High Frequency Numerical Solution to Evaluate the Impedance of the Vertical Grounding Electrode Using an Accurate Mathematical Approach

Document Type : Review Article

Authors

1 Electrical Engineering, University of Science and Technology of Mazandaran

2 University of Science and Technology of Mazandaran - Behshahr Branch

3 Mathematics, University of Science and Technology of Mazandaran

Abstract

Considering the air/earth interface to compute the electromagnetic field at the desired point is the most important problem in transient analysis of grounding system buried to lossy media like earth. In order to consider this issue in the available proposed method and to obtain a solution for the problem, one needs to account an integral solution of the so-called Semmerfeld integral in the cylindrical coordinate system. Analytical solution for such integral is almost impossible which is due to the presence of the oscillating the zeroth-order Bessel function of the first kind, and singularities and branch-cuts in its integrand function.  In this paper, we investigate the behavior of the vertical grounding electrode in a high-frequency electromagnetic transient state based on the near field theory using the method of moments (MoM). To compute the electromagnetic field at the desired point, the main problem is calculating the well-known Sommerfeld integral in the cylindrical coordinate system, which its integral kernel includes the zeroth-order Bessel function of the first kind along with some singularities and branch-cuts. Since the analytical solution of this integral is not available in literature, we propose a numerical method, as well as a strategy based on the exact solution for far and near filed calculations. A detailed analysis of the obtained results compared with other techniques are provided to confirm the accuracy and validity of the proposed method.

