There are two dominant approaches to voltage stability
studies, namely, Continuation Power Flow (CPF) and, more
recently, Optimal Power Flow (OPF) based approaches; the
latter are also referred to as OPF-Direct Methods (OPF-DM)
[3]. In the CPF method, the loading level is increased until
there is no feasible solution to the power flow equations
or the solution does not satisfy required ranges for certain
system variables such as voltages or power transfers [4].
The OPF-DM, on the other hand, is mainly an optimization
problem that maximizes the system loadability while satisfying
operational constraints, including the power flow equations as
well as limits on generator reactive powers, voltages and power
transfers, as discussed for example in [5], [6]. Depending on
the way the generator voltage control is modeled, the results
obtained from an OPF-DM can be shown to be basically the
same as those obtained from the CPF method [7]. In most of
these studies, generators’ Q-limits have been usually modeled
as simple fixed limits to reduced computational burden and
avoid convergence problems, in spite of the key role that these
limits play in voltage instability phenomenon, as discussed for
example in [2] and [8]. In the latter two papers, the generator
capability curves are better represented in voltage stability
studies, modeling the voltage dependence of generator Qlimits.