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Solution of Coupled Electromagnetic and Thermal Fields

  • Behzad ForghaniEmail author
Chapter

Abstract

The objective of this chapter is to discuss the electromagnetic and thermal simulation requirements when designing large power transformers; in particular, the focus will be on the study of overheat problems in the transformer tank due to the leakage flux and the induced eddy currents. There are a number of requirements for the model specification, the field solution, and the evaluation of the results, related to the electromagnetic performance, as there are a number of requirements for the model specification, the field solution and the evaluation of results, related to the thermal performance, of a power transformer. The model specification covers the geometric description, material properties of the components used in the device, current and voltage sources, as well as the numerical parameters, such as those related to the finite element method (FEM) (Silvester and Ferrari in finite elements for electrical engineers, Cambridge University Press, 1996 [1]). The coupled electromagnetic–thermal simulation requires the solution of two sets of equations. Since, in the overwhelming majority of cases, the time constants between the electromagnetic and thermal response are very different, the two sets of field equations can be solved separately; in other words, they are loosely coupled. The electromagnetic field equations may require a static, time-harmonic, or transient field solver, whereas the thermal field equations may require a static (steady-state) or transient field solver. The coupled electromagnetic–thermal simulation addresses both aspects of physics, i.e., electromagnetic and thermal, and the way the effect of one on the other is taken into account, by considering the temperature rise due to electromagnetic losses, and the effect on the material properties due to the change in temperature. Material property modeling plays a key role in the accurate simulation of the device. Since the magnetic properties of steel are nonlinear and hysteretic, and anisotropic for the grain-oriented steel used in transformers, advanced material models are needed for an accurate representation of the material, under the different operating conditions of a transformer. Simcenter™ MAGNET™ software is a general-purpose simulation tool on which the content of this chapter is based. This tool can be used for the design and analysis of many devices. More in-depth information on its general capabilities can be found at (Simcenter MAGNET knowledge base articles [2]).

Keywords

Leakage flux Overheat problems Coupled simulation Electromagnetic–thermal Material properties 

