Javor, Vesna

Rančić, Predrag D.

Digitale Bibliothek Thüringen

   Information Technology and Electrical  Engineering - Devices and Systems, Materials  and Technologies for the Future        Faculty of Electrical Engineering and Information Technology    Startseite / Index:  http://www.db-thueringen.de/servlets/DocumentServlet?id=14089 54. IWK Internationales Wissenschaftliches Kolloquium International Scientific Colloquium 07 - 10 September 2009 PROCEEDINGS Impressum  Herausgeber: Der Rektor der Technischen Universität llmenau  Univ.-Prof. Dr. rer. nat. habil. Dr. h. c. Prof. h. c. Peter Scharff  Redaktion: Referat Marketing   Andrea Schneider   Fakultät für Elektrotechnik und Informationstechnik  Univ.-Prof. Dr.-Ing. Frank Berger  Redaktionsschluss: 17. August 2009  Technische Realisierung (USB-Flash-Ausgabe):  Institut für Medientechnik an der TU Ilmenau  Dipl.-Ing. Christian Weigel  Dipl.-Ing. Helge Drumm  Technische Realisierung (Online-Ausgabe):  Universitätsbibliothek Ilmenau    Postfach 10 05 65  98684 Ilmenau  Verlag:   Verlag ISLE, Betriebsstätte des ISLE e.V.  Werner-von-Siemens-Str. 16  98693 llmenau   © Technische Universität llmenau (Thür.) 2009   Diese Publikationen und alle in ihr enthaltenen Beiträge und Abbildungen sind urheberrechtlich geschützt.   ISBN (USB-Flash-Ausgabe): 978-3-938843-45-1 ISBN (Druckausgabe der Kurzfassungen): 978-3-938843-44-4  Startseite / Index: http://www.db-thueringen.de/servlets/DocumentServlet?id=14089  CALCULATION OF LIGHTNING CHANNEL HEIGHT AND RETURN STROKE PROPAGATION SPEED FROM ELECTROMAGNETIC FIELD WAVEFORMS  Vesna Javor, Predrag D. Rancic  Faculty of Electronic Engineering, University of Nis, Serbia  ABSTRACT  For obtaining typically observed or measured light-ning electromagnetic field characteristics of the return stroke channel current different models can be used. Modified transmission line model with exponential decay with height, as an engineering model, and the functions earlier proposed by the authors for the channel-base current approximation, are used in this paper for lightning electric and magnetic field compu-tation. The relationships between the lightning chan-nel height, the return stroke propagation speed, the distance from the channel-base and time of the dis-continuity appearance in electric and magnetic field waveforms are presented in this paper. These rela-tionships can be used for obtaining any of these quan-tities of interest from other three experimentally de-termined or estimated. For different lightning channel heights the electric and magnetic field at ground surface points at different distances from the channel-base are presented in the paper for the chosen return stroke propagation speed.  Index Terms - Lightning, electromagnetic field, antenna, return stroke, channel-base current function  1. INTRODUCTION Different lightning return stroke channel models are described in [1]. Modified transmission line model with exponential decay with height (MTLE) [2] is often used as an engineering model for lightning electromagnetic field (LEMF) calculations. The func-tion CBC proposed in [3] and the function NCBC proposed in [4] for the approximation of channel-base currents, are used in this paper. Their parameters choice is analyzed in detail in [3] and [4]. The CBC function is simpler, but NCBC can better reproduce the channel-base current characteristics of the function proposed in [5] and often used by other authors. Relationships between the lightning channel height, the return stroke propagation speed, the dis-tance from the channel-base and time of the disconti-nuity appearance in electric and magnetic field waveforms are presented in this paper. These rela-tionships can be used for obtaining any of these four quantities of interest in the case of other three ex-perimentally measured or estimated. It is also shown in this paper that these relationships can be used in-dependently on the chosen channel-base current waveshape. For different lightning channel heights and for the chosen return stroke propagation speed the results for LEMF at ground surface points at dif-ferent distances from the channel-base are presented in the paper. 