Mohamed Mostafa Saied,
- Professor, (Emeritus- Kuwait University), Independent Researcher, IEEE Life Senior Member, Giza, Cairo,, Egypt
Abstract
This paper addresses the analysis of the electromagnetic transients developed in an important class of non-uniform high-voltage power lines. It deals particularly with compensated long overhead high- voltage transmission lines composed of several tower spans, which are connected in cascade. The derived mathematical model leads to a system composed of simultaneous partial differential and algebraic equations, which can be solved numerically in terms of parametric functions using the software Mathematica’s statement (ParametricNDSolve). The resulting current and voltage distributions along the line will be functions of the location x, the Laplace operators, as well as of the levels of eventually existing series capacitive and parallel inductive compensation. A code based on the Hosono algorithm can then be used for the numerical Laplace inversion of these expressions in order to get the corresponding results in the time-domain. The results of several representative case studies are presented and discussed in order to assess the impact of the different network parameters on the voltage and current distributions as well as the stresses in the compensating elements. It is believed that this study will be helpful to the high voltage and protection engineers, in addition to the power engineering students and trainees.
Keywords: Electromagnetic, transients, simulation, high-voltage lines, non-uniform, compensation, Mathematica, towers, span, partial differential equations, parametric functions, numerical Laplace inversion, Hosono algorithm, parameter study
[This article belongs to Trends in Electrical Engineering ]
Mohamed Mostafa Saied. Electromagnetic Transients in Compensated Overhead Lines with Multiple Tower Spans. Trends in Electrical Engineering. 2025; 15(02):1-9.
Mohamed Mostafa Saied. Electromagnetic Transients in Compensated Overhead Lines with Multiple Tower Spans. Trends in Electrical Engineering. 2025; 15(02):1-9. Available from: https://journals.stmjournals.com/tee/article=2025/view=212963
References
- El Dein AZE, Gouda OE, Lehtonen M, Darwish MMF. Mitigation of the electric and magnetic fields of 500-kV overhead transmission lines. IEEE Access. 2022;10:33900-8. doi:10.1109/ ACCESS.2022.3161932.
- Bewley LV. Traveling Waves on Transmission Systems. New York: Dover; 1963.
- Greenwood A, Selzer A. Electrical transients in power systems. IEEE Trans Syst Man Cybern. 1973;SMC–3:301–2. doi:10.1109/TSMC.1973.4309230
- Dommel HW. Bonneville Power Administration. Electromagnetic Transients Program Reference Manual: (EMTP) Theory Book. Portland, OR: Bonneville Power Administration; 1986.
- Van der Sluis L. Transients in Power Systems. New York: John Wiley & Sons; 2001. doi:10.1002/0470846186.
- Begamudre RD. Extra High-Voltage AC Transmission Engineering. New Delhi: New Age International; 2006.
- Ovick NL. Travelling waves on transmission lines, including corona effects [dissertation]. Pittsburgh: University of Pittsburgh; 1982.
- Scharlemann E. An EMTP Theory Book Correction. LLNL-TR-450052. Livermore, CA: Lawrence Livermore National Laboratory; 2010.
- Saied M, Safar Y, Salama M. Line transients with corona. J Univ Kuwait Sci. 1987;14:77–95.
- Saied MM, Safar YA. Electromagnetic transients on compensated lines under corona. Electr Mach Power Syst. 1989;16:441–62. doi:10.1080/07313568908909401.
- Tarditi AG, Besnoff JS, Duckworth R, Li FR, Li Z, Liu Y, Mcconnell BW, Olsen RG, Poole BR, Piesciorovsky EC, et al. High voltage modeling and testing of transformer, line interface devices, and bulk system components under electromagnetic pulse, geomagnetic disturbance, and other abnormal transients [Internet]. Oak Ridge (TN): Oak Ridge National Laboratory (US); 2019. doi: https://doi.org/10.2172/1515663.
- Saied MM. Corona modeling for the transient analysis, steady state and corona loss performance of transmission lines. Electr Power Qual Util J. 2013;16(2):11–20.
- Sellschopp FS, Arjona LM. An automated system for frequency response analysis with application to an undergraduate laboratory of electrical machines. IEEE Trans Educ. 2004;47:57–64. doi:10.1109/TE.2003.817621.
- Wolfram S. Differential equation solving with DSOLVE. Champaign, IL: Wolfram Research; 2008.
- Hosono T. Numerical inversion of Laplace transform and some applications to wave optics. Radio Sci. 1981;16:1015–9. doi:10.1029/RS016i006p01015.
- Lingaiah V. Exploring transmission lines overhead light. South Asian J Mark Manag Res. 2022 Jan;12(1, Suppl):97–107.

Trends in Electrical Engineering
| Volume | 15 |
| Issue | 02 |
| Received | 07/04/2025 |
| Accepted | 11/04/2025 |
| Published | 29/08/2025 |
| Publication Time | 144 Days |
Login
PlumX Metrics