Vol. 123
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2011-12-13
TM-TE Decomposition of Power Losses in Multi-Stranded Litz-Wires Used in Electronic Devices
By
Progress In Electromagnetics Research, Vol. 123, 83-103, 2012
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
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