电力系统自动化Issue(4)：19-24,6.DOI:10.7500/AEPS20130423007
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
摘要
Abstract
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Key words
sparse linear equations/block diagonal matrix/direct solver based on block matrix/whole process simulation with multi-time scale引用本文复制引用
宋新立,陈英时,王成山,叶小晖,汤涌,吴国旸..全过程动态仿真中大型线性方程组的分块求解算法[J].电力系统自动化,2014,(4):19-24,6.基金项目
国家高技术研究发展计划(863计划)资助项目(2011AA05A103) （863计划）
国家电网公司大电网重大专项资助项目(SGCC-MPLG001-2012)。This work is supported by National High Technology Research and Development Program of China (863 Program)(No.2011AA05A103) and State Grid Corporation of China,Major Projects on Planning and Operation Control of Large Scale Grid(No.SGCC-MPLG001-2012) （SGCC-MPLG001-2012）
