Bifurcations in a power system model

Bifurcations are performed for a power system model consisting of two generators feeding a load, which is represented by an induction motor in parallel with a capacitor and a combination of constant power and impedance PQ load. The constant reactive power and the coefficient of the reactive impedance load are used as the control parameters. The response of the system undergoes saddle-node, subcritical and supercritical Hopf, cyclic-fold, and period-doubling bifurcations. The latter culminate in chaos. The chaotic solutions undergo boundary crises. The basin boundaries of the chaotic solutions may consist of the stable manifold of a saddle or an unstable limit cycle. A nonlinear controller is used to control the subcritical Hopf and the period-doubling bifurcations and hence mitigate voltage collapse