Bifurcation subsystem and its application in power system analysis

The paper extends the concept of a bifurcation subsystem that experiences, produces, and causes the bifurcation in the full system model, and systematically describes a bifurcation subsystem method. The motivation for finding a bifurcation subsystem and its advantages over model reduction, slaving, and finding the center manifold dynamics are discussed. By using the theoretical results of the persistence on saddle-node and Hopf bifurcation of a full system model with both fast and slow singularly perturbed dynamics, a more precise definition of what constitutes a bifurcation subsystem for both saddle-node and Hopf bifurcation is given. Persistence of the center manifold for the reduced models of singularly perturbed fast and slow external dynamics thus is shown. These results are then used to show that the center manifold of the saddle-node and Hopf bifurcation lies in the bifurcation subsystem or is contained within the bifurcation subsystem if additional conditions are satisfied. The test conditions for the existence of a bifurcation subsystem are: 1) quickly reviewed and 2) then applied to compute a saddle-node and a Hopf bifurcation subsystem for a multiple machine differential algebraic example system. The results computationally validate the bifurcation subsystem method.