Vol. 123

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2011-12-13

TM-TE Decomposition of Power Losses in Multi-Stranded Litz-Wires Used in Electronic Devices

By Claudio Carretero, Jesus Acero, and Rafael Alonso
Progress In Electromagnetics Research, Vol. 123, 83-103, 2012
doi:10.2528/PIER11091909

Abstract

Efficiency often constitutes the main goal in the design of a power system because the minimization of power losses in the magnetic components implies better and safer working conditions. The primary source of losses in a magnetic power component is usually associated with the current driven by the wire, which ranges from low to medium frequencies. New power system tendencies involve increasing working frequencies in order to reduce the size of devices, thus reducing costs. However, optimal design procedures involve increasingly complex solutions for improving system performance. For instance, using litz-type multi-stranded wires which have an internal structure to uniformly share the current between electrically equivalent strands, reducing the total power losses in the windings. The power losses in multi-stranded wires are generally classified into conduction losses and proximity losses due to currents induced by a magnetic field external to the strand. Both sources of loss have usually been analyzed independently, assuming certain conditions in order to simplify the derivation of expressions for calculating the correct values. In this paper, a unified analysis is performed given that both power losses are originated by the electromagnetic fields arising from external sources where the wire is immersed applying the decomposition into transversal magnetic (TM) and transversal electric (TE) components. The classical power losses, the so called conduction and proximity losses, can be calculated considering the TM modes under certain conditions. In addition, a new proximity loss contribution emerges from the TE modes under similar conditions.

Citation


Claudio Carretero, Jesus Acero, and Rafael Alonso, "TM-TE Decomposition of Power Losses in Multi-Stranded Litz-Wires Used in Electronic Devices," Progress In Electromagnetics Research, Vol. 123, 83-103, 2012.
doi:10.2528/PIER11091909
http://jpier.org/PIER/pier.php?paper=11091909

References


    1. Lammeraner, J. and M. Stafl, Eddy Currents, Chemical Rubber Co., Cleveland, Ohio, 1964.

    2. Urling, A. M., et al., Characterizing high-frequency effects in transformer windings --- A guide to several significant articles, Applied Power Electronics Conference, 373-385, Baltimore, USA, 1989.

    3. Reatti, A. and M. K. Kazimierczuk, "Comparison of various methods for calculating the AC resistance of inductors," IEEE Transactions on Magnetics, Vol. 38, No. 3, 1512-1518, 2002.
    doi:10.1109/20.999124

    4. Nan, X. and C. R. Sullivan, An improved calculation of proximity-effect loss in high-frequency windings of round conductors, Power Electronics Specialist Conference, 853-860, Acapulco, Mexico, 2003.

    5. Dowell, P. L., "Effects of eddy currents in transformer windings," Proceedings of the Institution of Electrical Engineers, Vol. 113, No. 8, 1387-1394, 1966.
    doi:10.1049/piee.1966.0236

    6. Robert, F., "A theoretical discussion about the layer copper factor used in winding losses calculation," IEEE Transactions on Magnetics, Vol. 38, No. 5, 3177-3179, 2002.
    doi:10.1109/TMAG.2002.802406

    7. Sippola, M. and R. E. Sepponen, "Accurate prediction of high-frequency power-transformer losses and temperature rise," IEEE Transactions on Power Electronics, Vol. 17, No. 5, 835-847, 2002.
    doi:10.1109/TPEL.2002.802193

    8. Acero, J., et al., A model of losses in twisted-multistranded wires for planar windings used in domestic induction heating appliances, Applied Power Electronics Conference, 1247-1253, Anaheim, USA, 2007.

    9. Lotfi, A. W. and F. C. Lee, A high frequency model for Litz wire for switch-mode magnetics, Industry Applications Society Annual Meeting, 1169-1175, Toronto, Canada, 1993.

    10. Ferreira, J. A., "Analytical computation of AC resistance of round and rectangular litz wire windings," IEE Proceedings B, Electric Power Applications, Vol. 139, No. 1, 21-25, 1992.
    doi:10.1049/ip-b.1992.0003

    11. Lotfi, A. W., P. M. Gradzki, and F. C. Lee, "Proximity effects in coils for high frequency power applications," IEEE Transactions on Magnetics, Vol. 28, No. 5, 2169-2171, 1992.
    doi:10.1109/20.179432

    12. Albach, M., Two-dimensional calculation of winding losses in transformers, Power Electronics Specialists Conference, 1639-1644, Galway, Ireland, 2000.

