【摘要】 提出一种应用哈密顿-雅可比(Hamilton-Jacobi)偏微分方程求取电力系统稳定域的方法。该方法的主要思路是:在电力系统的状态空间预先设定一个小的稳定区域,将其作为目标集,逆时间求解目标集的可达集得到电力系统稳定域;目标集和可达集均由水平集函数描述,从而将可达集的计算转化为求解Hamilton-Jacobi方程的终值问题。该方法可以适应高阶模型、稳定域的非凸性,理论上可以求得精确的稳定域边界。通过单机无穷大电力系统的数值计算,验证了该方法的正确性和有效性。更多还原

【Abstract】 This paper presents a method to compute power system stability region using Hamilton-Jacobi partial differential equation. The big idea is that, determinate a small stability region in advance in power system’s state space as a target set, then compute the reachable set in backward time namely the stability region, the target set and the reachable set are both described by level set functions, thus computing the reachable set is converted into solving a terminal value problem of Hamilton-Jacobi equation. The method is adaptive to high-order models, nonconvex stability regions, and is able to calculate exactly stability boundary in theory. The correctness and effectiveness of the method is verified by numerical implementation for single machine and infinite bus systems.更多还原