基于Matlab的加窗FFT电力系统谐波分析

基于Matlab的加窗FFT电力系统谐波分析目录摘要：............................................................................................................................11绪论.............................................................................................错误!未定义书签。1.1课题背景、研究意义.......................................................错误!未定义书签。1.2谐波的危害与来源..........................................................错误!未定义书签。1.2.1谐波来源...................................................................错误!未定义书签。1.2.2电力系统谐波的危害...............................................................................31.3谐波检测..........................................................................错误!未定义书签。1.4谐波的标准与指标..........................................................错误!未定义书签。1.5国内外关于谐波的研究现状..........................................................................52谐波分析测量.............................................................................错误!未定义书签。2.1傅里叶级数与系数..........................................................错误!未定义书签。2.2傅里叶级数的复指数形式..............................................错误!未定义书签。2.3谐波相量的卷积..............................................................................................92.4傅里叶变换......................................................................错误!未定义书签。2.5快速傅里叶算法..............................................................错误!未定义书签。2.6傅里叶变换基本思想......................................................错误!未定义书签。2.7几种傅里叶变换的介绍.................................................................................142.7.1基-2FFT..............................................................错误!未定义书签。42.7.2实值FFT................................................................错误!未定义书签。2.7.3局部FFT................................................................错误!未定义书签。3基于FFT谐波法研究检测方法................................................错误!未定义书签。3.1FFT算法存在的问题.......................................................错误!未定义书签。3.1.1奈奎斯特频率和混叠............................................错误!未定义书签。3.1.2栅栏效应..............................................................................................193.1.3频谱泄露..............................................................错误!未定义书签。03.2算法的优化....................................................................错误!未定义书签。03.2.1窗函数..................................................................错误!未定义书签。03.2.2窗函数的选择........................................................错误!未定义书签。3.3FFT问题的优化.............................................................错误!未定义书签。44仿真实验与分析........................................................................错误!未定义书签。4.1仿真的理论依据...............................................................错误!未定义书签。4.2仿真实验与分析.............................................................错误!未定义书签。5参考文献......................................................................................错误!未定义书签。8致谢..............................................................................................错误!未定义书签。0附录................................................................................................错误!未定义书签。1基于Matlab的加窗FFT电力系统谐波分析摘要：随着电力系统中非线性电力元件的增多，电网中谐波分量大大增加，谐波污染的情况也日益严重，对电力系统的安全经济运行造成了极大的影响。谐波测量是谐波问题研究的主要依据，实时测量电网中的谐波含量，确切掌握电网中谐波的实际情况，对于防止谐波危害，维护电网的安全运行是十分必要的。对于谐波的分析，常用的分析方法有快速傅里叶变换（FFT），沃尔什变换（Walsh）,哈里特变换（Harley）和小波变换（Wavelets）等。快速傅里叶变换方法因为具有实现简单，精确度较好，功能较为丰富等优点，所以被用来作为常用的谐波检测方法，但是由于谐波分析时同步采样的难度较大，造成采样频谱泄露、栅栏效应，频率混叠等问题，使得算出的谐波精度不高。针对快速傅里叶变换测量谐波精度不足的缺点，通常采用加窗值FFT和全相位FFT等方式进行FFT的优化。本文的重点工作是：分析FFT算法存在的缺陷以及针对这些缺陷进行的改进，分析了多种窗函数的特性，并根据多种穿函数的优缺点，适当的将多个窗函数组合起来，达到更高的精度，仿真的结果表明，这种方法是切实可行的，能够达到足够的精度要求。关键词：电力系统，谐波，FFT，窗函数，加窗。2HarmonicanalysisofpowersystembasedonMatlabforFFTpowersystemAbstract：Withtheincreaseofpowersystemnonlinearelectricelements,harmoniccomponentisgreatlyincreased,harmonicpollutionisbecomingmoreandmoreserious,thesafeandeconomicoperationofpowersystemcausedagreatimpact.Harmonicmeasurementisamainbasisinthestudyofharmonicproblems,real-timemeasurementinpowergridharmoniccontent,theexactgrasptheactualconditionsofpowernetworkharmonic,topreventtheharmofharmonics,maintenanceandthesafetyoperationofthepowergridisverynecessary.Fortheharmonicanalysis,thecommonmethodsofanalysisarefastFouriertransform(FFT),Walshtransform(Walsh),Harriettransform(Harley)andwavelettransform(Wavelets),etc.FastFouriertransformmethodforitsrealizationissimple,goodaccuracyandmorefeaturerichandadvantages,itisusedforasacommonlyusedharmonicdetectionmethods,butduetotheharmonicanalysisofsynchronoussamplingdifficultyisgreater,causesamplingfrequencyspectrumleakageandpicketfenceeffect,frequencymixedstackandotherissues,makingthecalculatedharmonicprecisionisnothigh.InviewoftheshortcomingsofthefastFouriertransformformeasuringharmonicaccuracy,theoptimizationofFFTbyaddingwindowvalueFFTandfullphaseFFTisusuallyused.Thefocusofthispaperis:analysisofFFTalgorithminthepresenceofdefectsandimprovementforthesedefects,analysisthecharacteristicsofvariouswindowfunctions,andaccordingtotheadvantagesanddisadvantagesofwearingavarietyoffunctions,appropri