应用于电力谐波分析的改进插值算法

频谱泄漏是加窗插值傅里叶变换算法测量误差的主要来源,可通过加高阶窗抑制误差,但二次谐波及其他弱谐波的估计精度仍难显著提升,且带来复杂的频谱表达式和频率分辨率的损失。针对上述问题,提出一种改进插值算法。通过加低阶的sine窗函数,将传统离散傅里叶变换(DFT)平移1/2个谱线间隔到Odd-DFT域插值修正。利用相对频偏在所求谐波分量上减去其他分量的长程谱泄漏干扰之和,再进行插值修正,获得更精确的相对频偏。循环迭代若干次,用于抑制频谱泄漏对估计精度的影响。推导了修正公式,给出了算法流程,在不同环境下进行仿真分析,得出合理的迭代次数。研究结果表明,该算法的测量精度较传统加窗方法更高,并且弱谐波的估计精度得到提升,所需的采样时窗更少,提高了测量精度,满足电网测量的需要。

Improved Interpolation Algorithm Applied to Power Harmonic Analysis

The spectral leakage is the main cause of measurement error in windowed interpolation Fourier transform algorithm and the high-order window could be used to restrain it. However, it is still hard for improving the estimation accuracy of the second harmonic and other weak harmonics significantly. Moreover, it not only causes the loss of frequency resolution but also complicates the spectral expressions. An improved interpolation estimation algorithm is proposed to solve these problems. Using a low-order sine window, the traditional discrete Fourier transform(DFT)is shifted by 1/2 line spacing to the Odd-DFT domain for revision by the interpolated algorithm. The relative frequency offset of harmonics is used to subtract the sum of the long-range spectral leakage interference of other components, and then the interpolated algorithm is performed to obtain the more accurate relative frequency offset. Several iterations of loop are performed to restrain the impact of spectral leakage on estimation accuracy. The correction formula is deduced and the algorithm flow is given. The simulation analysis is carried out under different environments to obtain a reasonable number of iterations. The analysis results show that the measurement accuracy of this algorithm is higher than traditional windowing algorithm, the accuracy of weak harmonics is even more significantly improved and the number of required sampling time window is decreasing as well, which improve the measurement accuracy and meet the requirement of power grid.