基于apFFT和带约束条件的最小二乘拟合的间谐波检测算法

Inter-harmonic Detection Algorithm Based on apFFT and Least Square Fitting with Constraints

摘要:

在非整周期采样的情况下，使用传统的快速傅里叶变换（FFT）对邻近基波/谐波的密集谱间谐波进行参数估计时，由于频谱泄露的影响，间谐波检测误差较大，甚至难以判断密集谱的存在,因此，文中提出了一种基于全相位FFT和带约束条件的最小二乘拟合的间谐波检测算法。该算法的原理是先利用全相位FFT对间谐波参数进行预估，在预估参数的基础上构造拟合函数并设置约束方式，然后使用最小二乘拟合对间谐波参数进行校正。通过对比不同约束方式的效果，选择对幅值和相位分别进行约束为最佳约束方式。仿真实验表明，与其他基于FFT的算法相比，该算法可以有效地减少间谐波参数检测误差并具有良好的抗噪性。

Abstract:

In the case of non-integer period sampling, when using traditional fast Fourier transform (FFT) for parameter estimation of dense spectral inter-harmonics adjacent to the fundamental/harmonic, the inter-harmonic detection error is relatively high due to the influence of spectral leakage, and it is even difficult to judge the existence of dense spectrum. Therefore, an interharmonic detection algorithm based on allphase fast Fourier transform (apFFT) and least square fitting with constraints is proposed. The principle of the proposed algorithm is to first estimate the inter-harmonic parameters by using the apFFT, construct a fitting function and set constraints on the basis of the pre-estimated parameters, and then use the least square fitting to correct the inter-harmonic parameters. By comparing the effects of different constraint methods, the best constraint method is selected to constrain the amplitude and phase respectively. Simulation experiments show that, compared with other FFT-based algorithms, the proposed algorithm can effectively reduce the detection error of inter-harmonic parameters and has good noise immunity.