2. THE RETURN STROKE SPEED Lightning return stroke speed is one of the main parameters in lightning modeling, so as in evaluating lightning-induced effects [6]. It is known that the return stroke speed may vary along the lightning channel. Techniques for measuring return stroke speed were discussed by Idone and Orville [7]. "The optically measured return stroke speed probably represents the speed of the region of the upward-moving return stroke tip where power losses are the greatest. The peak of the power loss wave likely occurs earlier in time than the peak of the current wave" [8]. It was concluded in [8] that the often assumed relationship between the return stroke speed and the peak current is generally not supported by experimental data. On the basis of measurements for both natural and rocket-triggered lightning the propagation speed of a negative return stroke (both first and subsequent) is averaged over the channel below the lower cloud boundary and estimated to be from one-third to one-half of the speed of light. The negative return stroke speed within the bottom 100m or so is estimated to be from one-third to two-thirds of the speed of light. For a positive return stroke this speed is also of the order of . m/s108In most of the return stroke models and LEMF cal-culations the value of the return stroke speed is as-sumed to be constant over the channel. For the nega-tive return stroke the speed may vary non-monotoni-cally along the channel, initially increasing and then decreasing with height, and for the positive return stroke there are contradicting data regarding its varia-tion along the channel [8]. There are also discussions in [1] and [9] about the attempts of return stroke speed estimation by different authors.  In this paper one new and different approach is presented, trying to make use of electric and magnetic field waveforms at surface points at different distances from the lightning channel-base and the obtained relationships. If the return stroke speed is estimated in another way, then the use of them can be made for estimating lightning channel height.           © 2009 - 54th Internationales Wissenschaftliches Kolloquium3. THE DERIVED RELATIONSHIPS In the case of a thin straight vertical antenna modeling of the lightning channel it is necessary to choose a certain height of that antenna [10]. In natural cases there is a height at which the discharge stops for a while, even if it would be continued later and then stopped at some different height. Can this be notice-able in experimentally measured lightning electric and magnetic field waveforms? This paper presents results showing how this might be used for determining the lightning channel height or the return stroke speed.  On the basis of the governing relation of transmis-sion line models, it can be noticed [11] that the inter-rupt of the lightning channel at a certain height from the ground results in the discontinuity appearance in time moment  after the time of LEMF appearance at that point, , in both electric (Fig.1) and magnetic field (Fig.2) in a similar way at the distances of kilometers from the lightning channel-base. dtc/0 rt =For a chosen lightning channel height H and a re-turn stroke propagation speed v, at a distance r from the channel-base, the time of the discontinuity appear-ance can be calculated from the following expression   ( ) 1221 c−− −++= rrHvHtd , (1)  for c the speed of light. The results are presented in the following table for  which is usu-ally used in calculations as the average return stroke speed. If  is determined from the measured LEMF waveforms, and the return stroke propagation speed is assumed as , then the lightning channel height can be determined from the expression m/s103.1 8⋅=vdtm/s103.1 8⋅=v ( ) .ccc2c 11112222 −−−− −⎟⎠⎞⎜⎝⎛ ++−+= vvrtvtvrrtH ddd(2)  At the basis of experimentally determined light-ning channel height H and for the time of the dis-continuity appearance  in electric and magnetic field waveforms, the return stroke propagation speed along the channel could be determined from the ex-pression dt  ( )( ) .cc 11221 −−− +−+= rHrtHv d  (3)  The NCBC channel-base current function is       (4) [ ][ ]⎪⎩⎪⎨⎧∞<≤≤≤= ∑=−−τ1,eτ1τ0,eτ)(1τ)1(τ)1(nibimamicIIti for ,  the maximum current at , and the parameters a,  and  determining the current waveshape. For i=1 it becomes the simpler CBC function.   