Modeling of litz-wire losses in high-power medium-frequency transformers

A comprehensive closed-form analytical model for litz-wire losses in windings of medium-frequency transformers is provided. It is suitable for optimization, reasonably simple, yet physics based and thus fairly general, and covers in particular the effects of practical importance in the windings of medium- and high-frequency transformers. The model covers wire level, bundle-level, subbundle level, and strand-level proximity effect. It is assumed that at each level, the subconductors of the next lower level are twisted only, without radial transposition. For more than five subconductors, this leads to extra losses due to high reversed current in the inner subconductors. A first experimental comparison is provided for the winding arrangement of a medium-frequency transformer. It is shown that the wire-level proximity effect plays an important role for a wire of six top-level bundles and significantly improves the agreement with the measurements as compared with a model of strand-level proximity effect only.