Probabilistic Methodologies for Determining the Optimal Number of Substation Spare Transformers

This paper presents new probabilistic methodologies for computing the optimal number of transformer spares for power distribution substations. The basic idea consists of three steps: 1) the reliability evaluation of a given system of transformers with inventory of spares; 2) the calculation of investment and operational costs of the system for different alternatives of inventory composition; and 3) the identification of the number of spares that minimizes the total cost. Two new models are proposed for the reliability evaluation step. In the first one, the system operational states are represented by a Markov process. The second one uses a chronological Monte Carlo simulation model to assess the reliability performance of a system with inventory of spares. Both models are able to provide indices such as probability, frequency, and duration of failures, as well as estimates of energy not supplied and the corresponding costs. The proposed methodologies are applied to a 72-kV distribution transformer system, and the obtained results are compared to those from a widely used model based on a Poisson distribution.