快速求取节点阻抗矩阵的对称LR三角分解法

Fast calculating node impedance matrix with symmetrical LR triangular factorization algorithm

针对LR三角分解法计算过程中的问题,提出对称LR三角分解法,其中包括:合成阵应用、四角规则应用、对角元素取倒、对称LR三角分解法,大大加快前代计算。同时提出LR三角分解法求解节点阻抗矩阵Z的方法,并根据LR三角分解法计算过程的特点,综合应用Z_k阵的求取顺序、Z_k阵元素的求取方式、单位矩阵E元素结构特点,从而利用Z阵元素的对称性进行求解,并省去LR三角分解法中间矩阵的计算,大大加快回代计算。对IEEE各节点系统的验算表明,本方法与传统的或改进的LDU三角分解法和LR三角分解法相比,计算速度均大幅提高。

The symmetric LR triangular factorization algorithm is proposed based on the problems in the calculation process of the LR triangular factorization algorithm,which includes the application of composite matrix,the application of four-angle rule,the inversion of diagonal elements and the symmetric LR triangular factorization algorithm,which greatly accelerates the forward substitution calculation.Besides,the method that solving node impedance matrix Z with LR triangular factorization algorithm is also proposed,then according to the characteristics of calculation process of the LR triangular factorization algorithm,by comprehensively applying the calculating sequence of matrix Z_k,the calculating way of elements in matrix Z_k and the element structure features in unit matrix E,the symmetry of the elements in matrix Z can be used in solving process and the calculation of the intermediate matrix in LR triangular factorization algorithm can be left out,therefore the backward substitution calculation can be greatly accelerated.The check calculation of each node system in IEEE systems indicates that whether compared with the traditional or improved LDU triangular factorization algorithm or LR triangular factorization algorithm,the calculating speed of symmetric LR triangular factorization algorithm has always improved dramatically.