改进的模糊C均值法在负荷特性统计数据聚类中的应用毕业论文-

改进模糊C-均值法在静态负荷特性数据聚类中的研究改进模糊C-均值法在静态负荷特性数据聚类中的研究改进的模糊C均值法在负荷特性统计数据聚类中的应用摘要电力负荷是整个电力系统的安全稳定运行中较活跃的一部分。建立符合实际的动态负荷模型对电力系统规划、设计和运行等诸方面均有十分重要现实意义。本文采用实用化负荷建模思想，对负荷特性进行聚类，从而为变电站建立合适的负荷模型打下基础。基于目前负荷建模方面存在的问题，使用模糊C均值法，对同一地域不同地点变电站的负荷统计数据进行聚类分析。针对湖南电网48个变电站，对模糊C均值法实施改进后对其进行聚类，并与未改进的模糊C均值法的聚类结果进行比较，以说明改进方案的有效性。关键字：电力负荷；负荷特性；聚类；模糊C均值法APPLICATIONOFIMPROVEDFCMTOELECTRICLOADCHARACTERISTICSOFSTATISTICALDATACLUSTERINGABSTRACTThepowerloadisanactivepartinthesecurityandstableoperationoftheentireelectricalpowersystem.Itissignificantlyimportanttomakesuitableloadmodelforthepowersystemplanning,designandoperation.Inthispaperthepracticalloadmodelingmethodisemployed,andtheloadcharacteristicsisclusteredtoestablishtheactualloadmodelforsubstations.Basedonthecurrentproblems,FCMwithhierarchicalclusteringisusedtoperformtheclusteringoftheloadcharacteristicsdataofthedifferentsubstationsonthesamearea,theimprovedmethodisappliedfortheclusteringofHunangridsubstation.Theclusteringresultshowsthattheimprovedmethodiseffectivecomparingwiththeunimprovedmethod.KeyWords:powerload;loadcharacteristic;cluster,FCM目录第一章绪论11.1研究背景11.2发展及研究现状21.2.1发展21.2.2研究现状电力负荷建模的总体原则电力负荷建模的基本概念分类51.2.3实用化负荷建模思想统计综合法总体测辨法71.3聚类分析在负荷特性分析中的应用现状81.4本文主要研究内容9第二章聚类分析102.1聚类分析的基本概念102.2聚类方法112.3系统聚类法152.3.1最小张树聚类法162.3.2基于密度的聚类算法162.3.3基于网络的聚类方法162.3.4基于模型的聚类算法162.3.5基于划分的聚类算法162.4各算法优缺点比较17第三章模糊C均值在负荷特性聚类中的应用实例193.1聚类在电力系统中的应用综述193.2模糊C均值聚类算法203.2.1硬C均值聚类算法（HCM）203.2.2模糊C均值聚类223.2.3程序流程图233.3对模糊C均值法的改进253.3.1改进的各方案比较253.3.2最终改进方案的选定263.4聚类实例273.4.1原始数据聚类数据273.4.2未改进的模糊C均值法在实例中的应用273.4.3改进的模糊C均值法在实例中的应用283.4.4两种算法的比较293.5结果分析31第四章结语33参考文献34致谢35附录36附录A原始聚类数据36附录B系统聚类法所得的聚类中心生成的隶属度矩阵38附录C改进的模糊C均值法源程序41附录D类间距离计算源程序47附录E类内距离计算源程序48第⑥负荷聚类为没有安装布测点的变电站建立实用模型提供了有效途径，从而克服了广域电力系统为变电站均安装负荷测辨装置的不可行性，所带来的负荷模型建立的种种困难。负荷测辨装置安装在每一类的典型变电站中，记录下实测数据并为理想安装测点的典型变电站建立相应的负荷模型，而对于同类中未布测点则可以通过数学方法确定该类中其它没有安装测辨装置的变电站的综合负荷模型。这个过程考虑了负荷时变性特性，为综合测辨法应用于实用化负荷建模工作开辟了一条崭新的途径。结语1.随着电力系统规模和容量的不断扩张，电力系统安全经济运行的重要性和复杂性愈发显著地表现出来，安全性和经济性是相互关联又互相矛盾的两个方面，只有充分了认识到了电力系统的运行规律，才能找到即安全又经济的运行方式。2.本文基于目前负荷建模方面存在的问题，采用实用化负荷建模思想，认识到属于同一类的负荷具有相对稳定的性质和共同的特点，引入聚类分析法对同一地域不同地点电站的负荷统计数据进行聚类分析。本文对模糊C均值法加以改进后再对该数据进行聚类，并与未改进的模糊C均值法加以比较。3.本文研究内容及成果如下：查阅有关文献，总结了近年来负荷建模的研究现状，几种常用的聚类算法；深入学习了模糊C均值聚类算法，掌握了其基本理论和算法特点；了解了MATLAB软件及其工具箱。对传统的模糊C均值法做了改进，使其克服了对初值敏感，易受孤立点影响的不足。对改进算法和未改进算法的聚类结果进行了比较，结果表明，两项指标均有改善，改进后的模糊C均值法较改进以前有了一定的优势。模糊聚类计算结果中的聚类中心矩阵给我们对建模数据的采样点的选择即负荷测辨装置的安装地点提供了可靠依据，我们可根据聚类结果，将每类做成一个通用的模型，并且推广到同类的其他变电站中，负荷特性聚类是综合测辨法实用负荷建模过程的一个基础部分，因此，本文研究具有一定的实用价值。参考文献[1]孙即祥.现代模式识别[M].国防科技大学出版社，2001.[2]高惠璇.应用多元统计分析[M].北京大学出版社,2005.[3]肖健华.智能模式识别方法[M].华南理工大学出版社,2005.