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 2012 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 TLP, an adequate model to describe major events reliability data of power grids in the whole
range, and in the case of ENS and RT, is the best choice of the six alternative models analyzed.
