Análisis de impedancias de tierra de forma cerrada en estudios de cortocircuito de sistemas de distribución aérea
Contenido principal del artículo
Resumen
El objetivo de este estudio es evaluar la aplicabilidad de las principales fórmulas cerradas de impedancia de retorno por tierra en el análisis de cortocircuito de sistemas de distribución, así como identificar las configuraciones críticas en las cuales la elección del modelo de impedancia puede influir significativamente en los resultados del cortocircuito. La metodología adoptada en esta investigación se estructura en tres etapas. Primero, se desarrolló un algoritmo para implementar y comparar las formulaciones cerradas de impedancia de retorno por tierra, el cual fue validado con datos de referencia disponibles en la literatura. Segundo, se diseñó un algoritmo de análisis de cortocircuito que fue verificado con resultados publicados por la IEEE Power and Energy Society. Finalmente, se realizaron múltiples estudios de cortocircuito en varios alimentadores de prueba de distribución del IEEE. Los resultados muestran que la mayoría de las formulaciones cerradas de impedancia de retorno por tierra son adecuadas tanto para análisis de cortocircuito balanceados como desbalanceados, y que, en fallas monofásicas a tierra, la elección de la fórmula cerrada de impedancia resulta un factor crítico para obtener resultados precisos.
Detalles del artículo

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Referencias
[1] T. A. Papadopoulos, A. I. Chrysochos, C. K. Traianos, and G. Papagiannis, “Closed-form expressions for the analysis of wave propagation in overhead distribution lines,” Energies, vol. 13, no. 17, p. 4519, Sep. 2020. [Online]. Available: https://doi.org/10.3390/en13174519
[2] R. Cleenwerck, H. Azaioud, R. Claeys, T. Coosemans, J. Knockaert, and J. Desmet, “An approach to the impedance modelling of low-voltage cables in digital twins,” Electric Power Systems Research, vol. 210, p. 108075, Sep. 2022. [Online]. Available: http://doi.org/10.1016/j.epsr.2022.108075
[3] J. Zhang, F. Geth, R. Heidari, and G. Verbič, “Beyond simplifications: Evaluating assumptions for low-voltage network modelling in the DER era,” Sustainable Energy, Grids and Networks, vol. 43, p. 101860, Sep. 2025. [Online]. Available: http://doi.org/10.1016/j.segan.2025.101860
[4] J. R. Carson, “Wave propagation in overhead wires with ground return,” Bell System Technical Journal, vol. 5, no. 4, pp. 539–554, Oct. 1926. [Online]. Available: http://doi.org/10.1002/j.1538-7305.1926.tb00122.x
[5] W. H. Wise, “Effect of ground permeability on ground return circuits,” Bell System Technical Journal, vol. 10, no. 3, pp. 472–484, Jul. 1931. [Online]. Available: http://doi.org/10.1002/j.1538-7305.1931.tb01287.x
[6] W. Wise, “Propagation of high-frequency currents in ground return circuits,” Proceedings of the IRE, vol. 22, no. 4, pp. 522–527, Apr. 1934. [Online]. Available: http://doi.org/10.1109/JRPROC.1934.225868
[7] E. D. Sunde, Earth Conduction Effects in Transmission Systems. Dover Publications, 1968. [Online]. Available: https://upsalesiana.ec/ing35ar5r7
[8] H. Wohlfarth, “Calculation of ground impedances,” IEEE Transactions on Power Delivery, vol. 39, no. 4, pp. 2113–2124, Aug. 2024. [Online]. Available: https://doi.org/10.1109/TPWRD.2024.3388570
[9] C. Dubanton, “Calcul approché des parametres primaires et secondaires d’une ligne de transport,” EDF Bulletin de la Direction des Études et Recherches, no. 1, pp. 53–62, 1969, cited by: 16. [Online]. Available: https://upsalesiana.ec/ing35ar5r10
[10] A. Deri, G. Tevan, A. Semlyen, and A. Castanheira, “The complex ground return plane a simplified model for homogeneous and multi-layer Earth return,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-100, no. 8, pp. 3686–3693, Aug. 1981. [Online]. Available: https://doi.org/10.1109/TPAS.1981.317011
[11] F. Alvarado and R. Betancourt, “An accurate closed-form approximation for ground return impedance calculations,” Proceedings of the IEEE, vol. 71, no. 2, pp. 279–280, 1983. [Online]. Available: https://doi.org/10.1109/PROC.1983.12573
[12] M. Pizarro and R. Eriksson, “Modelling of the ground mode of transmission lines in time domain simulations,” 7th Int. Symp. on High Voltage Engineering, pp. 179–182, 1991.
