Vol. 51
Latest Volume
All Volumes
PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2013-04-26
Numerical Method of Computing Impedances in Shielded and Unshielded Three-Phase Rectangular Busbar Systems
By
Progress In Electromagnetics Research B, Vol. 51, 135-156, 2013
Abstract
In this paper, a new numerical method of calculating rectangular busbar impedance is proposed. This method is based on integral equation method and partial inductance theory. In particular, impedances of shielded and unshielded three-phase systems with rectangular phase and neutral busbars, conductive enclosure, and use of the method are described. Results for resistances and reactances for these systems of multiple rectangular conductors have been obtained, and skin and proximity effects have also been taken into consideration. The impact of the enclosure on impedances is also presented. Finally, two applications to three-phase shielded and unshielded systems busbars are described. The validation of the proposed method is carried out through FEM and laboratory measurements, and a reasonable level of accuracy is demonstrated.
Citation
Zygmunt Piatek Bernard Baron Pawel Jablonski Dariusz Kusiak Tomasz Szczegielniak , "Numerical Method of Computing Impedances in Shielded and Unshielded Three-Phase Rectangular Busbar Systems," Progress In Electromagnetics Research B, Vol. 51, 135-156, 2013.
doi:10.2528/PIERB13030205
http://www.jpier.org/PIERB/pier.php?paper=13030205
References

1. Salinas, E., "Conductive and ferromagnetic screening of 50 Hz magnetic field from a three-phase system of busbars," Journal of Magnetism and Magnetic Materials, No. 226-230, 1239-1241, 2001.
doi:10.1016/S0304-8853(00)01003-9

2. Ducluzaux, A., "Extra losses caused in high current conductors by skin and proximity effects," Schneider Electric, Cahier Technique, Vol. 83, 1983.

3. Du, Y. and J. Burnett, Power-frequency magnetic shielding of heavy-current conductors by rectangular shields, IEE Proc. --- Gener. Transm. Distrib., Vol. 146, No. 5, 223-228, 1999.

4. Koroglu, S., P. Sergeant, and N. Umurkan, "Comparison of analytical, finite element and neural network methods to study magnetic shielding," Simulation Modelling Practice and Theory, Vol. 18, 206-216, 2010.
doi:10.1016/j.simpat.2009.10.007

5. Copper Development Association, Copper for Busbars, 2001, available online at: http://www.cda.org.uk/Megab2/elecapps/pub22/index.htm.

6. Sarajcev, P. and R. Goic, "Power loss computation in high-current generator bus ducts of rectangular cross-section," Electric Power Components and Systems, Vol. 38, 1469-1485, 2010.
doi:10.1080/15325001003735192

7. Chiampi, M., D. Chiarabaglio, and M. Tartaglia, "A general approach for analyzing power busbar under AC conditions," IEEE Trans. on Magn., Vol. 20, No. 6, 2473-2475, 1993.
doi:10.1109/20.280979

8. Clavel, E., J. Roudet, and A. Foggia, "Electrical modeling of transformer connecting bars," IEEE Trans. on Magn., Vol. 38, No. 2, 1378-1382, 2002.
doi:10.1109/20.996028

9. Sigg, H. J. and M. J. O. Strutt, "Skin effect and proximity effect in polyphase systems of rectangular conductors calculated on an RC network," IEEE Trans. on Power Apparatus and Systems, Vol. PAS-89, No. 3, 470-477, 1970.
doi:10.1109/TPAS.1970.292726

10. Guo, J., A. W. Glisson, and D. Kajfez, "Analysis of resistance and internal reactance in systems of parallel conductors," Int. J. Electron. Commun. AEÜ, Vol. 52, No. 2, 57-64, 1998.

11. Piatek, Z., Impedances of Tubular High Current Busducts, Polish Academy of Sciences, Warsaw, 2008.

12. Piatek, Z., "Self and mutual impedances of a finite length gas insulated transmission line (GIL)," Elec. Pow. Syst. Res., Vol. 77, 191-203, 2007.
doi:10.1016/j.epsr.2006.02.017

13. Lovric, D., V. Boras, and S. Vujevic, "Accuracy of approximate formulas for internal impedance of tubular cylindrical conductors for large parameters," Progress in Electromagnetics Research M, Vol. 16, 171-184, 2011.

