BIFURCATION ANALYSIS IN A POWER SYSTEM MODEL

The dynamics of a 3-bus power system model is analyzed using bifurcation theory. This model has been widely studied concerning voltage collapse. This paper presents some additional results in this topic. It is shown that the cascade of period doubling bifurcations preceding the voltage collapse verifies the Feigenbaum's universal constant. In addition a Lorenz map for the chaotic attractor is derived resembling a one-dimensional unimodal curve. A two parameter bifurcation analysis reveals the presence of a Bogdanov-Takens codimension-two bifurcation for a positive value of the active power. Several dynamical scenarios, not directly related to the Bogdanov-Takens unfolding, have been detected. The presence of homoclinic, cyclic fold and period doubling bifurcations curves may indicate the existence of an organizing centre of global dynamics on the two parameter plane.