[13] T. Noda, “A double logarithmic approximation of Carson’s ground-return impedance,” IEEE Transactions on Power Delivery, vol. 21, no. 1, pp. 472–479, Jan. 2006. [Online]. Available: https://doi.org/10.1109/TPWRD.2005.852307
[14] W. Kersting and W. Phillips, “Distribution feeder line models,” IEEE Transactions on Industry Applications, vol. 31, no. 4, pp. 715–720, 1995. [Online]. Available: https://doi.org/10.1109/28.395276
[15] T. Theodoulidis, “On the closed-form expression of Carson’s integral,” Periodica Polytechnica Electrical Engineering and Computer Science, vol. 59, no. 1, pp. 26–29, 2015. [Online]. Available: https://doi.org/10.3311/PPee.7894
[16] T. Martins, A. Lima, and S. Carneiro, “Effect of approximate impedance formulae on the accuracy of transmission line modelling,” IET Generation, Transmission & Distribution, vol. 1, no. 4, pp. 534–539, Jul. 2007. [Online]. Available: https://doi.org/10.1049/iet-gtd:20060289
[17] O. Ramos-Leanos, J. L. Naredo, F. A. Uribe, and J. L. Guardado, “Accurate and approximate evaluation of power-line Earth impedances through the Carson integral,” IEEE Transactions on Electromagnetic Compatibility, vol. 59, no. 5, pp. 1465–1473, Oct. 2017. [Online]. Available: https://doi.org/10.1109/TEMC.2017.2679213
[18] S. Li and D. Tylavsky, “Analytic continuation as the origin of complex distances in impedance approximations,” International Journal of Electrical Power & Energy Systems, vol. 105, pp. 699–708, Feb. 2019. [Online]. Available: https://doi.org/10.1016/j.ijepes.2018.09.022
[19] K. Gampa, S. A. Vemprala, and S. M. Brahma, “Errors in fault analysis of power distribution systems using sequence components approach,” in IEEE PES T&D 2010. IEEE, 2010, pp. 1–6. [Online]. Available: https://doi.org/10.1109/TDC.2010.5484378
[20] R. S. F. Ferraz, R. S. F. Ferraz, A. C. Rueda-Medina, and M. H. M. Paiva, “Power flow and fault analysis using graph theory,” in 2021 IEEE URUCON. IEEE, Nov. 2021, pp. 6–11. [Online]. Available: https://doi.org/10.1109/URUCON53396.2021.9647053
[21] A. Suresh, K. Murari, S. Kamalasadan, and S. Paudyal, “Steady-state fault analysis of unbalanced power distribution network utilizing a novel sequence component based methodology,” in 2023 IEEE Industry Applications Society Annual Meeting (IAS). IEEE, Oct. 2023, pp. 1–6. [Online]. Available: https://doi.org/10.1109/IAS54024.2023.10406399
[22] J. He, Z. Li, W. Li, J. Zou, X. Li, and F.Wu, “Fast short-circuit current calculation of unbalanced distribution networks with inverter-interfaced distributed generators,” International Journal of Electrical Power & Energy Systems, vol. 146, p. 108728, Mar. 2023.
