基于高斯方法及Sherman-Morrison公式的暂态稳定性并行计算方法

并行计算是实现大规模电力系统暂态稳定性实时分析计算的有效途径。将s级2s阶的高斯方法和扩展的Sherman-Morrison矩阵求逆公式相结合，提出了一类新的暂态稳定性并行计算方法。该方法首先利用s级2s阶的高斯方法对微分-代数方程组进行多级离散，并利用严格的牛顿法对离散后的非线性方程组进行整体求解。在此基础上，按s个时间点将整体雅可比矩阵分裂成为一个分块对角矩阵和一个分块常系数矩阵。然后，以分裂后的分块对角矩阵为基础，利用扩展的Sherman-Morrison矩阵求逆公式将s个时间点上的计算任务进行“解耦”。所提方法在保持严格牛顿法的收敛性的同时具有很好的并行性。利用OpenMP并行计算技术在多核计算机上对2个不同的系统算例进行了测试，结果表明，所提出的并行方法可以获得较好的加速比以及并行效率。

Parallel algorithm for transient stability simulation using Gauss method and Sherman-Morrison formula

Parallel computing is an effective approach to transient stability real-time simulation of large-scale power system. A new parallel algorithm for power system transient stability simulation is proposed by combining Gauss integration method and the extended Sherman-Morrison formula. The algorithm adopts the s-stage 2s-order Gauss method to convert the differential-algebraic equations into a set of nonlinear algebraic equations by multi-stages discretization, while the algebraic system is solved using rigorous Newton method. On this basis, the whole Jacobian matrix involved in Newton method is splitted to a block diagonal matrix and a block constant coefficients matrix according to s time points, and then based on the block diagonal matrix, the computing tasks at s time points are fully decoupled through the extended Sherman-Morrison matrix inverse formula. The proposed algorithm preserves the good convergence of rigorous Newton method and meanwhile has a high degree of parallelism both in time and in space. For test, the proposed algorithm has been implemented on a multi-core computer by use of OpenMP technology, and the results for two example systems show that the proposed parallel algorithm can obtain effective speedup and parallel efficiency. This work is supported by National Natural Science Foundation of China (No. 51377098 and No. 50977052).