    13. Tourkhani, F. and P. Viarouge, "Accurate analytical model of winding losses in round Litz wire windings," IEEE Transactions on Magnetics, Vol. 37, No. 1, 538-543, 2001.
    doi:10.1109/20.914375

    14. Spang, M. and M. Albach, "Optimized winding layout for minimized proximity losses in coils with rod cores," IEEE Transactions on Magnetics, Vol. 44, No. 7, 1815-1821, 2008.
    doi:10.1109/TMAG.2008.920149

    15. Larouci, C., et al., "Copper losses of flyback transformer: Search for analytical expressions," IEEE Transactions on Magnetics, Vol. 39, No. 3, 1745-1748, 2003.
    doi:10.1109/TMAG.2003.810411

    16. Kazimierczuk, M. K., High-frequency Magnetic Components, John Wiley & Sons Ltd, Chichester, UK, 2009.

    17. Perry, M. P., "On calculating losses in current carrying conductors in an external alternating magnetic field," IEEE Transactions on Magnetics, Vol. 17, No. 5, 2486-2488, 1981.
    doi:10.1109/TMAG.1981.1061451

    18. Fawzi, T. H., P. E. Burke, and B. R. McLean, "Eddy losses and power shielding of cylindrical shells in transverse and axial magnetic fields," IEEE Transactions on Magnetics, Vol. 31, No. 3, 1452-1455, 1995.
    doi:10.1109/20.376302

    19. Carretero, C., R. Alonso, J. Acero, O. Lucia, and J. M. Burdio, "Dissipative losses evaluation in magnetic power devices with litz-wire type windings," PIERS Online, Vol. 7, No. 3, 246-250, 2011.

    20. Namjoshi, K. V., J. D. Lavers, and P. P. Biringer, "Eddy current power loss in structural steel due to cables carrying current in a perpendicular direction," IEEE Transactions on Magnetics, Vol. 30, No. 1, 85-91, 1994.
    doi:10.1109/20.272519

    21. Sullivan, C. R., "Optimal choice for number of strands in a litz-wire transformer winding," IEEE Transactions on Power Electronics, Vol. 14, No. 2, 283-291, 1999.
    doi:10.1109/63.750181

    22. Sullivan, C. R., "Computationally efficient winding loss calculation with multiple windings, arbitrary waveforms, and two-dimensional or three-dimensional field geometry," IEEE Transactions on Power Electronics, Vol. 16, No. 1, 142-150, 2001.
    doi:10.1109/63.903999

    23. Nan, X. and C. R. Sullivan, Simplified high-accuracy calculation of eddy-current loss in round-wire windings, Power Electronics Specialists Conference, 873-879, Aachen, Germany, 2004.

    24. Koertzen, H. W. E., J. D. van Wyk, and J. A. Ferreira, An investigation of the analytical computation of inductance and AC resistance of the heat-coil for induction cookers, Industry Applications Society Conference, 1113-1119, Houston, USA, 1992.

    25. Acero, J., et al., "Frequency-dependent resistance in litz wire planar windings for domestic induction heating appliances," IEEE Transactions on Power Electronics, Vol. 21, No. 4, 856-866, 2006.
    doi:10.1109/TPEL.2006.876894

    26. Hernandez, P., et al., Power losses distribution in the litz-wire winding of an inductor for an induction cooking appliance, Conference of the Industrial Electronics Society, 1134-1137, Sevilla, Spain, 2002.

    27. Podoltsev, A. D., I. N. Kucheryavaya, and B. B. Lebedev, "Analysis of effective resistance and eddy-current losses in multiturn winding of high-frequency magnetic components," IEEE Transactions on Magnetics, Vol. 39, No. 1, 539-548, 2003.
    doi:10.1109/TMAG.2002.806337

    28. Dular, P. and J. Gyselinck, "Modeling of 3-D stranded inductors with the magnetic vector potential formulation and spatially dependent turn voltages of reduced support," IEEE Transactions on Magnetics, Vol. 40, No. 2, 1298-1301, 2004.
    doi:10.1109/TMAG.2004.825153

    29. Gyselinck, J. and P. Dular, "Frequency-domain homogenization of bundles of wires in 2-D magnetodynamic FE calculations," IEEE Transactions on Magnetics, Vol. 41, No. 5, 1416-1419, 2005.
    doi:10.1109/TMAG.2005.844534

    30. Gyselinck, J., R. V. Sabariego, and P. Dular, "Time-domain homogenization of windings in 2-D finite element models," IEEE Transactions on Magnetics, Vol. 43, No. 4, 1297-1300, 2007.
    doi:10.1109/TMAG.2007.892408

