THE widespread use of lightning location systems provides

Transcription

1 112 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 57, NO. 1, FEBRUARY 2015 Effect of Frequency-Dependent Soil on the Propagation of Electromagnetic Fields Radiated by Subsequent Lightning Strike to Tall Objects Qilin Zhang, Tongtong Ji, and Wenhao Hou Abstract In this paper we have studied the propagation effect of frequency-dependent soil (FDS) on the far vertical electric fields radiated by subsequent lightning strike to tall objects with heights from 50 to 300 m. It is found that the field propagation attenuation along FDS is obviously less than that case where the parameters are assumed to be constant (low-frequency conductivity at 100 Hz, LFC), and with the decrease of LFC, the corresponding field attenuation increases. When LFC is equal to or larger than 0.01 S/m, the effect of FDS can be ignored. However, when LFC is S/m, the field peak for FDS may reach as much as 2.5 times of that earth with LFC for strike to a 300-m-tall object. Index Terms Attenuation, frequency-dependent conductivity, lightning subsequent return stroke, risetime of current wave (RT), strike to tall object. I. INTRODUCTION THE widespread use of lightning location systems provides lightning return stroke peak currents estimated from measured magnetic field peaks. The theoretical estimation of return stroke currents from remote electromagnetic fields depends on the adopted return stroke model [1]. Expressions relating radiated fields and return stroke channel base currents are usually assumed to be proportional to each other, with the proportionality coefficient being determined for striking to flat ground with the perfect conductivity [2]. However, the lightning usually strikes tall buildings (e.g., tall telecommunication objects) [3] [9]. For the case of strike to tall objects, as a result of transient process in the object, current waveforms can differ significantly at different heights along the object and can exhibit more than one peak (typically, secondary peak is larger than the initial one) [10] [12], and the presence of the object tends, in general, to increase substantially the electric and magnetic field peak values and their derivatives [13] [21]. It is worth noting that the high-frequency contents Manuscript received June 11, 2014; revised September 9, 2014; accepted October 1, Date of publication October 21, 2014; date of current version February 13, This work was supported in part by the National Key Basic Research Program of China (2014CB441405), in part by the National Natural Science Foundation of China under Grant and Grant , a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and by Commonwealth Industry Research Project of China (GYHY ). The authors are with the Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Key Laboratory for Aerosol- Cloud-Precipitation of China Meteorological Administration, Nanjing University of Information Science and Technology, Nanjing , China ( zhangqilin71@163.com; jitong0908@126.com; hwhnuist@163.com). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TEMC in the electromagnetic fields of lightning flashes striking tall structures are much different from the ones striking flat ground [22], [23], and the transient processes along the object result in more high-frequency components. Since the lightning electromagnetic fields change their signature as they propagate over a finitely conducting ground due to the selective attenuation of the high-frequency components [24] [38], the attenuation of the radiation field of lightning flashes striking tall objects is much larger than that striking flat ground. Cooray et al. [23] found that in the case where the ground conductivity is extremely poor, namely S/m, the attenuation of the peak radiation field may reach as much as 70% in the case of lightning flashes striking a 300-m-tall object. However, Cooray et al. [23] assumed that the soil conductivity and permittivity are constant and independent of lightning frequency. In fact, the soil conductivity and permittivity are frequency dependent [39], [40]. For example, recently, Cavka et al. [41] have presented a review and comparison of six different models representing the frequency dependence of the soil electrical parameters (conductivity and permittivity). The soil conductivity and permittivity usually increase with the increase of field frequency. In the following, we will analyze the propagation effect of the far vertical electric fields radiated by subsequent lightning strike to tall objects along the frequencydependent soil (FDS). II. MODEL INTRODUCTION Here, we will use the lumped sources in lightning return stroke models extended to include the presence of a tall strike object [42], [43], the object is modeled as a single, uniform and lossless transmission line. The return-stroke discharging current includes two components-a breakdown current and a corona current. Each of the two components is calculated by using the analytical expression suggested by Heidler [44]: I sc (h, t) = I 01 (t/τ 11 ) 2 η 1 1+(t/τ 11 ) 2 e( t/τ 12) + I 02 (t/τ 21 ) 2 η 2 1+(t/τ 21 ) 2 e( t/τ 22) ( η 1 = exp τ ( 11 2 τ ) ) 1/2 12 τ 12 τ 11 ( η 2 = exp τ ( 21 2 τ ) ) 1/2 22 τ 22 τ 21 (1) IEEE. 