Computing Rare Probabilities of Voltage Collapse

TL;DR

This paper presents a Large Deviation Theory-based framework for accurately computing rare probabilities of voltage collapse, improving efficiency over traditional Monte Carlo methods.

Contribution

It introduces a novel LDT-based approach to estimate voltage collapse probabilities, including higher-order approximations and extensions to non-Gaussian uncertainties.

Findings

LDT estimates closely match Monte Carlo results in rare-event regimes.

Second-order approximation improves accuracy over first-order methods.

Framework generalizes existing distance-based methods and is validated on test systems.

Abstract

This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on the stability boundary and derive both first-order and second-order approximations for the collapse probability. The second-order method incorporates the local curvature of the stability boundary, yielding higher accuracy. This LDT framework generalizes methods based on Mahalanobis distance and is extensible to non-Gaussian uncertainties. We validate our approach on test systems, demonstrating that the LDT estimates converge to Monte Carlo results in the rare-event regime where direct sampling becomes computationally prohibitive.