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New Journal of Physics

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Deutsche Physikalische Gessellschaft IOP Institute of Physics

Large-deviation properties of resilience of power grids

OPEN ACCESS Focus on Networks, Energy and the Economy

Timo Dewenter and Alexander K Hartmann

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Paper

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.

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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

PACS

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

02.30.Sa Functional analysis

84.40.Az Waveguides, transmission lines, striplines

02.50.Cw Probability theory

02.10.Ox Combinatorics; graph theory

02.40.Pc General topology

Subjects

Mathematical physics

Computational physics

Electronics and devices

Statistical physics and nonlinear systems

Dates

Issue 1 (January 2015)

Received 18 July 2014, accepted for publication 25 November 2014

Published 15 January 2015

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Funding

Lower Saxony Ministry of Science and Culture. Grant number: grant ZN2764/ZN 2896

Deutsche Forschungsgemeinschaft . Grant number: INST 184/108-1 FUGG

Annotations

Monte Carlo methods

Random graphs



  1. Large-deviation properties of resilience of power grids

    Timo Dewenter and Alexander K Hartmann 2015 New J. Phys. 17 015005

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