Quasi-Static Complex Image Method for a Current Point Source in Horizontally Stratified Multilayered Earth

doi:10.2528/PIERB11060301

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Progress In Electromagnetics Research B	ISSN: 1937-6472

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QUASI-STATIC COMPLEX IMAGE METHOD FOR A CURRENT POINT SOURCE IN HORIZONTALLY STRATIFIED MULTILAYERED EARTH

By Z. X. Li, G.-F. Li, J.-B. Fan, and Y. Yin

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Abstract:
Based on quasi-static electromagnetic field theory, recently grounding system under alternative currents (AC) substation has been studied with equal potential and unequal potential models. In these numerical models, the closed form of Green's function for a point source within a horizontal multilayered earth model and its quasi-static complex image method have been fully discussed. However, less information about how to achieve the closed form of Green's function through Matrix Pencil method is presented in these references. In this paper, we discuss how the kernel of the Green's function can be expanded into a finite exponential series.

Citation:
Z. X. Li, G.-F. Li, J.-B. Fan, and Y. Yin, "Quasi-static complex image method for a current point source in horizontally stratified multilayered earth," Progress In Electromagnetics Research B, Vol. 34, 187-204, 2011.
doi:10.2528/PIERB11060301
http://www.jpier.org/pierb/pier.php?paper=11060301

References:
1. Sakis Meliopoulos, A. P., F. Xia, and G. J. Cokkinides, "An advanced computer model for grounding system analysis," IEEE Transactions on Power Delivery, Vol. 8, No. 1, 13-23, 1993.
doi:10.1109/61.180314

2. Chow, Y. L., M. M. Elsherbiny, and M. M. A. Salama, "Surface voltages and resistance of grounding systems of grid and rods in two-layer earth by rapid Galerkin's moment method," IEEE Transactions on Power Delivery, Vol. 12, No. 1, 179-185, January 1997.
doi:10.1109/61.568239

3. Vujevic, S., "Numerical analysis of potential distribution for a point current source in horizontally stratified multilayer earth," Engineering Modelling, Vol. 8, 21-29, 1995.

4. Vujevic, S. and M. Kurtovic, "Numerical analysis of earthing grids buried in horizontal stratified multilayer earth," International Journal for Numerical Methods in Engineering, Vol. 41, 1297-1319, 1998.
doi:10.1002/(SICI)1097-0207(19980415)41:7<1297::AID-NME338>3.0.CO;2-Z

5. Zhang, L. P., J. S. Yuan, and Z. X. Li, "The complex image method and its application in numerical simulation of substation grounding grids," Communication in Numerical Methods in Engineering, Vol. 15, 835-839, 1999.
doi:10.1002/(SICI)1099-0887(199911)15:11<835::AID-CNM298>3.0.CO;2-I

6. Colominas, I., F. Navarrina, and M. Casteleiro, "A numerical formula for grounding system analysis in stratified soils," IEEE Transactions on Power Delivery, Vol. 17, No. 2, 587-595, 2002.
doi:10.1109/61.997943

7. Yuan, J. S., H. N. Yang, L. P. Zhang, X. Cui, and X. S. Ma, "Simulation of substation grounding grids with unequal-potential," IEEE Transactions on Magnetic, Vol. 36, No. 4, 1468-1471, 2000.
doi:10.1109/20.877715

8. Huang, L. and D. G. Kasten, "Model of ground grid and metallic conductor currents in high voltage a.c. substations for the computation of electromagnetic fields," Electric Power Systems Research, Vol. 59, 31-37, 2001.
doi:10.1016/S0378-7796(01)00112-2

9. Li, Z. X., G. F. Li, J. B. Fan, and C. X. Zhang, "Numerical calculation of grounding system buried in vertical earth model in low frequency domain based on the boundary element method," European Transactions on Electrical Power, Vol. 19, No. 8, 1177-1190, 2009.
doi:10.1002/etep.293