[4]章健.电力系统负荷建模方法的研究[D].华北电力大学博士学位论文,1997.[5]张红斌.电力系统负荷模型结构与参数辨识的研究[D].华北电力大学博士文,2003.[6]鞠平.综合负荷特性的分类综合方法及应用[J].电力系统自动化.2004,28(1):64-68[7]贺仁睦.电力系统负荷模型的分类与综合[J].电力系统及其自动化.1999,23(19):12-16.[8]熊传平.广域电力系统基于负荷分析与分类的负荷建模研究[D].河海大学硕士论文.2006.[9]金艳.综合动态负荷特性的分类与综合研究.河海大学硕士论文.2002.[10]贺仁睦，魏孝铭，韩民晓.电力负荷动特性实测建模的外推和内插[J].中国电机工程学报,1996(3):151-154.[13]李力，朱守真，沈善德等.负荷动态模型集结[J].电力自动化设备.Vol.19,No.4,Aug,1999:6-10,19.[14]陈柔伊，张尧，武至刚，陈泽怀改进的模糊聚类算法在负荷预测中的应用.电力系统及自动化学报2005.617卷.[15]王天行,张泽.多元统计分析学[M].成都:成都科技大学出社.1992:199～214.[16]吴元奇，冯荣扬.聚类分子计算方法的理论及结果比较.广东：湛江海洋大学学报.2002.2.[17]王成山，曹旌，陈光远.基于聚类分析的电力系统暂态稳定故障筛选.电网技术,2005.[18]徐南荣，宋文忠，夏安邦.系统辨识.南京:东南大学出版社，1991.[19]鞠平,马大强。电力系统负荷建模[M].水利电力出版社，1995.致谢本论文是在导师王进副教授的悉心指导下完成的，半年来，导师的教诲和关怀使我受益匪浅，特别是导师渊博的学识、严谨的、科学的治学态度和平易近人的工作作风是我终生学习的楷模，借此论文完成之际，谨向导师的辛勤培养表达我最诚挚的谢意！同时感谢徐超学长和王文生学长在我设计期间所给予的指导和无私帮助！最后向所有曾给予过帮助和关心的学长、亲人、朋友表示诚挚的感谢和深深的祝福！谢谢你们！XXX2010.6附录A原始聚类数据注：系统聚类法得到的冰柱图程序：Y=pdist(data);Z=linkage(Y,'average');H=dendrogram(Z,0);附录B系统聚类法所得的聚类中心生成的隶属度矩阵U=Columns1through110.02540.05710.04250.01880.13790.03640.03930.09610.09760.64120.01400.81510.59980.72610.82690.03800.60260.02050.03210.03060.01080.01570.02460.05790.02540.02260.08550.05050.09330.05750.08110.00870.01360.01540.03780.02320.01120.16230.02150.03140.05210.10450.23480.00690.02260.05080.02940.01980.35180.04220.68900.46070.48500.02780.02600.06650.12330.10280.07370.09430.18840.06720.17490.08330.02410.89460.03040.07330.05060.02690.13020.05830.05920.12660.11790.05270.0291Columns12through220.00810.05770.01920.07780.05990.20950.01860.03070.19190.00190.19610.01150.04600.02720.23030.43320.04660.00840.03020.03150.00250.06930.91570.10800.76640.13040.08740.04240.02610.69500.04540.97960.05910.00620.03490.01360.04750.03560.18610.01350.02510.11850.00140.09480.02430.27490.06930.11600.07310.13350.87110.11400.34700.00640.18670.02230.34560.07270.29240.23400.10550.03280.06360.10760.00540.21090.01180.13290.03150.10560.07680.27650.02950.04160.15800.00280.1832Columns23through330.31290.13120.07080.01440.02160.07740.13820.08670.08770.17520.07770.03570.01690.01920.00270.79170.30980.01880.17230.04040.03680.14400.03150.01750.01650.00210.01890.06590.01960.06350.02850.04870.04240.15540.68460.04760.00660.01160.04630.64410.05030.05560.20360.03560.11340.05030.04980.00720.02010.07730.05780.08520.07140.16420.07270.10340.03220.05450.00940.10560.26480.03650.31960.10470.09190.51590.24760.06740.74150.95760.03050.15860.08500.22250.61180.27950.1117Columns34through440.12570.39480.77630.88740.15150.74530.05460.16030.04770.24480.01760.04520.06420.01460.00430.01010.01700.05180.26740.12530.01500.87820.03480.02810.00860.00340.00