I. Introduction
Transformer design optimization seeks a constrained minimum cost solution by optimally setting the transformer geometry parameters and the relevant electrical and magnetic quantities. The difficulty in achieving the optimum balance between the transformer cost and performance is becoming even more complicated nowadays, as the manufacturing materials (copper, aluminum, steel) are highly variable stock exchange commodities. Techniques that include mathematical models employing analytical formulas, based on design constants and approximations for the calculation of the transformer parameters are often the base of the design process adopted by transformer manufacturers [1]. However, the relevant technical literature comprises a variety of other approaches in order to cope with the complex problem of transformer design optimization, based on stochastic optimization methods such as genetic algorithms (GAs) that have been used for power transformer cost minimization [2], performance optimization of cast-resin distribution transformers with stack core technology [3] or toroidal core transformers [4]. The computational complexity of stochastic methods becomes quite considerable in case of the numerous iterations that may be required in order to achieve overall transformer optimization, therefore limiting the application of such methods in certain aspects of transformer design, as in [5] and [6], where artificial intelligence techniques are used for winding material selection and prediction of transformer losses and reactance, respectively, or [7], where particle swarm optimization is applied for the transformer thermal parameters estimation. Moreover, the optimality of the solution provided by GAs and other stochastic methods cannot be guaranteed [8] and multiple runs may result to different suboptimal solutions, with a significant difference between the worst and the best one. On the other hand, deterministic methods may provide more robust solutions to the transformer design optimization problem. In this context, the deterministic method of geometric programming has been proposed in [9] in order to deal with the design optimization problem of both low-frequency and high-frequency transformer. An important improvement in deterministic design optimization methods can be implemented by the incorporation of numerical methods, and various approaches have been developed [10], [11].