基于总体最小二乘改进的SDFT三相交流电频率估计算法  

Improved SDFT algorithm based on total least squares for frequency estimation in three-phase power system

作　　者：刘勇[1] 王开[1] 刘航 沈佳佳 裴文江[1] 夏亦犁 

机构地区：[1]东南大学信息科学与工程学院,南京210096

出　　处：《东南大学学报（自然科学版）》2017年第6期1129-1134,共6页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金资助项目(61401094;61771124);江苏省自然科学基金资助项目(BK20140645);中央高校基本科研业务费专项资金资助项目(2242016K41050)

摘　　要：为了解决SDFT算法在含有噪声、谐波或突发干扰的电力网络中电压信号基频分量三点关系式不严格成立的问题,引入总体最小二乘算法(TLS-SDFT)进行改进.TLS-SDFT算法采用滑动窗截取的多个DFT基频分量样本点来扩展SDFT算法的三点关系式,引入扰动矩阵,并通过对系数矩阵进行奇异值分解,使扰动矩阵具有最小Frobenious范数,得到改进的频率估计值.由于系数矩阵结构的特殊性,该算法的额外复杂度为窗长的线性函数.仿真结果表明,在高斯白噪声干扰下,改进算法的估计偏差和均方误差远低于原SDFT算法.在高次谐波干扰、信号参数突变以及变电站实测环境下,改进算法的频率追踪精确度均有明显提升.In the smart discrete Fourier transform(SDFT) algorithm,the underlying relationship among the three consecutive fundamental components of the voltages does not hold when the threephase power system is contaminated by noises,harmonics,or encountered with sudden interrupts.To solve this problem,a total least squares SDFT(TLS-SDFT) algorithm is put forward.In the proposed algorithm,the original three point relation formula in the SDFT algorithm is extended based on the multiple DFT fundamental observations obtained by sliding windows.A perturbation matrix is introduced.The coefficient matrix is singular value decomposed to minimize the Frobenious norm of the perturbation matrix,and then the estimated frequency is improved.Due to the special structure of the coefficient matrix,the additional complexity of the proposed algorithm is a linear function with the length of the sliding window.The simulation results show that the estimation bias and the mean square error of the proposed algorithm are much smaller than those of the original SDFT algorithm under the interference of Gauss white noise.The frequency tracking accuracy of the proposed algorithm is obviously improved under the conditions of high harmonic interference,signal parameter mutation and real substation measurement.

关 键 词：频率估计 总体最小二乘 离散傅里叶变换 参数估计 

分 类 号：TM935.1[电气工程—电力电子与电力传动]