Lightning Return Stroke Models – A Critical Review Based On Comparison Of Lightning Parameters

Distributed Circuit Models, Electro-Magnetic Models, Engineering Models, Gas Dynamic Models, Lightning Attachment Models, Return stroke, Stepped leader.

ABSTRACT

Lightning is an intense bright discharge of the ionized sky or a thin channel of luminous spark directed towards the earth through the air that could present considerable risk to mankind and also possibly cause significant damage to buildings, monuments, transmission lines etc. Hence, it is necessary to provide appropriate protection against such large currents and strong electromagnetic radiation that are created from lightning phenomenon. A domain of considerable significance that continues to present considerable challenges to the scientific fraternity in the field of lightning protection is in understanding the underlying physical development process of lightning and the consequent disaster mechanism. Researchers have carried out diverse experimental analysis to ascertain the role and characteristics of lightning which occurs due to discharge of the large amount of charge accumulated in the cloud. Lightning discharge occurring between the nearest clouds called Cloud-to-Cloud (CC) flash or discharges which travel as a stepped leader which reaches earth forming Cloud-to-Ground (CG) flash are of significant interest. The hazards caused by the lightning are invariably modelled and inferred as a consequence of the resulting return stroke formed during the process of stepped leader descending on to the earth or a grounded system. In this context, several researchers have developed and postulated models by representing properties of lightning return stroke utilizing experimental data such as time-based changes in the base current and its derivatives, return stroke speed and electromagnetic field etc to a substantial degree of success. Though return models based to gas dynamics, electromagnetics, transmission line, hybrid and leader attachment representations has been widely utilized by the scientific community recently, there has been renewed focus in understanding and implementing modelling of lightning return strokes based on hybrid models and representation based on leader attachment methods. This research study focuses on providing a comprehensive overview and detailed comparison of various categories in lightning return stroke models, in addition to appropriate assumptions, merits and limitations to facilitate better understanding on characteristics of lightning phenomenon and provide vital clues into implementation of return stroke modelling.

REFERENCES

[1] V. Cooray, “The lightning flash,” IET, 2014.
[2] Shi, Wei, Qingmin Li, and Li Zhang, “A stepped leader model for lightning including charge distribution in branched channels,” J. App. Phys., Vol. 116, no. 10, (2014).
[3] A. Gayen, A. Dhar, B. N. Das, and D. R. Poddar, “A Simplified Approach to Understanding of the Phenomenon of Cloud to Ground Lightning and Modeling of Return Stroke Current,” Proc. 9th Int. Conf. Electromagn. Interf. Compat. (INCEMIC), no. 1, pp. 258–362, (2006).
[4] M.A. Uman, “The Lightning Discharge,” San Diego, CA: Acadamic, 1987.
[5] V. Cooray, “Lightning electromagnetics,” IET, 2012.
[6] C. Gomes and V. Cooray, “Concepts of lightning return stroke models,” IEEE Trans. Electromagn. Compat., Vol. 42, no. 1, pp. 82–96, (2000).
[7] Y. Lin, M. Uman, and R. Standler, “Lightning return stroke models,” J. Geophys. Res., Vol. 85, no. 9, pp. 1571–1583, 1980.
[8] V. A. Rokov, and M. A. Uman, “Lightning: physics and effects,” Cambridge University Press, 2003.
[9] V. A. Rakov and M. A. Uman, “Review and evaluation of lightning return stroke models including some aspects of their application,” IEEE Trans. Electromagn. Compat., Vol. 40, no. 4 PART 2, pp. 403–426, 1998.
[10] S. I. Drabkina, “The theory of the development of the spark channel,” J. Exper. Theoret. Phys., Vol. 21, pp. 473–483, 1951. (Engl. transl. AERE LIB/Trans. 621, Harwell, Berkshire, U.K.).
[11] S. I. Braginski, “Theory of the Development of a Spark Channel,” J. Exptl. Theor. Phys., Vol. 34, no. 34, pp. 1548–1557, 1958.
[12] R. D. Hill, “Channel heating in return-stroke lightning,” J. Geophys. Res., Vol. 76, no. 3, p. 637, 1971.
[13] R. D. Hill, “Energy dissipation in lightning,” J. Geophys. Res., Vol. 82, pp. 4967–4968, 1977.
[14] E. P. Krider, G. A. Dawson, and M. A. Uman, “The peak power and energy dissipation in a single-stroke lightning flash,” J. Geophys. Res., Vol. 73, pp. 3335–3339, (1968).