mtt /τ = mI mtib icTable 1 - Time  in  of the discontinuity appear-ance (counted from  of LEMP appearance at a dis-ance r in km) for different channel heights H in m dt μs0tt  Time  ( ) dt μsChannel height H (m) The distance  r (km) 2600 4500 7000 120000.5 27.16 48.04 75.57 130.681 25.95 46.65 74.08 129.115 22.12 40.37 65.85 118.97200 20.06 34.78 54.25   93.514. LEMF RESULTS For the distance of 5km from the channel-base the results for vertical electric field for three different channel heights and for the channel-base current function CBC [3] with parameters a=1.5, b=0.02, μs5826.0=mt  and kA11=mI , (approximately as the function in [5]), are presented in Fig.1, and for azimuthal magnetic field in Fig.2. Modified transmission line model (MTLE) with the channel current exponential decay with height z' is used, so λ)/'exp(),0(),'( ztitzi −= , for . The corre-sponding time intervals  of the discontinuity appearance in these waveforms can be noticed in Figs.1-9 for the chosen channel heights and the return stroke speed , also as in Table 1. m4500λ =dtm/s103.1 8⋅=v Figure 1  Vertical electric field at 5km for three different channel heights and for the CBC function  Figure 2  Azimuthal magnetic field at 5km for three different channel heights and for the CBC function  Figure 3  Vertical electric field at 5km for three dif-ferent CBC&NCBC channel-base current functions    Figure 4 Azimuthal magnetic field at 5km for three dif-ferent CBC&NCBC channel-base current functions    Figure 5  Vertical electric field at 200km for four different channel heights and for the CBC function   Figure 6 Azimuthal magnetic field at 200km for four different channel heights and for the CBC function For determining the electric and magnetic field above perfectly conducting ground from a straight vertical finite height antenna with a simple triangular current pulse in the channel-base the results are pre-sented in [10]. At three different distances, for the speed  and the height H=4km as in [10], the time of the discontinuity appearance  can be calculated from (1), and for the distance r=1km the value m/s103.1 8⋅=vdtμs41.60=dt  is obtained, for r=10km the value μs57.52=dt , for r=100km . The same time moments can be noticed in both electric and magnetic field waveforms for the three distances in the Fig.3 of paper [10]. It is interesting that the current derivative is constant in the rising part (equal to ), different from the current derivative of [5], that the channel-base current is of a finite time duration (chosen to be ) and different shape than usually used for such calculations, but the results from [10] prove the derived expressions (1)-(3).  μs27.50=dtμs1.2kA/10μs25This can be noticed also for the model proposed in [12], for H=9km, r=100km and , for which the value of m/s103.1 8⋅=vμs58.70=dt  is obtained from (1).  The three different channel-base current wave-shapes are chosen to show that these relationships are not influenced by the channel-base current function shape and its first derivative and that  is the same in these cases (Figs.3 and 4). For the first chosen chan-nel-base current the NCBC function parameters are dtkA11=mI , μs5826.0=mt  and , 1.1=a 25.01 =b , 34.01 =c , 006.02 =b , and . For the second channel-base current the CBC parameters are chosen as 66.02 =ckA11=mI , μs5826.0=mt , , , and for the third channel-base current the NCBC parame-ters are 5.1=a 02.0=bkA11=mI , μs472.0=mt , , 1.1=a 16.01 =b , 34.01 =c , 0047.02 =b , and  (the most ade-quate to the function in [5], with the same  and ). 66.02 =cmI mtThe results for four different channel heights and for the channel-base current function with parameters kA11=mI , μs5826.0=mt , a=1.5 and b=0.02, for ver-tical electric field are presented in Fig.5, and for azi-muthal magnetic field in Fig.6, for r=200km. The effect of lightning channel height at the dis-tance of hundreds of meters is different. For example at r=500m (Fig.7) and r=1km (Fig.8) from the chan-nel-base the increase of the vertical electric field ap-pears after time  from .  