Bifurcation subsystem identification

An algorithm is given for the identification of a bifurcation subsystem, which experiences, produces, and causes bifurcation in the full system model. The algorithm applies the bifurcation subsystem and geometric decoupling condition tests to a sequence of partitioned models where the internal systems are of increasing order and are associated with the largest right eigenvector elements. The simplicity of this algorithm makes its application to large systems possible. The bifurcation subsystem condition and geometric decoupling condition that are sufficient conditions for existence of a bifurcation subsystem are also theoretically extended in this paper. It is thus shown that bifurcation subsystem method is more rigorously established since specific norms are introduced to represent the different system properties that allow a bifurcation subsystem to exist. The theoretical results provide more insight into the bifurcation subsystem method and why and when a bifurcation subsystem exists. This analysis reveals that the existence of a bifurcation subsystem requires much weaker conditions than that required for slaving, model reduction, coherency reduction, and a-decomposition methods. The bifurcation subsystem identification algorithm is then applied to a relatively large two-area differential algebraic modeled system with multiple generators.