# Calculation of copper losses in case of Litz and twisted wires: 2D Modeling and application for switched reluctance machine

Calculation of copper losses in case of Litz and twisted wires: 2D Modeling and application for switched reluctance machine

Moustafa Al Eit
Fréderic Bouillault
Laurent Santandrea
Claude Marchand
Guillaume Krebs

GeePs|Group of electrical engineering - Paris UMR CNRS 8507, CentraleSupélec, Univ Paris-Sud, UPMC Université Paris 6 3-11 rue Joliot-Curie, Plateau de Moulon, 91192 Gif-sur-Yvette Cedex

Corresponding Author Email:
moustafa.aleit@supelec.fr
Page:
179-197
|
DOI:
https://doi.org/10.3166/EJEE.18.179-197
29/07/2015
|
Accepted:
3/11/2015
|
Published:
31 August 2016
| Citation

OPEN ACCESS

Abstract:

The strong correlation between the level of eddy current losses and the winding geometry shows the necessity to pay attention to the manner of disposition of coils in machine slots. The conductor type, whether it is solid or stranded, also has a crucial influence. Since the transposition of winding strands reduces the degree of skin and proximity effects, it is a recommended solution to reduce eddy current losses. This article suggests an electromagnetic analysis of complex stranded conductors such as Litz and twisted wires. Each conductor is decomposed into individual strands that are twisted or woven in the slot throughout the length of the machine. Combined with several electric circuit relationships that interpret the transposition of the strands, a 2D finite element model is developed in this article so that the copper losses in each strand can be calculated individually.

Keywords:

finite element analysis, eddy currents, twisted wire, Litz wire, switched reluctance machine.

1. Introduction
2. Finite element method formulation
3. 2D Modeling of Litz and twisted wires
4. Application examples
5. Conclusion
References

Bartoli M., Noferi N., Reatti A., Kazimierczuk M.K. (1996). Modeling Litz-wire winding losses in high-frequency power inductors. In 27th Annu. IEEE Power Electronics Specialists Conf., vol. 2, p. 1690-1696.

Besbes M., Multon B. (2004). MRVSIM Logiciel de simulation et d'aide à la conception de Machines à réluctance variable à double saillance à alimentation électronique. Deposit APP CNRS, 2004, IDDN.FR.001.430010.000.S.C.2004.000.30645.

Carsten B. (1986). High frequency conductor losses in switchmode magnetic. In Tech. Papers of the 1st Int. High Frequency Power Conversion 1986 Conf., p. 155-176.

Carstensen C. (2007). Eddy Currents in Windings of Switched Reluctance Machines. PhD Thesis in engineering and sciences, RWTH Aachen University.

Hannoun H., Hilairet M., Marchand C. (2011). Experimental validation of a switched reluctance machine operating in continuous-conduction mode. IEEE Trans. On Vehicular technology, vol. 60, n° 4, p. 1453-1460.

Howe G.W.O. (1917). The High-Frequency Resistance of Multiply-Stranded Insulated Wire. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 93, p. 468-492.

Klauz M., Dorrell D.G. (2006). Eddy current effects in a switched reluctance motor. IEEE Trans. On Magnetics, vol. 42, n° 10, p. 3437-3439.

Lotfi W., Lee F.C. (1993). A high frequency model for Litz wire for switch-mode magnetics. In Conf. Rec. 1993 IEEE Industry Applications Conf. 28th IAS Annu. Meeting, vol. 2, p. 1169-1175.

Piriou F., Razek A. (1988). Coupling of saturated electromagnetic systems to non linear power electronic device. IEEE Trans. On Magnetics, vol. 24, n° 1, p. 274-277.

Sullivan C.R (1999). Optimal Choice for Number of Strands in a Litz-Wire Transformer Winding. IEEE Trans. On Power Electronis, vol. 14, n° 2, p. 283-291.

Tang X., Sullivan C.R. (2003). Stranded wire with uninsulated strands as a low cost alternative to Litz wire. IEEE Power Electronics Specialist Conference 34th Annual, vol. 1, p. 298-295.