Global Topological Analysis of Power System Stability Boundary Considering Singularities at Infinity

新能源的接入给电网传统稳定性理论带来了挑战，本文从稳定域结构角度出发，研究了稳定域边界上流形的拓扑结构及无穷远奇点的分布特性，旨在为电网稳定运行提供更加全面的理论支撑。基于Poincare紧致性理论推导了电力系统经典模型的新向量场，提出一种改进收缩投影变换方法，获得位于(超)球面上的无穷远奇点位置。通过建立无穷远奇点与电力系统稳定性的之间映射关系，提出了判定电力系统稳定性的指标。仿真结果表明，所提出的收缩投影变换方法同样适用于不确定性的电力系统稳定域边界分析，且基于无穷远奇点的指标能够有效判定系统的稳定程度。New energy sources bring challenges to the stability theory. In this paper, the topology of the manifold on the boundary of the stability region and the distribution of the singularities at infinity are studied from the perspective of the region, aiming to provide more comprehensive theoretical support for the stable operation of the grid. Based on the Poincare converse theory, a new vector field of the classical model of the power system is derived, and an improved shrinking projection transformation is proposed to obtain the singularities at infinity located on the (hyper) sphere. By establishing the mapping relationship between the distribution of the singularities and the stability degree of the power system, a stability index based on the singularities is proposed. The simulation results show that the proposed method is also applicable to the boundary analysis of the non-deterministic power system, and the index based on the singularities can effectively determine the stability of the system.