改进加窗频谱峰值拟合算法及谐波分析应用

摘要

Windowed FFT algorithm is widely used for power harmonic analysis recently. However, there are some contradictions between the accuracy and computation burden in discrete spectral corrections. In this paper, the power harmonic analysis algorithm based on the least square method （LSM） and triangular self-convolution windows （TSCW） are proposed. Firstly, the signal is weighted by TSCW for reducing spectral leakage. Then, the polynomials for discrete spectral corrections, which are also adjustable by the computation accuracy, are founded based on the LSM. Finally, the computation formulas of amplitude, phase and frequency of harmonics are given based on the spectral correction polynomials. The power harmonic analysis experiments are taken under non-synchronized sampling and non-integral period truncation, including white noise and fundamental frequency changing, which verify the usefulness of the proposed method.%加窗FFT是目前应用最为广泛的谐波分析方法。但非同步采样时,离散频谱校正中存在计算准确度与实时性的矛盾。论文结合三角自卷积窗的频谱特性,建立了基于最小二乘法的三角自卷积窗加权电力谐波分析算法。首先利用三角自卷积窗对信号进行加权,以抑制频谱泄漏;其次,采用最小二乘法进行离散频谱校正,构造可以根据精度要求进行调节的频谱校正拟合多项式;最后,根据最小二乘拟合多项式,建立简单、易行的谐波幅值、初相角和频率计算式。非同步采样和非整数周期截断条件下,对白噪声、基波频率波动等情况的谐波参数分析仿真实验验证了算法的有效性和准确性。