一种基于改进傅立叶级数的高精度谐波分析算法  

A high accuracy harmonic analysis algorithm based on modified Fourier series

作　　者：徐志钮[1] 律方成[1] 

机构地区：[1]华北电力大学河北省输变电设备安全防御重点实验室,河北保定071003

出　　处：《电力系统保护与控制》2011年第10期27-30,36,共5页Power System Protection and Control

基　　金：国家重点基础研究发展计划项目(973项目)(2009CB724508)

摘　　要：为了提高在较短采样时间长度下的谐波分析精确度,提出了一种改进傅立叶级数的谐波分析算法。该算法根据加汉宁(Hanning)窗插值的傅立叶算法获得信号的频率,基于该频率获得计算傅立叶级数时整周期的区间,使用插值获得了边界点的信号值,根据梯形插值积分公式计算谐波幅值和相位,提高了精确度。加汉宁窗插值傅立叶算法对信号频率的分析精度要远高于谐波相位的分析精确度,尤其在较短采样时间长度时,获得信号频率后截取整周期信号的积分能有效提高了加窗插值傅立叶算法在短采样时间长度下的谐波分析的精确度。同时算法原理较为简单,编程实现较为容易。编程实现了多种基于傅立叶变换的谐波分析算法,计算结果表明所提算法在较短的采样时间长度下精确度远高于其他算法,同时长采样持续时间时算法的精度也要更高一些。For improving harmonic analysis accuracy of short sampling duration time,a modified Fourier series algorithm is proposed.The method obtains the signal frequency by Hanning windowed and interpolated algorithm,and then the integer period signal is gotten based on the signal frequency,and the signal value of boundary point is obtained by interpolation.The harmonic amplitude and phase are calculated by trapezoidal interpolation formula and the accuracy is improved.Signal frequency calculation accuracy of the Hanning windowed and interpolated algorithm is higher than that of the harmonic phase,especially in short sampling duration time.So the method using the obtained signal frequency to get integer period signal can improve harmonic analysis accuracy in short sampling duration time.In the meantime,the method has simple principle and easy program realization.Multiple harmonic analysis algorithms based on Fourier transform are implemented,and calculation result indicates that the proposed algorithm by this paper has higher accuracy than other algorithms in different sampling duration time,especially in short sampling duration time.

关 键 词：电力系统 谐波分析 傅立叶级数 汉宁窗 梯形插值 

分 类 号：TM744[电气工程—电力系统及自动化]