volume | PIER Journals

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.

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 Google Scholar

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

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

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. Google Scholar

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

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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

Prof. Zygmunt Piatek

Dr. Bernard Baron

Dr. Pawel Jablonski

Dr. Dariusz Kusiak

Dr. Tomasz Szczegielniak