References

  1. 1.
    P. P. Silvester, R. L. Ferrari, “Finite elements for electrical engineers”, Cambridge University Press, Third Edition 1996.Google Scholar
  2. 2.
    Simcenter MAGNET Knowledge Base articles at https://support.sw.siemens.com/en-US/knowledge-base/MG601540.
  3. 3.
    D. N. Dyck, B. S. Murray, “Transient Analysis of an Electromagnetic Shaker Using Circuit Simulation With Response Surface Models”, IEEE Trans. on Magnetics, Vol. 37, No. 5, September 2001.CrossRefGoogle Scholar
  4. 4.
    C. P. Steinmetz, “On the law of hysteresis,” Proceedings of the IEEE, vol. 72, no. 2, pp. 197–221, 1984.CrossRefGoogle Scholar
  5. 5.
    S. Hussain, K. Chang, “Effects of Incorporating Hysteresis in the Simulation of Electromagnetic Devices Using MAGNET v7.9”, White Paper, Mentor Graphics Corporation, 2018.Google Scholar
  6. 6.
    Z. Cheng, N. Takahashi, B. Forghani, G. Gilbert, J. Zhang, L. Liu, Y. Fan, X. Zhang Y. Du, J. Wang, and C. Jiao, “Analysis and measurements of iron loss and flux inside silicon steel laminations,” IEEE Trans. on Magnetics, vol. 45, no. 3, pp. 1222–1225, 2009.Google Scholar
  7. 7.
    Z. Cheng, N. Takahashi, B. Forghani, Y .Du, J. Zhang, L. Liu, Y. Fan, Q. Hu, C. Jiao, and J. Wang, “Large power transformer-based stray-field loss modeling and validation”, Electric Machines and Drives Conference, IEEE International, pp. 548–555 (Digital Object Identifier:  https://doi.org/10.1109/iemdc.2009.5075260), 2009.
  8. 8.
    Z. Cheng, N. Takahashi, B. Forghani, G. Gilbert, Y. Du, Y. Fan, L. Liu, Z. Zhai, W. Wu, and J. Zhang, “Effect of Excitation Patterns on both Iron Loss and Flux in Solid and Laminated Steel Configurations”, IEEE Trans. on Magnetics, vol. 46, no. 8, August 2010.CrossRefGoogle Scholar
  9. 9.
    Z. Cheng, N. Takahashi, B. Forghani, Y. Du, Y. Fan, L. Liu, Z. Zhao, and H. Wang, “Effect of Variation of B-H Properties on Loss and Flux Inside Silicon Steel Lamination”, IEEE Trans. on Magnetics, vol. 47, no. 5, May 2011.CrossRefGoogle Scholar
  10. 10.
    J. Zhang, L. Li, L. Liu, Y. Fan, B. Forghani, and Z. Cheng, “Measurement and 3D FEM Analysis of Additional Loss in Laminated Silicon Sheets Caused by Leakage Flux”, Transactions of China Electrotechnical Society, 2013, Vol. 28, Issue (5): 148–153.Google Scholar
  11. 11.
    Z. Cheng, N. Takahashi, B. Forghani, L. Liu, Y. Fan, T. Liu, Q. Hu, S. Gao, J. Zhang, and X. Wang, “Extended progress in TEAM Problem 21 Family”, COMPEL 2014, Vol. 33 Iss: 1/2 2014, pp. 234–244.Google Scholar
  12. 12.
    Z. Cheng, N. Takahashi, B. Forghani, A.J. Moses, P.I. Anderson, Y. Fan, T. Liu, X. Wang, Z. Zhao, and L. Liu, “Modeling of Magnetic Properties of GO Electrical Steel Based on Epstein Combination and Loss Data Weighted Processing”, IEEE Trans. on Magnetics, Vol. 50, No. 1, January 2014.CrossRefGoogle Scholar
  13. 13.
    Z. Cheng, B. Forghani, Y. Liu, Y. Fan, T. Liu, and Z. Zhao, “Magnetic Loss Inside Solid and Laminated Components under Extreme Excitations”, International Journal of Energy and Power Engineering, Vol. 5, Issue 1–1, pp. 21–30, September 2015.CrossRefGoogle Scholar
  14. 14.
    Z. Cheng, B. Forghani, T. Liu, Y. Fan, and L. Liu, “Extended P21-Based Benchmarking”, International Journal of Energy and Power Engineering, Issue 1–1, pp. 1–11, February 2016.MathSciNetCrossRefGoogle Scholar
  15. 15.
    Z. Zhao, Z. Cheng, B. Forghani, and L. Liu, “Analytical study and corresponding experiments for iron loss inside laminated core under ac-dc hybrid excitation”, International Journal of Applied Electromagnetics and Mechanics · August 2017.Google Scholar
  16. 16.
    Z. Cheng, B. Forghani, X. Wang, L. Liu, Y. Fan, X. Zhao, and Y. Liu, “Engineering-oriented investigation of magnetic property modeling and application”, International Journal of Applied Electromagnetics and Mechanics, August 2017.Google Scholar
  17. 17.
    S. Hussain, “Development of advanced material models for the simulation of low-frequency electromagnetic devices,” Ph.D. Thesis, McGill University, Montreal, Canada, Feb. 2017.Google Scholar
  18. 18.
    D. C. Jiles and D. L. Atherton, “Theory of ferromagnetic hysteresis,” Journal of Magnetism and Magnetic Materials, vol. 61, no. 1–2, pp. 48–60, 1986.CrossRefGoogle Scholar
  19. 19.
    Description of TEAM Problem 32: A Test-Case for Validation of Magnetic Field Analysis with Vector Hysteresis, O. Bottauscio, M. Chiampi, C. Ragusa, L. Rege and M. Repetto, https://www.compumag.org/wp/team/.
  20. 20.
    J. P. Webb, B. Forghani, “Adaptive Improvement of Magnetic Fields using Hierarchal Finite Elements”, IEEE Trans. on Magnetics, Vol. 30, No. 5, pp. 3511–3514, November 1994.Google Scholar
  21. 21.
    J.P. Webb, B. Forghani, “A T-Omega method using hierarchal edge elements”, IEE Proceedings, Sci. Meas. Technol., Vol. 142, no. 2, pp. 133–141, March 1995.Google Scholar
  22. 22.
    Description of TEAM Problem 3: Eddy Current Workshop (3), Bath Plate with 2 Holes, https://www.compumag.org/wp/wp-content/uploads/2018/06/problem3.pdf.
  23. 23.
    D. A. Lowther, B. Forghani, and E. Freeman, “On equivalent reluctances for time harmonic eddy current analysis”, Elsevier Studies in Applied Electromagnetics in Materials, Vol. 6, 1995, Pages 647–650.Google Scholar
  24. 24.
  25. 25.
    D.N. Dyck, J. P. Webb, “Solenoidal Current Flows for Filamentary Conductors”, IEEE Trans. on Magnetics, Vol. 40, No. 2, March 2004.Google Scholar
  26. 26.
    J. P. Webb, B. Forghani, and D.A. Lowther, “An Approach to the Solution of Three-Dimensional Voltage Driven and Multiply Connected Eddy Current Problems”, IEEE Trans. on Magnetics, Vol. 28, No. 2, pp. 1193–1196, March 1992.CrossRefGoogle Scholar

Copyright information

© Science Press, Beijing and Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Mentor Infolytica, a Siemens BusinessMontrealCanada

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