Probabilistic Method for Optimizing the Number and Timing of Substation Spare Transformers

This paper proposes a new probabilistic method based on chronological Monte Carlo simulation for computing optimal distribution substation spare transformers. The method allows the representation of events such as aging process, load growth, and other conditions not supported by traditional methods based on Poisson and Markov processes. The lifetimes of the transformers are represented by discrete probability distributions, determined by an algorithm that combines the aging of the insulating material, estimated by Arrhenius theory, with the loss of life caused by short-circuits, lightning and switching surges. To illustrate the importance of sizing the inventory based on reliability indices and costs, the proposed method is applied to a group of substations with 177 transformers of 138-13.8 kV, with power rating of 25 MVA. Finally, the proposed methodology is used in combination with a metaheuristic algorithm for determining the optimal timing strategy for composing of the stock of spare transformers over a pre-established planning horizon.