Keywords

Main Subjects

References

[1]    N. Ramezani, S. M. Shahrtash, "Calculating the transient behavior of grounding systems using inverse Laplace transform", Journal of Zhejiang University-SCIENCE C (Computers & Electronics), 12(3):250-262, 2011.
[2]    Cidras, J., Otero, A.F., Garrido, C., “Nodal frequency analysis of grounding systems considering the soil ionization effect”, IEEE Transactions on Power Delivery, 15(1):103-107, 2000.
[3]    Geri, A., “Behavior of ground systems excited by high impulse currents: the model and its validation”, IEEE Transactions on Power Delivery, 14(3):1008-1017, 1999.
[4]    Meliopoulos, A.P., Moharam, M.G., “Transient analysis of grounding systems", IEEE Transactions on Power Apparatus and System, 102(2):389-399, 1983.
[5]    Ramamoorty, M., Babu Narayanan, M.M., Parameswaran, S., Mukhedkar, D., “Transient performance of grounding grids”, IEEE Transactions on Power Delivery, 4(4):2053-2059, 1989.
[6]    Claudiner Mendes de Seixas, Sérgio Kurokaw, “Using circuit elements to represent the distributed parameters of a grounding system under lightning strokes”, Elsevier, Electric Power Systems Research, 172, 213-220, 2019.
[7]    Verma, R., Mukhedkar, D., “Impulse impedance of buried ground wire”, IEEE Transactions on Power Apparatus and System, 99(5):2003-2007, 1980.
[8]    Velazquez, R., Mukhedkar, D., “Analytical modeling of grounding electrodes transient behavior”, IEEE Transactions on Power Apparatus and System, 103(6):1314-1322, 1984.
[9]    Liu, Y.Q., Zitnik, M., Thottappillil, R., “An improved transmission line model of grounding systems”, IEEE Transactions on Electromagnetic Compatibility, 43(3):348-355, 2001.
[10]            Mentre, F.E., Grcev, L., “EMTP-based model for grounding system analysis”, IEEE Transactions on Power Delivery, 9(4):1838-1849, 1994.
[11]            Sofiane Chiheb, Omar Kherif, Madjid Teguar, Abdelouahab Mekhaldi, Noureddine Harid, “Transient behaviour of grounding electrodes in uniform and in vertically stratified soil using state space representation”, IET Science, Measurement & Technology, 12(4), 427-435, 2018.
[12]            Arnautovski-Toseva, V., Grcev, L., “Electromagnetic analysis of horizontal wire in two-layered soil”, Journal of Computational and Applied Mathematics, 168(1-2):21-29, 2004.
[13]            Doric, V., Poljak, D., Roje, V., “Transient analysis of the grounding electrode based on the wire antenna theory”, Engineering Analysis with Boundary Elements, 28(7): 801-807, 2004.
[14]            Poljak, D., Doric, V., “Wire antenna model for transient analysis of simple grounding systems, Part I: The vertical grounding electrode”, Progress in Electromagnetics Research, PIER 64, 149-166, 2006.
[15]            S.M. Shahrtash, and N. Ramezani,” A new approach to compute transient behavior of grounding electrodes in time-domain”, IEEE Intentional Conference on Power System Technology and Power, India, 1-5., 2008.
[16]            Silvestar Šesnić, Dragan Poljak, “Antenna model of the horizontal grounding electrode for transient impedance calculation: Analytical versus boundary element method”, Elsevier, Engineering Analysis with Boundary Elements, 37, 909-913, 2013.
[17]            Heimbach, M., Grcev, L.D., “Grounding system analysis in transients programs applying electromagnetic field approach”, IEEE Transactions on Power Delivery, 12(1):186-193, 1997.
[18]            Portela, C., “Frequency and transient behavior of grounding systems, Part I: Physical and methodological aspects", IEEE Intentional Symposium on Electromagnetic Compatibility, 379-384, 1997.
[19]            Andolfato, R., Bernardi, L., Fellin, L., “Aerial and grounding systems analysis by the shifting complex images method”, IEEE Transactions on Power Delivery, 15(3):1001-1009, 2000.
[20]            Zhang, B., He, J., Bok Lee, J., Cui, X., Zhao, Z., Zou, J., Chang, S., “Numerical analysis of transient performance of grounding systems considering soil ionization by coupling moment method with circuit theory”, IEEE Transactions on Magnetics, 41(5): 1440-1443, 2005.
[21]            Javad Gholinezhad, Reza Shariatinasab, “Interfacing electromagnetic model of tower-footing impedance with the EMTP software package”, International Journal of Electrical Power and Energy Systems, 105, 394-403,2019.
[22]            L. Qi, X. Cui, Z. Zhao, H. Li, “Grounding performance analysis of the substation grounding grids by finite element method in frequency domain”, IEEE Transactions on Magnetics, 43(4): 1181-1184, 2007.
[23]            P.L. Tokarsky, V.V. Dolzhikov, “Simple approximate formulas for evaluating Sommerfeld type integrals”, VIIth International Conference on Mathematical Methods in Electromagnetic Theory, 246-248, 1998.
[24]            A, Karwowski and J. Szymahda, “Vector potential of a vertical current element over a lossy ground”, IEE Proceedings H - Microwaves, Antennas and Propagation, 132(5), 326-328, 1985.
[25]            L. Grcev, “Transient electromagnetic fields near large earthing systems”, IEEE Transactions on Magnetics, 32(3): 1525-1528, 1996.
[26]            R.G. Olsen, M.C. Willis, “A comparison of exact and quasi-static methods for evaluating grounding systems at high frequencies”, IEEE Transactions on Magnetics, 11(2): 1071-1081, 1996.
[27]            L.Grcev, V.A.Toseva, “Grounding systems modeling for high frequencies and transient: some fundamental considerations”, IEEE Proceedings of powertech conference, 3: 1020-1026, 2003.
[28]            L. Grcev, F.Dawalibi, “An electromagnetic model for transient in grounding systems”, IEEE Transactions on Power Delivery, 5(4): 1773-1781, 1990.
[29]            B. Nekhoul, C. Guerin, P. Lapie, G. Meunier, R. Feuillet, “A finite element method for calculating the electromagnetic fields generated by substation grounding system”, IEEE Transactions on Magnetics, 31(3), 2150-2153, 1995.
[30]            B. Nekhoul,P.Lapie, X. Zgainski,G. Meunier,”Calculating the impedance of a grounding system”, IEEE Transactions on Magnetics, 32(3): 1509-1512, 1996.
[31]            A.Ishimaru، “Electromagnetic wave propagation، radiation، and scattering”، Prentice-Hall، Inc., A Division of Simon & Schuster Englewood Cliffs, N.J. 07632، 1991.
[32]            Maday Y, Pernaud-Thomas B, Vandeven H, “Reappraisal of Laguerre type spectral methods”, La Recherche Aerospatiale, 6: 13-35, 1985.
[33]            Funaro D, “Computational aspect of pseudo spectral Laguerre approximations”, Applied Numerical Mathematics, 6: 447-457, 1990.
[34]            Shen J, “Stable and efficient spectral methods in unbounded domains using Laguerre functions”, SIAM Journal on Numerical Analysis, 38: 1113-1133, 2000.
[35]            Guo B Y, Shen J,” Laguerre- Galerkin method for nonlinear partial differential equations on a semi-infinite interval”,Numerische Mathematik, 86: 635-654, 2000.
[36]            Siyyam H I, "Laguerre tau methods for solving higher order ordinary differential equations “, Journal of Computational Analysis and Applications, 3: 173-182, 2001.
[37]            Guo B Y, “Jacobi spectral approximation and its applications to differential equations on the half line”, An International Journal of Computers and Mathematics with Applications, 18: 95-112, 2000.
[38]            Gao B Y, “Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations”, Journal of Mathematical Analysis and Applications, 243: 373-408, 2000.
[39]            J. Stoer, R. Bulirsch, “Introduction to numerical analysis”, Springer-Verlag, New York, 1980.
 
 
AUT Journal of Electrical Engineering
Volume 53, Issue 1
June 2021
Pages 87-98

Files

Share

How to cite

Statistics