Boundary crises, fractal basin boundaries, and electric power collapses

Electric power systems are frequently nonlinear and, when faced with increasing power demands, may behave in unpredictable and rather irregular ways. We investigated the nonlinear dynamics of a single machine infinite bus power system model in order to study the appearance of coexistent periodic and chaotic attractors, characterizing multi-stable behavior. The corresponding basins of attraction present fractal boundaries, for which we have determined the uncertain fraction scaling in phase space. The bifurcation diagrams are studied with respect to variations of the mechanical power input and may lead to voltage collapse under certain circumstances, which we relate to a boundary crisis suffered by a chaotic attractor.