基于多孔分数阶小波变换的谐波检测新方法

基于分数阶小波变换的电力谐波检测方法是一项新兴的研究成果，其可较好地解决新型电力系统中谐波检测受噪声干扰的问题，提高谐波检测精度。然而传统离散分数阶小波变换均基于Mallat算法完成，其实现过程中的下采样操作将影响谐波信号的检测精度。针对这一问题，文章将非下采样多孔算法与分数阶小波变换相结合得到一种改进的离散分数阶小波变换实现方法，并在此基础上提出一种基于多孔分数阶小波变换的谐波检测新方法。此外，文章采用基于分数阶频谱四阶原点矩的方法确定最佳分数阶变换阶次，有效降低计算复杂度。实验结果表明，新方法对稳态谐波、短时谐波及时变谐波均能有效实现信号降噪和分离，并能对信号分量的幅值、频率及定位信息实现高精度检测。

A new method for harmonic detection based on fractional wavelet transform with A trous algorithm

The power harmonic detection method based on fractional wavelet transform is an emerging research achievement, which can effectively solve the problem of noise interference in new power systems and improve the accuracy of harmonic detection. However, traditional discrete fractional wavelet transform is based on Mallat algorithm, and the signal detection accuracy will be affected by the downsampling operation. To overcome this problem, A trous algorithm with non downsampling process is employed. Then a new method for harmonic detection based on fractional wavelet transform with A trous algorithm is proposed. In addition, the fourth order origin moment of fractional spectrum is used to determine the optimal fractional transform order, effectively reducing computational complexity. Experimental results show that the new method can effectively achieve noise reduction and signal separation for steady state harmonics, short time harmonics and time varying harmonics, and can achieve high-precision detection of the amplitude, frequency and positioning information of signal components.