Bayesian Modeling of Power Outages
Open AccessIn this dissertation, our objective is to model power outages and their consequences by measuring the total number of households affected and the total customer hours. In the first essay, we discuss the development of a Markov modulated compound Poisson process (MMCPP), to model the number of households affected by power outages. In doing so, we develop Bayesian inference for the model using a Gibbs sampler. We present an algorithm to predict the number of future outages and the number of household affected by those outages and discuss assessment of the number of states of the latent environmental process by computing marginal likelihood of different models. We consider several extensions of the proposed model including order restrictions to overcome the well known label switching problem, a non-homogeneous extension of the modulated process, taking into account covariates, and modeling customer outage hours. We use simulated, as well as actual, power outage data to demonstrate the implementation of our proposed model and the methodology. We present a comparison of the MMCPP model with a model using covariates and illustrate that the environmental process identifies the effect of covariates such as severe weather conditions. In the second essay, we consider modeling the number of households affected by power outages occurred 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 and jump size change with the changing state of the common environment which is a latent Markov process. Therefore, we refer to this model as Markov modulated multiple compound Poisson processes (MMMCPP). We extend the model to account for regional variation in a deterministic and stochastic manner by using covariates and autoregressive models respectively. In so doing, we introduce spatial version of MMMCPP's. We use simulated and real power outage data of five counties in northern Virginia to illustrate the proposed model.
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