Design optimization of distribution transformers with metaheuristic algorithms

Many economies in the world have adopted energy-efficiency requirements or incentive programs mandating or promoting the use of energy-efficient transformers. On the other hand, increases in transformer efficiency are subject to increases in transformer weight and size, sometimes as much as 50% or even more. The transformer manufacturing industry is therefore faced with the challenge to develop truly optimum designs. Transformer design optimization (TDO) is a mixed-integer nonlinear programming problem having complex and discontinuous objective function and constraints, with the objective of detailed calculation of the characteristics of a transformer based on national and/or international standards and transformer user requirements, using available materials and manufacturing processes, to minimize manufacturing cost or total owning cost, while maximizing operating performance. Detailed comparative analysis of the application of five modern metaheuristic optimization algorithms for the solution of TDO problem are carried out in this study, demonstrated on three test cases; and two algorithms are proposed, for which it has been verified that they possess guaranteed global convergence properties in spite of their inherent stochastic nature. A pragmatic benchmarking scheme is used for comparison of the algorithms. Transformer design optimization methods presented in the literature rarely yield solutions directly applicable in production; the design engineer usually needs to convert the theoretical solution to a practical one. This problem is addressed in this study, and a discrete transformer design optimization method is proposed which yields solutions with commercially available or productionally feasible dimensions Furthermore, a simple method is proposed to reduce the number of objective function and constraint calculations. The method is based on skipping calculations for design vectors recurring during the search process, by the use of caching technique Performance tests showed that global or near-global optimum solutions can be obtained with b6e6rl and CS for TDO, and CS and FPA algorithms for DTDO.