基于分块QR分解的一种状态估计算法

文中提出了一种基于分块QR分解的状态估计方法。该方法把虚拟测量处理为等式约束，避免了由于权因子分散而导致的数值病态问题。在每次迭代中，通过对两个分块矩阵的QR分解和一个稀疏三角线性方程组的求解，实现了系数矩阵的三角分解。与带有约束的正规方程(NE/C)法相比，不但消除了Jacobian矩阵叉乘造成的信息损失，而且保证了分解的数值稳定性。稀疏QR分解采用了基于Givens变换的方法并利用最小度列排序和变主元消元策略。减少注入元素的数目，提高了状态估计的计算效率。试验系统的仿真结果表明了该方法具有良好的数值稳定性和鲁棒性，而且有较高的计算效率，可以满足在线状态估计的要求。

A BLOCK QR BASED POWER SYSTEM STATE ESTIMATION ALGORITHM

This paper presents a stable block QR based method for solving power system state estimation problem. In the proposed method, virtual measurements are treated as equality constraints, which avoids the numerical ill-conditioning problem due to the disparity in weighting factors. At each iteration, triangular factorization of the coefficient matrix is carried out by performing QR decomposition on two partitioned matrices and by solving a set of linear equations involving a sparse triangular matrix. Compared with normal equations with constraints (NE/C) method, the proposed method circumvents the cross production of the Jacobian matrix which can cause the loss of information. And this method ensures the numerical stability of decomposition. In sparse QR decomposition based on Givens transformation, variable pivot row and column ordering techniques are used to reduce fill-ins and then computation efficiency is enhanced. Simulation results have shown that proposed method is stable and robust. Furthermore, it is very efficient and can meet the need of online state estimation.