Data-Driven Estimation of Failure Probabilities in Correlated Structure-Preserving Stochastic Power System Models

TL;DR

This paper introduces a data-driven, reduced-order method for efficiently estimating failure probabilities in stochastic power systems, outperforming traditional kernel density approaches especially for tail event and joint failure probability estimation.

Contribution

The paper develops a novel reduced-order equation derived from the Fokker-Planck equation to improve failure probability estimation in correlated stochastic power grid models.

Findings

More sample-efficient than kernel density estimation

More accurate joint failure probability estimates

Effective for spatiotemporally correlated noise

Abstract

We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed line energy probability density function is derived from the Fokker--Planck equation of the full-order continuous Markov process. Our method consists of estimates produced by numerically integrating this reduced equation. Numerical experiments for scalar- and vector-valued energy functions are conducted using the classical multimachine model under spatiotemporally correlated noise perturbation. The method demonstrates a more sample-efficient approach for computing probabilities of tail events when compared with kernel density estimation. Moreover, it produces vastly more accurate estimates of joint event occurrence when compared with independent models.