Probabilistic analysis of failures in power transmission networks and phase transitions: Study case of a high-voltage power transmission network

We present the failure analysis of a study case of a high-voltage power transmission network using the mathematical model of cascading blackouts introduced in Carreras et al. (Chaos 12:985-994, 2002). When the load of the network is randomly perturbed, we study the probability density function of the measure of the size of the resulting blackout as a function of the mean load level. The mathematical model used approximates the network with an undirected graph made of generator, load and junction nodes connected by branches representing the lines of the network. The electric flow in the network is found solving the optimal DC power-flow problem and the sequence of events causing a cascading blackout is simulated using a numerical scheme. The analysis points out the existence of values of the mean total power demand such that for higher values when the blackout size measure increases the decay of the blackout size measure probability density function changes from being best fitted by a negative exponential to being best fitted by an inverse power law. The analogies between this phenomenon and the phase transition phenomenon studied in statistical mechanics are discussed. The website: http://www.ceri.uniroma1.it/ceri/zirilli/w1 contains some auxiliary material including animations that helps the understanding of this paper.