This paper presents a scenario-based optimization framework for evaluating the life-cycle cost of right-sizing and replacement timing for distribution transformers under demand–growth uncertainty. The proposed formulation jointly considers the discrete commercial transformer ratings, the discounted investment cost, and the monetized iron and copper losses over a 15-year planning horizon. Demand uncertainty is represented by nine scenarios defined by combinations of initial apparent power demand and annual growth rate, with D1∈45, 50, 55 kVA and g∈3%, 4%, 5%. Under these assumptions, the demand envelope evolves from an initial range of 45–55 kVA to approximately 68. 1–108. 9 kVA in Year 15, while expected demand increases from 50 kVA to about 87 kVA. The optimization results show that the economically optimal policy is to install a 112. 5 kVA transformer in Year 1 and maintain that rating throughout the horizon, without triggering any replacement events. The selected transformer maintains expected loading between approximately 0. 44 p. u. and 0. 77 p. u. , while the upper-demand scenario remains below 1. 0 p. u. over the entire horizon. These results indicate that, for the demand–growth conditions analyzed, the preferred outcome is a single initial sizing decision rather than a phased replacement strategy. Therefore, the proposed framework provides a consistent scenario-based alternative to deterministic margin-based planning for distribution transformer asset management.
Muñoz-Pilco et al. (Mon,) studied this question.