Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system

A tutorial introduction in bifurcation theory is given, and the applicability of this theory to study nonlinear dynamical phenomena in a power system network is explored. The predicted behavior is verified through time simulation. Systematic application of the theory revealed the existence of stable and unstable periodic solutions as well as voltage collapse. A particular response depends on the value of the parameter under consideration. It is shown that voltage collapse is a subset of the overall bifurcation phenomena that a system may experience under the influence of system parameters. A low-dimensional center manifold reduction is applied to capture the relevant dynamics involved in the voltage collapse process. The need for the consideration of nonlinearity, especially when the system is highly stressed, is emphasized.< >