Line failure probability bounds for power grids

TL;DR

This paper introduces explicit upper bounds on line failure probabilities in power grids using Gaussian noise assumptions, enabling the characterization of safe operational regions that are convex and compatible with planning tools.

Contribution

The authors develop novel, explicit probabilistic bounds for line failures in power grids under the DC approximation, leveraging concentration inequalities.

Findings

Bounds are convex and polyhedral, facilitating integration into planning.

Probabilistic failure bounds are explicitly derived using concentration inequalities.

Tools are compatible with existing power grid planning methods.

Abstract

We develop upper bounds for line failure probabilities in power grids, under the DC approximation and assuming Gaussian noise for the power injections. Our upper bounds are explicit, and lead to characterization of safe operational capacity regions that are convex and polyhedral, making our tools compatible with existing planning methods. Our probabilistic bounds are derived through the use of powerful concentration inequalities.