Modelling electricity power cuts in the UK

Abstract

We consider a compound Poisson model for electricity power cuts. Cuts occur at rate ? and we associate with the ith cut a duration L i and size C i , where L i and C i are heavy tailed and positively correlated. Development of the model is complicated by the fact that we have no direct observations of (L i , C i ). Rather, if N is the number of power cuts in a year, we have observations of ? i=1 N C i L i and ? i=1 N C i . This necessitates the use of a parsimonious model for (L i , C i ), and we base ours on the Pareto distribution. To fit the model we apply kernel density estimation to simulated data to obtain estimates of the likelihood, which we then maximise using stochastic optimisation.