A refined continuation method for finding equilibrium points of power systems

This paper presents a method for finding equilibrium points of arbitrary index that lie on the boundary of the region of attraction of a stable 'operating point'. It is developed in the context of interconnected power system models, but is not limited to such models. The method exploits the fact that loss of stability of the attractor is preceded by a sequence of saddle-node bifurcations involving saddle equilibria on the boundary of its region of attraction. Thus, we use the procedure of continuing the stable point until it bifurcates and disappears. Using backtracking and elementary bifurcation theory, we find a number of one-saddles, depending on the path that led to the bifurcation. A refined search then yields equilibria of larger index. In the process, we obtain considerable information on the 'orbit' or Smale diagram of the flow. A number of medium to high dimension power system models were studied using our procedure.