基于汉宁双窗apFFT单谱线插值的电力谐波和间谐波检测算法

当利用快速傅里叶变换(FFT)对电力谐波或间谐波进行处理时,实际频率与频率分辨率不一定是整数倍关系,由此造成频谱泄漏,影响谐波或间谐波参数的估计精度。针对此问题,提出了一种基于汉宁双窗全相位FFT离散单谱线插值的频谱校正算法。算法的原理是:利用理论频率点附近的旁谱线幅值和主谱线幅值的比值,推导出各频率点的校正量。然后,根据估计出的频率校正量,并结合全相位FFT的线性时不变性(LTI)以及汉宁窗的归一化模函数估计出信号的幅值。由于全相位FFT的相位谱与频偏无关,因此可以取频率点处的主谱线相位值来估计信号的初相位。仿真算例对比表明:汉宁双窗apFFT单谱线插值频谱校正算法估计的谐波和间谐波参数更准确,综合误差更小,具有较强的抗白噪声干扰能力。

An electric power harmonic and inter-harmonic detection method based on single-spectrum-line interpolation of double hanning windows apFFT

When FFT is applied to analyze the harmonic or inter-harmonic signal of electric power,due to the non-integral multiple relationship between the real frequency and the frequency resolution,the spectral leakage will occur.As a result of that,the estimation accuracy of the harmonic or inter-harmonic parameters will degrade.To solve this problem,a discrete signal spectrum line interpolation correction method based on double Hanning windows apFFT is proposed in this paper.The principle of the algorithm is as follows: after the signal is processed by double Hanning windows apFFT,the modified values of each theory frequency point are deduced by the ratio of the side spectral line and main spectral line amplitudes.Then,according to these frequencies modified values and Hanning window mode function,and the LTI of apFFT to correct the corresponding amplitudes.Because the phase spectrum of apFFT has nothing to do with the frequency deviation,the initial phase of each frequency point is the phase of the main spectral line.Simulation examples show that the harmonic and inter-harmonic parameters estimated by the single-spectrum-line interpolation based on double Hanning windows apFFT are more accurate,the total errors are smaller,and the algorithm is more robust against white noise.