一种新型高斯塞德尔算法在电力系统潮流计算中的应用研究

:2010-09-19;:2010-11-09:(1980-),,,DSP第28卷第6期2010年12月江西科学JIANGXISCIENCEVo.l28No.6Dec.2010:1001-3679(2010)06-0807-04涂志军,曹晔,李伟,赵俊(,330031):主要介绍了一种新型高斯-塞德尔算法在电力系统潮流计算中的应用首先分别详细推导了基于传统和新型高斯-赛德尔法的潮流计算公式,新方法节点电压方程式的表达形式与传统方法不同,计算公式更加简单,迭代次数减少;然后使用C++程序语言对高斯-赛德尔法进行编程,最后将所提出的新型高斯赛德尔算法应用于电力系统潮流计算的实例中,计算结果表明高斯-塞德尔新方法与传统方法相比,迭代次数减少了30%,而且加速系数的适用范围更加广泛:高斯赛德尔法;直角坐标潮流计算;电力系统:TP272:AAppliedResearchofaNewTtpeofGaussSeidelMethodinthePowerFlowComputationofPowerSystemTUZhijun,CAOYe,LIWe,iZHAOJun(CollegeofInformationEngineering,NanchangUniversity,JiangxiNanchang330031PRC)Abstract:ThispapermainlyintroducesanewtypeofGaussSidelmethodintheappliedreasearchofpowerflowcomputationofpowersystem.Firs,toldandnewGaussSidelmethodisdeducedrespectivelybasedondetailedconventiona.lExpressionformsofnodevoltageequationofnewmethodvaryfromtraditionalmethod.ComputationalformulaismuchsimplerandthenumberofiterativetimesmaybedecreasedandthenusetheC++programminglanguageforGaussSeidelmethodforprogramming.Finallytheproposednewhighmethodisappliedtoinstancesofpowerflowcalculation.Calculationresultsshowthatthenumberofthenewmethodsiterativetimescomparedwithtraditionalmethodsreducesby30%,andtheapplicationrangeoftheaccelerationfactorextendsforawiderrange.Keywords:Gausssidelmethod,Rectangularcoordinates,Powerflowcalculation,Powersystem0引言,,,-,,,,,,,,,,[1~5]1高斯赛德尔法直角坐标潮流计算公式的推导,,,:Pi-jQiVi=ViiVi+!nj=1j∀iYijVj(1)(1):Vi=1Yii[Pi-jQiV*i-!nj=1j∀iYijVj](2)n,PQm,m+1PV,n(2):V(k+1)i=1Yii[Pi-jQiV*(k)i-YisUs-!i-1j=1YijU(k)j-!n-1j=i+1YijU(k)j](3)(3):ik+1,k,,,(3)V(k+1)i=1Yii[Pi-jQiV*(k)i-YisUs-!i-1j=1YijUk+1j-!n-1j=i+1YijU(k)j](4),(4)Pi=Gii(e2i+f2i)+ei!nj=1j∀i(Gijej+Bijfj)+fi!nj=1j∀i(Gijfj+Bijej)(5)-Qi=Bii(e2i+f2i)+ei!nj=1j∀i(Gijfi+Bijei)-fi!nj=1j∀i(Gijei-Bijfi)(6)A1=!i-1j=1(Gije(k+1)j-Bijf(k+1)j)+!nj=i+1(Gijf(k)j-Bijf(k)j)A2=!i-1j=1(Gijf(k+1)j+Bije(k+1)j)+!nj=i+1(Gijf(k)j+Bije(k)j)(7)(7)(5)(6)Pi=Gii(e2i+f2i)+eiA1+fiA2(8)-Qi=Bii(e2i+f2i)+eiA1-fiA2(9)(9)(8)e(k+1)i=GiiG2ii+B2ii(Pie(k)i+Qif(k)i(e(k)i)2+(f(k)i)2-A1)+BiiG2ii+B2ii(Pif(k)i+Qie(k)i(e(k)i)2+(f(k)i)2-A2)(10)f(k+1)i=GiiG2ii+B2ii(Pif(k)i-Qie(k)i(e(k)i)2+(f(k)i)2-A2)-BiiG2ii+B2ii(Pie(k)i+Qif(k)i(e(k)i)2+(f(k)i)2-A1)(11)(10)(11)2高斯赛德尔法直角坐标改进法潮流计算公式的推导2.1PQ:Pi=Gii(e2i+f2i)+eiA1+fiA2(12)-Qi=Bii(e2i+f2i)+eiA1-fiA2(13)(12):e(k+1)i=-Qi-e(k)iA2+f(k)iA1-Bii(f(k)i)2Bii(14)(14),ie(k+1)i,(12)f(k+1)i,(12)Bii,(13)Gii,:BiiPi+GiiQi=BiieiA1+BiifiA2-GiieiA2+GiifiA1,,:808201028f(k+1)i=BiiPi+GiiQi-(BiiA1-GiiA2)e(k+1)iGiiA1+BiiA2(15)(15),f(k+1)ie(k+1)i,(14)(15)A1A2,eifi2.2PVPP|V|,,P|V|,f(k)p,e(k)pe(k)p=|V|2-(f(k)p)2f(k)pe(k)p,Q(k)p(13),Q(k)p=-Bpp((e(k)p)2+(f(k)p)2-e(k)pA2+f(k)pA1(16)Q(k)p,(15)f(k+1)p=(BppP(k)p+GppQ(k)p-(BppA1-GppA2)e(k)p)/(GppA1+BppA2)(17)(17),f(k+1)p,,e(k+1)p=|V|2-(f(k+1)p)2(18)e(k+1)p,P,|V|3潮流计算的程序框图1,C++,,,PQPV,1,,1EF,1,PV,,,,,4计算实例,,图12种高斯赛德尔法潮流计算程序框图2,123PQ,4PV5,图2五节点电力系统图4.1S1=-1.6-j0.8,S2=-2.0-j1.0,S3=-3.7-j1.3,P4=5.0;(813)8096::[1],,,.ICP-AES[J].,2010,30(1):251-254.[2],.ICPAES[J].,1995,(3):53-56.[3],.15[J].,2009,29(10):36-39.[4],,,.ICPAES[J].,2009,28(2):150-156.(809)(|V(0)1|=|V(0)2|=|V(0)3|=|V(0)4|=1.00,|V4|=|V5|=1.05);e(0)1=e(0)2=e(0)3=1.00,e(0)4=e5=1.05,f(0)1=f(0)2=f(0)3=f(0)4=f5=04.21k1k212k1(GS)k2(NGS)11751451.11441171.2119921.396691.476441.559421.6214561.71021.81,5,=1.3~1.6,96~214,69~56,,,5总结,,,,,,12,,,,30%,:[1],.()[M].:,2002.[2].[M].:,2007.[3].[M].:,1988.[4].C++()[M].:,2003.[5]PowerandEnergyResearchUnit,SchoolofElectricalEngineering,SuranareeUniversityofTechnology.ConvergenceimprovementofGaussSeidelpowerflowsolutionusingloadtransfertechniqueThongkrajay[R].NakhonRatchasimaThailand30000.8136:ICPAES