HIGH FREQUENCY ENHANCEMENT OF THE HYBRID ELECTROMAGNETIC MODEL BY IMPLEMENTING COMPLEX IMAGES
A b s t r a c t: The well know hybrid electromagnetic model (HEM) is widely used for analysis of grounding systems. However, it has been proven that results obtained by HEM diverge from referent results in the high frequency (HF) domain. This paper presents implementation of complex image theory to take into account the earth-air interface instead of the quasi-static images used up-to-date with HEM. Parametric analysis of the achieved improvement in precision of the HEM method on high frequencies is visualized in multiple figures by comparison to referent results calculated by the renowned numerical electromagnetic code NEC-4. It may be concluded from the research presented in this paper that usage of complex images with HEM extends notably the applicability domain of the method.
Key words: hybrid electromagnetic model; complex images
Visacro S., Soares A. and Schroeder M. A.: An interactive computational code for simulation of transient behavior of electric system components for lightning currents, Proc. 2002 Int. Conf. Lightning Protection, pp. 732–737, 2002.
Visacro S. and Soares A.: HEM: A model for simulation of lightning – Related engineering problems, IEEE Trans. Power Delivery, vol. 20, no. 2, pp. 1206–1208, (2005).
Guimarães M., Araujo L., Castro R. V., Santos L. F. D., Murta Vale M. H. and Visacro S.: Impulse response of grounding grids: Experimental versus simulated results, Proc. 2012 Int. Conf. Lightning Protection, 2012.
Alípio R. S., Schroeder M. A. O., Afonso M. M. and Oliveira T. A. S.: Electromagnetic fields of buried conductors, Proc. Int. Conf. Grounding Earthing (GROUND 2008), pp. 399–402, 2008.
Alípio R. S., Schroeder M. A. O., Afonso M. M. and Oliveira T. A. S.: Electric fields of grounding electrodes: frequency and time domain analysis, Proc. X International Symposium on Lightning Protection 9th–13th November, Curitiba, Brazil, 2009.
Kuhar A., Ololoska-Gagoska L. and Grčev, L.: Numerical analysis of complex grounding systems using circuit based method, Proc. 12th Int. Conf. ETAI, Ohrid, Macedonia, Sep. 2015.
Jankoski R., Kuhar A. and Grčev L.: Frequency domain analysis of large grounding systems using hybrid circuit model, Proc. 8th Int. PhD Seminar on Computational and Electromagnetic Compatibility – CEMEC, Timisoara, Romania, Sep. 2014.
Kuhar A. and Grčev L.: Contribution to calculating the impedance of grounding electrodes using circuit equivalents, FACTA UNIVERSITATIS, Series: Electronics and Energetics, vol. 29, no. 4, pp. 721–732 (2016).
King R. W. P.: Antennas in material media near boundaries with application to communication and geophysical exploration, Part I: The baremetal dipole, IEEE Trans. Antennas Propag., vol. AP-34, no. 4, pp. 483–489, (1986).
Watt A. D., Personal communication, 1962.
Wait J. R., and Spies K. P.: On the image representation of the quasi-static fields of a line current source above the ground, Can. Journal of Physics, 47 (23), pp. 2731–2733, (1969).
Bannister P.: Applications of complex image theory, Radio Science, vol. 21, no.4, pp. 605–616 (1986).
Burke G. J.: Numerical Electromagnetics Code — NEC- 4, Method of Moments, Part II: Program Description—Theory, UCRL-MA-109338, Lawrence.
Livermore National Laboratory, Livermore, 1992. Arnautovski-Toševa V. and Grčev L.: On the image model of a buried horizontal wire, IEEE Trans. Electromagn. Compat., vol. 58, no. 1, pp. 278–286 (2016).
Otero A. F., Cidras J., Alemo J. L.: Frequency-dependent grounding system calculation by means of a conventional nodal analysis technique, IEEE Transactions on Power Delivery, Vol. 14, No. 3, pp. 873–878 (1999).
Park D.: Magnetic field of a horizontal current above a conducting earth, J Geophys. Res. 78 (16) pp. 3040–3043 (1973
 Chow Y. L., Yang, J. J. and Srivastava, K. D.: Complex images of a ground electrode in layered soils, Journal of Applied Physics (1992).
 Arnautovski-Toševa V.: Approximate closed-form solution of the electric field due to HED within finitely conductive earth. In: Proc. 2011 International Conference on Electromagnetics in Advanced Applications, ICEAA’11, Torino, Italy, pp. 670–673, 2011.
 Arnautovski-Toševa V, Grčev L. and Kacarska M.: Applicability of approximate Green’s functions in MPIE model of a horizontal wire conductor in lossy soil, 5 th International Symposium on Applied Electromagnetics – SAEM’2014, Skopje, Macedonia, 2014.