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For the enhancement of the transient stability of power systems, the key isto define a quantitative optimization formulation with system parameters asdecision variables. In this paper, we model the disturbances by Gaussian noiseand define a metric named Critical Escape Probability (CREP) based on theinvariant probability measure of a linearised stochastic processes. CREPcharacterizes the probability of the state escaping from a critical set. CREPinvolves all the system parameters and reflects the size of the basin ofattraction of the nonlinear systems. An optimization framework that minimizesCREP with the system parameters as decision variablesis is presented.Simulations show that the mean first hitting time when the state hits theboundary of the critical set, that is often used to describe the stability ofnonlinear systems, is dramatically increased by minimizing CREP. This indicatesthat the transient stability of the system is effectively enhanced. It alsoshown that suppressing the state fluctuations only is insufficient forenhancing the transient stability. In addition, the famous Braess' paradoxwhich also exists in power systems is revisited. Surprisingly, it turned outthat the paradoxes identified by the traditional metric may not exist accordingto CREP. This new metric opens a new avenue for the transient stabilityanalysis of future power systems integrated with large amounts of renewableenergy.

A Critical Escape Probability Formulation for Enhancing the Transient Stability of Power Systems with System Parameter Design