基于辛Radau方法的暂态稳定性并行计算方法

摘要

The research about parallel-in-time algorithms for transient stability parallel computation focuses on the solving effectively the contradiction between parallelism-in-time and convergence, which is the main problem existed for the research topic. In this paper, the s-stage and 2s-1 order symplectic Radau method is adopted for transient stability simulation. Based on the special matrix structure of the symplectic Radau method, a simple matrix transformation technique, which is similar to the so-called Jordan decomposition, is used for the decoupling of the computational task associated with the different time-points, and thus yields a new parallel-in-time algorithm where the computational task involved in different time-points can be solved independently or parallelly. The mathematical derivations and tests in IEEE 118-bus and IEEE 145-bus power system show that, the proposed algorithm is fully parallel-in-time, and at the same time keeps the convergence characteristics of Newton method, thus presents an efficient solution for the contradiction between parallelism-in-time and convergence.This work is supported by National Natural Science Foundation of China (No. 50977052).%电力系统暂态稳定性时间并行计算研究中所存在的主要问题是如何有效地解决时间并行度与收敛性之间的矛盾.将多级高阶辛Radau方法用于暂态稳定性计算,基于辛Radau方法的系数矩阵的结构特点,利用一个简单的、类似于矩阵约当(Jordan)分解方法的矩阵变换技巧,将多个时间点上的计算任务完全“解耦”,从而导出了一种新的暂态稳定性时间并行计算方法.数学推导以及在IEEE 118和IEEE 145节点系统中的对比测试结果表明,该方法具有很好的时间并行特性,保持了严格牛顿法的收敛特性,很好地解决了时间并行度与收敛性之间的矛盾.