Improvement on the Laminated Busbar of NPC Three-Level Inverters based on a Supersymmetric Mirror Circulation 3D Cubical Thermal Model

  • He, Feng-You (Dept. of Information and Electrical Engineering, China University of Mining and Technology) ;
  • Xu, Shi-Zhou (College of Electronic and Electrical Engineering, Henan Normal University) ;
  • Geng, Cheng-Fei (Dept. of Information and Electrical Engineering, China University of Mining and Technology)
  • Received : 2016.01.26
  • Accepted : 2016.07.11
  • Published : 2016.11.20


Laminated busbars with a low stray inductance are widely used in NPC three-level inverters, even though some of them have poor performances in heat equilibrium and overvoltage suppression. Therefore, a theoretical method is in need to establish an accurate mathematical model of laminated busbars and to calculate the impedance and stray inductance of each commutation loop to improve the heat equilibrium and overvoltage suppression performance. Firstly, an equivalent circuit of a NPC three-level inverter laminated busbar was built with an analysis of the commutation processes. Secondly, on the basis of a 3D (three dimensional) cubical thermal model and mirror circulation theory, a supersymmetric mirror circulation 3D cubical thermal model was built. Based on this, the laminated busbar was decomposed in 3D space to calculate the equivalent resistance and stray inductance in each commutation loop. Finally, the model and analysis results were put into a busbar design, simulation and experiments, whose results demonstrate the accuracy and feasibility of the proposed method.


