Duhamel数值积分算法在电力系统暂态稳定分析中的应用

Application of Duhamel integrals in power system transient stability analysis

基于Duhamel积分的数值求解方法被广泛地应用于非线性动力学研究中,为解决传统隐式梯形积分方法在电力系统暂态分析中的不足,将非线性动力学中的数学模型引入到电力系统暂态稳定分析中,对电力系统微分方程矩阵的齐次项部分作对角化处理,使矩阵指数函数的计算得到了简化,以提高计算效率,并对Duhamel项中非齐次项部分进行了线性拟合,形成了一种高效、稳定的数值积分方法;以电力系统综合程序(PSASP)的仿真结果作为标准值,比较了步长变化时对基于该算法和基于隐式梯形积分算法的暂态稳定计算结果的影响。研究结果证明,该算法在大步长下数值计算时具有比传统方法更好的准确性和稳定性,能够在电力系统的暂态稳定分析中得到利用,为基于时域仿真的电力系统紧急控制和预防控制做了准备。

The algorithm based on the duhamel integrals has been widely applied to solve non-linear system. Aiming at overcoming the weaknesses of the implicit trapezoidal integration, the mathematical model in non-linear system was used for transient stability analysis in power system. The homogeneous team of the power system characteristic matrix was diagonalized to simplify matrix exponent function and improve the efficiency of the computation burden. Besides, the nonhomogeneous team was linearized. The simulations of power system analysis software package（PSASP） of the proposed approach and the implicit trapezoidal integration were compared in order to explain the influence of integration step. The results indicate that the proposed time-integration method is better in the calculation precision and constancy than the traditional integration method with the big integration step. The method could be prepared for the emergency and preventive control of power system for its accuracy and stability.