An energy function method for determining voltage collapse during a power system transient

The occurrence of a voltage collapse is often described as a small-signal stability problem resulting from a bifurcation of the equilibrium load flow equations as the bus loads and generator power injections incur small changes. However, during a transient period, a voltage collapse may occur as a bifurcation of the transient load flow equations as the generator rotor angles vary. The purpose of this paper is to address voltage collapse in the general context of a transient stability problem for a differential algebraic equation (DAE) power system model. In particular, we define a stability region that guarantees both rotor angular stability and voltage stability. The stability region does not intersect the “impasse surface,” the surface on which the bus voltage variables are not defined as functions of the generator rotor angles. Bifurcation theory is used along with some recent results that characterize the stability boundary for DAE models, to show that an important component of the stability boundary is formed by the trajectories that are tangent to the impasse surface at a fold bifurcation point. An energy function transient stability method is developed that uses a sustained fault trajectory to find the first point of intersection with the impasse surface and then involves solving for the (stability) limiting trajectory that is tangent to the impasse surface at this point. This new transient stability method is somewhat similar in theory to the potential energy boundary surface method. Also, this method can be extended to develop stability estimates for power system models in which the stability region is more complex, possibly constrained by line power flow limits, voltage magnitude limits, etc