Modelling major failures in power grids in the whole range

Abstract: Empirical research with electricity transmission networks reliability data shows that the size of major failures - in terms of energy not supplied (ENS), total loss of power (TLP) or restoration time (RT) - appear to follow a power law behaviour in the upper tail of the distribution. However, this pattern - also known as Pareto distribution - is not valid in the whole range of those major events. We aimed to find a probability distribution that we could use to model them, and hypothesized that there is a two-parameter model that fits the pattern of those data well in the entire domain. We considered the major failures produced between 2002 and 2009 in the European power grid; analyzed those reliability indicators: ENS, TLP and RT; fitted six alternative models: Pareto II, Fisk, Lognormal, Pareto, Weibull and Gamma distributions, to the data by maximum likelihood; compared these models by the Bayesian information criterion; tested the goodness-of-fit of those models by a Kolmogorov-Smirnov test method based on bootstrap resampling; and validated them graphically by rank-size plots. We found that Pareto II distribution is, in the case of ENS and TLP, an adequate model to describe major events reliability data of power grids in the whole range, and in the case of RT, is the best choice of the six alternative models analyzed.