准同步DFT谐相角的线性修正算法

傅中君 王建宇 欧云 周根元 白凤娥 赵小荣

摘要：针对准同步DFT谐波分析方法在信号频偏时的短范围泄漏问题，研究准同步DFT谐相角的线性特性，建立准同步DFT谐相角与信号频偏率、谐次、迭代次数之间的线性修正模型，给出了准同步DFT谐相角的线性修正方法。该方法首先根据相邻采样点之间的基波相角差只与信号频率和采样频率相关的原理来测量信号频偏率，再按照只与信号频偏率、谐次、迭代次数相关的谐相角线性修正公式对准同步DFT的谐波分析结果进行修正。实验表明准同步DFT谐相角线性修正算法能够有效抑制短范围频谱泄漏，在较宽信号频偏范围内获得高精确度的谐相角分析结果。

关键词：谐波分析;准同步DFT;频谱泄漏;谐相角;线性修正

DOI：10.15938/j.emc.2019.09.014

中图分类号：TM 935

文献标志码：A

文章编号：1007-449X（2019）09-0108-07

Linear correcting algorithm for quasi synchronous DFT′s  harmonic phase

FU Zhong jun1，2，WANG Jian yu2，OU Yun3，ZHOU Gen yuan1， BAI Feng e1，ZHAO Xiao rong1

（1.School of Computer Engineering，Jiangsu University of Technology， Changzhou 213001， China;  2.School of Automation，Nanjing University of Science & Technology， Nanjing 210094， China;  3.Changzhou Foreign Languages School， Changzhou 213001， China）

Abstract：

Aiming at the short range leakage problem of quasi synchronous DFT （QSDFT） harmonic analysis method when signal frequency deviated， the linear characteristics of QSDFT′s harmonic phase angle were studied， and linear correction model between QSDFT′s harmonic angles and signal frequency deviation rate， harmonic order and iteration number were established. Furthermore， the linear correction method of QSDFT′s harmonic phase was given. Firstly， the signal frequency deviation rate was measured by the principle that the fundamental phase angle difference between adjacent sampling points is only related to the signal frequency and the sampling frequency. And then， the harmonic analysis result of QSDFT was corrected through the phase linearity correction formula. Simulation and experiment results show that this proposed algorithm can increase the accuracy of harmonic phase efficiently in the wide frequency range by minimizing short range spectral leakage.

Keywords：harmonic analysis; quasi synchronous DFT; spectral leakage; harmonic phase; linear correction

0引言

諧波分析技术能够把复杂信号分解成简单周期信号来认识事物的本质，因此它在电能质量监控、电子产品生产检验、电器设备监控等众多领域应用广泛。谐波分析的主要参数有谐幅值、谐相角两个，通常谐幅值应用较多，但是在应用谐波法进行相位测量的场合同样需要高精度的谐相角参数。在工程应用中，最常用的谐波分析方法是离散傅里叶变换（discrete Fourier transform，DFT）和快速傅里叶变换（fast Fourier transformation，FFT）。进行谐波分析时，总是有限点的采样和难以做到严格意义的同步采样，这样，在应用DFT和FFT进行谐波分析时就会存在由于截断效应导致的长范围泄漏以及栅栏效应导致的短范围泄漏，使得分析结果精度不高，甚至不可信。……