基于广义向后差分方法的电力系统暂态稳定性快速数值计算方法

为满足电力系统暂态稳定性实时分析计算的需求，将边界值类方法中的广义向后差分方法应用于暂态稳定性数值计算，提出了一种新的暂态稳定性快速数值计算方法。该方法利用广义向后差分方法对微分方程进行连续的时间差分离散，然后对离散后的非线性方程组采用牛顿法进行整体求解。利用雅克比矩阵所具有的带状结构特征，采用矩阵方程分裂—组合技巧，避免了对整体雅可比矩阵或多个分块子矩阵进行三角分解，从而提高了暂态稳定性数值计算的效率。对两个算例系统的测试结果表明:相对于经典的隐式梯形积分方法，所提出的算法在计算效率上具有明显的优势。

Fast power system transient stability simulations by generalized backward differentiation formulae

In order to meet the requirements of real-time analysis of power system transient stability, the Generalized Backward Differentiation Formulae (GBDF), which is a kind of boundary value methods, is applied to the transient stability numerical calculation, and a new algorithm is proposed. The proposed algorithm uses GBDF to carry on the continuous time discretization to the differential equations, and then uses the Newton method to solve the whole nonlinear system of the discretized nonlinear equations. Based on the band structure characteristic of the global Jacobian matrix, a special matrix equation split-combination technique is used to avoid the triangular factorization of the global Jacobian matrix or multiple block sub-matrices, thus to improve the efficiency of numerical calculation of transient stability. The test results of two example systems show that the proposed algorithm has obvious advantages over the classical implicit trapezoidal rule in terms of computational efficiency. This work is supported by National Natural Science Foundation of China (No. 51377098).