14. Fazljoo, S. A. and M. R. Besmi, A new method for calculation of impedance in various frequencies, 1st Power Electronic & Drive Systems & Technologies Conference (PEDSTC), 36-40, February 17-18, 2010.

15. Ametani, A., "Approximate method for calculating the impedance of multiconductors with cross section of arbitrary shapes ," Electrical Engineering in Japan, Vol. 111, No. 2, 117-123, 1992.
doi:10.1002/eej.4391120213

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

17. Paul, C. R., Inductance: Loop and Partial, J. Wiley & Sons, New Jersey, 2010.

18. Paul, C. R., Analysis of Multiconductor Transmission Lines, J. Wiley & Sons, New Jersey, 2010.

19. Silvester, P., "AC resistance and reactance of isolated rectangular conductors," IEEE Trans. on Power Apparatus and Systems, Vol. PAS-86, No. 6, 770-774, June 1967.
doi:10.1109/TPAS.1967.291888

20. Goddard, K. F., A. A. Roy, and J. K. Sykulski, Inductance and resistance calculations for isolated conductor, IEE Pro. --- Sci. Meas. Technol., Vol. 152, No. 1, 7-14, January 2005.

21. Goddard, K. F., A. A. Roy, and J. K. Sykulski, "Inductance and resistance calculations for a pair of rectangular conductor," IEE Pro. --- Sci. Meas. Technol., Vol. 152, No. 1, 73-78, January 2005.
doi:10.1049/ip-smt:20041058

22. Chen, H. and J. Fang, "Modeling of impedance of rectangular cross-section conductors," IEEE Conference on Electrical Performance of Electronic Packaging, 159-162, 2000.

23. Zhihua, Z. and M. Weiming, "AC impedance of an isolated flat conductor," IEEE Trans. on Electromagnetic Compatibility, Vol. 44, No. 3, 482-486, 2002.
doi:10.1109/TEMC.2002.801773

24. Piatek, Z. and B. Baron, "Exact closed form formula for self inductance of conductor of rectangular cross section," Progress In Electromagnetics Research M, Vol. 26, 225-236, 2012.

25. Piatek, Z., et al., "Exact closed form formula for mutual inductance of conductors of rectangular cross section," Przeglad Elektrotechniczny (Electrical Review), R. 89, No. 3a, 61-64, 2013.

26. Piatek, Z., et al., "Self inductance of long conductor of rectangular cross section," Przeglad Elektrotechniczny (Electrical Review), R. 88, No. 8, 323-326, 2012.

27. Piatek, Z., et al., "Mutual inductance of long rectangular conductors," Przeglad Elektrotechniczny (Electrical Review), R. 88, No. 9a, 175-177, 2012.

28. Broydé, F., E. Clavelier, and L. Broydé, A direct current per-unit-length inductance matrix computation using modified partial inductance, Proc. of the CEM 2012 Int. Symp. on Electromagnetic Compatibility, Rouen, April 25-27, 2012.

29. Hoer, C. and C. Love, "Exact inductance equations for rectangular conductors with application to more complicated geometries," J. Res. NBS, Vol. 69C, No. 2, 127-137, 1965.

30. Zhong, G. and C. K. Koh, "Exact form formula for mutual inductance of on-chip interconnects," IEEE Trans. on Circ. and Sys., I: FTA, Vol. 10, 1349-1353, 2003.
doi:10.1109/TCSI.2003.817778

31. Antonini, G., A. Orlandi, and C. R. Paul, "Internal impedance of conductor of rectangular cross section," IEEE Trans. on Microwave Theory and Tech., Vol. 47, No. 7, 979-984, 1999.
doi:10.1109/22.775429

32. Canova, A. and L. Giaccone, "Numerical and analytical modeling of busbar systems," IEEE Trans. on Power Delivery, Vol. 24, No. 3, 1568-1577, July 2009.
doi:10.1109/TPWRD.2009.2014270

33. Weeks, W. T., et al., "Resistive and inductive skin effect in rectangular conductors," IBM J. Res. Develop., Vol. 23, No. 6, 652-660, November 1979.
doi:10.1147/rd.236.0652

34. Barr, A. W., "Calculation of frequency dependent impedance for conductor of rectangular cross section," AMP J. of Technology, Vol. 1, 91-100, November 1991.

