Optimal distribution transformer sizing in a harmonic involved load environment via dynamic programming technique

Installation of a significant number of distributed generators (DGs), besides the application of non-sinusoidal loads such as; Plug-in Hybrid Electric Vehicles (PHEVs), in the emerging smart distribution networks and the industrial plants have posed a major challenge to the existing methods of optimal transformer sizing (OTS). The harmonic currents generated in these new environments not only substantially increase the transformer load losses, but also cause abnormal winding temperature rise and hence transformer excessive loss of life. Therefore, the harmonic contents of the loads currents should be accounted in choosing the appropriate size of distribution transformers. To address this concern of utilities, this paper introduces a new method to solve the OTS problem in such environments. It takes into account the effects of harmonics currents on excessive heat generation in a transformer and the transformer insulation loss of life due to these thermal stresses. This paper proposes a new dynamic programming (DP) framework to solve the OTS problem. Although the proposed DP method considers the transformer thermal equations, however, by introducing a novel variable named the depreciation cost, the consecutive stages of the proposed DP network are hold independent. Therefore, the proposed DP method does not require any supplementary heuristic algorithm to solve the OTS problem. In response, the proposed method is very fast and easy to implement. Comprehensive studies are carried out to validate the effectiveness of the proposed algorithm.