An Improvement of the Method for Estimating the Lightning Current from Measured Electromagnetic Fields in Lightning Locating Systems

Transcription

1 THE SCENCE AND ENGNEERNG REVEW OF DOSHSHA UNVERSTY, VOL. 9, NO. 3 October An mproement of the Method for Estimating the Lightning Current from Measured Electromagnetic Fields in Lightning Locating Systems Masashi TOR * and Yoshihiro BABA * (Receied July 3, ) Lightning locating systems (LLSs) proide lightning return-stroke peak s estimated from measured magnetic or electric field peaks as well as lightning striking locations. Direct measurements of lightning s on tall towers are used for testing the alidity of field-to- estimation equations employed in LLSs. The field and peaks are usually assumed to be proportional to each other, where the proportionality coefficient is determined for lightning strikes to flat ground or a grounded object of negligible height. Therefore, these estimation equations are not applicable to lightning strikes to tall towers. Furthermore, in the case of lightning strikes to tall towers, as a result of transient process in the tower, waeforms can differ significantly at different heights along the tower and can exhibit more than one peak. n such cases, the field-to- estimation coefficient depends on measurement location and on whether the first or second peak is used. Thus, for calibrating LLSs using measurements on towers, it is necessary to know appropriate far-field-to- estimation equations or coefficients. Electromagnetic field, lightning, lightning, lightning return stroke. Lightning Locating System LLS H.peak E z.peak d peak cdh.peak / peak = c de z.peak / c * Department of Electrical Engineering, Doshisha Uniersity, Kyoto Telephone : , Fax : , ybaba@mail.doshisha.ac.jp 1

2 13 1 m Gaisberg LLS.9 1) m Peissenberg. ) 3 m CN.3 3) LLS LLS Fig. 1 h = 1 3 m h h1 m Gaisberg h m Peissenberg h3 m CN TL representing channel ( ch ) TL representing tall object ( ob ) Ground surface Grounding impedance V (h,t) gr bot Reference ground Fig. 1. A lightning strike to a tall grounded object of height h, represented by lossless transmission lines connected in series with a lumped oltage source, V (h, t), and a lumped grounding impedance ( gr ). h gr 3 ch 9 ob 3 bot bot ob ob ob ob ch ch gr gr gr =3 ch =9 ob =3 (1)() bot =.9 =. Fig. 1 z h ) 1 ( z ', t ) n n bot n 1 n 1 bot sc n sc h, t (1) () h z ' nh c c h z ' nh h, t c c sc gr sc (3) V ( ), t (, t) () z h 1 z ' h ( z ', t ) sc h, t n1 (1 )(1 ) n bot ch sc h, t z' h h, t n1 (1 ) sc z ' h nh () c

3 137 1/3 =c/3 Fig. sc Fig. 1 ka1-9.1 s 3 s 1 ka s s 1 Risetime=.1 s Risetime=1. s 1 3 Time [s] Fig.. Waeforms of lightning short-circuit, sc, with different 1-to-9% risetimes:.1 and 1. s. sc.1 s 1. s Fig. 3 Fig. 3 (a) h=1 m(b) h= m(c) h=3 m h= Fig. 3 Table 1. Peak alues in kiloamperes of lightning at the and bottom of a tall object of different heights h=, 1,, and 3 m. Object Risetime =.1 s Risetime = 1. s height, h bottom bottom 1 m (1.) 11.1 m (1.) m (9.) (9.7) 1. * Value in ( ) is the second or largest peak if present. 1-m tower bottom 1 1-m tower Time [s] (a) 1 m -m tower bottom 1 1 -m tower Time [s] (b) m 3-m tower bottom m tower Time [s] Fig. 3. Current waeforms at the bottom and of a tall object of different heights h for the 1-to-9% risetime being equal to.1 s. Table 1 sc.1 s km Fig. Fig. sc 1 s Fig. 7 Fig. 3

4 m tower bottom 1-m tower 1 3 Time [s] 1 1 Strike to 1-m tower 1 3 Time [s] (a) 1 m (a) 1 m m tower bottom -m tower 1 3 Time [s] Strike to -m tower 1 3 Time [s] (b) m (b) m m tower bottom 3-m tower 1 3 Time [s] Strike to 3-m tower 1 3 Time [s] Fig.. Current waeforms at the bottom and of a tall object of different heights h for the 1-to-9% risetime being equal to 1 s. bot..peak (3) 1 1 () bot. peak sc. peak bot Fig.. Waeforms of ertical electric field E at d= km due to a lightning strike to a tall object of different heights h for the 1-to-9% risetime being equal to.1 s. =. bot =.9 sc.peak =1 ka bot.peak = 1.3 ka Fig. 3 (a), (b), (c)

5 Strike to 1-m tower 1 3 Time [s] (a) 1 m Strike to -m tower 1 3 Time [s] (b) m Strike to 3-m tower 1 3 Time [s] Strike to 1-m tower 1 3 Time [s] Strike to -m tower (a) 1 m 1 3 Time [s] (b) m Strike to 3-m tower 1 3 Time [s] Fig.. Waeforms of horizontal magnetic field H at d= km due to a lightning strike to a tall object of different heights h for the 1-to-9% risetime being equal to.1 s. 1 h m h 1 7. ka h1 m m 1. ka, h3 m 9. ka h/c 1 1.peak (3) Fig. 7. Waeforms of ertical electric field E at d= km due to a lightning strike to a tall object of different height h for the 1-to-9% risetime being equal to 1 s. 1 (7) 1. peak sc. peak. =. sc.peak =1 ka 1.peak =7. ka Fig. 3 (a), (b), (c) 1.peak sc (h, t) (3)