890.00980.30490.04990.10400.01580.01290.04560.08960.08820.05760.74160.10010.03690.07950.02710.55710.01020.12130.06950.02380.01190.02650.02660.26250.07480.08580.05700.01370.42930.16020.02970.01050.01970.03380.20220.21070.53440.03490.04540.19810.19370.05880.02490.04170.06740.08720.15720.07580.07530.0220Columns45through480.21930.14000.37740.17240.01100.05400.02620.01540.00900.03670.02680.01270.66290.07190.13010.67180.02620.09830.14260.03360.02160.15930.09100.02810.05000.43990.20600.0660附录C改进的模糊C均值法的源程序function[center,U,obj_fcn]=fcm(data,cluster_n,options)%FCMDatasetclusteringusingfuzzyc-meansclustering.%%[CENTER,U,OBJ_FCN]=FCM(DATA,N_CLUSTER)findsN_CLUSTERnumberof%clustersinthedatasetDATA.DATAissizeM-by-N,whereMisthenumberof%datapointsandNisthenumberofcoordinatesforeachdatapoint.The%coordinatesforeachclustercenterarereturnedintherowsofthematrix%CENTER.ThemembershipfunctionmatrixUcontainsthegradeofmembershipof%eachDATApointineachcluster.Thevalues0and1indicatenomembership%andfullmembershiprespectively.Gradesbetween0and1indicatethatthe%datapointhaspartialmembershipinacluster.Ateachiteration,an%objectivefunctionisminimizedtofindthebestlocationfortheclusters%anditsvaluesarereturnedinOBJ_FCN.%%[CENTER,...]=FCM(DATA,N_CLUSTER,OPTIONS)specifiesavectorofoptions%fortheclusteringprocess:%OPTIONS(1):exponentforthematrixU(default:2.0)%OPTIONS(2):maximumnumberofiterations(default:100)%OPTIONS(3):minimumamountofimprovement(default:1e-5)%OPTIONS(4):infodisplayduringiteration(default:1)%Theclusteringprocessstopswhenthemaximumnumberofiterations%isreached,orwhentheobjectivefunctionimprovementbetweentwo%consecutiveiterationsislessthantheminimumamountofimprovement%specified.UseNaNtoselectthedefaultvalue.%%Example%data=rand(100,2);%[center,U,obj_fcn]=fcm(data,2);%plot(data(:,1),data(:,2),'o');%holdon;%maxU=max(U);%%Findthedatapointswithhighestgradeofmembershipincluster1%index1=find(U(1,:)==maxU);%%Findthedatapointswithhighestgradeofmembershipincluster2%index2=find(U(2,:)==maxU);%line(data(index1,1),data(index1,2),'marker','*','color','g');%line(data(index2,1),data(index2,2),'marker','*','color','r');%%Plottheclustercenters%plot([center([12],1)],[center([12],2)],'*','color','k')%holdoff;%%SeealsoFCMDEMO,INITFCM,IRISFCM,DISTFCM,STEPFCM.%RogerJang,12-13-94,N.Hickey04-16-01%Copyright1994-2002TheMathWorks,Inc.