Analytical model for the equivalent impedances of the domestic induction heating system with rectangular cross‐sectional windings

Abstract

This study proposes an analytical model to evaluate the equivalent impedances of domestic induction heating systems. The method of separation of variables is employed to determine the vector potential produced by a filamentary coil under a semi-infinite conductor. Then, based on the superposition principle of linear problems, the total vector potential of the coaxial, coplanar, connected-in-series rectangular cross-sectional multi-windings with same thicknesses, which are made of enamelled Litz wire, is derived by integrating the vector potential of filaments. Finally, the total voltage on the windings and the equivalent impedance of the induction heating system are obtained. The proposed analytical method is flexible to be used for calculating the equivalent impedance of multi-windings with any number of windings in an induction heating system with any mixture of windings with different lengths in the radial direction, and any distance between two adjacent windings in the radial direction. The proposed generally analytical method is successfully verified by comparison with the finite element method and shows improvement with respect to the conventional analytical method.