Use of Markov Models in Assessing Spare Transformer Requirements for Distribution Stations

This paper describes a probabilistic method based on Markov models for assessing the number of spare transformers, regular units and mobile units, required for a group of distribution transformers. The proposed method uses two criteria in determining the required number of spare transformers. The first criterion assumes that a pre-determined level of the group availability is given and the number of spare units is determined when the calculated group availability exceeds the pre-determined level of the group availability. The second criterion uses a cost/benefit analysis method in calculating the number of the spare units. In the second criterion, the number of spare units (optimal number) is determined when the total cost (spare unit capital costs and unit outage costs) is minimum. The proposed method is also used to evaluate the impacts of multi-transformer stations (stations with transformer redundancy) and station capabilities for use of mobile unit transformers on the number of spare units. Two distribution transformer groups of the Hydro One's distribution system are used to illustrate the proposed method of assessment and to compare the results obtained using the two criteria.