[15] M. N. Plooster, “Shock Waves from Line Sources. Numerical Solutions and Experimental Measurements,” Phys. Fluids, Vol. 13, no. 11, p. 2665-2675, 1970.
[16] M. N. Plooster, “Numerical Simulation of Spark Discharges in Air,” Phys. Fluids, Vol. 14, no. 10, p. 2111-2123, 1971.
[17] M. N. Plooster, “Numerical Model of the Return Stroke of the Lightning Discharge,” Phys. Fluids, Vol. 14, no. 10, pp. 2124–2133, 1971.
[18] J. E. Borovsky, “Lightning energetics: Estimates of energy dissipation in channels, channel radii, and channel-heating risetimes,” J. Geophys. Res., Vol. 103, pp. 11537–11553, 1998.
[19] A. H. Paxton, R. L. Gardner, and L. Baker, “Lightning return stroke. A numerical calculation of the optic radiation,” Phys. Fluids, Vol. 29, no. 8, pp. 2736–2741, 1986.
[20] E. I. Dubovoy, V. I. Pryazhinsky, and V. E. Bondarenko, “Numerical modelling of the gasodynamical parameters of a lightning channel and radio-sounding reflection,” Izvestiya AN SSSR-Fizika Atmosfery I Okeana, Vol. 27, pp. 194–203, 1991.
[21] A. S. Podgorski and J. A. Landt, “Three-Dimensional Time Domain Modeling of Lightning,” IEEE Power Eng. Rev., Vol. PER-7, no. 7, pp. 72–73, 1987.
[22] R. Moini, V. A. Rakov, M. A. Uman and B. Kordi, “An antenna theory model for the lightning return stroke,” Proc. 12th Int. Zurich Symp. Electromag. Compat., Zurich, Switzerland, pp. 149–152. Feb. 1997.
[23] Baba. Yoshihiro and V. A. Rakov, “Electromagnetic models of the lightning return stroke,” J. Geophys. Res.: Atmospheres, Vol. 112, no. D4, 2007.
[24] Shoory, Abdolhamid, Rouzbeh Moini, SH Hesam Sadeghi and V. A. Rakov, “Analysis of lightning-radiated electromagnetic fields in the vicinity of lossy ground,” IEEE Trans. Electromagn. Compat., Vol. 47, no. 1, pp. 131-145, 2005.
[25] Y. Baba and M. Ishii, “Characteristics of electromagnetic return-stroke models,” IEEE Trans. Electromagn. Compat., Vol. 45, no. 1, pp. 129–135, 2003.
[26] J. E. Borovsky, “An electrodynamic description of lightning return strokes and dart leaders: Guided wave propagation along conducting cylindrical channels,” J. Geophys. Res., Vol. 100, no. D2, p. 2697, 1995.
[27] Chen, K, “Transient response of an infinite cylindrical antenna,” IEEE Trans. Antennas Propagat., Vol. 31, no. 1, pp. 170-172, 1983.
[28] CIGRE TF 33.01.03, “Lightning Exposure of Structures and Interception Efficiency of Air Terminals,” CIGRE Rep. 118, no. 3, Oct., p. 89, 1997.
[29] S. Visacro and F. H. Silveira, “Evaluation of current distribution along the lightning discharge channel by a hybrid electromagnetic model,” J. Electrostat., Vol. 60, no. 2-4, pp. 111-120, 2004.
[30] C. E. Baum and L. Baker, “Analytic return-stroke transmission-line model,” Light. Electromag., New York: Hemisphere, pp. 17–40, 1990.
[31] G. H. Price and E. T. Pierce, “The modelling of channel current in the lightning return stroke,” Radio Sci., Vol. 12, pp. 381–388, 1977.
[32] P. F. Little, “Transmission line representation of a lightning return stroke,” J. Phys. D: Appl. Phys., Vol. 11, pp. 1893–1910, 1978.
[33] N. Takagi and T. Takeuti, “Oscillating bipolar electric field changes due to close lightning return strokes,” Radio Sci., Vol. 18, pp. 391–398, 1983.
[34] D. W. Quinn, “Modeling of lightning,” Math. Comput. Simul., Vol. 29, no. 2, pp. 107–118, 1987.
[35] M. A. Da Frota Mattos and C. Christopoulos, “A nonlinear transmission line model of the lightning return stroke,” IEEE Trans. Electromagn. Compat., Vol. 30, no. 3, pp. 401–406, 1988.
