基于逆轨迹方法的简单电力系统稳定域的可视化

THE VISUALIZATION OF STABILITY REGIONS FOR SIMPLE POWER SYSTEMS BASED ON TRAJECTORY REVERSING METHOD

基于逆轨迹方法实现了对简单(2阶和3阶)电力系统稳定域的准确估计和可视化研究。依据非线性系统理论,稳定边界由该稳定边界上的所有不稳定平衡点的稳定流形的并集构成。首先,采用偏微分方程的Taylor级数解近似不稳定平衡点的稳定流形,从而得到了不稳定平衡点邻域内的近似稳定边界。进而,以该邻域内近似稳定边界上的点作为初值沿时间逆向积分,即采用逆轨迹来近似不稳定平衡点的稳定流形,从而实现了对稳定域的估计。实际仿真结果表明,采用该方法可以实现对简单电力系统(电力系统的两机经典模型、考虑发电机励磁控制的单机模型等)稳定域的可视化研究。

In this paper the trajectory reversing method is adopted to estimate and visualize the stability regions for simple power systems. Firstly, the Taylor series solution of a partial differential equation is used to approximate the stability boundary in the neighborhood of an unstable equilibrium point. Furthermore, the points on the approximate stability boundary are used as the initial values for numerical integration in reverse time. Hence the stability boundary is approximated by a series of trajectories in reverse time. Several examples such as a two-machine power system and a single-machine power system with excitation control are shown to prove the feasibility of the method.