    31. Sabariego, R. V., P. Dular, and J. Gyselinck, "Time-domain homogenization of windings in 3-D finite element models," IEEE Transactions on Magnetics, Vol. 44, No. 6, 1302-1305, 2008.
    doi:10.1109/TMAG.2007.915908

    32. Kong, J. A., "Electromagnetic fields due to dipole antennas over stratified anisotropic media," Geophysics, Vol. 37, No. 6, 985-996, 1972.
    doi:10.1190/1.1440321

    33. Clemmow, P. C., "The resolution of a dipole field into transverse electric and transverse magnetic waves," Proceedings of the Institution of Electrical Engineers, Vol. 110, No. 1, 107-111, 1963.
    doi:10.1049/piee.1963.0016

    34. Wilton, D., "A TM-TE decomposition of the electromagnetic field due to arbitrary sources radiating in unbounded regions," IEEE Transactions on Antennas and Propagation, Vol. 28, No. 1, 111-114, 1980.
    doi:10.1109/TAP.1980.1142285

    35. Lindell, I. V., "TE/TM decomposition of electromagnetic sources," IEEE Transactions on Antennas and Propagation, Vol. 36, No. 10, 1382-1388, 1988.
    doi:10.1109/8.8624

    36. Weiss, S. J. and W. K. Kahn, "Decomposition of electromagnetic boundary conditions at planar interfaces with applications to TE and TM field solutions," IEEE Transactions on Antennas and Propagation, Vol. 46, No. 11, 1687-1691, 1998.
    doi:10.1109/8.736622

    37. Janaswamy, R., "A note on the TE/TM decomposition of electromagnetic fields in three dimensional homogeneous space," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 9, 2474-2477, 2004.
    doi:10.1109/TAP.2004.834149

    38. Fawzi, T. H. and P. E. Burke, "Use of surface integral equations for analysis of TM-induction problem," Proceedings of the Institution of Electrical Engineers, Vol. 121, No. 10, 1109-1116, 1974.
    doi:10.1049/piee.1974.0257

    39. Fawzi, T. H., P. E. Burke, and M. Fabiano-Alves, "Use of surface-integral equations for the analysis of the TE-induction problem," Proceedings of the Institution of Electrical Engineers, Vol. 123, No. 7, 725-728, 1976.
    doi:10.1049/piee.1976.0159

    40. Carretero, C., R. Alonso, J. Acero, and J. M. Burdio, "Coupling impedance between planar coils inside a layered media," Progress In Electromagnetics Research, Vol. 112, 381-396, 2011.

    41. Carcione, J. M., "Simulation of electromagnetic diffusion in anisotropic media," Progress In Electromagnetics Research B, Vol. 26, 425-450, 2010.
    doi:10.2528/PIERB10100607

    42. Rothwell, E. J. and M. J. Cloud, Electromagnetics, CRC Press, Boca Raton, 2000.

    43. Ferreira, J. A., "Improved analytical modeling of conductive losses in magnetic components," IEEE Transactions on Power Electronics, Vol. 9, No. 1, 127-131, 1994.
    doi:10.1109/63.285503

    44. Silveira, F. E. M. and J. A. S. Lima, "Skin effect from extended irreversible thermodynamics perspective," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 2--3, 151-160, 2010.
    doi:10.1163/156939310790735787

    45. Voyer, D., R. Perrusel, and P. Dular, "Perturbation method for the calculation of losses inside conductors in microwave structures," Progress In Electromagnetics Research, Vol. 103, 339-354, 2010.
    doi:10.2528/PIER10031604

    46. Burke, P., T. Fawzi, and T. Akinbiyi, "The use of asymptotes to estimate TE- and TM-mode losses in long conductors," IEEE Transactions on Magnetics, Vol. 14, No. 5, 374-376, 1978.
    doi:10.1109/TMAG.1978.1059973

    47. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, U.S. Dept. of Commerce, Washington, D.C., 1970.

    48. Qian, Z.-G., M.-S. Tong, and W. C. Chew, "Conductive medium modeling with an augmented GIBC formulation," Progress In Electromagnetics Research, Vol. 99, 261-272, 2009.
    doi:10.2528/PIER09100702

    49. Fawzi, T., M. Ahmed, and P. Burke, "On the use of the impedance boundary conditions in eddy current problems," IEEE Transactions on Magnetics, Vol. 21, No. 5, 1835-1840, 1985.
    doi:10.1109/TMAG.1985.1063920

    50. Yuferev, S. and N. Ida, Surface Impedance Boundary Conditions. A Comprehensive Approach, CRC Press, Boca Raton, 2009.
    doi:10.1201/9781420044904