Journal
NEW JOURNAL OF PHYSICS
Volume 17, Issue -, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/17/1/015005
Keywords
power grids; large-deviation approach; complex networks
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Funding
- Lower Saxony research network 'Smart Nord' - Lower Saxony Ministry of Science and Culture through the 'Niedersachsisches Vorab' grant programme [ZN2764/ZN 2896]
- DFG through its Major Research Instrumentation Programme [INST 184/108-1 FUGG]
- Ministry of Science and Culture (MWK) of the Lower Saxony State
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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 Erdos-Renyi random graphs, Erdos-Renyi 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.
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