A New Method of Computing the Controlling Unstable Equilibrium Point of the Post-Fault Power System

Recently a new direct method for computing the controlling unstable equilibrium point has been proposed which is called the adjoint gradient system method. According to this method, the equilibrium points of the post-fault power system can be found by computing the equilibrium points of the adjoint gradient system which is derived from the original system. This paper presents a modification to the method mentioned above. It is found that there exists a family of adjoint gradient systems of a nonlinear autonomous dynamical system. And they share the same potential energy function. To compute the UEP of a past-fault power system more quickly, the appropriate adjoint gradient system should be chosen as the integral equation. To choose the adjoint gradient system, error control is taken into consideration. Simulation results on the IEEE 39-bus system prove that the modified method can help to compute the controlling unstable equilibrium point of a past-fault power system more quickly and efficiently.