利用小波傅里叶变换的谐波与间谐波检测

Measurement of Harmonic and Inter-harmonic Using Transform of Wavelet and Fourier

为有效检测快速变化和持续时间短的谐波与间谐波,分析了傅立叶变换检测谐波与间谐波的方法,并在此基础上探讨了利用小波变换进行检测的基本原理,提出了利用小波变换系数傅立叶变换幅值来分离谐波与间谐波的算法。该方法使用Morlet函数作为小波变换的小波基,根据小波变换系数傅里叶变换的幅频特性的突出点来检测谐波与间谐波的幅值与频率。仿真结果与理论分析表明,小波变换具有良好的时域与频域局部化特性,小波变换系数傅里叶变换幅值能有效检测谐波与间谐波,并在检测持续时间短的谐波与间谐波方面有很大优越性。

This paper analyses a Fourier transform method of measurement of harmonic and inter-harmonic, it probes into the basic principium of wavelet transform measurement of harmonics and inter-harmonics, and puts forward an arithmetic using coefficient of wavelet transform and maximal values of Fourier transform to separate harmonics and inter-harmonics from original signals. In the proposed method, a Morlet function is served as the wavelet function of wavelet transform, and the characteristic between maximal values and frequencies of coefficient of wavelet transform and Fourier transform are introduced to measure the maximal values and frequencies of harmonics and inter-harmonics. In order to prove the validity of the proposed method, this paper has done simulations with Matlab. The theoretical analyses and simulative results show that wavelet transform has a good localized characteristic in time domain and frequency domian. The method of coefficient of wavelet transform and maximal values of Fourier transform is able to measure the harmonics and inter-harmonics in power system efficaciously. Especially, there are advantages in the measurement of the harmonics and inter-harmonics of short duration.