Timo Dewenter and Alexander K Hartmann 2015 New J. Phys. 17 015005 doi:10.1088/1367-2630/17/1/015005
Timo Dewenter and Alexander K Hartmann
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Part of Focus on Networks, Energy and the Economy
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 numerically investigate the probability density functions (pdfs) down to the tails to gain insight into very resilient and very vulnerable networks. This is achieved via large-deviation techniques, which allow us to study very rare values that 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.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
84.40.Az Waveguides, transmission lines, striplines
Issue 1 (January 2015)
Received 18 July 2014, accepted for publication 25 November 2014
Published 15 January 2015
Total article downloads: 407
Lower Saxony Ministry of Science and Culture. Grant number: grant ZN2764/ZN 2896
Deutsche Forschungsgemeinschaft . Grant number: INST 184/108-1 FUGG
Monte Carlo methods
Random graphs
Timo Dewenter and Alexander K Hartmann 2015 New J. Phys. 17 015005