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arXiv · 1411.5233

Large-deviation properties of resilience of power grids

Timo Dewenter·Alexander K. Hartmann
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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 Erd\H{o}s-R\'enyi random graphs, Erd\H{o}s-R\'enyi 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 $10^{-160}$. 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.

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Timo Dewenter, Alexander K. Hartmann. 2014-11-19. Large-deviation properties of resilience of power grids. https://doi.org/10.1088/1367-2630/17/1/015005

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