36874.29866.371614.2622-11.2314-9.9761-155.15230.39874.53246.963417.7068-15.5638-14.9672-255.15980.40014.59886.999818.1298-16.3027-15.0021-3005.16120.41114.60097.052618.3811-16.3105-15.0053242,2,V.,V,,.,,,.,1,-Vq13.82;2,-V,a1,b1,,,.,.2,V=152.2(x2-(a2,b2)),a2490,5.1.,5.15,0;b2470,0.40.,0.3987,0,.529:-V/图24节点2发电机系统效益前沿图Fig.2ThemaximumprofittrendgraphindifferentriskfactorV4293V,IEEE9bus.393,1,2,3,.4,5,6ISO.图3IEEE9节点系统图Fig.39node3generatorstructurechart4Tab.4Lineparameters/(/(hW#h)/(/(kW#h-1)(1,4)0.65(4,9)0.12.5(4,5)0.32(8,9)0.032.5(5,6)0.11.5(2,8)0.45(3,6)0.25(7,8)0.0053.5(6,7)0.121.55Tab.5GeneratingtechnicalandeconomicparametersAiBiqminqmax13.150.003050220.015050330.0120506Tab.6LoadnodeparameterPj∃jPj∃j4100.0737100.0535100.0178100.1376100.0699100.0937,89IEEE91,2,3VR.:V,a2,b2,42,.442,V.71VTab.7The1stgenerationcompany+sresultforagiven