dt 0tThe discontinuity is noticeable also in magnetic field waveforms at hundreds of meters from the chan-nel-base, but as a decreasing step (Fig.9).  In experimentally obtained results for electric and magnetic field waveforms these discontinuities can be noticed and the unknown values can be estimated from relationships (1)-(3) if other quantities assumed.        Figure 7  Vertical electric field at 500m for four different channel-base current functions    Figure 8  Vertical electric field at 1km for four different channel heights and for the CBC function   Figure 9  Azimuthal magnetic field at1km for four different channel heights and for the CBC function 5. CONCLUSION From experimentally measured lightning electric and magnetic field waveforms, on the basis of time of discontinuity appearance at different distances from the channel-base, the return stroke speed can be estimated if the lightning channel height is assumed or known (e.g. in rocket-triggered lightning experi-ments). The derived relationships can be used also for estimating the lightning channel height if the return stroke speed is assumed. The distance from the lightning channel-base can also be estimated using measured electric and magnetic field waveforms and chosen return stroke speed and the channel height.    6. REFERENCES [1] Rakov, V. A., M. A. Uman, “Review and evalua-tion of lightning return stroke models including some aspects of their application,” IEEE Trans. on Elec-tromagnetic Compatibility, Vol.40, No.4, pp.403-426, Nov. 1998.  [2] Nucci, C. A., C. Mazzetti, F. Rachidi, and M. Ianoz, “On lightning return stroke models for LEMP calculations,” in Proc. 19th Int. Conference on Light-ning Protection, Graz, Austria, Apr. 1988.  [3] Javor, V., P. D. Rancic, “Application of one suitable lightning return-stroke current model,” Int. Symposium on EMC Europe 2006, Proceedings of full papers, pp. 941-946, Barcelona, Sep. 2006.  [4] Javor, V., “Approximating decaying part of the lightning return stroke channel-base current,” in Book of Abstracts 3rd Int. Symp. on Lightning Physics and Effects, pp.26, Vienna, Austria, Apr. 2008.  [5] Nucci, C. A., G. Diendorfer, M. A. Uman, F. Ra-chidi, M. Ianoz, and C. Mazzetti, “Lightning return stroke current models with specified channel-base current: A review and comparison,” J. Geophys. Res., Vol.95, pp.20395-20408, 1990.  [6] Rachidi, F., C. A. Nucci, M. Ianoz, C. Mazzetti, “Influence of a lossy ground on lightning-induced voltages on overhead lines,” IEEE Trans. on Elec-tromagnetic Compatibility, Vol.38, No.3, pp.250-264, Aug. 1996.  [7] Idone, V. P., Orville R. E., “Lightning return stroke velocities in the Tunderstorm Research International Program (TRIP),” J. Geophys. Res., Vol.87, pp.4903-4915, 1982.  [8] Rakov, V. A., “Lightning return stroke speed,” J. of Lightning Research, Vol.1, pp.80-89, 2007.  [9] Gomes, C., V. Cooray, “Concepts of lightning re-turn stroke models,” IEEE Trans. on Electromagnetic Compat., Vol.42, No.1, pp.82-96, Feb. 2000.  [10] Uman, M. A., D. K. McLain, E. P. Krider, “The electromagnetic radiation from a finite antenna,” Am. J. of Physics, Vol.43, pp.33-38, 1975.  [11] Javor, V., P. D. Rancic: "The effect of lightning return stroke channel height on electric and magnetic field waveforms," 29th Int. Conference on Lightning Protection  ICLP 2008, Uppsala, CD Proceedings of Full Papers, Paper 3a-07.1-10, Uppsala, Jun. 2008.  [12] Baba, Y., M. Ishii, “Lightning return stroke model incorporating current distortion,” IEEE Trans. on Electromagnetic Compatibility, Vol.44, No.3, pp.476-478, Aug. 2002. 

Calculation of lightning channel height and return stroke propagation speed from electromagnetic field waveforms

https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00019046/54_IWK_2009_3_1_05.pdf

Calculation of lightning channel height and return stroke propagation speed from electromagnetic field waveforms

Abstract

Similar works

Full text

Available Versions

Digitale Bibliothek Thüringen