Large-deviation properties of resilience of power grids

TL;DR

This study analyzes the probability distributions of power grid resilience against line failures across different network models, revealing how network topology influences extreme resilience or vulnerability using large-deviation techniques.

Contribution

It introduces a large-deviation approach to quantify rare resilience events in power grids and compares different network ensembles, including real-world data.

Findings

Right tail of resilience distribution follows an exponential decay.

Resilient networks tend to have small diameters and high power sign ratios.

Adding links generally increases network resilience.

Abstract

We study the distributions of the resilience of power flow models against transmission line failures via a so-called backup capacity. We consider three ensembles of random networks and in addition, the topology of the British transmission power grid. The three ensembles are Erd\H{o}s-R\'enyi random graphs, Erd\H{o}s-R\'enyi random graphs with a fixed number of links, and spatial networks where the nodes are embedded in a two dimensional plane. We investigate numerically the probability density functions (pdfs) down to the tails to gain insight in very resilient and very vulnerable networks. This is achieved via large-deviation techniques which allow us to study very rare values which occur with probability densities below $10^{-160}$. We find that the right tail of the pdfs towards larger backup capacities follows an exponential with a strong curvature. This is confirmed by the rate function which approaches a limiting curve for increasing network sizes. Very resilient networks are basically characterized by a small diameter and a large power sign ratio. In addition, networks can be made typically more resilient by adding more links.