用于电力系统谐波分析的加窗插值FFT算法研究

Study on Windows and Interpolated FFT Algorithm for Harmonic Analysis in Power System

分析了传统傅利叶算法的误差原因 ,提出了运用加窗减少泄漏误差、通过插值算法限制栅栏效应的方法。与以往加窗插值法不同的是 :利用卡当公式 (Cardan)推导出 3、4项窗的一般求解公式。用此法仿真计算电网信号的结果表明 :对于频率和幅值 ,各种窗具有很高的精度 ;4项窗所得相位误差较大。综合考虑频率、幅值和相位 3个因素 ,则用 3项窗精度最高 ,其旁瓣最小衰减达到 5 9 7dB ,满足电力系统谐波分析的需要。

In this paper the reasons causing the error of conventional FFT algorithm are studied. A method to diminish the leakage error by adding windows and then limit the picket fence effect by the interpolating algorithm is presented. Unlike the conventional interpolating windowed algorithm, the newly proposed algorithm deduces calculating formulas of 3-term and 4-term windows using Cardan formula. Power system signals are simulated and calculated with this method, all kinds of windows have high accuracy for the frequency and magnitude, however, for the phase the result obtained by 4-term windows have notable error. Three factors including frequency, magnitude and phase are taken into comprehensive consideration, when 3-term windows are chosen this method have the highest accuracy and the least attenuation of its side-lobe can reach to -59.7 dB, it meets the requirement of harmonic analysis in power system.