基于Blackman自乘-卷积窗的FFT谐波检测算法

电网中存在的大量谐波严重影响着电力系统的安全稳定运行,快速傅里叶变换(Fast Fourier Transform,FFT)算法被广泛应用于电网谐波的检测,由于存在频谱泄漏和栅栏效应导致谐波参数检测的误差较大,通过加窗函数和插值算法可以提高FFT算法的精度。对窗函数进行自乘和卷积运算可以改善旁瓣性能,以Blackman窗作为母窗,进行自乘和卷积运算,提出了Blackman自乘-卷积窗,该窗函数具有较优的主瓣和旁瓣性能。结合三谱线插值算法,推导出频率、幅值、相位的插值修正公式。采用Blackman自乘-卷积窗和其他余弦窗对含弱幅值信号的复杂信号进行对比仿真,验证了Blackman自乘-卷积窗三谱线插值算法在检测弱幅值信号时依然具有很高的精度,对含白噪声的信号进行仿真,验证了该算法对谐波信号参数检测的相对误差较小,抗干扰能力强。

An algorithm for FFT harmonic detection based on Blackman self-multiplication-convolution window

The existence of a large number of harmonics in the power network seriously affects the safe and stable operation of the power system. Fast Fourier transform algorithm is widely used in the detection of harmonic in the power network. Because of the spectrum leakage and fence effect, the error of harmonic parameter detection is large. The precision of FFT algorithm can be improved by windowing function and interpolation algorithm. The sidelobe performance of window function is improved by multiplication and convolution.The Blackman self-multiplication convolution window is obtained by multiplying and convolution of Blackman window. The window function has better main lobe and sidelobe performance.The interpolation correction formula of frequency, amplitude and phase is derived by using the interpolation algorithm of triple-spectral-line.Using this window function and other windows simulate the complex signal with weak amplitude signal, it is verified that the triple-spectral-line interpolation algorithm of Blackman self-multiplication convolution window still has high accuracy in detecting weak amplitude signal. The simulation of the signal with white noise verifies that the algorithm has small relative error and strong anti-jamming ability to the harmonic signal parameter detection.