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 andLeast Square Fitting with Constraints

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。

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.