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244Vol.24No.4Apr.200420044ProceedingsoftheCSEE©2004Chin.Soc.forElec.Eng.0258-8013200404-0050-08TM715;O225A470·405111213000722200223ANIAHP-BASEDMADMMETHODINURBANPOWERSYSTEMPLANNINGXIAOJun1,WANGCheng-shan1,ZHOUMin21.SchoolofElectricalEngineeringandAutomation,TianjinUniversity,Tianjin300072,China;2.ShinanPowerSupplyCompany.SMEPC,Shanghai200233,ChinaABSTRACT:Inordertosolvemulti-attributedecision-making(MADM)probleminurbanpowersystemplanning,anintervalanalytichierarchyprocess(IAHP)-basedmethodisproposedandappliedtoapracticalplanningcase.Inthiscase,awholeprocessoftheIAHP-basedMADMmethodisillustratedstepbystep.Insidetheproposedmethod,anindextoevaluatetheconsistenceofIAHPjudgmentmatrixisbuiltup;andthealgorithmofweightsolutioninIAHPisalsoimproved.Furthermore,thehierarchysetupinthecasecanbewidelyappliedtosimilarcasesinurbanpowernetworkplanning.ThecasestudyindicatesthatthepresentedapproachsignificantlysimplifiesthecomplicatedMADMproblemsintheplanning,andcombinestheadvantagesofbothhumanexpertiseandcomputingpowerfrommachinecalculation.Meanwhile,theintervaltechnologyenablesthemethodtosuccessfullydealwithuncertaintiesinMADMattributesandvagueofexperts’judgment.itissummarizedthattheIAHP-basedMADMmethodisapracticalsolutioninurbanpowersystemplanning.KEYWORDS:Urbanpowersystemplanning;MADM;AHP;Interval;Judgmentmatrix;Consistence;WeightAHP99C26221200375ProjectSponsoredbyInnovationFundforSmallTechnology-basedFirmsofChina99C262212003751[1]MADMMCDM[2][3][4]AHPLP451AHPLP[5]AHP/Tradeoff/Risk[6]AHP[7]2AnalyticHierarchyProcessAHP1977Satty[8]AHP[9](IntervalAHPIAHP)IAHPAHPX=[x-,x+]x+x-AHPIAHPAHPIAHPIAHP3762km27.43km22.4km2CNP2.5[1]789.6MW14.5MW/km235kV110kV3135kV35kV471735kV35kV35kVT220kV35kV220kV52242110kV35kV110kV110kV1435kV10220kV9110kV3110kV10kV35kV113110kV35kV110kV635kV2212220kV34IAHP4.1AHPAHPAHP1GAB2CDA2A1B1B2D13C1C2D2A1135kVTA12A13A14A21A22D34B21B22D31D32A141A142N-112341AHPFig.1AHPhierarchyofthecase3GABCDGABCDA1A2A1AHPAHPAHPA453BCDG123D31GGABCDABCDGABCD4.211611Tab.1Decisiontableofalternatives1(35kV)2(110kV)3()35kVT(23%~26%)(3%~32%)(25%~32%)/km2.9722.7802.837/km0.7031.0050.703/808957689879710/%0.980.680.73/%0.120.180.1247()24()28()()()()()()()35kV35kV110,35220kV35kV110kV123%~26%220kV23%220kV26%4.31ABCDGABCDG4×44G[8]1116[2,3]AHP[8]154242AHPAHPAHPAHPAHP1163×322Tab.2Judgmentmatrixofalternatives1A11P-35kVT2A12P-3A13P-4A141P-5A142P-6A21P-7A22P-8B1P-9B21P-10B22P-11C1P-12C2P-13D1P-14D2P-15D31P--16D32P--2D31P220kV3AHP1-9[8]3211220kV35kV35kV2220kV35kV35kV211-9[69