Finite Element Magnetic Models via a Coupling of Subproblems of Lower Dimensions

Abstract

International audienceModel refinements of magnetic circuits are performed via a subdomain finite element method based on a perturbation technique. A complete problem is split into subproblems, some of lower dimensions, to allow a progression from 1-D to 3-D models. Its solution is then expressed as the sum of the subproblem solutions supported by different meshes. A convenient and robust correction procedure is proposed allowing independent overlapping meshes for both source and reaction fields, the latter being free of cancellation error in magnetic materials. The procedure simplifies both meshing and solving processes, and quantifies the gain given by each model refinement on both local fields and global quantities

Model refinements of transformers via a subproblem finite element method

“…Indeed, a lower dimension model actually defines some perfect magnetic walls that are made permeable when increasing the dimension [2].…”

“…It is based on a finite element (FE) subproblem (SP) method (SPM) with magnetostatic and magnetodynamic problems solved in a sequence on different adapted meshes [1]- [5], from simple 1-D models up to accurate 3-D models, in a large frequency range, of the magnetic circuits and their windings (stranded or massive coils). Each step of the SPM aims at improving the solution obtained at previous steps via any coupling of the following changes, defining model refinements: change from ideal to real (with leakage flux) flux tubes [1], change from 1-D to 2-D to 3-D [2], change of material properties [1]- [3] (e.g., from linear to nonlinear), change from perfect to real materials [4], change from single wire to volume conductor windings [4], [5], and newly developed change from homogenized [6] to fine models (cores as lamination stacks and coils as wire or foil windings, with the details affecting their high frequency behaviors). The methodology involves and couples numerous techniques that have been developed by the authors and, up to now, only applied for simplified test problems [1]- [5].…”

Perfect Conductor and Impedance Boundary Condition Corrections via a Finite Element Subproblem Method

“…To allow a natural progression from simple to more elaborate models, a complete problem is split into a series of SPs that define a sequence of changes, with the complete solution being replaced by the sum of the SP solutions [3]. Each SP is defined in its particular domain, generally distinct from the complete one and usually overlapping those of the other SPs.…”

“…for changes from µ q and σ q for SP q to µ p and σ p for SP p in some regions [3]. Also, BCs have to be defined for surface sources (SSs), possibly expressed from previous solutions, i.e.…”

“…It is here proposed to perform successive FE refinements via a subproblem (SP) method (SPM) [3] to correct the models with approximate BCs. Accurate skin and proximity effects, i.e.…”