[23] R. Galloway, W. Shorrocks, and L. Wedepohl, “Calculation of electrical parameters for short and long polyphase transmission lines,” Proceedings of the Institution of Electrical Engineers, vol. 111, no. 12, p. 2051, 1964. [Online]. Available: https://doi.org/10.1049/piee.1964.0331
[24] M. Cenký, J. Bendík, B. Cintula, P. Janiga, A. Belan, and Z. Eleschová, “Three-phase and single-phase measurement of overhead power line capacitance evaluation,” Electrical Engineering, vol. 105, no. 2, pp. 1045–1065, Jan. 2023. [Online]. Available: https://doi.org/10.1007/s00202-022-01714-1
[25] W. Kersting, “Radial distribution test feeders,” in 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings IEEE, 2001, pp. 908–912. [Online]. Available:
https://doi.org/10.1109/PESW.2001.916993
[26] K. P. Schneider, B. A. Mather, B. C. Pal, C.-W. Ten, G. J. Shirek, H. Zhu, J. C. Fuller, J. L. R. Pereira, L. F. Ochoa, L. R. de Araujo, R. C. Dugan, S. Matthias, S. Paudyal, T. E. McDermott, and W. Kersting, “Analytic considerations and design basis for the IEEE distribution test feeders,” IEEE Transactions on Power Systems, vol. 33, no. 3, pp. 3181–3188, May 2018. [Online]. Available: https://doi.org/10.1109/TPWRS.2017.2760011
[27] I. Kim, “A short-circuit analysis algorithm capable of analyzing unbalanced loads and phase shifts through transformers using the Newton-Raphson power-flow calculation, sequence, and superposition methods,” International Transactions on Electrical Energy Systems, vol. 31, no. 4, Oct. 2020. [Online]. Available: https://doi.org/10.1002/2050-7038.12653
[28] G. Meena, A. Mathur, V. P. Singh, K. Murari, and S. Kamalasadan, “Efficient evaluation of short-circuit faults in active distribution networks,” in 2024 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES). IEEE, Dec. 2024, pp. 1–6. [Online]. Available: https://doi.org/10.1109/PEDES61459.2024.10961501
[29] T. F. Garbelim Pascoalato, A. R. Justo de Araújo, S. Kurokawa, and J. P. Filho, “Effects of frequency-dependent soil electrical parameters on sequence parameters of double-circuit transmission lines,” Electric Power Systems Research, vol. 247, p. 111724, Oct. 2025. [Online]. Available: https://doi.org/10.1016/j.epsr.2025.111724
[30] A. A. Castillo, A. L. López, N. A. Barboza Tello, I. Uriarte, and A. Jiménez, “A comparison of models for calculating distribution lines impedance,” in 2018 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC). IEEE, Nov. 2018, pp. 1–6. [Online]. Available: https://doi.org/10.1109/ROPEC.2018.8661470
[31] IEEE. Resources – IEEE PES Test Feeder. Institute of Electrical and Electronics Engineers. [Online]. Available: https://upsalesiana.ec/ing35ar5r32
[32] W. H. Kersting, Distribution System Modeling and Analysis, Third Edition. CRC Press, 2012. [Online]. Available: https://upsalesiana.ec/ing35ar5r33
[33] W. H. Kersting and G. Shirek, “Short circuit analysis of IEEE test feeders,” in PES T&D 2012. IEEE, May 2012, pp. 1–9. [Online]. Available: http://doi.org/10.1109/TDC.2012.6281539
[34] W. H. Kersting and R. K. Green, “The application of Carson’s equation to the steady-state analysis of distribution feeders,” in 2011 IEEE/PES Power Systems Conference and Exposition. IEEE, Mar. 2011, pp. 1–6. [Online]. Available: http://doi.org/10.1109/PSCE.2011.5772579
[35] F. Rongqi, L. Kuan, H. Qiang, J. Panpan, and W. Anning, “Calibration of distributed PV setting calculation model and simulation calculation model based on short-circuit test of distribution network,” in 2023 IEEE 11th Joint International Information Technology and Artificial Intelligence Conference (ITAIC). IEEE, Dec. 2023, pp. 603–607. [Online]. Available: http://doi.org/10.1109/ITAIC58329.2023.10408848
[36] J. Hoeksema, R. Torkzadeh, J. Van Waes, S. Cobben, and V. Ćuk, “A case study on the future changes in short circuit power to analyze the impact on voltage dips,” IET Conference Proceedings, vol. 2023, no. 6, pp. 1330–1334, Jul. 2023. [Online]. Available: http://doi.org/10.1049/icp.2023.0707