Skin effect and active resistance of power transmission line wires
https://doi.org/10.21285/1814-3520-2025-1-33-50
Abstract
The study aims to analyze the skin effect as applied to the active resistance of aluminum wires using a mathematical model based on the theory of electromagnetic fields. The study uses the Elcut finite element simulation software. The simulated object includes round aluminum and cylindrical steel-aluminum wires with a cross-section of 339 mm2 each, as well as AS 300/39 wire. The nonuniformity of a real power transmission line with steel-aluminum wires is considered. Calculations were verified in the Elcut software by dividing the aluminum wire into two components: a circle with a cross-section of 39 mm2 and an outer ring with a cross-section of 300 mm2. The results of aluminum wire simulation at different harmonics have established a coincidence of the obtained skin effect coefficients with the mathematical model. This coefficient reflects an increase in the active resistance of the wire at the highest harmonic in relation to direct current resistance. For an aluminum wire with a cross-section of 339 mm2, the active resistance at the 5th, 7th,11th, and 13th harmonic has increased by 24, 40, 71, and 84%, respectively. This circumstance confirmed the need to consider the skin effect in the assessment of power losses in power transmission lines at higher harmonics. We propose to simulate the AS wire as a cylindrical nonuniform wire consisting of a steel circle inside an aluminum ring. For AS 300/39 wire, the error of determining the skin effect coefficient using this method is below 5% in the studied harmonic range. Thus, the proposed research method considering AS wires as round cylindrical shows the possibility of refining their mathematical model.
Keywords
About the Authors
A. V. BelosvetovRussian Federation
Anton V. Belosvetov, Postgraduate Student
33, Shchetinkina str., Novosibirsk 630099
V. Z. Manusov
Russian Federation
Vadim Z. Manusov, Dr. Sci. (Eng.), Professor, Professor of the Physics and Mathematics School
16, Chekhova str., Khanty-Mansiysk 628011
References
1. Levačić G., Župan A., Čurin M. An overview of harmonics in power transmission networks. In: First International Colloquium on Smart Grid Metrology. 2018. https://doi.org/10.23919/SMAGRIMET.2018.8369828.
2. Arrillaga J., Bradley D., Bodger P. Power system harmonics. (Russ. ed.: Garmoniki v elektricheskih sistemah. Moscow: Energoatomizdat; 1990, 320 р.)
3. Shandrygin D.A., Dovgun V.P., Egorov D.E., Manshin M.V. An analysis of resonant modes in electric power systems with a traction load. Proceedings of Irkutsk State Technical University. 2020;24(2):396-407. (In Russ.). https://doi.org/10.21285/1814-3520-2020-2-396-407. EDN: MPFYPK.
4. Bui Ngoc Hung, Kovernikova L.I. The applicability of active filters for reduction of voltage non-sinusoidality in the power supply system of a coal mine in Vietnam. Proceedings of Irkutsk State Technical University. 2020;24(2):318-332. (In Russ.). https://doi.org/10.21285/1814-3520-2020-2-318-332. EDN: KCTRQU.
5. Panteleev V.I., Kuzmin I.S., Zavalov A.A., Tikhonov A.V., Umetskaya E.V. Power quality in power supply systems of mining and processing enterprises in Russia. Proceedings of Irkutsk State Technical University. 2021;25(3):356-368. (In Russ.). https://doi.org/10.21285/1814-3520-2021-3-356-368. EDN: SRSSJA.
6. Bebikhov Yu.V., Egorov A.N., Matul G.A., Semenov A.S., Kharitonov Ya.S. Search of ways to improve the efficiency of application of high-voltage frequency-regulated electric drive in conditions of mining production. Natural and Technical Sciences. 2018;8:228-234. (In Russ.).
7. Ashraf N., Abbas G., Abbassi R., Jerbi H. Power quality analysis of the output voltage of AC voltage and frequency controllers realized with various voltage control techniques. Applied Sciences. 2021;11(2):538. https://doi.org/10.3390/app11020538. EDN: BSGOVR.
8. Dutta N., Kaliannan P., Subramaniam U. Experimental analysis of PQ parameter estimation of VFD drives. In: Materials Science and Engineering: IOP Conference Series. 2020;937(1):012042. https://doi.org/10.1088/1757-899X/937/1/012042.
9. Jyothi R., Sumitgupta, Rao K.U., Jayapal R. IoT application for real-time condition monitoring of voltage source inverter driven induction motor. Innovative Data Communication Technologies and Application. 2021;59:97-105. https://doi.org/10.1007/978-981-15-9651-3_8.
10. Akhmedov S.B., Klimov P.L. Effect of renewable energy-based distributed generation with power invertors on resonance at harmonic frequencies. Proceedings of Irkutsk State Technical University. 2020;24(1):97-111. (In Russ.). https://doi.org/10.21285/1814-3520-2020-1-97-111. EDN: JZCIJV.
11. Zakaryukin V.P., Kryukov A.V., Cherepanov A.V. Modelling of highest harmonics resonant processes in alternating current traction nets. Modern technologies. System analysis. Modeling. 2016;3:214-221. (In Russ.). EDN: WMELHD.
12. Hu Haitao, Shao Yang, Tang Li, Ma Jin, He Zhengyou, Gao Shibin. Overview of harmonic and resonance in railway electrification systems. IEEE Transactions on Industry Applications. 2018;54(5):5227-5245. https://doi.org/10.1109/TIA.2018.2813967.
