An approach for determining the subsystem experiencing and producing a bifurcation in a power system dynamic model

This paper presents a method for determining reduced-order subsystems called bifurcation subsystems, that experience bifurcation, and produce the bifurcation in the full power system dynamic model. The bifurcation subsystem is generally a subset of the center manifold subsystem. The bifurcation subsystem is in fact the singular perturbation determined slow subsystem within the center manifold dynamics that actually experiences and produces the bifurcation in the center manifold dynamics. The test procedure used to determine a bifurcation subsystem is described in this paper and does not require performing a nonlinear transformation required to determine the center manifold. The theory provides two singular perturbation based test conditions for existence of bifurcation subsystems. Examples that demonstrate the systematic use of this test procedure are presented for saddle-node and Hopf bifurcations in a single-machine-infinite-bus-model. Results when the test procedure for finding a bifurcation subsystem is applied to the large dominant elements of the tight eigenvector and the participation factor of a bifurcating eigenvalue are compared.