Bifurcation and chaos in power systems

A detailed example of a power system model with load dynamics is studied by investigating qualitative changes or bifurcations in its behaviour as a reactive power demand at one load bus is increased. In addition to the saddle-node bifurcation often associated with voltage collapse, we find other bifurcation phenomena which include Hopf bifurcation, cyclic fold bifurcation, period doubling bifurcation, and the emergence of chaos. The presence of these dynamic bifurcations motivates a re-examination of the role of saddle-node bifurcations in the voltage collapse phenomenon. In fact, simulation results suggest that voltage collapse may take place before the reactive power demand is increased to the system steady-state operating limit where a saddle-node bifurcation is detected. We also consider the role that the algebraic constraints imposed by some load models may play in the global analysis of the attractors of the system. Implications for power system operations are drawn.