与退化Hopf分岔有关的小扰动稳定域拓扑性质

小扰动稳定域的边界是由描述电力系统的微分代数方程的3类分岔点构成的,文中通过对由Hopf分岔点构成的小扰动稳定域的研究发现:稳定域的边界并非连续光滑,它会由于边界上系统结构稳定性的破坏而出现几何形状的突然改变.表明所发现的稳定域边界性质的变化与系统中出现的退化Hopf分岔有关,并由此导致二维参数空间中同时出现2个小扰动稳定域,这2个稳定域之间的互相吸引以至最终的融合造成了稳定域边界几何形状的极不规则变化.最后在三维空间中演示了小扰动稳定域并讨论了稳定域的连通性.研究表明,深入探讨非线性动力系统中的退化Hopf分岔等更为复杂的动态行为,是揭示电力系统小扰动稳定域拓扑性质的重要途径.

Topological Characteristics of the Small Signal Stability Region with Degenerate Hopf Bifurcation

The boundary of small signal stability region(SSSR)is consisted of three types of local bifurcations of power system modeled by differential-algebraic equations.This paper focuses on the SSSR composed of Hopf bifurcation points.It is found that the boundaries of SSSR are not continuous smoothly and its shape can be changed roughly when the structural stability of system on the boundary is broken.The study shows that the change of characteristics of boundary of SSSR is related with degenerate Hopf bifurcation closely.The degenerate Hopf bifurcation leads to the appearance of two SSSR in 2-dimension parameter space,then attraction and coupling of the two regions result in the sudden changes of boundaries of SSSR.At last it illustrates the SSSR and its connectivity in 3-dimension space.The article shows that the research on the complicated dynamics of nonlinear system is the essential approach to reveal the topological characteristics of SSSR of power system.