  For the enhancement of the transient stability of power systems, the key is
to define a quantitative optimization formulation with system parameters as
decision variables. In this paper, we model the disturbances by Gaussian noise
and define a metric named Critical Escape Probability (CREP) based on the
invariant probability measure of a linearised stochastic processes. CREP
characterizes the probability of the state escaping from a critical set. CREP
involves all the system parameters and reflects the size of the basin of
attraction of the nonlinear systems. An optimization framework that minimizes
CREP with the system parameters as decision variablesis is presented.
Simulations show that the mean first hitting time when the state hits the
boundary of the critical set, that is often used to describe the stability of
nonlinear systems, is dramatically increased by minimizing CREP. This indicates
that the transient stability of the system is effectively enhanced. It also
shown that suppressing the state fluctuations only is insufficient for
enhancing the transient stability. In addition, the famous Braess' paradox
which also exists in power systems is revisited. Surprisingly, it turned out
that the paradoxes identified by the traditional metric may not exist according
to CREP. This new metric opens a new avenue for the transient stability
analysis of future power systems integrated with large amounts of renewable
energy.
