对称高斯消元法的快速求解及其应用  

Fast solutions and application on symmetrical Gaussian eliminating algorithms

作　　者：庄广宇 张洁[2] 戴雨心 陈恳[1] ZHUANG Guangyu;ZHANG Jie;DAI Yuxin;CHEN Ken(Information Engineering School,Nanchang University,Nanchang 330031,China;Jiangxi Electric Power Design Institute,Nanchang 330096,China)

机构地区：[1]南昌大学信息工程学院,江西南昌330031 [2]江西省电力设计院,江西南昌330096

出　　处：《南昌大学学报（工科版）》2018年第2期189-193,198,共6页Journal of Nanchang University(Engineering & Technology)

基　　金：江西省教育厅科学技术研究重点基金资助项目(60009);江西省研究生创新专项基金资金项目(YC2016-S065);南昌大学研究生创新专项基金资金项目(CX2016268)

摘　　要：引入四角规则,可将高斯消元法计算过程形象化,无需依赖计算公式直接完成消元计算,大大方便编程;根据对称矩阵的特点,提出2种对称高斯消元法,分别用四角规则或三角规则直接完成消元计算。与高斯消元法相比,对称高斯消元法可减少50%非对角元素的计算以及相应的除法计算,大大提高计算速度。分别用高斯消元法和2种对称高斯消元法求取IEEE-30、-57、-118系统的节点阻抗矩阵,后者的计算速度大大高于前者。以IEEE-118系统为例,后者的前代过程时间比前者快约38%或53%。后者的前代+回代过程时间比前者快约16%或28%。By introducing a four-angle rule,the calculating process of the Gaussian eliminating algorithm can be visualized in order that the eliminating calculating can be directly completed without using the formula,which can be greatly convenient to program,Then according to the characteristics of symmetric matrices,two kinds of symmetric Gaussian eliminating algorithm were proposed,and the eliminating calculation can be directly completed by the four-angle rule or the three-angle rule. Compared with the Gaussian eliminating algorithm,the symmetric ones can reduce the calculation on 50% non-diagonal elements and the corresponding division calculation,which can greatly improve the calculation speed. The bus impedance matrices of IEEE-30,-57 and-118 were obtained by the Gaussian eliminating algorithm and the two symmetric ones and the latters were much higher than the former in the speed. Taking IEEE-118 system as an example,the times on the process of forward substitution for the lattersare about 38% or 53% faster than the former,and the times on the process of backward substitution for the thelattersare about 16% or 28% faster than the former.

关 键 词：高斯消元法 对称矩阵 前代计算 回代计算 节点导纳矩阵 节点阻抗矩阵 电力系统 

分 类 号：TM711[电气工程—电力系统及自动化]