Dynamic Bifurcations in a Power System Model Exhibiting Voltage Collapse

Abstract

Dynamic bifurcations, including Hopf and period-doubling bifurcations, are found to occur in a power system dynamic model recently employed in voltage collapse studies. The occurrence of dynamic bifurcations is ascertained in a region of state and parameter space linked with the onset of voltage collapse. The work focuses on a power system model studied by Dobson and Chiang (1989). The presence of the dynamic bifurcations, and the resulting implications for dynamic behavior, necessitate a re- examination of the role of saddle node bifurcations in the voltage collapse phenomenon. The bifurcation analysis is performed using the reactive power demand at a load bus as the bifurcation parameter. Due to numerical ill-conditioning, a reduced-order model is employed in some of the computations. It is determined that the power system model under consideration exhibits two Hopf bifurcations in the vicinity of the saddle node bifurcation. Between the Hopf bifurcations, i.e., in the "Hopf window," period-doubling bifurcations are found to occur. Simulations are given to illustrate the various types of dynamic behaviors associated with voltage collapse for the model. In particular, it is seen that an oscillatory transient may play a role in the collapse.