基于三次样条插值的算术傅里叶谐波分析方法  

Study on harmonic analysis based on cubic spline interpolated arithmetic fourier transform

作　　者：武婕[1] 刘开培[1] 乐健[1] 陈宜皇 

机构地区：[1]武汉大学电气工程学院,武汉430072

出　　处：《电测与仪表》2016年第1期15-18,31,共5页Electrical Measurement & Instrumentation

基　　金：国家自然科学基金(51007065)

摘　　要：数字化变电站采用固定采样频率10 k Hz采样数据,每周期采样点数为200,不为2的整数次幂;且基波频率的波动会导致非同步采样,直接运用离散傅里叶或快速傅里叶变换分析谐波,会对测量结果产生较大误差,不满足电力系统谐波分析精度的要求。算术傅里叶变换(AFT)算法简单且并行性好,对计算点数无限制,适用于分析离散信号的频谱。但该算法需要不均匀的采样点,目前电力系统所得到的是均匀采样的数据,因此运用AFT时需先对均匀采样的离散信号进行插值,而插值过程将不可避免地引入误差,影响到AFT算法的谐波分析精度。AFT常用的插值算法为零次插值,此方法存在较大误差,严重影响谐波分析精度,不能满足电力系统的要求。对比了四种平面插值算法,通过仿真分析比较了这四种方法对AFT谐波分析精度的影响。最后选用三次样条插值算法来提高AFT的谐波分析精度。仿真结果表明:在非同步采样条件下,用三次样条插值的AFT谐波分析方法精确度高,稳定性好,满足谐波分析精度的要求,为电力系统谐波分析开辟了新思路。The data sampling frequency of the signals in digital substation is normally a fixed 10 k Hz. The sampled points in every period are 200,not an integer power of 2. Meanwhile,the fluctuating frequency of fundamental wave will result in non-synchronized sampling. Analyzing harmonic by using Discrete Fourier or Fast Fourier transform could bring great errors in the results,and the accuracy can＇t meet the requirements in power system. The Arithmetic Fourier transform（ AFT） is more appropriate for analyzing discrete signals due to the advantages such as simple computation,good parallelism and no limitation on sampled numbers. It requires non-uniform sampling points,while the sampled points in power system are uniformed,so the uniform sampled signals should be interpolated when using AFT.The interpolation method of AFT keeps using is the zero interpolation. It produces a negative effect on the accuracy of the harmonic analysis,which can＇t satisfy the requirements in power system. This paper proposes a new interpolation method of AFT after comparing the accuracy performance of four interpolation methods. Finally,the cubic spline interpolation is selected to improve the accuracy due to its higher precision and better stability. The MATLAB simulation results show that the new interpolation can meet the requirements of power system harmonic analysis in non- synchronization sampling and provides new ways for harmonic analysis.

关 键 词：算术傅里叶变换 插值法 非同步采样 精度 

分 类 号：TM762[电气工程—电力系统及自动化]