Modelling and optimization of winding resistance for litz wire inductors

Optimization of winding resistance for litz wire inductors is essential to reduce losses and improve energy transfer efficiency in electrical power systems. In this study, an approximate model for the optimization of winding resistance in litz wire inductors based on Dowell's equation is developed in three frequency ranges. The proximity and skin effects are analysed separately and subsequently combined to obtain an approximation with minimum theoretical error. Two error functions are defined to determine the frequency ranges for which the approximation is valid. Based on this Dowell's model approximation, it is found that, with the other parameters of the inductors fixed, both the porosity factor and conductivity have an optimal value that minimizes AC resistance for the litz wire windings. Thus, expressions for the optimum porosity factor and conductivity are derived, the optimization schemes under different practical engineering conditions are also given. The theoretical results are in good agreement with the experimental measurements, which indicates that the proposed model is valid for three frequency ranges, and the proposed optimization method is practical and suitable.