基于Nuttall窗双谱线插值FFT的电力谐波分析方法_卿柏元

第28卷第25期中国电机工程学报 V ol.28 No.25 Sep. 5, 2008

2008年9月5日 Proceedings of the CSEE ©2008 Chin.Soc.for Elec.Eng. 153 文章编号：0258-8013 (2008) 25-0153-06 中图分类号：TM 935 文献标志码：A 学科分类号：470⋅40

基于Nuttall窗双谱线插值FFT的

电力谐波分析方法

卿柏元，滕召胜，高云鹏，温和

(湖南大学电气与信息工程学院，湖南省长沙市 410082)

An Approach for Electrical Harmonic Analysis Based on Nuttall Window

Double-spectrum-line Interpolation FFT

QING Bai-yuan, TENG Zhao-sheng, GAO Yun-peng, WEN He

(College of Electrical and Information Engineering, Hunan University, Changsha 410082, Hunan Province, China)

ABSTRACT: The fast Fourier transform (FFT) had already become a main method of the electrical harmonic analysis since it’s easily realized in embedded system, but there were difficulties in performing synchronized sampling and integral period truncation in the electric power harmonic analysis, and the accuracy of the analysis result would be disturbed by the frequency leakage. Some efforts had been made, such as the utilization of window functions and interpolation algorithms, to improve the accuracy of harmonic parameters computation by FFT. The sidelobe characteristic of Nuttall window and the double-spectrum-line interpolation algorithm were both discussed, an approach for electrical harmonic analysis based on the Nuttall window double-spectrum-line interpolation FFT was proposed, the applicable rectification formulas of the double-spectrum-line interpolation was obtained by using polynomial curve fit functions, and subsequently calculating burden was dramatically reduced. The simulation results indicate that, by using the approach presented in this paper under the non-synchronized sampling and non-integral period truncation conditions, the errors of calculating amplitudes of 21 orders harmonics are no more than 0.0009%, as well as that of calculating phases no more than 0.04%.

KEY WORDS: harmonic analysis; Nuttall window; sidelobe; double-spectrum-line interpolation; fast Fourier transform; polynomial fit

摘要：快速傅里叶变换(fast Fourier transform，FFT)因其易于嵌入式系统实现而被作为电力谐波分析的主要方法，但电力谐波分析时很难做到同步采样和整数周期截断，由此造成的频谱泄漏将影响测量结果的准确性。加窗和插值修正算法可改善基于FFT的谐波参数计算的准确度。该文讨论Nuttall 窗的旁瓣特性和双谱线插值算法，提出基于Nuttall窗双谱线插值FFT的电力谐波分析方法，用曲线拟合函数求出实用的双谱线插值修正公式，大大减少了计算量。仿真结果表明，提出的谐波分析方法在非同步采样和非整数周期截断条件下，21次谐波幅值计算误差小于等于0.0009%，初相位计算误差小于等于0.04%。

关键词：谐波分析；Nuttall窗；旁瓣；双谱线插值；快速傅里叶变换；多项式拟合

0 引言

电力系统中非线性负荷的大量增加，特别是电力电子装置的广泛应用，使电网中产生了大量的高次谐波[1-3]，造成电能质量严重恶化，危及电力系统安全和经济运行。对谐波分量的准确分析将有利于电能质量的评估，并可采取必要的措施加以治理。快速傅里叶变换已成为电力谐波分析最主要的方法，但采用FFT进行电力谐波分析时很难做到同步采样和整数周期截断，由此造成频谱泄漏和栅栏效应[4-6]，导致信号参数(频率、幅值、相位)计算结果不准，无法达到谐波测量的国标要求[4]。采用性能优良的窗函数可减小频谱泄漏引起的误差，对计算结果进行插值修正可减小栅栏效应引起的误差[7]。针对现有文献[8-18]在插值算法的实现、修正公式的求解及计算精度等方面存在的不足，本文分析Nuttall窗的旁瓣特性[19]，提出基于Nuttall窗双谱线插值FFT的高精度电力谐波分析方法，推导Nuttall窗的双谱线插值算法，利用曲线拟合函数[20]求出实用的修正公式，大大减少了计算量，易于嵌入式系统实现。仿真结果表明，在非同步采样和非整数周期截断条件下，本文提出的电力谐波分析方