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

TL;DR

This paper introduces the Critical Escape Probability (CREP), a new metric for optimizing power system parameters to significantly improve transient stability by reducing the likelihood of system states escaping critical regions.

Contribution

It formulates CREP based on stochastic process invariant measures and demonstrates its effectiveness in enhancing stability through parameter optimization.

Findings

Minimizing CREP increases mean first hitting time, improving stability.

CREP provides a comprehensive measure reflecting basin of attraction size.

Traditional metrics may not detect paradoxes identified by CREP.

Abstract

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.