Magnetic Field Conforming Formulations for Foil Windings

Denis, Louis; Paakkunainen, Elias; Rasilo, Paavo; Schops, Sebastian; Vanderheyden, Benoît; Geuzaine, Christophe

doi:10.1109/TMAG.2025.3584111

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Magnetic Field Conforming Formulations for Foil Windings

Denis, Louis; Paakkunainen, Elias; Rasilo, Paavo et al.

2025 • In IEEE Transactions on Magnetics, 61 (8), p. 1-7

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https://hdl.handle.net/2268/337107

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10.1109/TMAG.2025.3584111

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Keywords :

Finite element analysis; foil winding; homogenization methods; inductors; Foil windings

Abstract :

[en] We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the magnetic scalar potential in non-conducting regions to improve the efficiency of the model. This leads to a significant reduction in the number of degrees of freedom, particularly in 3-D applications. The proposed models are verified on two frequency-domain benchmark problems: a 2-D axisymmetric problem and a 3-D problem. They reproduce results obtained with magnetic flux density conforming formulations and with resolved conductor models that explicitly discretize all turns. Moreover, the models are applied in the transient simulation of a high-temperature superconducting coil. In all investigated configurations, the proposed models provide reliable results while considerably reducing the size of the numerical problem to be solved.

Disciplines :

Electrical & electronics engineering

Author, co-author :

Denis, Louis ; Université de Liège - ULiège > Montefiore Institute of Electrical Engineering and Computer Science

Paakkunainen, Elias ; Institute for Accelerator Science and Electromagnetic Fields, Technical University of Darmstadt, Darmstadt, Germany ; Tampere University, Electrical Engineering Unit, Tampere, Finland

Rasilo, Paavo ; Tampere University, Electrical Engineering Unit, Tampere, Finland

Schops, Sebastian ; Institute for Accelerator Science and Electromagnetic Fields, Technical University of Darmstadt, Darmstadt, Germany

Vanderheyden, Benoît ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Electronique et microsystèmes

Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)

Language :

English

Title :

Magnetic Field Conforming Formulations for Foil Windings

Publication date :

2025

Journal title :

IEEE Transactions on Magnetics

ISSN :

0018-9464

eISSN :

1941-0069

Publisher :

Institute of Electrical and Electronics Engineers Inc.

Volume :

Issue :

Pages :

1-7

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://xplorestaging.ieee.org/ielx8/20/11097315/11059313.pdf?arnumber=11059313

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique
TU Darmstadt - Technical University of Darmstadt

Funding text :

The work of Louis Denis was supported by F.R.S.-FNRS. The work of Elias Paakkunainen is supported by the Graduate School CE in Computational Engineering at the Technical University of Darmstadt.

