Abstract
Cross-linked polyethylene (XLPE), the most commonly used insulation system in underground cables, and gas-insulated substations are often subjected to high-voltage stresses of time-varying nature. Lightning overvoltages, fast transients, very fast transients, and AC voltages are the most common overvoltages striking the insulation. These stresses cause degradation of insulation, which is called treeing, and are considered as the major cause of the reduction in life of the insulation. The purpose of our work is the development of a stochastic model to inspect the spread of electrical trees under lightning impulse voltage. A numerical solution of Poisson’s equation in the material is obtained first. The electric field distributions obtained on the surface of the material are used to compute the path of tree propagation by developing a program based on a probabilistic approach. The key parameters of the damage are evaluated by plotting histograms of the results obtained from many iterations. A statistical analysis of the obtained results has also been done, and the model has been found efficient.
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Sarathi, R.; Oza, K.H.; Pavan Kumar, C.L.G.; Tanaka, T.: Electrical treeing in XLPE cable insulation under harmonic AC voltages. IEEE Trans. Dielectr. Electr. Insul. 22(6), 3177–3185 (2015)
Schurch, R.; Ardila-Rey, J.; Montana, J.; Angulo, A.; Rowland, S.M.; Iddrissu, I.; Bradley, R.S.: 3D characterization of electrical tree structures. IEEE Trans. Dielectr. Electr. Insul. 26(1), 220–228 (2019)
Ying, L.; Xiaolong, C.: A novel method for the insulation thickness design of HV XLPE cable based on electrical treeing tests. IEEE Trans. Dielectr. Electr. Insul. 21(4), 1540–1546 (2014). https://doi.org/10.1109/TDEI.2014X.004250
Chen, G.; Tham, C.H.: Electrical treeing characteristics in XLPE power cable insulation in frequency range between 20 and 500 Hz. IEEE Trans. Dielectr. Electr. Insul. 16(1), 179–188 (2009). https://doi.org/10.1109/TDEI.2009.4784566
Du, B.X.; Zhu, L.W.: Electrical tree characteristics of XLPE under repetitive pulse voltage in low temperature. IEEE Trans. Dielectr. Electr. Insul. 22(4), 1801–1808 (2015). https://doi.org/10.1109/TDEI.2015.005183
Liu, H.; Liu, Y.; Li, Y.; Zheng, P.; Rui, H.: Growth and partial discharge characteristics of electrical tree in XLPE under AC-DC composite voltage. IEEE Trans. Dielectr. Electr. Insul. 24(4), 2282–2290 (2017). https://doi.org/10.1109/TDEI.2017.006537
Vidya, M.S.; Sunitha, K.; Ashok, S.; Mishra, D.; Chandra, V.: A model based on bag of visual words to predict the category of damage in XLPE insulation under the application of combined AC and repeated lightning impulses of both polarities. Electr. Eng. 103, 2825–2836 (2021)
Su, J.; Du, B.; Li, J.; Li, Z.: Electrical tree degradation in high-voltage cable insulation: progress and challenges. High Voltage 5(4), 353–364 (2020)
Niemeyer, L.; Pietronero, L.; Wiesmann, H.J.: Fractal dimension of dielectric breakdown. Phys. Rev. Lett. 52(12), 1033–1036 (1984). https://doi.org/10.1103/PhysRevLett.52.1033
Wiesmann, H.J.; Zeller, H.R.: A fractal model of dielectric breakdown and prebreakdown in solid dielectrics. J. Appl. Phys. 60(5), 1770–1773 (1986). https://doi.org/10.1063/1.337219
Sarathi, R.; Ramu, T.S.: Stochastic simulation of tree propagation in XLPE under different voltage profiles. Solid State Commun. 87(5), 401–404 (1993). https://doi.org/10.1016/0038-1098(93)90785-L
Schwab, A.J.; Sack, M.; Malinovski, A.S.; Noskov, M.D.: Self-consistent modeling of electrical tree propagation and PD activity. IEEE Trans. Dielectr. Electr. Insul. 7(6), 725–733 (2000). https://doi.org/10.1109/94.891982
Barclay, A.L.; Sweeney, P.J.; Dissado, L.A.; Stevens, G.C.: Stochastic modelling of electrical treeing: fractal and statistical characteristics. J. Phys. D. Appl. Phys. 23(12), 1536–1545 (1990). https://doi.org/10.1088/0022-3727/23/12/009
Parpal, J.L.; Crine, J.P.; Dang, C.: Electrical aging of extruded dielectric cables: a physical model. IEEE Trans. Dielectr. Electr. Insul. 4(2), 197–209 (1997). https://doi.org/10.1109/94.595247
Kupershtokh, A.L.; Charalambakos, V.; Agoris, D.; Karpov, D.I.: Simulation of breakdown in air using cellular automata with streamer to leader transition. J. Phys. D. Appl. Phys. 34(6), 936–946 (2001). https://doi.org/10.1088/0022-3727/34/6/315
