Kl. Praprost et Ka. Loparo, AN ENERGY FUNCTION-METHOD FOR DETERMINING VOLTAGE COLLAPSE DURING A POWER-SYSTEM TRANSIENT, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 41(10), 1994, pp. 635-651
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.