Large-deviation properties of resilience of power grids

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 $10^{-160}$. 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.

16 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

References in corpus (4)

• The large deviation approach to statistical mechanics
• Analysis of a power grid using the Kuramoto-like model
• Robustness of the European power grids under intentional attack
• Synchrony-optimized Networks of Non-identical Kuramoto Oscillators

Cited by in corpus (4)

• Observing symmetry-broken optimal paths of stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media
• Synchronization in the presence of time delays and inertia: Stability criteria
• First-passage area distribution and optimal fluctuations of fractional Brownian motion
• Numerical Aspects of Large Deviations