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since 26 October 2025

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Bibliography

G. Calderon-Lopez, J. Scoltock, Y. Wang, I. Laird, X. Yuan, and A. J. Forsyth, "Power-dense bi-directional DC-DC converters with high-performance inductors," IEEE Trans. Veh. Technol., vol. 68, no. 12, pp. 11439-11448, Dec. 2019.
A. K. Das and B. G. Fernandes, "Accurate capacitance calculation of multi-layer foil windings in a Medium/High-frequency high-power transformer," in Proc. IEEE Energy Convers. Congr. Expo. (ECCE), Oct. 2020, pp. 5834-5841.
M. Rios, G. Venkataramanan, A. Muetze, and H. Eickhoff, "Thermal performance modeling of foil conductor concentrated windings in electric machines," IEEE Trans. Ind. Appl., vol. 54, no. 5, pp. 4104-4113, Sep. 2018.
M. Rios and G. Venkataramanan, "Design and construction of a foil winding permanent magnet machine," in Proc. IEEE Energy Convers. Congr. Expo. (ECCE), Oct. 2020, pp. 2026-2033.
M. El Feddi, Z. Ren, A. Razek, and A. Bossavit, "Homogenization technique for Maxwell equations in periodic structures," IEEE Trans. Magn., vol. 33, no. 2, pp. 1382-1385, Mar. 1997.
J. Gyselinck and P. Dular, "Frequency-domain homogenization of bundles of wires in 2-D magnetodynamic FE calculations," IEEE Trans. Magn., vol. 41, no. 5, pp. 1416-1419, May 2005.
R. V. Sabariego, P. Dular, and J. Gyselinck, "Time-domain homogenization of windings in 3-D finite element models," IEEE Trans. Magn., vol. 44, no. 6, pp. 1302-1305, Jun. 2008.
H. De Gersem and K. Hameyer, "A finite element model for foil winding simulation," IEEE Trans. Magn., vol. 37, no. 5, pp. 3427-3432, Sep. 2001.
P. Dular and C. Geuzaine, "Spatially dependent global quantities associated with 2-D and 3-D magnetic vector potential formulations for foil winding modeling," IEEE Trans. Magn., vol. 38, no. 2, pp. 633-636, Mar. 2002.
C. A. Valdivieso, G. Meunier, B. Ramdane, J. Gyselinck, C. Guerin, and R. V. Sabariego, "Time-domain homogenization of foil windings in 2-D axisymmetric finite-element models," IEEE Trans. Power Del., vol. 36, no. 3, pp. 1264-1269, Jun. 2021.
J. Bundschuh, Y. Spack-Leigsnering, and H. De Gersem, "Considering capacitive effects in foil winding homogenization," IEEE J. Multiscale Multiphys. Comput. Techn., vol. 9, pp. 179-187, 2024.
E. Paakkunainen, J. Bundschuh, I. C. Garcia, H. De Gersem, and S. Schops, "A stabilized circuit-consistent foil conductor model," IEEE Access, vol. 12, pp. 1408-1417, 2024.
S. Weinert, J. Bundschuh, Y. Spack-Leigsnering, and H. De Gersem, "Magneto-Thermally coupled field simulation of homogenized foil winding models," 2025, arXiv:2503.13010.
E. Paakkunainen, L. Denis, C. Geuzaine, P. Rasilo, and S. Schops, "Foil conductor model for efficient simulation of HTS coils in large scale applications," IEEE Trans. Appl. Supercond., vol. 35, no. 5, pp. 1-5, Aug. 2025.
J. Dular, C. Geuzaine, and B. Vanderheyden, "Finite-element formulations for systems with high-temperature superconductors," IEEE Trans. Appl. Supercond., vol. 30, no. 3, pp. 1-13, Apr. 2020.
P. Dular, F. Henrotte, and W. Legros, "A general and natural method to define circuit relations associated with magnetic vector potential formulations," IEEE Trans. Magn., vol. 35, no. 3, pp. 1630-1633, May 1999.
S. Schops, H. De Gersem, and T. Weiland, "Winding functions in transient magnetoquasistatic field-circuit coupled simulations," COMPEL, vol. 32, no. 6, pp. 2063-2083, Nov. 2013.
E. Creuse, P. Dular, and S. Nicaise, "About the gauge conditions arising in finite element magnetostatic problems," Comput. Math. Appl., vol. 77, no. 6, pp. 1563-1582, Mar. 2019.
P. Dlotko, B. Kapidani, S. Pitassi, and R. Specogna, "Fake conductivity or cohomology: Which to use when solving eddy current problems with h-formulations?" IEEE Trans. Magn., vol. 55, no. 6, pp. 1-4, Jun. 2019.
P. Dular, C. Geuzaine, and W. Legros, "A natural method for coupling magnetodynamic H-formulations and circuit equations," IEEE Trans. Magn., vol. 35, no. 3, pp. 1626-1629, May 1999.
M. Pellikka, S. Suuriniemi, L. Kettunen, and C. Geuzaine, "Homology and cohomology computation in finite element modeling," SIAM J. Sci. Comput., vol. 35, no. 5, pp. B1195-B1214, Jan. 2013.
I. Babuška and G. N. Gatica, "On the mixed finite element method with Lagrange multipliers," Numer. Methods Partial Differ. Equ., vol. 19, no. 2, pp. 192-210, Mar. 2003.
D. S. Malkus and T. J. R. Hughes, "Mixed finite element methodsreduced and selective integration techniques: A unification of concepts," Comput. Methods Appl. Mech. Eng., vol. 15, no. 1, pp. 63-81, Jul. 1978.
C. R. Vargas-Llanos, F. Huber, N. Riva, M. Zhang, and F. Grilli, "3D homogenization of the T-A formulation for the analysis of coils with complex geometries," Superconductor Sci. Technol., vol. 35, no. 12, Dec. 2022, Art. no. 124001.
P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, "A general environment for the treatment of discrete problems and its application to the finite element method," IEEE Trans. Magn., vol. 34, no. 5, pp. 3395-3398, May 1998.
C. Geuzaine and J. Remacle, "Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities," in Proc. Int. J. Numer. Meth. Eng., vol. 79, May 2009, pp. 1309-1331.
L. Denis, E. Paakkunainen, P. Rasilo, S. Schops, B. Vanderheyden, and C. Geuzaine, "GetDP models: Magnetic field conforming formulations for foil windings," Zenodo, 2025, doi: 10.5281/zenodo.15203011.
J. Rikabi, C. F. Bryant, and E. M. Freeman, "An error-based approach to complementary formulations of static field solutions," Int. J. Numer. Methods Eng., vol. 26, no. 9, pp. 1963-1987, Sep. 1988.