Perturbation Finite Element Method for Magnetic Model Refinement of Air Gaps and Leakage Fluxes

Abstract

Model refinements of magnetic circuits are performed via a subproblem finite element method based on a perturbation technique. An approximate problem considering ideal flux tubes and simplified air-gap models is first solved. It gives the sources for a finite element perturbation problem considering the actual air gaps and flux tubes geometries with the exterior regions. The procedure simplifies both meshing and solving processes, and allows to quantify the gain given by each model refinement.Index Terms-Finite-element method (FEM), magnetic circuits, perturbation method.

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

“…The source fixes the current density in inductors. With the perturbation method, is also used for expressing changes of permeability and for adding portions of inductors [3], [4]. In magnetodynamic problems, also expresses changes of conductivity [2], [6].…”

“…The canonical problem (1a)-(1h) is defined in with the magnetic vector potential formulation [3], [4], expressing the magnetic flux density in as the curl of a magnetic vector potential . The related -formulation is obtained from the weak form of the Ampère equation (1a), i.e.…”

“…A subproblem FE method is herein developed for coupling solutions of various dimensions, starting from simplified models [7], based on ideal flux tubes defining 1-D models, that evolve towards 2-D and 3-D accurate models, allowing leakage flux and end effects. It is an extension of the method proposed in [3]- [5], applied to refinements up to 3-D models. With the former method, material and interface condition changes were combined separately.…”

Model refinements of transformers via a subproblem finite element method

“…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]. It can also help in education with a progressive understanding of the various aspects of transformer design.…”

Comparison of implementation techniques for Galerkin projection between different meshes

“…The accuracy of the solution is ensured by the quasi-best property of the Galerkin method. Similar applications of Galerkin projection can also be found in domain decomposition methods [5][6][7][8][9].…”