基于三次样条插值的算术傅里叶谐波分析方法

武婕; 刘开培; 乐健; 陈宜皇

武婕,刘开培,乐健,陈宜皇.基于三次样条插值的算术傅里叶谐波分析方法[J].电测与仪表,2016,53(1):.
Wu Jie,Liu kaipei,Le Jian,Chen YiHuang.Study on Harmonic Analyzing Based on Cubic Spline Interpolated Arithmetic Fourier Transform[J].Electrical Measurement & Instrumentation,2016,53(1):.

基于三次样条插值的算术傅里叶谐波分析方法

Study on Harmonic Analyzing Based on Cubic Spline Interpolated Arithmetic Fourier Transform

DOI：

中文关键词: 算术傅里叶变换插值法非同步采样精度

英文关键词:Arithmetic Fourier transform, interpolation methods, harmonic in power system, precision

基金项目:国家自然科学基金（51007065）

作者中文名	作者英文名	单位
武婕	Wu Jie	武汉大学电气工程学院
刘开培	Liu kaipei	武汉大学电气工程学院
乐健	Le Jian	武汉大学电气工程学院
陈宜皇	Chen YiHuang	武汉大学电气工程学院

摘要点击次数: 2080

中文摘要:

摘要：数字化变电站采用固定采样频率10kHz采样数据，每周期采样点数为200，不为2的整数次幂；且基波频率在规定范围内波动，很难做到同步采样，直接运用快速傅里叶变换分析谐波将存在较大误差，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，而目前电力系统所得到的均是均匀采样的数据，因此应用AFT时首先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AFT算法的谐波分析精度。AFT常用的插值算法为零次插值，该算法存在较大误差，严重影响谐波分析精度，不能满足电力系统的要求。本文对比了四种常用的平面插值算法，包括零次插值、一阶线性插值、分段三阶Hermite插值和三次样条插值。通过仿真分析比较了这四种插值方法对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，满足谐波分析的精度要求，为谐波分析开辟了新思路。

英文摘要:

Abstract：The data sampling frequency of the signals in digital substation is normally a fixed 10kHz. The sampled points in every period are 200, not an integer power of 2. Meanwhile, it is very difficult to perform synchronized sampling for the fundamental frequency is fluctuating in the prescribed scope. The Fast Fourier transform may not suitable for its harmonic analysis. 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, so the uniform sampled signals should be interpolated when using AFT. The interpolation method 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, i.e. the zero interpolation、the first-order linear interpolation、the piecewise cubic hermit interpolation and the cubic spline interpolation. 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, and provides new ways for harmonic analysis.

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