General Analytical Model for the Thermal Resistance of Windings Made of Solid or Litz Wire

In this paper, an analytical method to model the thermal resistance of windings made either of solid or litz wire is presented and validated by measurements. In addition, an extended numerical approach for litz wire windings, which also considers the twist pitch, is shown. With the presented model, it is possible to describe the thermal resistance of arbitrary wire arrangements. This approach can be used in straightforward thermal designs of magnetic devices, or it can be integrated in optimization procedures to improve the thermal designs of magnetic components. The analytical models are verified by measurements with nonpotted and epoxy-potted solid wire test setups and test setups for litz wire, which all show a good matching between the calculated and measured values. Besides the models for the thermal resistance between the winding layers, a method to simplify the thermal network of multilayer windings is presented. Finally, a thermal equivalent circuit of a test transformer has been calculated, which shows a good match between the measured and the predicted temperature distribution.