小扰动稳定域微分拓扑学性质初探 (一)小扰动稳定域非凸边界和空洞现象示例

Tentative Study on Differential Topological Characteristics of the Small Signal Stability Region Part One Illustration of Nonconvex Boundary and Instability Region(Hole) in Small Signal Stability Region

对电力系统小扰动稳定域的微分拓扑学性质进行了初步探讨。首先,简单回顾了小扰动稳定域的相关定义、边界组成及其性质;然后,给出一种基于优化过程实现对小扰动稳定域Hopf分岔界面追踪的算法;最后,利用一个简单的3节点系统,示例了小扰动稳定域边界面非凸和内部存在封闭不稳定(空洞)区域的现象,并对小扰动稳定域内部空洞区域随系统参数变化的规律进行了研究。该工作对于进一步深化对电力系统小扰动稳定域微分拓扑学性质的研究具有一定帮助。

Differential topological characteristics of the small signal stability region （SSSR） in power systems are tentatively studied in this paper. A brief review is firstly given on SSSR＇s definition, boundary composition and its characteristics. Then, a method based on optimal algorithm is presented for properly tracing the Hopf bifurcation segment on SSSR＇s boundary. Finally, based on the algorithm proposed and a simple power system, illustrations are given to the phenomenon that there is a closed instability region （hole） inside of the SSSR and that the SSSR＇s boundary is not convex. And the phenomenon also implies that. The change rules of the hole in the SSSR with system parameters are then discussed. Studies of this paper are helpful to understand the differential topological characteristics of SSSR of real power systems.