Due to the wide use of non-linear components, harmonic problem becomes increasingly serious. It is difficult to perform accurate harmonic analysis with fast Fourier transform (FFT) under the unsynchronized sampling conditions. Windowed interpolation methods can improve the accuracy of FFT for harmonic analysis. An improved algorithm with high accuracy is proposed based on the attenuation characteristics of the Hanning-windowed discrete spectrum of signal. Via a specific polynomial transform of the spectral sequence, the algorithm reduces the spectral leakage further, and then the interpolation is applied to derive the practical correction formulas of the harmonic frequency, amplitude and phase. Comparison with Harming and Blackman-Harris interpolation FFT methods is carried out by Matlab simulations, which verifies the higher analysis accuracy of the proposed algorithm. An experiment on capacitor harmonic current demonstrates its validity further.%大量非线性元件的应用导致电网谐波问题愈发严重,快速傅立叶变换(FFT)在非同步采样条件下难以实现谐波的精确检测,通过加窗插值可以改善FFT算法的准确度.根据信号加Hanning窗离散频谱的衰减特性,提出一种高精度改进算法.该算法通过对加窗信号的离散频谱序列进行特定的多项式变换,进一步减轻各次谐波频谱之间的互相干扰,继而应用插值运算推导出各次谐波频率、幅值和相位的高精度校正公式.对该算法与Hanning窗和Blackman-Harris窗插值FFT算法进行Matlab仿真对比,验证了该算法具有更高的分析精度.对电容器谐波电流的实验研究进一步证明了改进算法的有效性.
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