]3431-9Tab.3Reciprocal1-9scalarsystem135792,4,6,84D31PTab.4Pair-wisecomparisonofjudgmentmatrixD31P21-[69]31-[69]32[12]ijaijjiajiaij1/aij221[69]12[1/91/6]455ijaijij21a2121[69]a1212[69][1/91/6]aiii[11]5D31PTab.5JudgmentmatrixD31Paij1231[1.0000,1.0000][0.1111,0.1667][0.1111,0.1667]2[6.0000,9.0000][1.0000,1.0000][0.5000,1.0000]3[6.0000,9.0000][1.0000,2.0000][1.0000,1.0000]C2P4552124472147/241.9538[1.95381.9538]66C2PTab.6JudgmentmatrixC2P1231[1.0000,1.0000][0.5106,0.5106][0.5957,0.5957]2[1.9538,1.9538][1.0000,1.0000][1.1667,1.1667]3[1.6786,1.6786][0.8571,0.8571][1.0000,1.0000]211077Tab.7Judgmentmatrixofattributes1G42A23B24C25D36A147A228A142-9B2210D32-DD1D2D3DD2D1[11.5]D3D1[78]D3D2[68]88DTab.8JudgmentmatrixDD1D2D31[1.0000,1.0000][0.6667,1.0000][0.1250,0.1429]2[1.0000,1.5000][1.0000,1.0000][0.1250,0.1667]3[7.0000,8.0000][6.0000,8.0000][1.0000,1.0000]4.4312132321-93[10,11]AHPCR[8]nA=[aij]n×nW={W1,W2,..,Wn}3.5λmax[8]iniinW/)(1max∑==AWλ(1)(AW)iAWiλmaxCR[8]CR0.1A56899Tab.9ConsistenceindexofjudgmentmatrixCRCRD31P[0.00000,0.11614]0.05807C2P[0.00000,0.00000]0.00000D[0.00000,0.10802]0.054019[11]C2PCR[00]D31PDCR0.0580.0540.1[11]56244.5(IEM)[10][9]λmaxW1-9AnxnAW=λmaxW(2)Guass-SiederW(k+1)=(1/λmax(k))AW(k)(3)kW(k+1)k+1λmax(k)(1)()()()max1()/nkkkiiinWλ==∑AW(4)||W(k+1)–W(k)||ee||·||X={xi}xi=[xi-,xi+]||X||=max{|xi+|},i=1,,n(5)λmaxW[9]λmaxλmax(1)[9]IAHPD31PC2PD1010Tab.10JudgmentmatrixweightvectorW1W2W3D31P[0.0528,0.0719][0.3326,0.4955][0.4170,0.6301]C2P[0.2157,0.2157][0.4223,0.4223][0.3620,0.3620]D[0.0897,0.1112][0.1021,0.1342][0.7098,0.8530]10W1W2W33D31P3[0.05280.0719][0.033260.4955][0.41700.6301]13232123310C2P4.6)(1)()1(kjnjkijkiWWW∑=+=i=1,2,…,m(6)mWi(k+1)ik+1A(k+1)nA(k+1)Wj(k)A(k+1)kjWij(k)ij1G01C2C1C21C1C2W11(2)W12(2)W11(2)=[0.4129,0.4943]W12(2)=[0.2157,0.2157]C1C2CW1(2)W2(2)W1(2)=[0.1206,0.1525]W2(2)=[0.7625,0.9645]1C0.2834][0.2142,)2(2)2(12)2(1)2(11)2(21)2(1)1(1=+==∑=WWWWWWWjjj(6)123[0.152,0.388][0.226,0.568][0.233,0.581][12]X=[x-,x+],Y=[y-,y+]X≥Ymax[(0,()()max(0,)]()()()LXLYyxPXYLXLY+−+−−≥=+(7)L(X)=x+-x-L(Y)=y+-y-(7)4571111Tab.11Judgmentmatrixofglobalweightsortpossibility12310.50000.28090.265720.71910.50000.484930.73430.51510.50000-1[12]0.2330.3790.389332123112331051AHP2CR3[1]YuYixinWangChengshanXiaoJunetalAcomputerdecisionsupportsystemofurbanpowersystemplanning[J]AutomationofElectricPowerSystems200024(15)59-62[2],HuangZhongwuZhongDanhongWuJieetalApplicationoffuzzycomprehensivedecisiontolongtermpowersystemplanning[J]Distribution&Utilization2001018(005)7-9[3]WuLiZhouLerongWuJieetalFuzzymulti-objec