Robustness of Power-law Behavior in Cascading Failure Models

TL;DR

This paper investigates the conditions under which large cascading failures in power networks follow a power-law distribution, highlighting the risk of severe outages in electric transmission systems.

Contribution

It analyzes the robustness of power-law behavior in cascading failure models, providing insights into when such heavy-tailed risks are likely to occur.

Findings

Power-law distribution observed under specific critical conditions.

Risk of large failures can be quantitatively characterized.

Robustness of power-law behavior depends on network assumptions.

Abstract

Inspired by reliability issues in electric transmission networks, we use a probabilistic approach to study the occurrence of large failures in a stylized cascading failure model. In this model, lines have random capacities that initially meet the load demands imposed on the network. Every single line failure changes the load distribution in the surviving network, possibly causing further lines to become overloaded and trip as well. An initial single line failure can therefore potentially trigger massive cascading effects, and in this paper we measure the risk of such cascading events by the probability that the number of failed lines exceeds a certain large threshold. Under particular critical conditions, the exceedance probability follows a power-law distribution, implying a significant risk of severe failures. We examine the robustness of the power-law behavior by exploring under which assumptions this behavior prevails.