  This paper is concerned with estimating critical clearing times in the
transient stability problem of power grids without extensive time-domain
simulations. We consider a highdimensional post-fault system (the grid after
the fault is cleared) which we decouple into many smaller subsystems. Then, for
each subsystem, we find the so-called safety sets and simulate the faulted
system once to deduce the so-called safe and unsafe critical clearing times,
which specify the intervals of time over which the fault may remain active
before safety is compromised. We demonstrate the approach with a numerical
example involving the IEEE 14 bus system.
