volume | PIER Journals

Abstract

There are applications of the finite difference time domain (FDTD) method, which need to model thin wires in dispersive media. However, existing thin wire techniques in the FDTD method are developed only for the conductive and dielectric media. The article presents a modification of oblique thin wire formalism proposed by Guiffaut et al. and a minor modification for the technique proposed by Railton et al. for applications with Debye media. The modifications are based on auxiliary differential equation (ADE) method. The modifications are validated by calculations of grounding potential rise (GPR) of a horizontal electrode buried in soil with dispersive properties.

1. Kuklin, D., "Choosing configurations of transmission line tower grounding by back flashover probability value," Front. Energy, Vol. 10, No. 2, 213-226, 2016.
doi:10.1007/s11708-016-0398-6

2. Alipio, R. and S. Visacro, "Frequency dependence of soil parameters: effect on the lightning response of grounding electrodes," IEEE Trans. Electromagn. Compat., Vol. 55, No. 1, 132-139, 2013.
doi:10.1109/TEMC.2012.2210227

3. Diaz, L., C. Miry, A. Reineix, C. Guiffaut, and A. Tatematsu, "FDTD transient analysis of grounding grids. A comparison of two different thin wire models," 2015 IEEE International Symposium on Electromagnetic Compatibility (EMC), 501-506, 2015.
doi:10.1109/ISEMC.2015.7256213

4. De Conti, A. and S. Visacro, "Analytical representation of single- and double-peaked lightning current waveforms," IEEE Trans. Electromagn. Compat., Vol. 49, No. 2, 448-451, 2007.
doi:10.1109/TEMC.2007.897153

5. Visacro, S. and R. Alipio, "Frequency dependence of soil parameters: experimental results, predicting formula and influence on the lightning response of grounding electrodes," IEEE Trans. Power Delivery, Vol. 27, No. 2, 927-935, 2012.
doi:10.1109/TPWRD.2011.2179070

6. Kelley, D. F., T. J. Destan, and R. J. Luebbers, "Debye function expansions of complex permittivity using a hybrid particle swarm-least squares optimization approach," IEEE Trans. Antennas Propag., Vol. 55, No. 7, 1999-2005, 2007.
doi:10.1109/TAP.2007.900230

7. Okoniewski, M., M. Mrozowski, and M. A. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microw. Guided Wave Lett., Vol. 7, No. 5, 121-123, 1997.
doi:10.1109/75.569723

8. Holland, R. and L. Simpson, "Finite-difference analysis of EMP coupling to thin struts and wires," IEEE Trans. Electromagn. Compat., Vol. 23, No. 2, 88-97, 1981.
doi:10.1109/TEMC.1981.303899

9. Guiffaut, C. and A. Reineix, "Cartesian shift thin wire formalism in the FDTD method with multiwire junctions," IEEE Trans. Antennas Propag., Vol. 58, No. 8, 2658-2665, 2010.
doi:10.1109/TAP.2010.2050427

10. Ledfelt, G., "A stable subcell model for arbitrarily oriented thin wires for the FDTD method," Int. J. Numer. Model. Electron. Netw. Devices Fields, Vol. 15, No. 5-6, 503-515, 2002.
doi:10.1002/jnm.466

11. Edelvik, F., "A new technique for accurate and stable modeling of arbitrarily oriented thin wires in the FDTD method," IEEE Trans. Electromagn. Compat., Vol. 45, No. 2, 416-423, 2003.
doi:10.1109/TEMC.2003.811294

12. Guiffaut, C., A. Reineix, and B. Pecqueux, "New oblique thin wire formalism in the FDTD method with multiwire junctions," IEEE Trans. Antennas Propag., Vol. 60, No. 3, 1458-1466, 2012.
doi:10.1109/TAP.2011.2180304

13. Umashankar, K. and A. Taflove, "Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity," IEEE Trans. Antennas Propag., Vol. 35, No. 11, 1248-1257, 1987.
doi:10.1109/TAP.1987.1144000

14. Mäkinen, R. M., J. S. Juntunen, and M. A. Kivikoski, "An improved thin-wire model for FDTD," IEEE Trans. Microw. Theory Techn., Vol. 50, No. 5, 1245-1255, 2002.
doi:10.1109/22.999136

15. Noda, T. and S. Yokoyama, "Thin wire representation in finite difference time domain surge simulation," IEEE Trans. Power Delivery, Vol. 17, No. 3, 840-847, 2002.
doi:10.1109/TPWRD.2002.1022813

16. Railton, C. J., D. L. Paul, I. J. Craddock, and G. S. Hilton, "The treatment of geometrically small structures in FDTD by the modification of assigned material parameters," IEEE Trans. Antennas Propag., Vol. 53, No. 12, 4129-4136, 2005.
doi:10.1109/TAP.2005.860008

17. Taniguchi, Y., Y. Baba, N. Nagaoka, and A. Ametani, "An improved thin wire representation for FDTD computations," IEEE Trans. Antennas Propag., Vol. 56, No. 10, 3248-3252, 2008.
doi:10.1109/TAP.2008.929447

18. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, 2005.

19. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, 1989.

Mr. Dmitry Kuklin