基于Kaiser窗相位差校正的电力谐波分析与应用

Harmonic analysis based on Kaiser window phase difference correction and its application

采用基本窗函数和广义余弦窗函数对信号加权可减少频谱泄漏和栅栏效应的影响,但其效果受到窗函数固定旁瓣性能的制约。Kaiser窗可定义一组可调的窗函数,自由选择主瓣与旁瓣衰减之间的比重,因此能全面地反映主瓣与旁瓣衰减之间的交换关系。对信号非同步采样和非整周期截断时的频谱进行了分析,讨论了Kaiser窗的主、旁瓣特性,提出了基于Kaiser窗相位差校正的电力谐波分析方法,推导了信号基波与各次谐波频率、幅值、初相角的计算式。仿真结果表明:Kaiser窗函数设计实现灵活、抑制频谱泄漏效果好,Kaiser窗相位差校正算法克服了基波频率波动对谐波分析的影响,对含21次谐波信号的基波频率计算相对误差仅为1.0×10-7%,幅值计算相对误差≤0.000 6%,初相位计算相对误差≤0.008%,三相谐波分析与谐波电能计量应用实践证明了该方法的正确性。

The fundamental windows and generalized cosine windows have been used to eliminate the errors caused by spectral leakage and picket fence effect, but the analysis result is restricted by the performance of the fixed side lobes of these windows. Kaiser window can define a group of adjustable window functions and the specific weight between the major lobe and side lobes fall off of Kaiser window can be freely selected, so the commutation rejection between the major lobe and side lobes fall off can be presented in the round. The signal spectral under non-synchronized sampling and non-integral period truncation conditions is analyzed. The characteristics of major lobe and side lobes of Kaiser window are both discussed, and an approach for electrical harmonic analysis based on Kaiser window phase difference correction is proposed. The arithmetic expressions of the frequencies, amplitudes and initial phases of fundamental and every harmonics have been deduced. Simulation results show that Kaiser window function can be designed and realized neatly and restrains spectral leakage well; the influences of fundamental frequency fluctuation on harmonic analysis are restrained by using the approach presented in this paper; the relative errors of calculating fundamental frequencies with 21 order harmonics are no more than 1.0 ×10^-7% , the relative errors of calculating amplitudes are no more than 0. 000 6% , and those of calculating initial phases are no more than 0. 008%. Threephase harmonic analysis and harmonic energy measurement application have proved the validity of the approach presented in this paper.