In this paper, an inverse procedure algorithm is proposed in the time domain to evaluate lightning return stroke currents along a lightning channel using measured magnetic flux density at an observation point while the current velocity along a lightning channel is assumed to be a height dependent variable. The proposed method considers all field components and it can evaluate the full shape of currents and the current velocity at different heights along a lightning channel. Moreover, a sample of measured magnetic flux density from a triggered lightning experiment is applied to the proposed algorithm and the evaluated currents and current velocities are validated using a measured channel base current and magnetic flux density at another observation point.
Mohd Zainal Abidin Ab Kadir,
"Evaluation of Lightning Current and Velocity Profiles Along Lightning Channel Using Measured Magnetic Flux Density," Progress In Electromagnetics Research,
Vol. 130, 473-492, 2012. doi:10.2528/PIER12060612
1. Rakov, V., M. Uman, and K. Rambo, "A review of ten years of triggered-lightning experiments at Camp Blanding, Florida," Atmospheric Research, Vol. 76, 503-517, 2005. doi:10.1016/j.atmosres.2004.11.028
2. Vujevic, S., D. Lovric, and I. Juric-Grgic, "Least squares estimation of Heidler function parameters," European Transactions on Electrical Power, Vol. 21, 329-344, 2011. doi:10.1002/etep.445
3. Lovric, D., S. Vujevic, and T. Modric, "On the estimation of Heidler function parameters for reproduction of various standardized and recorded lightning current waveshapes ," European Transactions on Electrical Power, 2011. doi:10.1002/etep.445
4. Andreotti, A., D. Assante, S. Falco, and L. Verolino, "An improved procedure for the return stroke current identification," IEEE Transactions on Magnetics, Vol. 41, 1872-1875, 2005. doi:10.1109/TMAG.2005.846283
5. Andreotti, A., U. De Martinis, and L. Verolino, "An inverse procedure for the return stroke current identification," IEEE Transactions on Electromagnetic Compatibility, Vol. 43, 155-160, 2002. doi:10.1109/15.925535
6. Andreotti, A., F. Delfino, P. Girdinio, and L. Verolino, "An identification procedure for lightning return strokes," Journal of Electrostatics, Vol. 51, 326-332, 2001. doi:10.1016/S0304-3886(01)00097-3
7. Ceclan, A., D. Micu, and L. Czumbil, On a return stroke lightning identification procedure by inverse formulation and regularization, IEEE Conference on Electromagnetic Field Computation (CEFC), 1, Biennial, 2010.
8. Popov, M., S. He, and R. Thottappillil, "Reconstruction of lightning currents and return stroke model parameters using remote electromagnetic fields," Journal of Geophysical Research, Vol. 105, 24469-24481, 2000. doi:10.1029/2000JD900283
9. Uman, M. A. and D. K. McLain, "Lightning return stroke current from magnetic and radiation field measurements," Journal of Geophysical Research, Vol. 75, 5143-5147, 1970. doi:10.1029/JC075i027p05143
10. Uman, M. A., D. K. McLain, and E. P. Krider, "The electromagnetic radiation from a finite antenna," Amer. J. Phys., Vol. 43, 33-38, 1975. doi:10.1119/1.10027
11. Rachidi, F. and C. Nucci, "On the Master, Uman, Lin, Standler and the modi¯ed transmission line lightning return stroke current models ," Journal of Geophysical Research, Vol. 95, 20389-20393, 1990. doi:10.1029/JD095iD12p20389
12. Shoory, A., F. Rachidi, M. Rubinstein, R. Moini, and S. H. Hesamedin Sadeghi, "Analytical expressions for zero-crossing times in lightning return-stroke engineering models," IEEE Transactions on Electromagnetic Compatibility, Vol. 51, 963-974, 2009. doi:10.1109/TEMC.2009.2029699
13. Rachidi, F., J. Bermudez, M. Rubinstein, and V. Rakov, "On the estimation of lightning peak currents from measured fields using lightning location systems ," Journal of Electrostatics, Vol. 60, 121-129, 2004. doi:10.1016/j.elstat.2004.01.010
15. Cooray, V. and The Lightning Flash, , IET Press, 2003.
16. Andreotti, A., F. Delfino, P. Girdinio, and L. Verolino, "A field-based inverse algorithm for the identification of different height lightning return strokes," The International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), Vol. 20, 724-731, 2011. doi:10.1108/03321640110393716
17. Rakov, V., Characterization of lightning electromagnetic fields and their modeling, 14th Int. Zurich Symposium on Electromagnetic Compatibility, 3-16, Zurich, 2001.
