Complex Dynamics in Swing Equations of a Power System Model

Complex dynamics in the reduced swing equations of a power system are investigated. As the change of bifurcation parameter μ, the system exhibits complex bifurcations, such as saddle-node bifurcation, Hopf bifurcation, cyclic fold bifurcation and torus bifurcations and complex dynamics, such as periodic orbits, quasiperiodic orbits, period-doubling orbits and chaotic attractors which link with the system instability or collapse. The sufficient conditions for saddle-node bifurcation and Hopf bifurcation are derived. Specifically, between the Hopf bifurcations, i.e., in the “Hopf window”, a cascade of period-doubling bifurcation, which leads to chaos, is shown to occur. The periodic orbits, period-doubling orbits, quasiperiodic orbits and chaotic behavior are shown in numerical simulation based on the computations of the orbits, the eigenvalues, the Floquet multipliers and Lyapunov exponents.