Distribution of blackouts in the power grid and the Motter and Lai model

TL;DR

This paper compares empirical blackout data with models, showing that network topology and failure rules influence blackout size distributions more than physical flow laws, reconciling different observed behaviors.

Contribution

It demonstrates how model parameters affect blackout distributions and shows similar results across different models, emphasizing the role of topology and failure dynamics.

Findings

Blackout sizes can follow power-law or bimodal distributions.

Model parameters significantly influence blackout size distribution.

Similar results are observed across different cascade models.

Abstract

Carreras, Dobson and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them by computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal as in a first order phase transition, resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system. Here we reconcile the two approaches and investigate how the distribution of the blackouts change with model parameters, including the tolerance criteria and the dynamic rules of failure of the overloaded lines during the cascade. In addition, we study the same problem for the Motter and Lai model and find similar results, suggesting that the physical laws of flow on the network are not as important as network topology, overload conditions, and dynamic rules of failure.