Failure and avalanches in complex networks

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 $-2.0\pm 0.05$ for the regular networks and $-1.5\pm 0.05$ for the irregular networks. A presented mean field theory is in good agreement with these numerical results.

Added new references and some minor extentions on request from referee. Changed figure order. Added journal ref

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• The structure and function of complex networks
• Cascade-based attacks on complex networks
• Renormalization group analysis of the small-world network model
• Structural Vulnerability of the North American Power Grid
• Anomalous Transport in Complex Networks
• Robustness of the avalanche dynamics in data packet transport on scale-free networks

Cited by in corpus (9)

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• Dynamic Effects Increasing Network Vulnerability to Cascading Failures
• Efficiency of attack strategies on complex model and real-world networks
• A limited resource model of fault-tolerant capability against cascading failure of complex network
• Stochastic Load-Redistribution Model for Cascading Failure Propagation
• How Many Nodes are Effectively Accessed in Complex Networks?
• Limits of Predictability of Cascading Overload Failures in Spatially-Embedded Networks with Distributed Flows
• Load Dependence of Power Outage Statistics
• Revisiting and modeling power-law distributions in empirical outage data of power systems