Frequency-domain homogenization for litz-wire bundles in finite element calculations

This work deals with a frequency-domain homogenization method for litz-wire bundles embedded in a finite element (FE) model. The approach consists in adopting a frequency-dependent complex reluctivity in the litz-wire bundles and a frequency-dependent complex impedance in the electrical circuit in terms of dimensionless coefficients. The litz-wire bundles become homogeneous conductors which are easy to integrate into a finite element model. The homogenization methods in previous works are also reviewed. The complex permeability achieved with our model is compared to the most accurate expression found in literature. The agreement is very good despite the different elementary cell and condition setting. Moreover, the homogenization method in this paper is validated for both 2-D and 3-D FE calculations with the translational-symmetry transformer model and the axisymmetric inductor model respectively. The reference solutions of those models are computed by finely discretizing each conductor inside the litz-wire bundle. The results of the computed resistance and inductance agree well with those computed by the reference fine model, resulting in less than 3% and 0.05% maximum errors respectively in 2-D FE model, and 4% and 1.8% respectively in 3-D FE model with several times less computational cost.