Probability Models for Optimal Sparing of Distribution Network Transformers

A probabilistic approach for the determination of the optimum number of spare transformers is presented providing minimum annual cost consisting of capital cost for spares and transformer outage costs. The model suggested can cover any transformer unit lifetime and renewal time probability distribution. This makes it possible to account for the effects of transformer deterioration due to aging and to realistically, based upon empirical data, assess the impacts of the renewal time by treating it as a stochastic rather than as a deterministic variable lasting the entire planning period. The comparison of the model presented with the Poisson distribution based approach, widely used in sparing analyses in the past, has shown that the negligence of aging and of the stochastic nature of renewal times can lead to worse than optimal solutions.