6 1 3 Strike to 1-m tower Time [s] (a) 1 m E z..peak H.peak ) 3 1 Strike to -m tower E H (9a) z. peak b. peak c d (9b) cd. peak b. peak 1 3 Time [s] (b) m 3 Strike to 3-m tower Time [s] Fig.. Waeforms of horizontal magnetic field H at d= km due to a lightning strike to a tall object of different heights h for the 1-to-9% risetime being equal to 1 s. 1. peak sc. peak 1 bot bot. =. bot =.9, sc.peak =1 ka.peak =1.9 ka Fig. 3 (a) (b) z =) () c b.peak c d b. peak E z. peak (1a) cd H (1b) b. peak. peak LLS Fig. 3 Fig. Fig. h/c h c peak d >> h E z.peak H.peak

7 11 c E (11a) z. peak 1. peak 1. peak c d c d c H. p eak 1. peak 1. peak cd (11b) cd (7) (1a)(1b) h/c 1 c c d 1. peak E z. peak c cd H c 1. peak. peak (1a) (1b) E z H (7)() h/c 1 (1a)(1b) /(+c) =c/3. Fig. 3 1 (1a)(1b) Table Table.1 s h=1, 3 m 1 7. ka 1 s h=3 m Table. First peak alues ealuated from Fig. 3 and those estimated using approximate expression (1a) or (1b) in kiloamperes of lightning at the of a tall object of different heights h=, 1,, and 3 m. Object Risetime =.1 s Risetime = 1. s height, h Actual Actual 1 m m m peak sc. peak 1 bot bot 1 bot bot 1. peak (1a)(1b)(13) c d. peak 1 bot bot Ez. peak 1 c cd H c. peak bot bot. peak (13) (1a) (1b) (1a)(1b) (1+ bot + bot ) /(+c) =c/3, bot =.9 =..3 CN LLS.3 3) Fig. 3 (1a)(1b) Table 3 Table 3.1 s h=1 m 7

8 1 h=3 m () (1a)(1b) sc (h, t) sc (h, t) Fig. Table 3. Second peak alues ealuated from Fig. 3 and those estimated using approximate expression (1a) or (1b) in kiloamperes of lightning at the of a tall object of different heights h=, 1,, and 3 m. Object Risetime =.1 s Risetime = 1. s height, h Actual Actual 1 m m m ()(7) bot.peak 1 1 () bot. peak bot. peak (1a)(1b)() c d bot. peak 1 bot E z. peak 1 c cd H c bot. peak bot. peak (a) (b) (1a) (1b) (1+ bot )/(+c)=c/3, bot =.9. Fig. 3 (a)(b) Table Table.1 s (a)(b) Fig. 3 1 s Table. Peak alues ealuated from Fig. 3 and those estimated using approximate expression (a) or (b) in kiloamperes of lightning at the bottom of a tall object of different heights h=, 1,, and 3 m. Object Risetime =.1 s Risetime = 1. s height, h Actual Actual 1 m m m FDTD 7) =c/ sfdtd km km 1 m (f) -1/ (f=1 MHz, =1 ms/m m, =.1 ms/m m) 1 km(i) (ii) =1 ms/m r =1 r =1(iii) =1 ms/m r =1 r =1(i) =.1 ms/m r =1 r =1 h= m gr =3, ch =9, ob =3

9 perfect conductor 1 ms/m 1 ms/m.1 ms/m 1 3 Time [s] (a) E z at d= km for h= m perfect conductor 1 ms/m 1 ms/m.1 ms/m 1 3 Time [s] (b) H at d= km for h= m perfect conductor 1 ms/m 1 ms/m.1 ms/m 1 3 Time [s] (c) E z at d= km for h= perfect conductor 1 ms/m 1 ms/m.1 ms/m 1 3 Time [s] (d) H at d= km for h= Fig. 9. Waeforms of ertical electric field E z and horizontal magnetic field H at a distance of km from a ertical lightning channel on lossy ground for different conductiity alues, calculated using the D-cylindrical FDTD method. bot.9. 1 ns d= km E z H Fig. 9 s LLS 1 ms/m1 ms/m.1 ms/m

10 1 3 1/3 H.peak E z.peak 1 1.peak.peak bot.peak.peak =(1+ bot + bot )cd H.peak /(+c) bot b.peak =cdh.peak / b.peak (1+ bot + bot )/(+c) km h/ch c 1 (1+ bot + bot )/(+c) =c/3 =. bot = m CN LLS.3 LLS h/c 1 m 1 7 1) G. Diendorfer, and H. Pichler, Properties of lightning discharges to an instrumented tower and their implication on the location of those flashes by lightning location systems, Proc. th nternational Workshop on Physics of Lightning, Guadeloupe, France () ) G. Diendorfer, W. Schulz, and F. Fuchs, Comparison of correlated data from the Austrian lightning location system and measured lightning s at the Peissenberg tower, Proc. nternational Conference on Lightning Protection, Birmingham, UK (199) 3) A. Lafkoici, A. M. Hussein, W. Janischewskyf, and K. L. Cummins, Performance analysis of the north American lightning detection network using CN tower lightning data, Proc. 19th nternational Lightning Detection Conference, Tucson, Arizona, USA () ) Y. Baba, and V. A. Rako, On the use of lumped sources in lightning return stroke models, J. Geophys. Res., ol. 11, no. D311, doi: 1.19/JD () ) V. A. Rako, Lightning return stroke speeds, J. Lightning Res., ol. 1, pp. -9 (7) ) M. A. Uman, D. K. McLain, and E. P. Krider, The electromagnetic radiation from a finite antenna, American Journal of Physics, ol. 3, pp.33-3 (197) 7) K. S. Yee, Numerical solution of initial boundary alue problems inoling Maxwell s equations in isotropic media, EEE Trans. Antennas and Propagation, ol. 1, no. 3, pp (19) 1