Probabilistic method for optimizing the number and timing of substation spare transformers

This paper presents a new probabilistic methodology based on Chronological Monte Carlo Simulation for sizing inventories of distribution substation spare transformers.The proposed method allows the representation of events such as: equipment aging; load growth and system expansion; inventory management; gradual increasing in the number of spares; and other conditions not supported by traditional methods based on Poisson and Markov processes. Several reliability indices and costs can be calculated. The lifetimes of the transformers are represented by discrete probability distributions, determined by a chronological simulation algorithm, considering: The aging process of the insulating material (estimated by the Arrhenius Theory), and; The loss of life caused by short-circuits, lightning, and switching surges (statistics from historical data); The proposed method is applied to a group of substations with 177 transformers of 138-13.8 kV, with power rating of 25 MVA; The idea is to demonstrate the importance of the inventory sizing on reliability indices and system costs.