基于抗差总体最小二乘法的电力系统谐波状态估计

摘要

The mathematical model of harmonic state estimation and total least squares method are introduced. Harmonic state estimation is analyzed using robust total least squares method, considering the effect of measurement error and parameter error. This paper analyzes the shortcoming of total least squares that it is less capable of resisting gross error and proposes that the robust total least squares is used for harmonic state estimation. A mathematical model of IEEE-14 bus system is built in Matlab. Normal distribution error of gross error is added to measurement data, so as to normal distribution error to parameter matrix. The probability density curve and a comparison among total least squares, robust least squares and robust total least squares show that harmonic state estimation based on robust total least squares is the most accurate.%介绍了谐波状态估计的数学模型及最小二乘和总体最小二乘的求解算法，综合考虑测量误差和参数误差的影响，利用总体最小二乘法进行谐波状态估计。分析了测量粗差对估计结果的影响，针对总体最小二乘法不具备抑制粗差能力的缺点，提出利用抗差总体最小二乘法进行谐波状态估计。用Matlab搭建了IEEE-14节点谐波测试系统仿真模型，在测量数据和参数矩阵中分别加入含有粗差的正态分布误差及正态分布误差，画出概率密度曲线图，并对总体最小二乘法、抗差最小二乘法和抗差总体最小二乘法进行比较，结果表明利用抗差总体最小二乘法能够得到更精确的谐波状态估计结果。