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

This paper presents a method to compute unstable equilibrium points on the transient stability boundary of power systems with detailed generator modeling. According to the stability region theory of nonlinear dynamic systems, relations of unstable equilibrium points on different stability region boundaries in periodic nonlinear dynamic systems are deduced. It is proved that, when all loads are modeled as constant impedances, transient stability equations are equivalent to ordinary differential equations. Combined with the adjoint method, unstable equilibrium points on certain transient stability region boundary are found according to angular periodicities of transient stability equations. The method is shown to be efficient and reliable from the numerical simulations of WSCC 4-machine test system.