10. Rancic, P. D., L. V. Stefanovic, and D. R. Djordjevic, "A new model of the vertical ground rod in two-layer earth," IEEE Transactions on Magnetic, Vol. 28, No. 2, 1497-1500, 1992.
doi:10.1109/20.123980

11. Rancic, P. D., L. V. Stefanovic, and D. R. Djordjevic, "An improved linear grounding system analysis in two-layer earth," IEEE Transactions on Magnetic, Vol. 32, No. 5, 5179-5187, 1996.
doi:10.1109/20.538620

12. Li, Z. X., J. B. Fan, and W. J. Chen, "Numerical simulation of substation grounding grids buried in both horizontal and vertical multilayer earth model," International Journal for Numerical Methods in Engineering, Vol. 69, 2359-2380, 2007.
doi:10.1002/nme.1853

13. Vujevic, S. and P. Sarajcev, "Potential distribution for a harmonic current point source in horizontally stratified multilayer medium," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 27, 624-637, 2008.
doi:10.1108/03321640810861070

14. Li, Z. X., G. F. Li, and J. B. Fan, "Numerical simulation of substation grounding system in low-frequency domain based on the boundary element method with linear basis function," Communication in Numerical Methods in Engineering, Vol. 26, No. 12, 1819-1914, December 2010.

15. Sarajcev, P., S. Vujevic, and D. Lovric, "Time-harmonic current distribution on conductor grid in horizontally stratified multilayer medium," Progress In Electromagnetics Research B, Vol. 31, 67-87, 2011.

16. Otero, A. F., J. Cidras, and J. L. Alamo, "Frequency-dependent grounding system calculation by means of a conventional nodal analysis technology," IEEE Transactions on Power Delivery, Vol. 14, No. 3, 873-877, July 1999.
doi:10.1109/61.772327

17. Dawalibi, F., "Electromagnegtic fields generated by overhead and buried short conductors, Part 1 --- Single conductor," IEEE Transactions on Power Delivery, Vol. 1, No. 4, 105-1111, 1986.
doi:10.1109/TPWRD.1986.4308036

18. Dawalibi, F. and R. D. Southey, "Analysis of electrical interference from power lines to gas pipelines, Part 1 --- Computational methods," IEEE Transactions on Power Delivery, Vol. 4, No. 3, 1840-1846, 1989.
doi:10.1109/61.32680

19. Dawalibi, F., "Electromagnegtic fields generated by overhead and buried short conductors, Part 2 --- Ground networks," IEEE Transactions on Power Delivery, Vol. 1, No. 4, 112-119, 1986.
doi:10.1109/TPWRD.1986.4308037

20. Li, Z. X., W. J. Chen, J. B. Fan, and J. Y. Lu, "A novel mathematical modeling of grounding system buried in multilayer earth," IEEE Transactions on Power Delivery, Vol. 21, No. 3, 1267-1272, 2006.
doi:10.1109/TPWRD.2006.875857

21. Li, Z. X. and W. J. Chen, "Numerical simulation grounding system buried within horizontal multilayer earth in frequency domain," Communication in Numerical Methods in Engineering, Vol. 23, 11-17, 2007.

22. Li, Z. X., "Numerical calculation of grounding system in low-frequency domain based on the boundary element method," International Journal for Numerical Methods in Engineering, Vol. 73, 685-705, 2008.
doi:10.1002/nme.2097

23. Sarkar, T. K. and O. Pereira, "Using the matrix pencil method to estimate the parameters of a sum of complex exponentials," IEEE Antenna and Propagation Magazine, Vol. 37, No. 1, 48-55, February 1995.
doi:10.1109/74.370583

24. Chow, Y. L., J. J. Yang, and K. D. Srivastava, "Complex images of a ground electrode in layered soils," Journal of Applied Physics, Vol. 71, No. 2, 569-574, 1992.
doi:10.1063/1.350407

25. Hua, Y. and T. K. Sarkar, "Generalized pencil-of-function method for extracting poles of an EM system from its transient response," IEEE Transactions on Antenna and Propagation, Vol. 37, No. 2, 229-234, February 1989.
doi:10.1109/8.18710