A Mixed Surface Volume Integral Formulation for the Modeling of High-Frequency Coreless Inductors

Abstract

An original integral formulation dedicated to the high frequency modeling of electromagnetic systems without magnetic materials is presented. The total current density (i.e. conduction plus displacement currents) is approached by facet elements so that resistive, inductive and capacitive effects are all modeled. The method avoids moreover the volume mesh of the conductors, which is too dense at high frequencies, due to the skin and proximity effects appearing e.g. in wound inductors. Surface impedance boundary conditions are employed to that end. The formulation is general and suitable for non simply connected domains. It is first compared with the finite element method on an academic test case, and is then experimentally validated on a coreless wound inductor, using an impedance analyzer.

3D eddy currents computation by BEM using the modified magnetic vector potential and the reduced magnetic scalar potential

“…In this test, we focus on the calculation of Joule losses. With the proposed formulation, the losses are calculated by the expression (19) and will be compared to the losses obtained by other methods such as FEM, BEM-FEM 14 or SIBC (Surface Impedance Boudary Condition) 17 . A volume mesh and a surface mesh with the same discretion of the surface will be used.…”

Unstructured PEEC method with the use of surface impedance boundary condition

“…In this work, we propose a new formulation dedicated to electromagnetic regions treated by the surface impedance condition (Yuferev and Di Rienzo, 2010). This work is an extension of a previous volume integral approach based on three-dimensional facet interpolations of the current density and of the magnetic flux density (Meunier et al, 2015;Torchio et al, 2019) and SIBC approaches in the case of conductive but non-magnetic regions (De Grève et al, 2016). The main interest is that volume conductive regions only require a surface mesh and that the air is not discretized (unlike finite element approaches combined with SIBC).…”