A cluster distribution as a model for estimating high-order-event probabilities in power systems

We propose the use of the cluster distribution, derived from a negative binomial probability model, to estimate the probability of high-order events in terms of number of lines outaged within a short time, useful in long-term planning and also in short-term operational defense to such events. We use this model to fit statistical data gathered for a 30-year period for North America. The model is compared to the commonly used Poisson model and the power-law model. Results indicate that the Poisson model underestimates the probability of higher-order events, whereas the power-law model overestimates it. We use the strict chi-square fitness test to compare the fitness of these three models and find that the cluster model is superior to the other two models for the data used in the study.