13. Annenkov E.O., Zubova E.V., Seleznev A.S., Fedosov D.S. Effectiveness of the method of two measurements in determining the parameters of equivalent circuits of electrical network elements for the highest harmonic components of currents and voltages. iPolytech Journal. 2022;26(3):401-414. (In Russ.). https://doi.org/10.21285/1814-3520-2022-3-401-414.
14. Silvério E.T., Macedo Junior J.R. Measuring and modeling the skin effect for harmonic power flow studies. Energies. 2023;16(23):7913. https://doi.org/10.3390/en16237913.
15. Zhang Xiao-Ping, Yan Zuanhong. Energy quality: a definition. IEEE Open Access Journal of Power and Energy. 2020;7:430-440. https://doi.org/10.1109/OAJPE.2020.3029767.
16. Borovikov V.S., Volkov M.V., Litvak V.V., Kharlov N.N., Mel’nikov V.A., Pogonin A.I., et al. Regime properties of electrical networks 110 kV in the south of Russia in ensuring efficient transport of electricity. Tomsk: STT; 2013, 268 р. (In Russ.). EDN: TZMHRJ.
17. Borovikov V.S., Volkov M.V., Ivanov V.V., Litvak V.V., Mel’nikov V.A., Pogonin A.I., Kharlov N.N. Experience of orporate surveying of 110 kV electrical networks in Siberia. Tomsk: Tomsk Polytechnic University; 2010, 227 р. (In Russ.). EDN: QMLILB.
18. Kharlov N.N. Resonance modes of multi-wire power transmission lines. Elektrichestvo. 2009;12:9-13. (In Russ.).
19. Kharlov N.N., Ivanov V.V., Pogonin A.V., Melnikov V.A. Formation of equations of steady non-sinusoidal modes of electric systems subject to state of distribution of power line parameter. Bulletin of the Tomsk Polytechnic University. 2009;314(4):56-59. (In Russ.). EDN: KVYIBF.
20. Kharlov N.N., Borovikov V.S., Litvak V.V., Pogonin A.V., Mel’nikov V.A. Energy survey of non-sinusoidal modes of multi-wire power transmission lines. Elektrichestvo. 2011;12:12-15. (In Russ.).
21. Borovikov V.S., Kharlov N.N., Akimzhanov T.B. On the need to include additional losses from higher current harmonics in process losses during electric power transmission. Bulletin of the Tomsk Polytechnic University. 2013;322(4):91-93. (In Russ.). EDN: QAREGB.
22. Akimzhanov T.B., Kharlov N.N., Borovikov V.S., Ushakov V.Y. Development of calculation methods for additional electrical power losses during transportation. In: The 9th International Forum on Strategic Technology. 21–23 October 2014, Cox’s Bazar. Cox’s Bazar: IEEE; 2014, p. 351-354. (In Russ.). https://doi.org/10.1109/IFOST.2014.6991138. EDN: UFWCJV.
23. Payne A. Skin effect, proximity effect and the resistance of circular and rectangular conductors. 2021. Available from: https://www.researchgate.net/publication/351306996_SKIN_EFFECT_PROXIMITY_EFFECT_AND_THE_RETSISTANCE_OF_CIRCULAR_AND_RECTANGULAR_CONDUCTORS [Accessed 25th September 2024].
24. Ramo S., Whinnery J.R., Van Duzer T. Fields and waves in communication electronics. John Wiley & Sons; 1994, 858 р.
25. Ramo S., Whinnery J.R. Fields and waves in modern radio. 2nd ed. John Wiley & Sons; 1953, 576 p.
26. Monteiro J.H.A., Costa E.C.M., Pinto A.J.G., Kurokawa S., Gatous O.M.O., Pissolato J. Simplified skin-effect formulation for power transmission lines. IET Science, Measurement & Technology. 2014;8(2):47-53. https://doi.org/10.1049/iet-smt.2013.0072.
27. Raven M.S. Skin effect in the time and frequency domain–comparison of power series and Bessel function solutions. Journal of Physics Communications. 2018;2(3):035028. https://doi.org/10.1088/2399-6528/aab4a8.
28. Terman F.E. Radio engineer’s handbook. Electrical and electronic engineering series. New York; London: McGraw-Hill Book Company; 1943, 1015 р.
29. Kaftanova Yu.V. Special functions of mathematical physics. Har’kov: Novoe slovo; 2009, 596 р. (In Russ.).
30. Angot A. Complements de mathematiques. A lusage des ingenieurs de lelekеrotechnique et des telecommunications. Paris, 1957. (Russ. ed.: Matematika dlya elektro- i radioinzhenerov. Moscow: Nauka; 1965, 780 р.)
31. Kennelly A.E., Laws F.A., Pierce P.H. Experimental researches on skin effects in conductors. Transactions of the American Institute of Electrical Engineers. 1915;34(2):1953-2021. https://doi.org/10.1109/T-AIEE.1915.4765283.
Review
For citations:
Belosvetov A.V., Manusov V.Z. Skin effect and active resistance of power transmission line wires. iPolytech Journal. 2025;29(1):33-50. (In Russ.) https://doi.org/10.21285/1814-3520-2025-1-33-50