paper

Large-deviation properties of resilience of power grids

arXiv:1411.5233 · doi:10.1088/1367-2630/17/1/015005

Abstract

We study the distributions of the resilience of power flow models against transmission line failures via a so-called backup capacity. We consider three ensembles of random networks and in addition, the topology of the British transmission power grid. The three ensembles are Erdős-Rényi random graphs, Erdős-Rényi random graphs with a fixed number of links, and spatial networks where the nodes are embedded in a two dimensional plane. We investigate numerically the probability density functions (pdfs) down to the tails to gain insight in very resilient and very vulnerable networks. This is achieved via large-deviation techniques which allow us to study very rare values which occur with probability densities below . We find that the right tail of the pdfs towards larger backup capacities follows an exponential with a strong curvature. This is confirmed by the rate function which approaches a limiting curve for increasing network sizes. Very resilient networks are basically characterized by a small diameter and a large power sign ratio. In addition, networks can be made typically more resilient by adding more links.

arXiv comment16 pages, 6 figures; Corrected smaller errors (Omega=2π*50 rad/s and n_P is number of poles) and added additional information for some references

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