全过程动态仿真中大型线性方程组的分块求解算法

发布时间：2018-01-22 16:44

本文关键词： 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　出处：《电力系统自动化》2014年04期 　论文类型：期刊论文

【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。
[Abstract]:The whole process dynamic simulation of power system can unify the electromechanical transient, medium and long term dynamic processes to carry on the digital simulation. In the process of simulation, it is necessary to solve the large sparse linear equations, which are formed by the algebraic equations after differential-algebraic equations of the power system equipment model and the algebraic equations of the transmission network model. The fast solution algorithm is one of the difficulties in power system dynamic simulation. In this paper, a fast and direct block algorithm based on the characteristics of matrix structure in simulation is proposed. A sparse solver for linear equations in large power systems is developed and implemented. The sparse matrix is divided into four block matrices in this algorithm. Then, the largest diagonal block is further subdivided into several smaller diagonal block matrices, and the LU symbolic decomposition and numerical decomposition of the matrix are carried out by using some small blocks with the same structure. Compared with other existing solvers, ESS has obvious global solution speed advantage, especially in matrix LU decomposition.
【作者单位】：智能电网教育部重点实验室天津大学;上海智琢软件公司;中国电力科学研究院;
【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)~~
【分类号】：TM743
【正文快照】： 0引言电力系统全过程动态仿真是将电力系统机电暂态、中期和长期过程有机地统一起来进行数字仿真,用于研究电力系统在受到干扰之后系统较长时间的机电过渡过程。仿真时间可从几秒到数十分钟甚至若干个小时。它是电力系统规划设计、调度运行和科学研究的重要仿真计算工具之一[1

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