Frequency- and time-domain homogenization of windings in two-dimensional finite-element models

This paper deals with novel homogenization methods for the inclusion of skin and proximity effect in windings in finite-element (FE) models of electromagnetic devices. A general frequency-domain approach and its original extension to the time domain are proposed. In a preprocessing step the conductors (i.e. type of cross-section and packing, and fill factor) are characterized in the frequency domain by means of a reduced FE model, producing six dimensionless and frequency-dependent skin- and proximity-effect coefficients. The latter coefficients are readily taken into account in a frequency-domain FE analysis of a complete device. A time-domain FE analysis with homogenized winding requires the introduction of additional unknowns and equations; this extension to the time domain is analogous to the approximation of a frequency-dependent inductive impedance by a ladder circuit consisting of constant resistances and inductances. By way of illustration and validation, the homogenization methods are applied to a 2D FE model of an inductor. For the winding, different types of wire cross-section and packing, viz round/hexagonal and rectangular/rectangular, are considered. A precise reference solution is obtained with a FE model in which all wires are finely discretized. An excellent agreement is achieved while reducing the computation time considerably