[36] M. A. da F Mattos and C. Christopoulos, “A model of the lightning channel, including corona, and prediction of the generated electromagnetic fields,” J. Phys. D. Appl. Phys., Vol. 23, no. 1, pp. 40–46, 1990.
[37] M. V. Kostenko, “Electrodynamic characteristics of lightning and their influence on disturbances of high-voltage lines,” J. Geophys. Res. Atmos., Vol. 100, no. D2, pp. 2739–2747, 1995.
[38] V. Amoruso and F. Lattarulo, “The Electromagnetic Field of an Improved Lightning Return-Stroke Representation,” IEEE Trans. Electromagn. Compat., Vol. 35, no. 3, pp. 317–328, 1993.
[39] S. Visacro and A. De Conti, “A distributed-circuit return-stroke model allowing time and height parameter variation to match lightning electromagnetic field waveform signatures,” J. Geophys. Res. Lett., Vol. 32, no. 23, pp. 1–5, 2005.
[40] V. A. Rakov, “Some inferences on the propagation mechanisms of dart leaders and return strokes,” J. Geophys. Res.: Atmospheres, Vol. 103, no. D2, pp. 1879-1887, 1998.
[41] G. N. Oetzel, “Computation of the diameter of a lightning return stroke,” J. Geophys. Res., Vol. 73, no. 6, pp. 1889–1896, 1968.
[42] H. Norinder, “Quelques essais recents relatifs a¨ la determination des surtensions indirectes,” CIGRE, Paris, pp. 303, 29th Jun. – 8th Jul. 1939.
[43] C. E. R. Bruce and R. H. Golde, “The lightning discharge,” J. Inst. Elect. Eng., Vol. 88, pp. 487–520, 1941.
[44] R. Lundholm, “Spectral theory of quantum systems with exotic symmetries,” Ph.D. dissertation, KTH, Stockholm, Sweden, 1957.
[45] A. S. Dennis and E. T. Pierce, “The return stroke of the lightning flash to earth as a source of VLF atmospherics,” J. Res. Natl. Bur. Stand. Sect. D Radio Sci., Vol. 68D, no. 7, p. 777, 1964.
[46] M. A. Uman and D. K. Mclain, “Magnetic Field of Lightning Return Stroke,” J. Geophys. Res., Vol. 74, pp. 6899–6910, 1969.
[47] V. Cooray and R. E. Orville, “The effects of variation of current amplitude, current risetime and return stroke velocity along the return stroke channel on the electromagnetic fields generated by return strokes,” J. Geophys. Res., Vol. 95, no. D11, pp. 18617–18630, 1990.
[48] V. Rakov and A. A. Dulzon, “A modified transmission line model for lightning return stroke field calculations,” Proc. 9th Int. Symp. Electromagn., pp. 229–234, 1991.
[49] M. Master, Y. T. Lin, M. A. Uman and R. B. Standler, “Calculations of lightning return stroke electric and magnetic fields above ground,” J. Geophys. Res., Vol. 86, pp. 12127–12132, 1981.
[50] F. Rachidi, and C. A. Nucci, “On the Master, Uman, Lin, Standler and the modified transmission line lightning return stroke current models,” J. Geophys. Res.: Atmospheres, Vol. 95, no. D12, pp. 20389-20393, 1990.
[51] V. Cooray and N. Theethayi, “Effects of corona on pulse propagation along transmission lines with special attention to lightning return stroke models and return stroke velocity,” Proc. VIII Int. Symp. Light. Prot., Brazil, (2005).
[52] C. F. Wagner, “A new approach to the calculation of the lightning performance of transmission lines,” AIEE Trans., Vol. 75, pp. 1233–1256, 1956.
[53] F. Heidler, “Traveling current source model for LEMP calculation,” Proc. 6th Int. Symp. EMC, Zurich, Switzerland, 29F2, pp. 157–162, 1985.
[54] P. Hubert, “New model of lightning return stroke – confrontation with triggered lightning observations,” Proc. 10th Int. Aerospace and Ground Conf. Lightning and Static Electricity, pp. 211–215, Paris, 1985.
[55] V. Cooray, “A return stroke model,” Proc. Int. Conf. Lightning and Static Electricity, University of Bath, Sep. 1989.
[56] V. Cooray, “A model for the subsequent return strokes,” J. Electrostat., Vol. 30, pp. 343–354, 1993.