18. Rakov, V. and M. Uman, "Review and evaluation of lightning return stroke models including some aspects of their application," IEEE Transactions on Electromagnetic Compatibility, Vol. 40, 403-426, 1998. doi:10.1109/15.736202
19. Baba, Y., S. Miyazaki, and M. Ishii, "Reproduction of lightning electromagnetic field waveforms by engineering model of return stroke ," IEEE Transactions on Electromagnetic Compatibility, Vol. 46, 130-133, 2004. doi:10.1109/TEMC.2004.823625
20. Bruce, C. E. R. and R. H. Golde, "The lightning discharge," J. Inst. Elect. Eng., Part 2, Vol. 88, 487-520, 1941.
21. Uman, M. A. and D. K. McLain, "Magnetic field of lightning return stroke," Journal of Geophysical Research, Vol. 74, 6899-6910, 1969. doi:10.1029/JC074i028p06899
22. Jones, R. D., "On the use of tailored return-stroke current representations to simplify the analysis of lightning effects on systems," IEEE Transactions on Electromagnetic Compatibility, 95-96, 1977. doi:10.1109/TEMC.1977.303552
23. Pierce, E. T., "Triggered lightning and some unsuspected lightning hazards (Lightning triggered by man and lightning hazards)," ONR Naval Res. Rev., Vol. 25, 1972.
24. Djalel, D., H. Ali, and C. Benachiba, "Coupling phenomenon between the lightning and high voltage networks," Proceedings of Word Academy of Science, Engineering and Technology (PWASET), Vol. 21, 95-101, 2007.
25. Heidler, F. and Analytische blitzstromfunktion zur LEMP-berechnung, 18th ICLP, Munich, Germany, 1985.
26. Diendorfer, G. and M. Uman, "An improved return stroke model with specified channel-base current," Journal of Geophysical Research --- Atmospheres, Vol. 95, 13621-13644, 1990. doi:10.1029/JD095iD09p13621
27. Nucci, C. A., G. Diendorfer, M. Uman, F. Rachidi, and C. Mazzetti, "Lightning return-stroke models with channel-base specified current: A review and comparison ," Journal of Geophysical Research, Vol. 95, 20395-20408, 1990. doi:10.1029/JD095iD12p20395
28. Bizjaev, A., V. Larionov, and E. Prokhorov, Energetic characteristics of lightning channel, 20th Int. Conf. Lightning Protection, 1.1, Switzerland, 1990.
29. Dubovoy, E., V. Pryazhinsky, and G. Chitanava, "Calculation of energy dissipation in lightning channel," Meteorologiya i Gidrologiya, Vol. 2, 40-45, 1991.
30. Moini, R., S. Sadeghi, and B. Kordi, "An electromagnetic model of lightning return stroke channel using electric field integral equation in time domain," Engineering Analysis with Boundary Elements, Vol. 27, 305-314, 2003. doi:10.1016/S0955-7997(02)00118-2
31. Baba, Y. and V. Rakov, "Electromagnetic models of the lightning return stroke," J. Geophys. Res., Vol. 112, 1-17, 2007. doi:10.1029/2006JD007222
33. Da Frota Mattos, M. A. and C. Christopoulos, "A nonlinear transmission line model of the lightning return stroke," IEEE Transactions on Electromagnetic Compatibility, Vol. 30, 401-406, 1988. doi:10.1109/15.3321
34. Gomes, C. and V. Cooray, "Concepts of lightning return stroke models," IEEE Transactions on Electromagnetic Compatibility, Vol. 42, 82-96, 2000. doi:10.1109/15.831708
35. Izadi, M., M. Z. A. Ab Kadir, C. Gomes, and W. F. W. Ahmad, "Numerical expressions in time domain for electromagnetic fields due to lightning channels ," International Journal of Applied Electromagnetics and Mechanics, Vol. 37, 275-289, 2011.
36. Nucci, C., "Lightning-induced voltages on overhead power lines. Part I: Return stroke current models with specified channel-base current for the evaluation of the return stroke electromagnetic fields ," Electra, Vol. 161, 75-102, 1995.
