Analytical modelling of high‐frequency losses in toroidal inductors

Abstract

Toroidal inductors are widely used in power electronic systems. With the increasing switching frequency of power devices, the AC losses of high‐frequency inductor windings have become an issue that cannot be ignored in design. A method with low computational time cost and high accuracy is urgently needed by designers. This paper proposes a modified analytical method for winding loss calculation of toroidal inductors based on the one‐dimensional Dowell method and the two‐dimensional Ferreira method, and proposes a compensated analytical model considering the proximity effect of inter‐turn conductors of toroidal windings. The analytical method calculates the non‐linear porosity of toroidal windings, and can accurately solve the AC losses of toroidal inductors with arbitrary porosity winding encapsulation. The analytical results are in good agreement with the finite element method (FEM) and experimental data. The experimental measurement data verifies the validity of the proposed model within 1‐MHz frequency, the calculation error of the modified analytical method is less than 25%, and the calculation error of the compensated analytical model is reduced to 10%.

Loss-Optimized Design of Magnetic Devices

“…The total loss of the winding can be obtained from the sum of ( 21) and (27). The partial derivatives of the total loss with respect to the number of turns are used to compute the poles.…”

“…Winding losses are influenced by the skin effect and proximity effect of the conductor, while core losses are directly linked to the material and size of the core, determined by the excitation source during operation. Various methods exist for predicting winding losses, including analytical and numerical approaches [ 26 , 27 ]. Notably, loss models for Litz wire devices [ 28 ] and 2D copper foil devices are continuously optimized [ 29 , 30 , 31 ].…”

AC-Winding-Resistance Calculation of Toroidal Inductors with Solid-Round-Wire and Litz-Wire Winding Based on Complex Permeability Modeling

“…Numerous studies have proposed original and modified approaches to calculate the frequency-dependency of the winding losses, including the homogenization method based on the complex permeability [5][6][7][8][9], unit-cell simulations [10,11], and partial element equivalent circuit (PEEC) [12], as well as the hybrid method [13,14], and analytical models [15][16][17][18][19][20][21]. Sullivan et al [5] and Gyselinck et al [6,7] calculated the frequency-dependent complex permeability of a winding region based on finite element analysis (FEA).…”

“…However, this method has been used for the transformer windings where the turns in each layer exhibit the same structure. To overcome the limitation of the original method, some authors proposed an analytical formulation of AC-winding losses for a solidround wire winding by modifying Dowell's model to account for the layered structure of the toroidal inductor [20,21].…”