Computation of the voltage oscillatory stability boundary by a direct method

This paper propose a methodology to directly compute Hopf bifurcation points in electric power systems and the voltage stability boundary associated with them. The mathematical formulation is based on the set of differential-algebraic equations regarding the power system and a set of equations related to the conditions that must be satisfied for occurrence of Hopf bifurcations. Both sets of nonlinear algebraic equations are solved in a unified framework based on the Newton method. A homotopy method with artificial parameter is used to compute proper initial conditions of the set of variables to be solved and to overcome most difficulties of the traditional Newton based techniques towards convergence when the initial solution is far away from the bifurcation point. Finally, the effectiveness of the proposed methodology is presented through numerical examples using the IEEE 3-generators 9-bus test system.