Computation of unstable equilibrium points on the transient stability boundary of power systems with detailed generator modeling

This paper presents a method to compute multiple unstable equilibrium points on transient stability region boundary considering complex generator modeling. For a nonlinear dynamic system, there exists an adjoint system, constructed by system equations and its Jacobian matrix. The adjoint system is a gradient system with an analytic Lyapunov function. All equilibrium points of the dynamic system are stable equilibrium points in the adjoint system. Stable equilibrium point of the dynamic system is a type-I unstable equilibrium point and its unstable manifolds can be acquired in minus system. Minimum points of Lyapunov function are found along the unstable manifolds in the adjoint system. Trajectories in the adjoint system from these minimum points generally converge to stable equilibrium points which are unstable equilibrium points of the dynamic system. Therefore, unstable equilibrium points on the stability boundary could be found efficiently. IEEE 11-bus system and IEEE 162-bus system are used for the valification of the proposed method.