37. Rakov, V. and A. Dulzon, "Calculated electromagnetic fields of lightning return stroke," Tekh. Elektrodinam, Vol. 1, 87-89, 1987.
38. Nucci, C. A., C. Mazzetti, F. Rachidi, and M. Ianoz, "On lightning return stroke models for LEMP calculations," Proc. 19th Int. Conf. Lightning Protection, 463-469, Austria, 1988.
39. Baba, Y. and M. Ishii, "Lightning return-stroke model incorporating current distortion," IEEE Transactions on Electromagnetic Compatibility, Vol. 44, 476-478, 2002. doi:10.1109/TEMC.2002.801770
40. Heidler, F., "Travelling current source model for LEMP calculation," Proc. of the 6th Symposium and Technical Exhibition on Electromagnetic Compability, 157-162, Zurich, 1985.
41. Izadi, M., M. Z. A. Ab Kadir, C. Gomes, and W. F. W. Ahmad, "An analytical second-FDTD method for evaluation of electric and magnetic fields at intermediate distances from lightning channel," Progress In Electromagnetic Research, Vol. 110, 329-352, 2010. doi:10.2528/PIER10080801
42. Wang, V. R. and M. Uman, "Observed leader and return-stroke propagation characteristics in the bottom 400m of a rockettriggered Iightning channel," triggered Iightning channel, Vol. 104, 14369-14376, 1999.
43. Olsen, R. C., D. M. Jordan, V. A. Rakov, M. A. Uman, and N. Grimes, "Observed two-dimensional return stroke propagation speeds in the bottom 170m of rocket-triggered lightning channel," J. Geophys. Res., Vol. 31, 2004.
44. Thottappillil, R. and V. Rakov, "Review of three equivalent approaches for computing electromagnetic fields from an extending lightning discharge," Journal of Lightning Research, Vol. 1, 90-110, 2007.
45. Kreyszig, E., "Advanced Engineering Mathematics," Wiley, India, 2007.
46. Engelbrecht, A. P., Fundamentals of Computational Swarm Intelligence, 1st Ed., Wiley Chichester, UK, 2005.
47. Clerc, M., Particle Swarm Optimization, Wiley-ISTE, 2006.
48. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, 397-407, 2004. doi:10.1109/TAP.2004.823969
49. Zaharis, Z. D., S. K. Goudos, and T. V. Yioultsis, "Application of boolean PSO with adaptive velocity mutation to the design of optimal linear antenna arrays excited by uniformamplitude current distribution ," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 10, 1422-1436, 2011.
50. Li, Y., S. Sun, F. Yang, and L. J. Jiang, "Design of dual-band slotted patch hybrid couplers based on PSO algorithm," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 17-18, 2409-2419, 2011. doi:10.1163/156939311798806220
51. Wang, D., H. Zhang, T. Xu, H. Wang, and G. Zhang, "Design and optimization of equal split broadband microstrip Wilkinson power divider using enhanced Particle Swarm Optimization algorithm," Progress In Electromagnetics Research, Vol. 118, 321-334, 2011. doi:10.2528/PIER11052303
52. Wang, W.-B., Q. Feng, and D. Liu, "Application of chaotic Particle Swarm Optimization Algorithm to pattern synthesis of antenna arrays ," Progress In Electromagnetics Research, Vol. 115, 173-189, 2011.
53. Wang, J., B. Yang, S. H. Wu, and J. S. Chen, "A novel binary Particle Swarm Optimization with feedback for synthesizing thinned planar arrays," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 14-15, 1985-1998, 2011. doi:10.1163/156939311798071965
54. Naghavi, A. H., M. Tondro-Aghmiyouni, M. Jahanbakht, and A. A. Lotfi Neyestanak, "Hybrid wideband microstrip Wilkinson power divider based on lowpass filter optimized using Particle Swarm method ," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 14-15, 1877-1886, 2010.
55. Izadi, M., M. Z. A. Ab Kadir, and C. Gomes, "Evaluation of electromagnetic fields associated with inclined lightning channel using second order FDTD-hybrid methods," Progress In Electromagnetics Research, Vol. 177, 209-236, 2011.
56. Izadi, M., M. Z. Ab Kadir, C. Gomes, and W. F. H. W. Ahmad, "Analytical expressions for electromagnetic fields associated with the inclined lightning channels in the time domain ," Electric Power Components and Systems, Vol. 40, 414-438, 2012. doi:10.1080/15325008.2011.639130