一种快速求取节点阻抗矩阵的方法

A method for fast solving bus impedance matrixes

提出了一种含规格化的高斯消元法快速求取电力系统节点阻抗矩阵Z的方法。根据单位矩阵E的结构特点以及本方法中Z阵元素的计算顺序,找出并利用进行k-1次和进行n-1次含规格化的高斯消元后节点导纳矩阵Y和E阵元素的变化规律。然后根据变化的Y阵以及E阵,从Z阵的最后一列开始,计算对角元及对角元所在列以上的元素,再根据对称性得到对角元所在行以左的元素。依次从右向左、从下向上逐列、逐行地求取Z阵元素,以得到整个Z阵。本方法原理简单、计算快捷。用本方法对IEEE-57~300节点系统的Y阵求取相应的Z阵,与传统的高斯消元法、LDU三角分解法相比,可将计算速度提高约40%-60%。

A method based on Gaussian elimination algorithm with normalization for fast solving bus impedance matrixes Z was presented in the paper. According to the characteristic of the structure in the unit matrix E and the calculating order for the elements in matrix Z in the method,the changed laws of structure will be found and used after the normalization and elimination has been made k- 1 or n- 1 times for a bus admittance matrix Y and the matrix E. Then based on the changed matrix Y and the matrix E,the diagonal element and the off-diagonal elements on the diagonal element in a column was calculated beginning from the last column of the matrix Z. After then,based on the symmetry,the off-diagonal elements on the left of the diagonal element will be got. In order to get the matrix Z,all the elements in the matrix Z were calculated from the right to left and from the bottom to the top. The principle of the method was very simple,and the calculating speed was faster than other methods. The method has been used to solve the matrixes Z from the matrixes Y for IEEE- 57- 300 bus systems,and the calculating speed has increased about 40%- 60% compared with the original Gaussian elimination algorithm and the LDU triangular decomposition algorithm.