K. Hollaus, J. Schöberl:

"Various two dimensional multi-scale finite element formulations for the eddy current problem in iron laminates";

Talk: EMF 2016 10th International Symposium on Electric and Magnetic Fields, Lyon (invited); 2016-04-12 - 2016-04-14; in: "EMF 2016 10th International Symposium on Electric and Magnetic Fields", R. Scorretti, L. Krähenbühl (ed.); Ampère Laboratory (CNRS and Université de Lyon), 1 (2016), 1 pages.

An efficient as well as an accurate simulation of the eddy currents in laminated iron

cores of electrical machines and transformers is important to facilitate the design

process. Modeling of each laminate requires many finite elements. The fine meshes

are the reason why large equation systems arise, which may require prohibitively

large amounts of computer resources to obtain an accurate solution. The multi-scale

finite element method (MSFEM) has proven to overcome this restriction.

Laminated iron cores are observed as a periodic structure in the context of MSFEM.

The smooth variation of the solution due to the macroscopic structure of the iron

core is taken into account by standard polynomial shape functions. Orthogonal

periodic micro-shape functions consider the local rough behavior of the solution

caused by the microscopic structure.

Various two dimensional multi-scale formulations using a magnetic vector potential

or a current vector potential are discussed. The potential formulations are either

vector valued or get along with a single component. Formulations will be presented

which make use of the finite element spaces H1; L2;H(curl) and H(div). Depending

on the problem even or odd polynomials are used for the micro-shape functions.

Particular attention is paid to the edge effect, air gaps, arbitrary penetration depths

and nonlinear material properties.

Two dimensional models, i.e. no dependency in the third dimension, represent a

simplification of real world problems. The case, where the current density is perpendicular

to the plane of projection and its average value equals to zero is studied.

This case approximates a problem which has a large but finite extension in the third

dimension. Neither an application of a single component magnetic vector potential

nor a use of a two component current vector potential provides the required solution.

Both options only provides solutions where the average value of the current

density over all laminates is zero. To overcome this shortcoming balanced currents

in the individual laminates are enforced by additional conditions. This leads to a

saddle point problem, the associated system is simply solved by PARDISO.

Multi-scale approaches proposed up to now do not explicitly fulfill divergence free

eddy currents. A formulation will be presented which fulfills this requirement exactly.

The formulation deals with the vector valued magnetic vector potential, the

magnetic field is perpendicular to the plane of projection.

Numerical simulations demonstrate excellent accuracy and very low computational

costs.

http://publik.tuwien.ac.at/files/publik_255642.pdf

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