基于模糊层次分析法的城市电网规划决策综合评判(1)

,,(,300072)AFAHP-BASEDMADMMETHODINURBANPOWERSYSTEMPLANNINGChenDayu,XiaoJun,WangChengshan(SchoolofElectricalEngineering&AutomationTianjinUniversity,Tianjin300072,China)ABSTRACT:Thedecisionmakersofurbanpowersystemplanningoftenfaceacomplexsystemincludingseveralparts.ThesedecisionproblemsofthecomplexsystemaremostlyMADMproblems.Howtodeterminetheoptimumsolutioninthenoninferiorsolutionsisthekey.ThispaperintroducesaFAHP-basedMADMmethodinurbanpowersystemplanningandtheprocedureofapplyingthismethod.ThemethodwillbeanewwayforurbanpowersystemplanningMADM.KeyWords:urbanpowersystemplanningMADM;trian-gularfuzzynumber;fuzzyAHP:,,,,:;;1,[1],,,(AHP),(MADM):1),;2),,[2],(FUZZYAHP),,,2AHP,,,AHP,,,,2.12.1.1　三角模糊数的定义[3]:F(R)R,MF(R),:1)Mm:R[0,1]m(x)=xm-l-lm-lx[l,m]xm-u-um-ux[m,u]0(1),lmn;2)x0R,m(x0)=1;3)(0,1),M={xm(x)}M,(l,m,u)2.1.2　三角模糊数的运算15420038ProceedingsoftheEPSAVol.15No.4Aug.20032003417M1=(l1,m1,u1),M2=(l2,m2,u2),:1)M1M2=(l1+l2,m1+m2,u1+u2)[]2)M1M2=(l1l2,m1m2,u1u2)[]3)M1=(l1,m1,u1)R[]4)1/M1=(1/u1,1/m1,1/l1)[]2.2FUZZYAHP2.2.1　建立层次结构并构造模糊判断矩阵,T,Q,m[3]n,,()(),,T,,T(M=(Mij)nn,Ek=(Ekij)QQk,k=1n),[4]:aij=1T(a1ij+a2ij++atij)=[lij,mij,uij](2):aijij,atijtij,,aij=(aij)-1=[1uij,1mij,1lij]2.2.2　计算局部权重及综合权重(3):Sk=nj=1Mij(ni=1nj=1Mij)-1(3),Sk,S=[S1,S2,Sn]T:Fkq=Qj=1Ekij(Qi=1Qj=1Ekij)-1(4):Fkqqk,q=1QF=[Fkq]nQ,Nx[5]Nx=SF(5),,,33.162km2,7.43km2,35kV110kV,,::,35kV35kV,,35kVT,,220kV35kV,35kV220kV,220kV35kV,,:110kV,,220kV,9110kV,,110kV10kV,35kV,,,:110kV,35kV,220kV,,,,,84200343.2FUZZYAHP:1),;2);3)(2);4)(3)(4)(5),;5),;6)5)3.3FUZZYAHP3.3.1　建立层次结构,,,,,,11N-1,,1G,ABCD,GABCD,A1A2A,1AHPAHPAHP,,,,,,ABCDG;,,D31G,GABCDABCDG,ABCD,,3.3.2　建立因素判断矩阵和方案判断矩阵,1ABCDG,ABCDG,4X4,,4G,1)116,,311A14218520034:[6,7]111(1,3](3,5](5,7](7,9)135kV,35kV,110kV,,1,1,,1.5,2,[1,1.5,2],[6][0.5,0.667,1],[5],[1,1,1]122(A142)(1)[1.000,1.000,1.000][1.000,1.500,2.000][5.000,6.000,7.000][0.500,0.667,1.000][1.000,1.000,1.000][4.000,5.500,7.000][0.143,0.167,0.200][0.143,0.182,0.250][1.000,1.000,1.000]C2,,,,,244747/24,1.958,[1.958,1.958,1.958]3:3(C2)(1)[1.000,1.000,1.000][0.511,0.511,0.511][0.596,0.596,0.596][1.958,1.958,1.958][1.000,1.000,1.000][1.167,1.167,1.167][1.679,1.679,1.679][0.857,0.857,0.857][1.000,1.000,1.000]2)11011,4,6,4.85,[4,4.85,6],[0.167,0.207,0.250][1,1,1]4:4(1)[1.000,1.000,1.000][0.167,0.207,0.250][4.000,4.850,6.000][1.000,1.000,1.000]3.3.3　求得综合判断矩阵并进行一致性校验,(A14),(2)3,,35(,5,)5(3)[1.000,1.000,1.000][1.000,1.000,1.000][1.000,1.000,1.000][0.167,0.207,0.250][0.167,0.210,0.250][0.167,0.207,0.250][4.000,4.850,6.000][4.000,4.750,6.000][4.000,4.850,6.000][1.000,1.000,1.000][1.000,1.000,1.000][1.000,1.000,1.000][5](8620034,)(2),(),6,78,6[1.000,1.000,1.000][0.167,0.208,0.250][4.000,4.808,6.000][1.000,1.000,1.000]7(A141)[1.000,1.000,1.000][0.200,0.225,0.250][0.250,0.292,0.333][4.000,4.444,5.000][1.000,1.000,1.000][2.000,2.500,3.000][3.000,3.429,4.000][0.333,0.400,0.500][1.000,1.000,1.000]8(A142)[1.000,1.000,1.000][1.000,1.500,2.000][5.000,6.000,7.000][0.500,0.667,1.000][1.000,1.000,1.000][4.000,5.500,7.000][0.143,0.167,0.200][0.143,0.182,0.250][1.000,1.000,1.000]3.3.4　求局部权重和综合权重(3)6,S=[(0.141,0.172,0.203),(0.606,0.828,1.135)]T(4)78,F=(0.090,0.106,0.124)(0.342,0.500,0.725)(0.435,0.556,0.704)(0.269,0.421,0.653)(0.269,0.338,0.430)(0.063,0.079,0.105)NA14=SF=[(0.220,0.432,0.848),(0.224,0.444,0.884),(0.076,0.124,0.206)]NA14A14,,GN=[(0.075,0.193,0.319),(0.131,0.297,0.413),(0.117,0.237,0.532)]3.3.5　综合权重的排序[8]N1=(l1,m1,u),N2=(l2,m2,u2),p(N1N2)=min{1-max(m1-l2m1-l1+m2-l2,0),1}+(1-)min{max(u1-m2u1-m1+u2-m2,0),0}(6)N1N2[8]0.5,;=0.5,;0.5,,=1p(N1N2)N1N2;=0,p(N1N2)N1N2,=0.5p(NiNj),pij,i,jN,P=(pij)33:P=0.50.3910.3400.6090.50.1850.6600.8150.58720034:[8],i=1Q(Qj=1pij+1-Q2)(7)[4],,=(0.244,0.265,0.491):,,,,,,4,,,,,,,,,,51,..,2000,24(15):59622PanJ,TekluY,RahmanS,DeCastroA.Aninterval-basedMADMapproachtothedentificationofcandi-datealternativesinstrategicresourceplanning.IEEETransactionsonPowerSystems,2000,15(4):144114463,..,2002,20(2):89924,.AHP.,1997,27(2):1651805,..:,19996SattyTL.TheAnalyticHierarchyProcess.McGraw-Hill,NewYork,19807,,,..,2001,18(5):798..,2002,16(1):4750(69),,,,,,,4,,,,,51,,..,2001,18(2):502,,,.Delphi5.:,20003.Delphi.:,20014,,,..,2002,28(3):318820034