基于VSS-CDFE的三相非平衡电力系统频率无偏估计

Unbalanced three-phase power systems frequency estimation based on CDFE algorithm

为了实现含噪三相非平衡电力系统高精度频率无偏估计,引入了复数域直接频率估计(CDFE)算法,分析其原理并对其进行了改进。CDFE算法基于正弦信号的线性预测,求取误差函数的瞬时平方值关于频率的偏导数,并以该值作为频率估计的更新值。在此基础上,进一步提出变步长CDFE(VSS-CDFE)算法,根据最速下降法则动态更新步长因子来代替CDFE算法的固定步长。仿真分析及实验结果表明,在噪声干扰下,VSS-CDFE算法可以准确地对基于复数建模的三相非平衡电力系统进行频率追踪,其估计均方误差和理论值相吻合。相比CDFE算法,VSS-CDFE算法在相同的收敛速度下,估计均方误差更小,在相同的估计均方误差下,收敛速度更快。

In order to solve the frequency estimation problem in unbalanced three-phase power systems,the Complex-valued DFE(CDFE)algorithm is analyzed and improved.The CDFE algorithm is based on the linear prediction of sinusoidal signal,in which the instantaneous squared value of the error function is first defined,and its first derivative is used to track the frequency of the unbalanced three-phase power system.Furthermore,variable step-size CDFE(VSS-CDFE)algorithm is also derived based on the CDFE algorithm by using the steepest descent method.The experimental results show that CDFE algorithm is able to accurately track the frequency in the unbalanced power systems that based on complex-model under white Gaussian measurement noise,and the estimated mean square error(MSE)is also consistent with that obtained by the theoretical analysis.Compared with the traditional CDFE algorithm,the VSS-CDFE algorithm has smaller estimated variance at the same convergence rate.On the other hand,its convergence rate is faster than the conventional CDFE algorithm for a predefined variance requirement.Both algorithms provide unbiased and robust frequency estimates and the VSS-CDFE algorithm is more superior in terms of estimation variances.