A Two-Dimensional Equivalent Complex Permeability Model for Round-Wire Windings

Eddy currents at high frequencies affect both active power and reactive power in a winding. Recently a two-dimensional (2-D) model for calculating power loss in round-wire windings was introduced and was shown to have higher accuracy than the Dowell model and the Bessel-function method. The model was given in terms of proximity-effect loss normalized by the square of field magnitude and conductivity. In order to find the total proximity-effect loss, the field distribution in the winding window should also be known, which requires the modeling of not only how the eddy currents in windings affect power loss but also how they affect the field distribution in the window. Based on the proximity-effect loss model and the Kramer-Kronig relation, we derive an equivalent complex permeability model of a round-wire winding that agrees with finite element analysis results. This model can be used to calculate high-frequency winding loss and inductances (especially leakage inductance) in transformers and inductors with two-dimensional geometry. Numerical simulation results and experimental results validate the complex permeability model