PERTANIKA JOURNAL OF SCIENCE AND TECHNOLOGY

 

e-ISSN 2231-8526
ISSN 0128-7680

Home / Regular Issue / JST Vol. 31 (4) Jul. 2023 / JST-3912-2022

 

Self-Consistent Positive Streamer-Leader Propagation Model Based on Finite Element Method (FEM) and Voltage Distortion Method (VDM)

Ziwei Ma, Jasronita Jasni, Mohd Zainal Abidin Ab Kadir and Norhafiz Azis

Pertanika Journal of Science & Technology, Volume 31, Issue 4, July 2023

DOI: https://doi.org/10.47836/pjst.31.4.30

Keywords: COMSOL, FEM, leader progression model, space charge, streamer, voltage distortion method

Published on: 3 July 2023

Researchers have worked on positive leader propagation models and proposed different theoretical and numerical approaches. The charge simulation method (CSM) has traditionally been chosen to model the quasi-static electric field of each stage of leader propagation. The biggest drawback of the CSM is that the calculation is complicated and time-consuming when dealing with asymmetric electric field structures. On the contrary, the finite element method (FEM) is more suitable and reliable for solving electrostatic field problems with asymmetric and complex boundary conditions, avoiding the difficulties of virtual charge configuration and electric field calculation under complex boundary conditions. This paper modeled a self-consistent streamer-leader propagation model in an inverted rod-plane air gap based on FEM and the voltage distortion method (VDM). The voltage distortion coefficient was analyzed to calculate the streamer length and space charge. The physical dynamic process of the discharge was simulated with the help of COMSOL Multiphysics and MATLAB co-simulation technology. The results show that the initial voltage of the first corona is -1036 kV, close to the experiment value of -1052 kV. The breakdown voltage of -1369 kV is highly consistent with the experimental value of -1365 kV. The largest streamer length is 2.72 m, slightly higher than the experimental value of 2.3 m. The leader velocity is 2.43×104 m/s, close to the experiment value of 2.2×104 m/s. This model has simple calculations and can be used in complex electrode configurations and arbitrary boundary conditions without simplifying the model structure, making the model more flexible.

  • Arevalo, L., Cooray, V., Wu, D., & Jacobson, B. (2012). A new static calculation of the streamer region for long spark gaps. Journal of Electrostatics, 70(1), 15-19. https://doi.org/10.1016/j.elstat.2011.07.013

  • Becerra, M. (2013). Glow corona generation and streamer inception at the tip of grounded objects during thunderstorms: Revisited. Journal of Physics D: Applied Physics, 46(13), Article 135205. https://doi.org/10.1088/0022-3727/46/13/135205

  • Becerra, M., & Cooray, V. (2006a). A simplified physical model to determine the lightning upward connecting leader inception. IEEE Transactions on Power Delivery, 21(2), 897-908. https://doi.org/10.1109/TPWRD.2005.859290

  • Becerra, M., & Cooray, V. (2006b). A self-consistent upward leader propagation model. Journal of Physics D: Applied Physics, 39(16), 3708-3715. https://doi.org/10.1088/0022-3727/39/16/028

  • Bondiou, A., & Gallimberti, I. (1994). Theoretical modelling of the development of the positive spark in long gaps. Journal of Physics D: Applied Physics, 27(6), 1252-1266. https://doi.org/10.1088/0022-3727/27/6/024

  • Brezmes, A. O., & Breitkopf, C. (2014). Simulation of inductively coupled plasma with applied bias voltage using COMSOL. Vacuum, 109, 52-60. https://doi.org/10.1016/j.vacuum.2014.06.012

  • Chen, S., He, H., Zou, Y., He, J., & Chen, W. (2016, September 19-22). Simulation of corona space charge generated from the ±800kV UHVDC overhead transmission line in a thunderstorm. [Paper presentation]. 2016 IEEE International Conference on High Voltage Engineering and Application (ICHVE), Chengdu, China. https://doi.org/10.1109/ICHVE.2016.7800706

  • Cigre, W. G. (2021). Procedures for Estimating the Lightning Performance of Transmission Lines – New Aspects. CIGRE.

  • Cooray, V. (2014). The Lightning Flash (2nd ed.). Institution of Engineering and Technology.

