Analytical Formulation of Copper Loss of Litz Wire With Multiple Levels of Twisting Using Measurable Parameters

Abstract

Litz wire has been widely utilized in power transformers and inductors as a wire with low copper loss at high-frequency operation. The Litz wire is commonly made of many thin isolated strands twisted in multiple levels. Due to its complicated structure, the copper loss prediction of the Litz wire has been difficult, hindering the design optimization of the Litz wire structure. To overcome this difficulty, preceding studies have investigated the analytical copper loss models of the constituting elements of the Litz wire, i.e., the strands and the bundles of strands. The purpose of this article is to propose an analytical copper loss model of the Litz wire by utilizing these preceding knowledge. The proposed model is formulated only with parameters that can be measured by basic testing instruments. Besides, the proposed model considers the bundle structure of the Litz wire, which affects the local ac current distribution, and the twisting pitch, which causes the inclination of the Litz wire strands. The proposed model was tested by comparing the analytical prediction and experimental measurements of the ac resistance of commercially available Litz wires. As a result, the predicted ac resistance showed good agreement with the measured ac resistance, suggesting the appropriateness of the proposed model.