基于Nuttall窗双谱线插值FFT的电力谐波分析方法

An Approach for Electrical Harmonic Analysis Based on Nuttall Window Double-spectrum-line Interpolation FFT

快速傅里叶变换(fast Fourier transform,FFT)因其易于嵌入式系统实现而被作为电力谐波分析的主要方法,但电力谐波分析时很难做到同步采样和整数周期截断,由此造成的频谱泄漏将影响测量结果的准确性。加窗和插值修正算法可改善基于FFT的谐波参数计算的准确度。该文讨论Nuttall窗的旁瓣特性和双谱线插值算法,提出基于Nuttall窗双谱线插值FFT的电力谐波分析方法,用曲线拟合函数求出实用的双谱线插值修正公式,大大减少了计算量。仿真结果表明,提出的谐波分析方法在非同步采样和非整数周期截断条件下,21次谐波幅值计算误差小于等于0.0009%,初相位计算误差小于等于0.04%。

The fast Fourier transform （FFT） had already become a main method of the electrical harmonic analysis since it＇s easily realized in embedded system, but there were difficulties in performing synchronized sampling and integral period truncation in the electric power harmonic analysis, and the accuracy of the analysis result would be disturbed by the frequency leakage. Some efforts had been made, such as the utilization of window functions and interpolation algorithms, to improve the accuracy of harmonic parameters computation by FFT. The sidelobe characteristic of Nuttall window and the double-spectrum-line interpolation algorithm were both discussed, an approach for electrical harmonic analysis based on the Nuttall window double-spectrum-line interpolation FFT was proposed, the applicable rectification formulas of the double-spectrum-line interpolation was obtained by using polynomial curve fit functions, and subsequently calculating burden was dramatically reduced. The simulation results indicate that, by using the approach presented in this paper under the non-synchronized sampling and non-integral period truncation conditions, the errors of calculating amplitudes of 21 orders harmonics are no more than 0.000 9%, as well as that of calculating phases no more than 0.04%.