AN ENERGY FUNCTION-METHOD FOR DETERMINING VOLTAGE COLLAPSE DURING A POWER-SYSTEM TRANSIENT

Several recent papers have focused on the subject of voltage collapse in power systems. The occurrence of a voltage collapse is often descri bed as a small-signal stability problem resulting from a bifurcation o f the equilibrium load how equations as the bus loads and generator po wer 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 tran sient stability problem for a differential algebraic equation (DAE) po wer system model. In particular, we define a stability region that gua rantees both rotor angular stability and voltage stability. The stabil ity region does not intersect the ''impasse surface,'' the surface on which the bus voltage variables are not defined as functions of the ge nerator rotor angles. Bifurcation theory is used along with some recen t results that characterize the stability boundary for DAE models, to show that an important component of the stability boundary is formed b y the trajectories that are tangent to the impasse surface at a fold b ifurcation point. An energy function transient stability method is dev eloped 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 su rface at this point. This new transient stability method is somewhat s imilar 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.