Rodríguez-Serna, J.M.; Albarracín-Sánchez, R.; Carrillo, I.: An improved physical-stochastic model for simulating electrical tree propagation in solid polymeric dielectrics. Polymers (Basel) (2020). https://doi.org/10.3390/polym12081768
Jörgens, C.; Clemens, M.: “Modeling the electric field at interfaces and surfaces in high-voltage cable systems.” COMPEL – Int. J. Comput. Math. Electr. Electron. Eng. (2020). https://doi.org/10.1108/COMPEL-01-2020-0041
Satrazanis, C.; Mavrikakis, N.C.; Siderakis, K.G.; Danikas, M.G.: A short review and a comparison of simulation models of electrical treeing development in solid insulation. J. Eng. Sci. Technol. Rev. 13(4), 69–75 (2020)
Cai, Z.; Wang, X.; Li, L.; Hong, W.: Electrical treeing: a phase-field model. Extrem. Mech. Lett. 28, 87–95 (2019). https://doi.org/10.1016/j.eml.2019.02.006
Jayakrishnan, A.; Kavitha, D.; Arthi, A.; Nagarajan, N.; Balachandran, M.: Simulation of electric field distribution in nanodielectrics based on XLPE. Mater. Today Proc. 3(6), 2381–2386 (2016). https://doi.org/10.1016/j.matpr.2016.04.151
Velasco, J.; Frascella, R.; Albarracín, R.; Burgos, J.; Dong, M.; Ren, M.; Yang, L.: Comparison of positive streamers in liquid dielectrics with and without nanoparticles simulated with finite-element software. Energies 11(2), 361 (2018)
Isa, M.A.M., et al.: Investigation on partial discharge activities in cross-linked polyethene power cable using finite element analysis. J. Phys. Conf. Ser. 1432, 012024 (2020). https://doi.org/10.1088/1742-6596/1432/1/012024
Sadiku, M.N.: Elements of Electromagnetics. Oxford University Press, New York (2007)
Kawai, T.; Muto, H.; Hirotsu, K.; Nakatsuka, T.: A study of treeing phenomena in the development of insulation for 500 kV XLPE cables. IEEE Trans. Dielectr. Electr. Insul. 5(5), 695–706 (1998)
Murata, Y.; Katakai, S.; Kanaoka, M.: Impulse breakdown superposed on ac voltage in XLPE cable insulation. IEEE Trans. Dielectr. Electr. Insul. 3(3), 361–365 (1996). https://doi.org/10.1109/94.506207
Ying, L.; Xiaolong, C.: Electrical tree initiation in XLPE cable insulation by application of DC and impulse voltage. IEEE Trans. Dielectr. Electr. Insul. 20(5), 1691–1698 (2013). https://doi.org/10.1109/TDEI.2013.6633699
Karafyllidis, I.; Danikas, M.G.; Thanailakis, A.; Bruning, A.M.: Simulation of electrical tree growth in solid insulating materials. Electr. Eng. 81(3), 183–192 (1998). https://doi.org/10.1007/BF01236238
Vardakis, G.; Danikas, M.: Simulation of electrical tree propagation in a solid insulating material containing spherical insulating particle of a different permittivity with the aid of cellular automata. Facta Univ. - Ser. Electron. Energ. 17(3), 377–389 (2011). https://doi.org/10.2298/fuee0403377v
El-Zein, A.; Talaat, M.; El Bahy, M.: A numerical model of electrical tree growth in solid insulation. IEEE Trans. Dielectr. Electr. Insul. 16(6), 1724–1734 (2009). https://doi.org/10.1109/TDEI.2009.5361596
Schurch, R.; González, C.; Aguirre, P.; Zuniga, M.; Rowland, S. M.; Iddrissu, I.: “Calculating the Fractal Dimension From 3D Images of Electrical Trees,” In: The 20th International Symposium on High Voltage Engineering, Buenos Aires, Argentina, August 27 – September 01, pp. 4–9, (2017)
Schurch, R.; Rowland, S.; Bradley, R.; Withers, P.: Imaging and analysis techniques for electrical trees using X-ray computed tomography. IEEE Trans. Dielectr. Electr. Insul. 21(1), 53–63 (2014). https://doi.org/10.1109/TDEI.2013.003911
Kudo, K.: Fractal analysis of electrical trees. IEEE Trans. Dielectr. Electr. Insul. 5(5), 713–727 (1998). https://doi.org/10.1109/94.729694
Drissi-Habti, M.; Raj-Jiyoti, D.; Vijayaraghavan, S.; Fouad, E.C.: Numerical simulation for void coalescence (water treeing) in XLPE insulation of submarine composite power cables. Energies 13(20), 5472 (2020). https://doi.org/10.3390/en13205472
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Vidya, M.S., Sunitha, K., Ashok, S. et al. A Mathematical Modeling Approach to Characterize the Growth of the Electrical Tree in XLPE Insulation Under Lightning Impulse Overvoltage. Arab J Sci Eng 47, 14293–14304 (2022). https://doi.org/10.1007/s13369-022-06739-z
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DOI: https://doi.org/10.1007/s13369-022-06739-z