Multiobjective optimal design of high frequency transformers using genetic algorithm

This paper deals with the multiobjective optimization (MO) design of high frequency (HF) transformers using genetic algorithms (GAs). In its most general form, the design problem requires minimizing the mass or overall dimensions of the core and windings as well as the loss of the transformer while ensuring the satisfaction of a number of constraints. In this contribution, the area product (i.e. the product of the core cross section and the winding area) and the power loss are used as objective functions whereas the operating frequency and the maximum flux density are chosen as optimization variables. The constraints include, as for them, appropriate limits on efficiency, maximum surface temperature rise and maximum ratio no-load/full load current. The area product is optimized in place of weight or volume of the transformer because these two quantities can be easily expressed in terms of area product. It is an elegant mean to limit the number of objective functions. The major advantage of the suggested design procedure is that it proposes to the designer a set of optimal transformers - instead of a single solution - so he can choose a posteriori which of them best fits the application under consideration. Finally, in order to illustrate the design procedure, the optimal design of a transformer supplied with square voltage waveform is performed and the results are discussed.