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Asymptotic modeling and discretisation of magnetic components in eddy current problems

Abstract : Modeling of integrated magnetic components in electrical engineering (such as high frequency transformers) leads to several issues related to frequency increase. This frequency increase induces eddy currents in conducting material which require very fine meshes and consequently, it leads to large systems of equations and prohibit computational cost, especially for 3D structures. The commercial scientific software only partially tackle these issues due notably to the presence of airgaps (modeling "infinite" medium by radiating conditions), the presence of thin layers (very heterogeneous meshes), and the inclusion of winding multi-layers. To deal with these difficulties, dedicated tools have been implemented. The primary issue that is the presence of airgaps is treated by solving a coupled "Finite Element Method (FEM)/ Boundary Element Method (BEM)" system in 3D. The BEM is adapted to general field problems with unbounded structures because no artificial boundaries are needed, this is not the case for the FEM. Moreover, the BEM requires only a surface discretisation which reduces the number of unknowns and then the computational time. The secondary issue is to deal with thin conductive layers used in a wide range of applications for shielding purpose. Modeling such conductive regions require very fine volume discretisation due to the rapid decay of fields through the surface for high frequencies. To avoid this difficulty, we derive an equivalent model for 3D Eddy Current problem with a conductive thin layer of slight thickness, where the conductive sheet is replaced by its mid-surface, and its shielding behaviour is satisfied by an equivalent transmission condition which connects the electric and magnetic fields around the surface. In addition, an efficient discretisation using the BEM is provided to solve numerically the problem with the transmission condition. The last issue is to tackle the foil winding problems. We proceed by considering the simple case of a problem of laminar stacks. We provide an effective modeling of the laminar stacks in 1D and 2D by deriving the classical homogenisation in the domain of the laminar stacks. Then, we study the influence of the interface (with air) on the vector potential to treat the problem in the whole domain. We also consider the case where the skin depth is kept less than or equal to the thickness of the metal sheet.
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Submitted on : Friday, March 6, 2020 - 11:26:09 AM
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  • HAL Id : tel-02500653, version 1



Mohammad Issa. Asymptotic modeling and discretisation of magnetic components in eddy current problems. Electromagnetism. Université Paul Sabatier - Toulouse III, 2019. English. ⟨NNT : 2019TOU30177⟩. ⟨tel-02500653⟩



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