Bifurcation theory applied to the analysis of power systems - Revel, Gustavo (2008)
In this paper, several nonlinear phenomena found in the study of power system networks are described in the context of bifurcation theory. Toward this end, a widely studied 3-bus power system model is considered. The mechanisms leading to static and dynamic bifurcations of equilibria as well as a cascade of period doubling bifurcations of periodic orbits are investigated. It is shown that the cascade verifies the Feigenbaum’s universal theory. Finally, a two parameter bifurcation analysis reveals the presence of a Bogdanov-Takens codimension-two bifurcation acting as an organizing center for the dynamics. In addition, evidence on the existence of a complex global phenomena involving homoclinic orbits and a period doubling cascade is included.