%$Revision:1.13$$Date:2002/04/1422:20:38$ifnargin~=2&nargin~=3, error('Toomanyortoofewinputarguments!');enddata_n=size(data,1);in_n=size(data,2);%Changethefollowingtosetdefaultoptionsdefault_options=[2; %exponentforthepartitionmatrixU 100; %max.numberofiteration 1e-5; %min.amountofimprovement 1]; %infodisplayduringiterationifnargin==2, options=default_options;else %If"options"isnotfullyspecified,paditwithdefaultvalues. iflength(options)<4, tmp=default_options; tmp(1:length(options))=options; options=tmp; end %Ifsomeentriesof"options"arenan's,replacethemwithdefaults. nan_index=find(isnan(options)==1); options(nan_index)=default_options(nan_index); ifoptions(1)<=1, error('Theexponentshouldbegreaterthan1!'); endendexpo=options(1); %ExponentforUmax_iter=options(2); %Max.iterationmin_impro=options(3); %Min.improvementdisplay=options(4); %Displayinfoornotobj_fcn=zeros(max_iter,1); %ArrayforobjectivefunctionU=initfcm(cluster_n,data_n); %Initialfuzzypartition%Mainloopfori=1:max_iter, [U,center,obj_fcn(i)]=stepfcm(data,U,cluster_n,expo); ifdisplay, fprintf('Iterationcount=%d,obj.fcn=%f\n',i,obj_fcn(i)); end %checkterminationcondition ifi>1, ifabs(obj_fcn(i)-obj_fcn(i-1))<min_impro,break;end, endenditer_n=i; %Actualnumberofiterationsobj_fcn(iter_n+1:max_iter)=[];Function[U_new,center,obj_fen]=stepfcm(data,U,cluster_n,expo)%STEPFCMOnestepinfuzzyc-meanclustering%[U_NEW,CENTER,ERR]=STEPFCM(DATA,U,CLUSTER_N,EXPO)%performsoneiterationoffuzzyc-meanclustering,where%%DATA:matrixofdatatobeclustered.(Eachrowisadatapoint.)%U:partitionmatrix.(U(i,j)istheMFvalueofdatajinclusterj.)%CLUSTER_N:numberofclusters.%EXPO:exponent(>1)forthepartitionmatrix.%U_NEW:newpartitionmatrix.%CENTER:centerofclusters.(Eachrowisacenter.)%ERR:objectivefunctionforpartitionU.%%Notethatthesituationof"singularity"(oneofthedatapointsis%exactlythesameasoneoftheclustercenters)isnotchecked.%However,ithardlyoccursinpractice.%%SeealsoDISTFCM,INITFCM,IRISFCM,FCMDEMO,FCM.%RogerJang.11-22-94.%Copyright1994-2002TheMathWorks,Inc.%$Revision:1.13$$Date:2002/04/1422:21:02$Mf=U,^expo;%MFmatrixafterexponentialmodificationcenter=mf*data./((ones(size(data,2),1)*sum(mf))`);%newcenterdist=distfcm(center,data);%fillthedistancematrixobj_fcn=sum(sum((dist.^2).*mf));%objectivefunctiontmp=dist.^(-2/(expo-1));%calculatenewU,supposeexpo!=1U_new=tmp./(ones(cluster_n,1)*sum(tmp));Functionout=distfcm(center,data)%DISTFCMDistancemeasureinfuzzyc-meanclustering.%OUT=DISTFCM(CENTER,DATA)calculatestheEuclideandistance%betweeneachrowinCENTERandeachrowinDATA,andreturnsa%distancematrixOUTofsizeMbyN,whereMandNarerow%dimensionsofCENTERandDATA,respectively,andOUT(I,J)is%thedistancebetweenCENTER(I,:)andDATA(J,:).%%SeealsoFCMDEMO,INITFCM,IRISFCM,STEPFCM,andFCM.%RogerJang,11-22-94,6-27-95.%Copyright1994-2002TheMathWorks,Inc.%$Revision:1.13$$Date:2002/04/1422:20:29$out=zeros(size(center,1),size(data,1));%f