基于Kaiser窗双谱线插值FFT的谐波分析方法

为进一步减少加窗插值FFT的频谱泄漏和栅栏效应,提出了基于Kaiser窗的双谱线插值FFT的电力谐波分析方法,运用多项式拟合求出了实用的插值修正算式,推导了信号基波与各次谐波频率、幅值、初相角的计算式。仿真结果表明,Kaiser窗函数设计实现灵活、抑制频谱泄漏效果好,基于Kaiser窗的双谱线插值FFT方法能有效克服基波频率波动与白噪声对谐波分析的影响,在非整数周期截断条件下,对含21次谐波信号的频率计算相对误差仅为1.4×10%,幅值计算相对误差≤0.002%,初相位计算相对误差≤0.0001%,三相谐波电能计量应用实践证明了该方法的正确性。

Harmonic analysis based on Kaiser window double spectrum line interpolation FFT

To further reduce the errors caused by spectral leakage and picket fence effect, an approach for electrical harmonic analysis based on Kaiser window double spectrum line interpolation FFT is proposed in this paper. The applicable rectification formulas of the interpolation are obtained by using polynomial curve fitting. The arithmetic expressions of the fundamental and harmonic frequencies, amplitudes and initial phases are deduced. Simulation results show that Kaiser window function can be designed and realized easily and restrain the spectral leakage well, the influences caused by fundamental frequency fluctuation and white noise on harmonic analysis are all restrained by using the presented approach, and under non-integral period truncation conditions, the relative errors of frequency calculation for 21 order harmonics are no more than 1.4×10~(-9)%, the relative errors of amplitude calculation are no more than 0.002%, and those of phase calculation are no more than 0.000 1%. Three-phase harmonic energy measurement application proves the validity of the presented approach.