  • Diaz, O., Cooray, V., & Arevalo, L. (2018). Numerical modeling of electrical discharges in long air gaps tested with positive switching impulses. IEEE Transactions on Plasma Science, 46(3), 611-621. https://doi.org/10.1109/TPS.2018.2802039

  • Ding, Y., Lv, F., Zhang, Z., Liu, C., Geng, J., & Xie, Q. (2016). Discharge Simulation of typical air gap considering dynamic boundary and charge accumulation. IEEE Transactions on Plasma Science, 44(11), 2615-2621. https://doi.org/10.1109/TPS.2016.2600179

  • El-Zein, A., Talaat, M., & Samir, A. (2018). Positive streamer in gases: Physical approach from low to high energies. Vacuum, 156, 469-474. https://doi.org/10.1016/j.vacuum.2018.07.051

  • Gallimberti, I., Bacchiega, G., Bondiou-Clergerie, A., & Lalande, P. (2002). Fundamental processes in long air gap discharges. Comptes Rendus Physique, 3(10), 1335-1359. https://doi.org/10.1016/S1631-0705(02)01414-7

  • Gao, J., Wang, L., Li, G., Fang, Y., Song, B., Xiao, B., & Liu, K. (2020). Discharge of air gaps during ground potential live-line work on transmission lines. Electric Power Systems Research, 187, Article 106519. https://doi.org/10.1016/j.epsr.2020.106519

  • Goelian, N., Lalande, P., Bondiou-Clergerie, A., Bacchiega, G. L., Gazzani, A., & Gallimberti, I. (1997). A simplified model for the simulation of positive-spark development in long air gaps. Journal of Physics D: Applied Physics, 30(17), 2441-2452. https://doi.org/10.1088/0022-3727/30/17/010

  • Gu, J., He, K., Yu, H., Chen, W., Bian, K., & Shi, W. (2020, September 6-10). Effect of space charge on lightning shielding performance of UHVDC transmission line under lightning downward leader. [Paper presentation]. 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), Beijing, China. https://doi.org/10.1109/ICHVE49031.2020.9279506

  • Gu, S., Chen, W., Chen, J., He, H., & Qian, G. (2010). Observation of the streamer–leader propagation processes of long air-gap positive discharges. IEEE Transactions on Plasma Science, 38(2), 214-217. https://doi.org/10.1109/TPS.2009.2037004

  • Gu, S., Xiang, N., Chen, J., He, H., Xie, S., & Chen, W. (2012, September 2-7). Observation of 3m rod-rod discharges under switching impulse voltage. [Paper presentation]. 2012 International Conference on Lightning Protection (ICLP), Vienna, Australia. https://doi.org/ 0.1109/ICLP.2012.6344360

  • He, H., He, J., Chen, W., Xie, S., Xiang, N., Chen, J., & Gu, S. (2012). Comparison of positive leader propagation in rod–plane and inverted rod-plane gaps. IEEE Transactions on Plasma Science, 40(1), 22-28. https://doi.org/ 10.1109/TPS.2011.2172002

  • Hnatiuc, B., Sabau, A., & Astanei, D. (2019). Classic spark simulation using COMSOL software. IOP Conference Series: Materials Science and Engineering, 591, Article 012050. https://doi.org/10.1088/1757-899X/591/1/012050

  • Lalande, P., Bondiou-Clergerie, A., Bacchiega, G., & Gallimberti, I. (2002). Observations and modeling of lightning leaders. Comptes Rendus Physique, 3(10), 1375-1392. https://doi.org/10.1016/S1631-0705(02)01413-5

  • Les Renardières Group. (1973). Research on Long Air Gap Discharges at Les Renardières. https://e-cigre.org/publication/ELT_023_3-research-on-long-air-gap-discharges-at-les-renardieres

  • Les Renardières Group. (1974). Research on Long Air Gap Discharges at Les Renardières:1973 Results. https://e-cigre.org/publication/ELT_023_3-research-on-long-air-gap-discharges-at-les-renardieres

  • Li, Z., Zeng, R., Yu, Z., Chen, S., Liao, Y., & Li, R. (2013). Research on the upward leader emerging from transmission line by laboratory experiments. Electric Power Systems Research, 94, 64-70. https://doi.org/10.1016/j.epsr.2012.05.016

  • Mohammadi, R., Vahidi, B., & Rahiminejad, A. (2019). Estimation of HVDC transmission lines shielding failure using LPM method and an adapted SLIM model. IET Science, Measurement & Technology, 13(9), 1345-1351. https://doi.org/10.1049/iet-smt.2018.5180

  • Naidu, M. S., & Kamaraju, V. (2013). High voltage engineering. McGraw-Hill Education (India) Pte Ltd.

