基于四项余弦窗四谱线插值FFT的电力谐波算法分析

An Approach for Electrical Harmonic Analysis Based on Four Terms Cosine Window and Quadplex-spectrum-line Interpolation FFT

快速傅里叶变换是谐波检测中的主要方法,但在谐波分析中很难做到同步采样、整数周期截断,从而造成频谱泄露影响谐波测量的准确性。为了提高谐波的检测精度,利用FFT分析了Nuttall窗的旁瓣特性和四谱线插值算法。提出了一种基于4项3阶Nuttall窗四谱线插值的电力谐波检测算法,该算法通过分析加Nuttall窗信号傅里叶变换的频域表达式,利用谐波频点附近的4根离散频谱的幅值确定谐波谱线的准确位置,进而得到谐波的幅值、频率及相位。通过用曲线拟合函数求得实用的修正公式,简化了复杂的计算过程,并对修正公式进行了Matlab仿真。仿真结果表明:所提出的算法在非同步或非整周期采样时对谐波幅值和相位的检测精度较高,应用该算法处理信号的幅值相对误差小于4.29×10^(-6)%,相位相对误差小于5.7×10^(-4)%。相对于双谱线Hanning、三谱线Blackman-harris算法精度得到了显著提高。并结合沈阳农业大学光伏电站并网算例,将研究检测方法对用户型光伏电站谐波进行分析,并且与分析检测结果进行对比来验证本研究方法的有效性。更加有效的检测谐波幅值和相位,有利于更好的减少农业用户光伏电站对电力系统稳定运行的影响。

The Fast Fourier Transform （FFT） is a major method of harmonic detection, but i t＇s hard to achieve synchronous sampling and integer cycle truncation during the period of the harmonic analysis, which resulting in Spectrum leakage,affecting the accuracy of harmonic measurement. In order to improve the detection accuracy of harmonic, the FFT was used to analyze sidelobe characteristics of Nuttall window and Four-Line interpolation algorithm. A power harmonic detection algorithm based on Four third-order Nuttall Window Four-Line Interpolation was proposed, this algorithm analyzed frequency domain expressions of add Nuttall window signal to Fourier transform, using the amplitude of four discrete spectra that near harmonic frequency to determine the accurate position of the harmonic line, and then get the amplitude, frequency and phase of the harmonic. Through using practical correction formula that obtained by curve fitting functions, simplified the complicated calculation process, and the modified formula was simulated by Matlab. The simulation results showed that the algorithm proposed in this study had high detection accuracy for harmonic amplitude and phase when sampled in non-synchronous or non-integer period. The algorithm was applied to deal with the amplitude relative error of the signal which is less than 4.29X10＂6%, the phase relative error was less than 5.7×10-4%. Compared with the bispectrum Hanning, the precision of the Three - l ine Blackman -harr is algorithm has been significantly improved. In this paper, a Grid-connected example of photovoltaic power station in Shenyang Agricultural University was presented,Harmonics of the User -type photovoltaic power plant have been analyzed by studying detection methods,and compared with the results of the test analysis to verify the effectiveness of this research method, which obtains more effective detection of harmonic amplitude and phase, and is beneficial to reduce the influence of users photovoltaic power station＇s on the stable operation of the power system.