  1. C. R. Paul, Introduction to Electromagnetic Compatibility, 2nd ed., John Wiley & Sons, 93(7-8), pp.1-12, 2006.
  2. G. L. Skibinski and D. M. Divan, "Design methodology and modeling of low inductance planar bus structures," European Conference on Power Electronics and Applications, Vol. 3, pp. 98-105, Sep. 1993.
  3. M. C. Caponet, F. Profumo, R. W. De Doncker, and A. Tenconi, "Low stray inductance bus bar design and construction for good EMC performance in power electronic circuit," IEEE Trans. Power Electron., Vol. 17, No. 2, pp. 225-231, Mar. 2002.
  4. R. Yi, Z. M. Zhao, and L. Q. Yuan, "Busbar optimization design for high power converters," Trans. China Electrotechnical Society, Vol. 23, No. 8, pp. 94-100, Aug. 2008.
  5. A. T. Bryant, K. K. Vadlapati, J. P. Starkey, A. P. Goldney, S. Y. Kandilidis, and D. A. Hinchley, "Current distribution in high power laminated busbars," in Proc. 14th European Conference on Power Electronics and Applications, pp.1-10, 2011.
  6. C. Chen, X. Pei, Y. Chen, and Y. Kang, "Investigation, evaluation, and optimization of stray inductance in laminated busbar," IEEE Trans. Power Electron., Vol. 29, No. 7, pp. 3679-3693, Sep. 2014.
  7. B. Gultekin and M. Ermis, "Cascaded multilevel converter-based transmission statcom: System design methodology and development of a 12 kv ${\pm}12$ mvar power stage," IEEE Trans. Power Electron., Vol. 28, No. 11, pp. 4930-4950, Jan. 2013.
  8. F. Zare and G. F. Ledwich, "Reduced layer planar busbar for voltage source inverters," IEEE Trans. Power Electron., Vol. 17, No. 4, pp. 508-516, Jul. 2002.
  9. L. Smirnova, R. Juntunen, K. Murashko, T. Musikka, and J. Pyrhonen, "Thermal analysis of the laminated busbar system of a multilevel converter," IEEE Trans. Power Electron., Vol. 31, No.2, pp. 1479-1488, Apr. 2016.
  10. H. Wen and W. Xiao, "Design and optimization of laminated busbar to reduce transient voltage spike," in Proc. 2012 IEEE International Symposium on Industrial Electronics (ISIE), pp.1478-1483, 2012.
  11. H. Yu, Z. Zhao, T. Lu, L. Yuan, and S. Ji, "Laminated busbar design and stray parameter analysis of three-level converter based on HVIGBT series connection," in Proc. IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 3201-3207, 2015.
  12. A. Plesca, "Busbar heating during transient conditions. Electric Power Systems Research," Vol. 89, pp. 31-37, Aug. 2012.
  13. J. Hus, "Estimating busbar temperatures," IEEE Trans. Ind. App., Vol. 26, No. 5 , pp. 926-934, Oct. 1990.
  14. R. T. Coneybeer, W. Z. Black, and R. A. Bush, "Steady-state and transient ampacity of bus bar," IEEE Trans. Power Del., Vol. 9, No. 4 , pp.1822-1829, Oct. 1994.
  15. H. T. Chen, D. Y. Lin, S. C. Tan, and S. Y. R. Hui, "Chromatic, photometric and thermal modeling of led systems with nonidentical LED devices," IEEE Trans. Power Electron., Vol. 29, No.12, pp. 6636-6647, Jan. 2014.
  16. D. Zhou, F. Blaabjerg, M. Lau, and M. Tonnes, "Thermal analysis of multi-mw two-level wind power converter," in Proc. IEEE Press, Vol. 2, No.1, pp. 5858-5864, 2012.
  17. X. W. Wu, N. Q. Shu, H. T. Li, and L. Li, "Contact temperature prediction in three-phase gas-insulated bus bars with the finite-element method," IEEE Trans. Mag., Vol. 50, No.2, pp. 277-280, Feb. 2014.
  18. Y. Alexandrova, R. S. Semken, and J. Pyrhonen, "Permanent magnet synchronous generator design solution for large direct-drive wind turbines: Thermal behavior of the lc dd-pmsg," Applied Thermal Engineering, Vol. 65, No. 1-2, pp. 554-563, Apr. 2014.
  19. N. Rostami, M. R. Feyzi, and J. Pyrhonen, A. Parviainen, and M. Niemela, "Lumped-parameter thermal model for axial flux permanent magnet machines," IEEE Trans. Mag., Vol. 49, No. 3, pp. 1178-1184, Jul. 2013.
  20. C. Chen, X. Pei, Y. Shi, and X. Lin, "Modeling and optimization of high power inverter three-layer laminated busbar," in Proc. Energy Conversion Congress and Exposition, Vol. 11, pp.1380-1385, 2012.
  21. A. Hino and K. Wada, "Resonance analysis for DC-side laminated bus-bar of a high speed switching circuit," in Proc. IEEE Future Energy Electronics Conference, pp. 751-756, 2013.
  22. T. Hong, "Current capability enhancement of bus bars or PCBs by thermal conduction," in Power Conversion Intelligent Motion, 2012.
  23. H. Li, "Study on key thchnology of high power three-level converter and dirve control system of synchronous motor," Ph.D. Dissertation, China University of Mining and Technology, China, 2010.
  24. B. Cadilhon, L. Pecastaing, T. Reess, and A. Gibert, "Low-stray inductance structure to improve the rise-time of a marx generator," IET Electric Power Applications, Vol. 2, No. 4, pp. 248-255, Jul. 2008.
  25. R. J. Pasterczyk, C. Martin, J. M. Guichon, and J. L. Schanen, "Planar busbar optimization regarding current sharing and stray inductance minimization," in Proc. IEEE 2005 European Conference on Power Electronics and Applications, pp. 9 -P.9, 2005.
  26. R. Wrobel and P. H. Mellor, "A general cuboidal element for three-dimensional thermal modeling," IEEE Trans. Mag., Vol. 46, No.8, pp. 3197-3200, Aug. 2010.

Cited by

  1. Power Device Thermal Fault Tolerant Control of High-Power Three-Level Explosion-Proof Inverter Based on Holographic Equivalent Dual-Mode Modulation vol.2017, pp.1563-5031, 2017,