Abstract

In this paper we consider modeling the number of households affected by power outages occurring in multiple locations. In so doing, we assume that the power distribution systems in those locations operate under a common environment. For each location, we consider a compound Poisson process to model the number of affected households, whose jump rate (outage rate) and jump size (the number affected by each outage) change with the changing environment which is modelled as a latent Markov process. Therefore, we refer to this model as Markov modulated multiple compound Poisson processes. Given the state of the environment, the occurrence of power outages in different regions and the number of households affected by each power outage are assumed to be conditionally independent. We extend the model to account for regional variation in a deterministic manner by using covariates on outage rates and the number of affected households. We use simulated and real power outage data from five counties in Northern Virginia to illustrate the proposed model.