Cascading Link Failure in the Power Grid: A Percolation-Based Analysis

TL;DR

This paper analyzes cascading link failures in power grids modeled as random geometric graphs, providing new analytical conditions for the existence of large operational components after failures, using a percolation-based approach.

Contribution

It introduces a novel percolation-based model for cascading link failures in power networks and derives the first analytical conditions for large component existence post-failure.

Findings

Derived conditions for large component existence after degree-dependent failures

Mapped links to a dual graph to facilitate analysis

Provided analytical thresholds for cascading failures

Abstract

Large-scale power blackouts caused by cascading failure are inflicting enormous socioeconomic costs. We study the problem of cascading link failures in power networks modelled by random geometric graphs from a percolation-based viewpoint. To reflect the fact that links fail according to the amount of power flow going through them, we introduce a model where links fail according to a probability which depends on the number of neighboring links. We devise a mapping which maps links in a random geometric graph to nodes in a corresponding dual covering graph. This mapping enables us to obtain the first-known analytical conditions on the existence and non-existence of a large component of operational links after degree-dependent link failures. Next, we present a simple but descriptive model for cascading link failure, and use the degree-dependent link failure results to obtain the first-known analytical conditions on the existence and non-existence of cascading link failures.