  With the growth of renewable generation (RG) and the development of
associated ride through curves serving as operating limits, during
disturbances, on violation of these limits, the power system is at risk of
losing large amounts of generation. In order to identify preventive control
measures that avoid such scenarios from manifesting, the power system must be
modeled as a constrained dynamical system. For such systems, the interplay of
feasibility region (man-made limits) and stability region (natural dynamical
system response) results in a positively invariant region in state space known
as the constrained stability region (CSR). After the occurrence of a
disturbance, as it is desirable for the system trajectory to lie within the
CSR, critical clearing time (CCT) must be defined with respect to the CSR
instead of the stability region as is done traditionally. The sensitivity of
CCT to system parameters of constrained systems then becomes beneficial for
planning/revising protection settings (which impact feasible region) and/or
operation (which impact dynamics). In this paper, we derive the first order CCT
sensitivity of generic constrained power systems using the efficient power
system trajectory sensitivity computation, pioneered by Hiskens in [1]. The
results are illustrated for a single-machine infinite-bus (SMIB) system as well
as a multi-machine system in order to gain meaningful insight into the
dependence between ability to meet constraints, system stability, and changes
occurring in power system parameters, such as, mechanical power input and
inertia.