[57] G. Diendorfer and M. A. Uman, “An improved return stroke model with specified channel base current,” J. Geophys. Res., Vol. 95, pp. 13621–13644, 1990.
[58] R. Thottappillil, D. K. Mclain, M. A. Uman and G. Diendorfer, “Extension of Diendorfer-Uman lightning return stroke model to the case of a variable upward return stroke speed and a variable downward discharge current speed,” J. Geophys. Res., Vol. 96, pp. 17143–17150, 1991.
[59] R. Thottappillil and M. A. Uman, “Lightning return stroke model with heightvariable discharge time constant,” J. Geophys. Res., Vol. 99, pp. 22773– 22780, 1994.
[60] V. Cooray, “Predicting the spatial and temporal variation of the current, the speed and electromagnetic fields of subsequent return strokes,” IEEE Trans. Electromagn. Compat., Vol. 40, pp. 427–435, 1998.
[61] V. Cooray and V. Rakov, “A current generation type return stroke model that predicts the return stroke velocity,” J. Light. Res., Vol. 1, pp. 32–39, 2007.
[62] V. Cooray, R. Montano and V. Rakov, “A model to represent first return strokes with connecting leaders,” J. Electrostat., Vol. 40, pp. 97–109, 2004.
[63] V. Cooray, “A novel procedure to represent lightning return strokes – current dissipation return stroke models,” IEEE Trans. EMC, Vol. 51, pp. 748 – 755, 2009.
[64] A. J. Eriksson, “An improved electrogeometric model for transmission line shielding analysis,” IEEE Power Engg. Review., Vol. 2, no. 3, pp. 871–77, 1987.
[65] Hartono, Z. A., I. Robiah, and M. Darveniza, “A database of lightning damage caused by bypasses of air terminals on buildings in Kuala Lumpur, Malaysia,” 6th Int. Symp. Light. Protec. (SIPDA), Santos, Brazil, pp. 211 – 16, 2001.
[66] Mousa, Abdul M., “Proposed research on the collection volume method/field intensification method for the placement of air terminals on structures,” Power Engineering Society General Meeting, IEEE, Vol. 1, pp. 301-305, 2003.
[67] Hartono, Z. A., and I. Robiah, “The field intensification method (FIM): An assessment based on observed bypass data on real buildings in Malaysia,” Public comment submitted to the Australian standardization committee, EL-24, 2002.
[68] L. Dellera and E. Garbagnat, “Lightning strike simulation by means of the Leader Progression Model, Part I: Description of the model and evaluation of free-standing structures,” IEEE Trans. Power Deliv., Vol. 5, no. 4, pp. 2009-2022, 1990.
[69] L. Dellera and E. Garbagnati, “Lightning strike simulation by means of the Leader Progression Model: II. Exposure and shielding failure evaluation of overhead lines with assessment of application graphs,” IEEE Trans. Power Deliv., Vol. 5, no. 4, pp. 2023-2029, 1990.
[70] F. Rizk, “Modelling of transmission lines: exposure to direct lightning strokes,” IEEE Trans. Power Deliv., Vol. 5, no. 4, pp. 1983-1997, 1990.
[71] F. A. M. Rizk, “Modeling of Lightning Incidence to Tall Structures Part II: Application,” IEEE Trans. Power Deliv., vol. 9, no. 1, pp. 172–193, 1994.
[72] M. Becerra and V. Cooray, “A self-consistent upward leader propagation model,” J. Phys. D. Appl. Phys., Vol. 39, no. 16, pp. 3708–3715, 2006.
[73] M. Becerra and V. Cooray, “On the velocity of positive connecting leaders associated with negative downward lightning leaders,” J. Geophys. Res. Lett., Vol. 35, no. 2, 2008.
[74] V. Cooray, “The lightning flash,” IET, 2014.
[75] Shi, Wei, Qingmin Li, and Li Zhang, “A stepped leader model for lightning including charge distribution in branched channels,” J. App. Phys., Vol. 116, no. 10, 2014.
[76] A. Gayen, A. Dhar, B. N. Das, and D. R. Poddar, “A Simplified Approach to Understanding of the Phenomenon of Cloud to Ground Lightning and Modeling of Return Stroke Current,” Proc. 9th Int. Conf. Electromagn. Interf. Compat. (INCEMIC), no. 1, pp. 258–362, 2006.
[77] M.A. Uman, “The Lightning Discharge,” San Diego, CA: Acadamic, 1987.