用于迭代法潮流计算的改进Jacobi预处理方法

摘要

In order to improve the speed of power flow calculation and meet the requirement of real-time calculation,the iterative methods for linear equations are applied to the power flow calculation.When the spectral distribution of the coefficient matrix is relatively scattered,however,the speed of iterative method is slow and even not convergent.The coefficient matrix is needed to be pre-treated to solve the problems mentioned above.Firstly,the characteristic of Jacobi matrix in the power flow calculation is analyzed and segmentally processed based on the PV and PQ nodes.The bigger numbers are found and act as preconditioners.Then,the inverse matrix of the preconditioners is multiplied by the coefficient matrix A and the constant item b,and the original linear system is transformed into a new equivalent linear system which can be easily solved.The speed of solving linear equations in power flow calculation is highly improved.The simulation result shows that the algorithm can solve the power flow equations efficiently.%为提高潮流计算速度,满足实时计算的要求,线性方程组迭代法被用于电力系统潮流计算.但是当系数矩阵谱分布较为分散时,迭代法求解线性方程组存在收敛速度慢甚至不收敛等问题,为了解决这个问题,需对系数矩阵进行预处理.首先,分析电力系统潮流计算时Jacobi矩阵的特点,对其按PV,PQ节点进行分块处理,找出其中数值上较大的元素作为预处理子.然后,将预处理子的逆矩阵分别与系数矩阵A和常量项b相乘,将原线性方程组转换为新的更容易求解的等价线性方程组,大幅提高了潮流计算中线性方程组求解的速度.实验表明,该方法能有效解决大规模电网潮流求解问题.