Europhys. Lett.
Volume 76, Number 4, November 2006
Page(s) 717 - 723
Section Interdisciplinary physics and related areas of science and technology
Published online 18 October 2006
Europhys. Lett., 76 (4), pp. 717-723 (2006)
DOI: 10.1209/epl/i2006-10324-1

Failures and avalanches in complex networks

J. Ø. H. Bakke1, A. Hansen1 and J. Kertész2

1  Department of Physics, Norwegian University of Science and Technology N-7491 Trondheim, Norway
2  Institute of Physics, Budapest University of Technology - Budafoki út. 8 H-1111 Budapest, Hungary

received 7 June 2006; accepted in final form 25 September 2006
published online 18 October 2006

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.

89.75.Fb - Structures and organization in complex systems.
89.75.Hc - Networks and genealogical trees.
84.70.+p - High-current and high-voltage technology: power systems; power transmission lines and cables.

© EDP Sciences 2006