静态状态估计中权重矩阵确定的方法研究

Method for Determining the Weight Matrix in Static State Estimation

加权最小二乘估计是电力系统静态估计的常用算法,特点是收敛性能好,估计质量高。静态状态估计中权重矩阵取各量测量的方差阵的逆矩阵,使估计具有最小的误差方差阵,因为系统运行状态随时间变化方差矩阵难以确定,在实际估计过程中方差阵一般取为单位阵。提出了通过分析历史数据,假设在系统运行过程中量测误差服从均值一定、方差一定的概率分布,以估计值近似真值,以状态估计的残差近似量测量的误差,得到量测量的误差分布,再进行统计分析从而确定权重矩阵的方法,使得静态状态估计具有最小的方差阵,获得概率意义下的最优估计。最后通过仿真验证了所提方法的有效性。

Weighted least squares estimation is a common algorithm for static power estimation, which is characterized by good convergence performance and high quality. In conventional estimator with a weight matrix of the inverse of the variance for the measurements, however, the variance matrix is usually taken as a unit matrix in actual process as it is indefinable when the power system operation state changes. In this paper, a weight matrix of the inverse of the variance for the residual is adopted by analyzing historical data, Which is assumed that the measurement error obeys a probability distribution with a mean value and a certain variance, and with the residual as measurement error, the residual data are analyzed to get the error distribution of measurement to determine the variance matrix by statistical method, which reaches the minimum variance matrix and the optimal estimation in the sense of probability. Effectiveness of the strategy is verified by simulation.