基于预处理共轭梯度法的电力系统机电暂态仿真

Electrical-Machanical Transient Simulation of Power System Based on Preconditioned Conjugate Gradient Method

把基于不完全LU分解的预处理共轭梯度法(ILUCG)用于电力系统暂态稳定仿真计算,提出了一种与矩阵方程直接求解法相结合的混合算法。该方法采用不完全LU分解对暂态稳定计算中的雅可比矩阵进行预处理,以改善其条件数;对预处理之后的方程组,采用改进的共轭梯度法进行迭代求解,在系统收敛困难的情况下,改用直接求解法求解矩阵方程;在迭代过程中,充分利用当前已有的预处理后的等价雅可比矩阵进行迭代计算,而当雅可比矩阵及相关变量变化较大时,重新计算雅可比矩阵并进行相应的预处理操作,以提高算法的效率和计算速度;多个算例表明,对于电力系统暂态仿真的计算,本文算法的计算速度明显优于直接分解求解法和单纯的ILUCG,并易于在并行计算平台上实现,具有一定的实际应用前景。

A hybrid simulation method which combines direct LU decomposition method and the incomplete LU factorization based preconditioned conjugate gradient （ILUCG） method is presented for the power systems transient stability simulation calculation in this paper. The method adopts incomplete LU factorization to precondition on the Jacobian matrix in order to reduce the condition number; and then the linear equations are solved with improved conjugate gradient method, and the direct method would be adopted when convergence of iterative method could not be achieved. During the iteration, the current jacobian matrix being preconditioned on is utilized repeatedly and not to be recalculated until the changing of Jacobian matrix and relative variable is large. The results of the samples demonstrate that, for the transient stability simulation of power system, the calculation speed of the hybrid simulation method is obviously superior to that of direct LU decomposition method and pure ILUCG, since most of the calculation of the hybrid simulation method is done by preconditioned conjugate gradient method, it is easy to be implemented at all kinds of parallel platform and owns the potential to be applied for practice.