Development of probabilistic models for computing optimal distribution substation spare transformers

This paper presents probabilistic models developed based on Poisson probability distribution for determining the optimal number of transformer spares for distribution transformer systems. The outage of a transformer is a random event and the probability mathematics can best describe this type of failure process. The developed models have been illustrated using illustrative 72 kV distribution transformer systems. Industry average catastrophic transformer failure rate and a one-year transformer repair or procurement time have been utilized in the examples considered in the paper. Among the models developed for determining the optimum number of transformer spares, the statistical economics model provides the best result as it attempts to minimize the total system cost including the cost of spares carried in the system