  • Nijdam, S., Teunissen, J., & Ebert, U. (2020). The physics of streamer discharge phenomena. Plasma Sources Science and Technology, 29(10), Article 103001. https://doi.org/10.1088/1361-6595/abaa05

  • Petrov, N. I., & Waters, R. T. (2021). Lightning to earthed structures: Striking distance variation with stroke polarity, structure geometry and altitude based on a theoretical approach. Journal of Electrostatics, 112, Article 103599. https://doi.org/10.1016/j.elstat.2021.103599

  • Ping, W., Yaxi, C., Xiuyuan, Y., Yujian, D., Jianghai, G., Fangcheng, L., Ling, J., & Weidong, S. (2022). Transformation characteristics of large-size ball-plate gap discharge under positive polarity operating impact at an altitude of 2200m. Chinese Journal of Electrical Engineering, 1-11. Advance online publication. https://kns.cnki.net/kcms/detail/11.2107.TM.20220708.1730.031.html

  • Rizk, F. A. M. (1989). A model for switching impulse leader inception and breakdown of long air-gaps. IEEE Transactions on Power Delivery, 4(1), 596-606. https://doi.org/10.1109/61.19251

  • Rizk, F. A. M. (2009). Modeling of proximity effect on positive leader inception and breakdown of long air gaps. IEEE Transactions on Power Delivery, 24(4), 2311-2318. https://doi.org/10.1109/TPWRD.2009.2027494

  • Rizk, F. A. M. (2020). New approach for assessment of positive streamer penetration of long air gaps under impulse voltages. IEEE Transactions on Dielectrics and Electrical Insulation, 27(3), 791-798. https://doi.org/10.1109/TDEI.2020.008588

  • Rodrigues, E., Pontes, R., Bandeira, J., & Aguiar, V. (2019). Analysis of the incidence of direct lightning over a HVDC transmission line through EFD model. Energies, 12(3), Article 555. https://doi.org/10.3390/en12030555

  • Talaat, M., El-Zein, A., & Samir, A. (2019). Numerical and simulation model of the streamer inception at atmospheric pressure under the effect of a non-uniform electric field. Vacuum, 160, 197-204. https://doi.org/10.1016/j.vacuum.2018.11.037

  • Tao, Y., Xiaotian, W., Wenxia, S., & Ming, Y. (2022). Space charge criterion of the initial streamer for the stable inception of positive upleader under lightning strikes. Chinese Journal of Electrical Engineering, 1-13. Advance online publication. https://kns.cnki.net/kcms/detail/11.2107.tm.20220419.1016.004.html

  • Wang, X., He, J., Yu, Z., Zeng, R., & Rachidi, F. (2016). Influence of ground wire on the initiation of upward leader from 110 to 1000 kV AC phase line. Electric Power Systems Research, 130, 103-112. https://doi.org/10.1016/j.epsr.2015.08.022

  • Xu, Y., & Chen, M. (2013). A 3-D self-organized leader propagation model and its engineering approximation for lightning protection analysis. IEEE Transactions on Power Delivery, 28(4), 2342-2355. https://doi.org/10.1109/TPWRD.2013.2263846

  • Yang, N., Zhang, Q., Hou, W., & Wen, Y. (2017). Analysis of the lightning-attractive radius for wind turbines considering the developing process of positive attachment leader: Attractive radius for wind turbines. Journal of Geophysical Research: Atmospheres, 122(6), 3481-3491. https://doi.org/10.1002/2016JD026073

  • Zeng, R., Li, Z., Yu, Z., Zhuang, C., & He, J. (2013). Study on the influence of the dc voltage on the upward leader emerging from a transmission line. IEEE Transactions on Power Delivery, 28(3), 1674-1681. https://doi.org/10.1109/TPWRD.2013.2252371

  • Zhou, Q., Liu, C., Bian, X., Lo, K. L., & Li, D. (2018). Numerical analysis of lightning attachment to wind turbine blade. Renewable Energy, 116, 584-593. https://doi.org/10.1016/j.renene.2017.09.086

  • Zixin, G., Qingmin, L., Wanshui, Y., Hongbo, L., Li, Z., & Wah Hoon, S. (2020). The dynamic critical length criterion of initial streamer for the stable upward leader inception under negative lightning strikes. Proceedings of the CSEE, 40(5), 1713-1721. https://doi.org/10.13334/j.0258-8013.pcsee.190881