全过程动态仿真中大型线性方程组的分块求解算法  

An Algorithm of Large Linear Equations Based on Block Matrix for Whole Process Dynamic Simulations

作　　者：宋新立[1] 陈英时 王成山[1] 叶小晖[3] 汤涌[3] 吴国旸[3] 

机构地区：[1]智能电网教育部重点实验室,天津大学,天津市300072 [2]上海智琢软件公司,上海市200863 [3]中国电力科学研究院,北京市100192

出　　处：《电力系统自动化》2014年第4期19-24,共6页Automation of Electric Power Systems

基　　金：国家高技术研究发展计划(863计划)资助项目(2011AA05A103);国家电网公司大电网重大专项资助项目(SGCC-MPLG001-2012)~~

摘　　要：电力系统全过程动态仿真能够将机电暂态、中期和长期动态过程有机地统一起来进行数字仿真,仿真过程中需要多次求解大型稀疏线性方程组。该方程组由电力系统设备模型的微分—代数方程式差分后的代数方程和输电网络模型的代数方程形成,其快速求解算法是电力系统全过程动态仿真的难点之一。文中提出一种利用仿真中矩阵结构特点的分块快速直接求解算法,并开发实现了大型电力系统线性方程组稀疏求解器(ESS)。该算法首先将稀疏矩阵分为4个分块矩阵,然后将其中规模最大的对角块进一步细分为多个更小的对角分块矩阵,并利用部分小分块具有相同结构的特点进行矩阵LU符号分解和数值分解,最后根据分块矩阵进行前代和回代求解计算。与现有其他求解器进行的算例对比表明,ESS具有较为明显的整体求解速度优势,特别是在矩阵LU分解方面。Power system whole process dynamic simulation is such a method in which the electro-mechanical transient,medium-and long-term dynamic phenomena are organically unified.During the whole process of dynamic simulation,it is one of the key steps to solve sparse systems of linear equations composed of two kinds of equations：difference equations from dynamic equipment and algebraic equations from power network.Because of its very high order and large numbers of solving,the algorithm for fast solving is very important for this kind of dynamic simulation.This paper proposes a new method based on the block matrix for fast solving this linear equation and has developed an electric sparse solver （ESS）.It first divides the sparse matrix into four big blocks.Many decoupled diagonal smaller blocks which are related to the equipment on buses in the power system are further divided from the largest diagonal block.Next,by utilizing the same structure among these small blocks,these diagonal blocks are symbolically and numerically LU factorized one by one.Finally,the equations are solved block by block using conventional forward and backward substitution.This algorithm has been implemented in a new linear system solver called ESS.The results from several linear equations in power system whole process dynamic simulations show that compared with other solvers,ESS can achieve higher computational efficiency,especially in the factorization phase.

关 键 词：稀疏线性方程组 分块对角矩阵 分块直接求解算法 多时间尺度全过程仿真 

分 类 号：TM743[电气工程—电力系统及自动化]