Comparison of analytical methods for calculating the AC resistance and leakage inductance of medium-frequency transformers

In this paper, a detailed investigation and comparison of different analytical expressions for the high-frequency resistance of medium-frequency transformers is presented. The comparison is made by 2D FEM simulations and experimental tests with suitable transformers. The deviations between the FEM and the various analytical calculations are presented explicitly via error contour maps to characterize the formulas for different geometrical parameters of common transformers. The comparison shows that the modified Dowell-based method features accurate results. The same study is also done to get an accurate prediction of the desired leakage inductance of transformers by modifying the formula based on Dowell.

[1]  E.C. Tatakis,et al.  A new model for the determination of copper losses in transformer windings with arbitrary conductor distribution under high frequency sinusoidal excitation , 2007, 2007 European Conference on Power Electronics and Applications.

[2]  Irma Villar,et al.  Multiphysical Characterization of Medium-Frequency Power Electronic Transformers , 2010 .

[3]  Marian K. Kazimierczuk,et al.  Analytical winding foil thickness optimisation of inductors conducting harmonic currents , 2013 .

[4]  G.S. Dimitrakakis,et al.  High-Frequency Copper Losses in Magnetic Components With Layered Windings , 2009, IEEE Transactions on Magnetics.

[5]  J. D. van Wyk,et al.  A new method for the more accurate determination of conductor losses in power electronic converter magnetic components , 1988 .

[6]  W. G. Hurley,et al.  Calculation of leakage inductance in transformer windings , 1994 .

[7]  E.C. Tatakis,et al.  A Semiempirical Model to Determine HF Copper Losses in Magnetic Components With Nonlayered Coils , 2008, IEEE Transactions on Power Electronics.

[8]  J. Uceda,et al.  Errors obtained when 1D magnetic component models are not properly applied , 1999, APEC '99. Fourteenth Annual Applied Power Electronics Conference and Exposition. 1999 Conference Proceedings (Cat. No.99CH36285).

[9]  J.-P. Schauwers,et al.  Eddy current losses in SMPS transformers round wire windings: a semi-analytical closed-form formula , 2005, 2005 European Conference on Power Electronics and Applications.

[10]  Charles R. Sullivan,et al.  Computationally efficient winding loss calculation with multiple windings, arbitrary waveforms, and two-dimensional or three-dimensional field geometry , 2001 .

[11]  V. A. Niemela,et al.  Characterizing high-frequency effects in transformer windings-a guide to several significant articles , 1989, Proceedings, Fourth Annual IEEE Applied Power Electronics Conference and Exposition.

[12]  F. C. Lee,et al.  Two-dimensional skin effect in power foils for high-frequency applications , 1995 .

[13]  Sidney C. Larson,et al.  Effective resistance to alternating currents of multilayer windings , 1940, Electrical Engineering.

[14]  Jan Abraham Ferreira,et al.  Improved analytical modeling of conductive losses in magnetic components , 1994 .

[15]  P. L. Dowell,et al.  Effects of eddy currents in transformer windings , 1966 .

[16]  Marian K. Kazimierczuk,et al.  High-Frequency Magnetic Components , 2009 .

[17]  Wei Yuan,et al.  Simplified 2-D Analytical Model for Winding Loss Analysis of Flyback Transformers , 2012 .

[18]  F. Robert,et al.  The layer copper factor, although widely used and useful, has no theoretical base [SMPS transformers] , 2000, 2000 IEEE 31st Annual Power Electronics Specialists Conference. Conference Proceedings (Cat. No.00CH37018).

[19]  J.A. Ferreira,et al.  Appropriate modelling of conductive losses in the design of magnetic components , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[20]  Colonel William T. McLyman,et al.  Transformer and inductor design handbook , 1978 .

[21]  Marian K. Kazimierczuk,et al.  Transformer winding loss caused by skin and proximity effects including harmonics in pulse-width modulated DC¿DC flyback converters for the continuous conduction mode , 2011 .

[22]  Rik W. De Doncker,et al.  A contribution to the design of isolated DC-DC converters for utility applications , 2012 .

[23]  Marian K. Kazimierczuk,et al.  Analytical optimisation of solid-round-wire windings conducting dc and ac non-sinusoidal periodic currents , 2013 .

[24]  Charles R. Sullivan,et al.  An improved calculation of proximity-effect loss in high-frequency windings of round conductors , 2003, IEEE 34th Annual Conference on Power Electronics Specialist, 2003. PESC '03..

[25]  J. A. Ferreira Analytical computation of AC resistance of round and rectangular litz wire windings , 1992 .

[26]  N. H. Kutkut,et al.  A simple technique to evaluate winding losses including two-dimensional edge effects , 1998 .

[27]  Marian K. Kazimierczuk,et al.  Harmonic winding losses in the transformer of a forward pulse width modulated DC-DC converter for continuous conduction mode , 2012 .

[28]  Alex Van den Bossche,et al.  Improved calculation of winding losses in gapped inductors , 2005 .

[29]  H. Grotstollen,et al.  Improved analytical modeling of conductive losses in gapped high-frequency inductors , 1998, Conference Record of 1998 IEEE Industry Applications Conference. Thirty-Third IAS Annual Meeting (Cat. No.98CH36242).

[30]  Torbjorn Thiringer,et al.  An Accurate Pseudoempirical Model of Winding Loss Calculation in HF Foil and Round Conductors in Switchmode Magnetics , 2014, IEEE Transactions on Power Electronics.

[31]  M. Albach,et al.  Two-dimensional calculation of winding losses in transformers , 2000, 2000 IEEE 31st Annual Power Electronics Specialists Conference. Conference Proceedings (Cat. No.00CH37018).

[32]  W. Roshen,et al.  Fringing Field Formulas and Winding Loss Due to an Air Gap , 2007, IEEE Transactions on Magnetics.

[33]  M. Kazimierczuk High-Frequency Magnetic Components: Kazimierczuk/High-Frequency Magnetic Components , 2013 .

[34]  Marian K. Kazimierczuk,et al.  Modelling Winding Losses in High-Frequency Power inductors , 1995, J. Circuits Syst. Comput..

[35]  Frédéric Robert A theoretical discussion about the layer copper factor used in winding losses calculation , 2002 .

[36]  J.-P. Schauwers,et al.  Two-dimensional analysis of the edge effect field and losses in high-frequency transformer foils , 2005, IEEE Transactions on Magnetics.

[37]  M. Kazimierczuk,et al.  Comparison of various methods for calculating the AC resistance of inductors , 2002 .

[38]  Phoivos D. Ziogas,et al.  A novel approach for minimizing high-frequency transformer copper losses , 1988 .

[39]  V. A. Niemela,et al.  Calculating the short-circuit impedances of a multiwinding transformer from its geometry , 1989, 20th Annual IEEE Power Electronics Specialists Conference.

[40]  J. W. Kolar,et al.  Optimized design of medium frequency transformers with high isolation requirements , 2010, IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society.

[41]  J.-P. Schauwers,et al.  A closed-form formula for 2D ohmic losses calculation in SMPS transformer foils , 1999, APEC '99. Fourteenth Annual Applied Power Electronics Conference and Exposition. 1999 Conference Proceedings (Cat. No.99CH36285).

[42]  Norbert Frohleke,et al.  Automated optimization of high frequency inductors , 1998, IECON '98. Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (Cat. No.98CH36200).

[43]  S. Butterworth Eddy-Current Losses in Cylindrical Conductors, with Special Applications to the Alternating Current Resistances of Short Coils , 1922 .