Failure and avalanches in complex networks

TL;DR

This paper analyzes the size distribution of power blackouts in complex networks, revealing power-law behaviors and proposing a model that reproduces these distributions across different network types.

Contribution

It introduces a load redistribution model that explains blackout size distributions and validates it with empirical data and theoretical analysis.

Findings

Power-law distribution of blackout sizes in real power grids

Model reproduces observed power-law exponents in simulations

Mean field theory aligns with numerical results

Abstract

We study the size distribution of power blackouts for the Norwegian and North American power grids. We find that for both systems the size distribution follows power laws with exponents $-1.65 \pm 0.05$ and $-2.0 \pm 0.1$ respectively. We then present a model with global redistribution of the load when a link in the system fails which reproduces the power law from the Norwegian power grid if the simulation are carried out on the Norwegian high-voltage power grid. The model is also applied to regular and irregular networks and give power laws with exponents $-2.0\pm0.05$ for the regular networks and $-1.5\pm0.05$ for the irregular networks. A presented mean field theory is in good agreement with these numerical results.