35. Baron, B., et al., "Impedance of an isolated rectangular conductor," Przeglad Elektrotechniczny (Electrical Review), R. 89, No. 4, 278-280, 2013.

36. Comellini, E., A. Invernizzi, and G. Manzoni, "A computer program for determining electrical resistance and reactance of any transmission line," IEEE Trans. on Power Apparatus and Systems, Vol. PAS-92, 308-314, 1973.
doi:10.1109/TPAS.1973.293628

37. Tsuboi, K., M. Tsuji, and E. Yamada, "A simplified method of calculating busbar inductance and its application for stray resonance analysis in an inverter DC link," Electrical Engineering in Japan, Vol. 126, No. 3, 49-63, 1999.
doi:10.1002/(SICI)1520-6416(199902)126:3<49::AID-EEJ6>3.0.CO;2-A

38. Angi, H., M. Weiming, and Z. Zhihua, New numerical methods of computing internal inductance of conductor of rectangular cross-section, Asia-Pacific Symposium on Electromagnetic Compatibility and 19th International Zurich Symposium on Electromagnetic Compatibility, 674-677, 2008.

39. Matsuki, M. and A. Matsushima, "Improved numerical method for computing internal impedance of a rectangular conductor and discussions of its high frequency behavior," Progress In Electromagnetics Research M, Vol. 23, 139-152, 2012.
doi:10.2528/PIERM11122105

40. Matsuki, M. and A. Matsushima, "Efficient impedance computation for multiconductor transmission lines of rectangular cross section," Progress In Electromagnetics Research B, Vol. 43, 373-391, 2012.

41. Battauscio, O., M. Chiampi, and D. Chiarabaglio, "Experimental validation of a numerical model of busbar systems," IEE Proceedings --- Generation, Transmission and Distribution, 65-72, 1995.
doi:10.1049/ip-gtd:19951489

42. Birtwistle, D. and P. Pearl, "Measurement of impedance, power loss and current distribution in three-phase busbars," J. of Electrical and Electronics Engineering, Australia --- IE Aust. & IREE Aust., Vol. 8, No. 1, 37-46, 1988.

43. Du, J., J. Burnett, and Z. C. Fu, "Experimental and numerical evaluation of busbar trunking impedance," Electric Power Systems Research, No. 55, 113-119, 2000.
doi:10.1016/S0378-7796(99)00104-2

44. Battauscio, O., et al., "Numerical and experimental evaluation of magnetic field generated by power busbar systems," IEE Proc. --- Gener. Transm. Distrib., Vol. 143, No. 5, 455-460, 1996.
doi:10.1049/ip-gtd:19960557

45. Konrad, A., "Interodifferential finite element formulation of two-dimensional steady-state skin effect problems," IEEE Trans. on Magn., Vol. MAG-18, 284-292, 1982.
doi:10.1109/TMAG.1982.1061775

46. Deeley, E. M. and E. E. Okon, "An integral method for computing the inductance and A.C. resistance of parallel conductors," International Journal for Numerical Methods in Engineering, Vol. 12, 625-634, 1978.
doi:10.1002/nme.1620120407

47. Kamon, M., M. J. Tsuk, and J. K. White, "FASTHENRY: A multipole-accelerated 3-D inductance extraction program," IEEE Trans. on Microwave Theory and Techniques, Vol. 42, No. 9, 1750-1758, September 1994.
doi:10.1109/22.310584

48. Meeker, D., Finite Element Method Magnetics, version 4.2 (April 11, 2012, Mathematica Build), http://www.femm.info .