  Standard power system models are parameter dependent differential-algebraic
equation (DAE) type. Following a transient event, voltage collapse can occur as
a bifurcation of the transient load flow solutions which is marked by the
system trajectory reaching a singular surface in state space where the voltage
causality is lost. If a fault is expected to cause voltage collapse, preventive
control decisions such as changes in AVR settings need to be taken in order to
get enhance the system stability. In this regard, the knowledge of sensitivity
of critical clearing time (CCT) to controllable system parameters can be of
great help. The quasi-stability boundary of DAE systems is more complicated
than ODE systems where in addition to unstable equilibrium points (UEP) and
periodic orbits, singularity plays an important role making the problem
challenging. The stability boundary is then made up of a number of dynamically
distinct components. In the present work, we derive the expression for CCT
sensitivity for the phenomenon where the critical fault-on trajectory
intersects the singular surface itself which is one such component forming the
stability boundary. The results are illustrated for a small test system in
order to gain visual insights.
