Frequency-domain homogenization of bundles of wires in 2-D magnetodynamic FE calculations

A general approach for the frequency-domain homogenization of multiturn windings in two-dimensional (2-D) finite element (FE) calculations is presented. First, a skin and proximity effect characterization of the individual conductors, of arbitrary cross-section and packing, is obtained using a representative 2-D FE model. Herein, three excitation modes are considered, viz current and flux density in two perpendicular directions. In practical cases, the three modes are independent and the obtained frequency-dependent impedance and complex reluctivity tensor can be readily used in a FE model of the complete device. By way of example and validation, the method is applied to an inductor having an airgap and one of three different windings. The homogenized model produces global results (impedance versus frequency) that agree well with those obtained with a more precise FE model. In the latter, each turn of the winding is explicitly modeled and finely discretized.