Scaling of AC copper loss in thermal modeling of electrical machines

The accurate prediction of the ac copper loss together with its thermal behaviour is crucial in the design of electrical machines, transformers and inductors. The commonly used figure of merit, when describing the ac copper loss, is a ratio of the equivalent ac and dc resistance (Rac/Rdc). This ratio defines the average ac copper loss as a function of frequency. However, as the ac and dc components of the copper loss scale differently with temperature a single value of Rac/Rdc derived for one temperature might be inadequate when used in thermal modelling. In this paper, the authors discuss limitations and applicability of the existing scaling techniques. The emphasis is placed on the method proposed earlier by the authors. The proposed scaling approach is illustrated on example test coils. Both theoretical and experimental data is provided and discussed.

[1]  T. Suzuki,et al.  Theoretical Analysis of AC Resistance in Coil Using Magnetoplated Wire , 2009, IEEE Transactions on Magnetics.

[2]  K.W.E. Cheng,et al.  Calculation of winding losses in high-frequency toroidal inductors using single strand conductors , 1994 .

[3]  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).

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

[5]  G. Jewell,et al.  Proximity Loss Study In High Speed Flux-Switching Permanent Magnet Machine , 2009, IEEE Transactions on Magnetics.

[6]  Jonathan Bremner,et al.  Influence of PWM on the Proximity Loss in Permanent-Magnet Brushless AC Machines , 2008, IEEE Transactions on Industry Applications.

[7]  P. D. Evans,et al.  Reduction of proximity losses in coupled inductors , 1991 .

[8]  Lixiang Wei,et al.  Analysis of Strap Losses for High Power High Frequency Inductors , 2007, 2007 IEEE Industry Applications Annual Meeting.

[9]  Marian K. Kazimierczuk,et al.  Inductor winding loss owing to skin and proximity effects including harmonics in non-isolated pulse-width modulated dc-dc converters operating in continuous conduction mode , 2010 .

[10]  M. Kazimierczuk,et al.  Harmonic winding loss in buck DC-DC converter for discontinuous conduction mode , 2010 .

[11]  M. Albach,et al.  Optimized Winding Layout for Minimized Proximity Losses in Coils With Rod Cores , 2008, IEEE Transactions on Magnetics.

[12]  T. M. Jahns,et al.  Analysis of bundle losses in high speed machines , 2010, The 2010 International Power Electronics Conference - ECCE ASIA -.

[13]  J. R. Brauer,et al.  Finite element prediction of losses and temperatures of laminated and composite inductors for AC drives , 2003, IEEE International Electric Machines and Drives Conference, 2003. IEMDC'03..

[14]  William Gerard Hurley,et al.  Derivation of optimum winding thickness for duty cycle modulated current waveshapes , 1997, PESC97. Record 28th Annual IEEE Power Electronics Specialists Conference. Formerly Power Conditioning Specialists Conference 1970-71. Power Processing and Electronic Specialists Conference 1972.

[15]  Diego Puyal,et al.  Frequency-dependent resistance in Litz-wire planar windings for domestic induction heating appliances , 2006, IEEE Transactions on Power Electronics.

[16]  R. Wrobel,et al.  Investigation of Proximity Losses in a High Speed Brushless Permanent Magnet Motor , 2006, Conference Record of the 2006 IEEE Industry Applications Conference Forty-First IAS Annual Meeting.

[17]  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..

[18]  Theodore. P. Bohn,et al.  Transposition effects on bundle proximity losses in high-speed PM machines , 2009, 2009 IEEE Energy Conversion Congress and Exposition.

[19]  J.-P. Schauwers,et al.  A closed-form formula for 2-D ohmic losses calculation in SMPS transformer foils , 2001 .

[20]  J. W. Kolar,et al.  Loss modeling of inductive components employed in power electronic systems , 2011, 8th International Conference on Power Electronics - ECCE Asia.

[21]  A. Van den Bossche,et al.  Practical Wide Frequency Approach for Calculating Eddy Current Losses in Transformer Windings , 2006, 2006 IEEE International Symposium on Industrial Electronics.

[22]  Ka Wai Eric Cheng,et al.  Optimisation of high frequency inductor design of series resonant converter , 1992, PESC '92 Record. 23rd Annual IEEE Power Electronics Specialists Conference.

[23]  T. Watanabe,et al.  Measuring the temperature dependence of resistivity of high purity copper using a solenoid coil (SRPM method) , 1991, [1991] Conference Record. IEEE Instrumentation and Measurement Technology Conference.

[24]  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 .

[25]  M. Sippola,et al.  Accurate prediction of high-frequency power-transformer losses and temperature rise , 2002 .

[26]  Charles R. Sullivan,et al.  Aluminum Windings and Other Strategies for High-Frequency Magnetics Design in an Era of High Copper and Energy Costs , 2007, APEC 07 - Twenty-Second Annual IEEE Applied Power Electronics Conference and Exposition.

[27]  T. Suzuki,et al.  Reduction of Proximity Effect in Coil Using Magnetoplated Wire , 2007, IEEE Transactions on Magnetics.

[28]  Z.Q. Zhu,et al.  Strand-level proximity losses in PM machines designed for high-speed operation , 2008, 2008 18th International Conference on Electrical Machines.

[29]  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).

[30]  Marian K. Kazimierczuk,et al.  Winding resistance of litz-wire and multi-strand inductors , 2012 .

[31]  Rafal Wrobel,et al.  Contribution of End-Winding Proximity Losses to Temperature Variation in Electromagnetic Devices , 2012, IEEE Transactions on Industrial Electronics.

[32]  M. Albach,et al.  The influence of air gap size and winding position on the proximity losses in high frequency transformers , 2001, 2001 IEEE 32nd Annual Power Electronics Specialists Conference (IEEE Cat. No.01CH37230).