基于m次重启的简化广义最小残差法的电力系统暂态稳定仿真

Power System Transient Stability Simulation Based on Simpler Generalized Minimal Residual Algorithm of m-Times Restart

提出了一种基于m次重启的简化广义最小残差法(simpler generalized minimal residual algorithm of m times restart,SGMRES(m))的电力系统暂态稳定仿真新算法,即采用SGMRES(m)方法对暂态稳定仿真中形成的线性方程组进行求解,通过修正标准正交基的生成过程,使得m阶上Hessenberg矩阵成为上三角矩阵。这样,只要通过简单的上三角线性方程组的求解即可求得解的修正量,避免了求解广义最小残差法每次迭代中的最小二乘问题,从而有效地减少了计算量。为进一步加快计算速度,文中算法进一步结合了伪牛顿策略和不完全LU预处理技术。多个算例的计算结果表明,所提出方法是有效的。

A new simpler generalized minimal residual algorithm of m-times restart （SGMRES（m）） is proposed, namely the linear equations, which form in the transient stability simulation during the iteration from the n-th step to （n＋1）-th step, are solved by SGMRES（m）. Through modifying the generative process of normal orthogonal basis, the m-order upper Hessenber matrix is turned into upper triangular matrix, thus so long as simply solving the upper triangular linear equations the correction value of the solution is attained, thus the trouble of solving least square problem that appears in each iteration during the solution of generalized minimum residual method can be avoided, and the calculation burden can be effectively reduced. To fiarther accelerate the calculation, the proposed algorithm is integrated with dishonest Newton method and incomplete LU precondition. Simulation results of calculation examples show that the proposed algorithm is efficient.