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2 ZHANG et al.: EFFECT OF FREQUENCY-DEPENDENT SOIL ON THE PROPAGATION OF ELECTROMAGNETIC FIELDS 113 where I 01 and I 02 are the current peaks of the breakdown current and corona current, η 1 and η 2 are the peak correction factors, τ 11 and τ 21 determine the risetime (RT) of the breakdown current and corona current, and τ 12 and τ 22 determine the decay time of the currents. In order to study the transient process of lightning current in the object with different height, we choose the lightning shortcircuit current waveforms (I sc (h, t)) with different current RT for subsequent lightning flashes, but for the same peak. In the analysis, the current along the tall object is simulated by using the lumped voltage model and the current along the lightning channel is simulated by using the TL model as shown in Baba and Rakov [42, see the equations (6a) and (6b) in their paper]. Fig. 1 shows the lighting current waveform at the top and bottom of 50-m and 300-m-tall objects, respectively. RT with 0.2 and 2 μs, respectively, corresponds to 10 90% RT of subsequent lightning current waveforms. h is the height of tall object. ρ t is the reflection coefficient at the object top for the upwardpropagation waves, and ρ b is the reflection coefficient at the object bottom for the downward-propagation waves: ρ t = (Z t Z ch ) / (Z t + Z ch ) (2) ρ b = (Z t Z g ) / (Z t + Z g ) (3) where Z t is the impedance of tall objects, z ch is the impedance of the lightning channel and Z g is the lumped grounding impedance. We assume that ρ b =1.0 and ρ t = 0.5 (e.g., Z ch = 900 Ω, Z t = 300 Ω and Z g =0Ω), as shown in Baba and Rakov [42], [43]. In Fig. 1, the solid lines correspond to the short-circuit current waveforms (I sc (t)), which is defined here as the lightning current that would be measured at an ideally grounded object of negligible object height. The dashed lines correspond to the current waveform at the top of tall object (I top (t)) and the dash dotted lines correspond to the current waveform at the bottom of object (I bot (t)). Note that, the tall objects may cause the current waveform to sharply rise or decline at several time moments, corresponding to the reflections at the top or bottom of tall object, which are attributive to strong radiation field pulses with high-frequency components. The current at the bottom of the tower is higher than that at the top because of the successive multiple reflections occurring at the two ends of the strike object, which is similar to that measured values as shown in [45]. On one side, based on the frequency contents of lightning strike current, the model of Baba and Rakov [42] as well as Rachidi et al. [9] assumes that the equivalent impedances of lightning channel and strike object are constant (although in reality it varies with lightning current waveform), without considering the current attenuation along the strike object, and the object is modeled as a single, uniform and lossless transmission line. On the other side, because the characteristic impedance of strike object is larger than grounding impedance, the reflection coefficient at the bottom of tall object is assumed to be ρ b =1.0, while the reflection coefficient at the top of tall object is ρ t = 0.5. Therefore, the superposition of waves due to the successive multiple reflections at the two ends of the strike object results in a larger peak value at the top. Fig. 1. Lighting current waveforms at the top and bottom of 50-m and 300- m-tall objects ρ t = 0.5 for subsequent lightning return stroke with RT of 0.2 and 2 μs ρ b =1.0, respectively. The reflection coefficients at the top and bottom of tall object are ρ t = 0.5 and ρ b =1.0, respectively. The solid lines correspond to short-circuit current waveforms (I sc (h, t) ), the dashed lines correspond to the current waveform at the object top (I bot (t)) andthe dash dotted lines correspond to the current waveform at the object bottom (I bot (t)).

3 114 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 57, NO. 1, FEBRUARY 2015 Also, the effect of tall objects on the lightning current waveforms depends on the reflection coefficients of lightning current waves at two ends of object and lightning current RT. With the increase of RT, the effect of tall objects becomes less [see Fig. 1(c)]. Further analysis shows that, the current magnitude along the strike object for p b =0.7 (ρ t = 0.5) is less about 10% than that for ρ b =1.0 (ρ t = 0.5). Therefore, in this paper we do not consider the effect of different reflection coefficients on our simulated results. Based on the distribution of lightning current along the tall object and channel as show in Fig. 1, the far vertical electric fields on a perfectly conducting ground are calculated according to the equations presented by Bermudez et al. [14]. The channel height H is assumed to be 10 km and the object height ranges from 50 to 300 m, and the return stroke speed is v = m/s. Then, the propagation effect of the FDS can be computed as follows (e.g., [32], [33], [46], [47]): E σ,tall (0,d,t)= t 0 E,tall (0,d,t τ) W (0,d,τ) dτ (4) where E,tall (0,d,t) and E σ,tall (0,d,t) are the vertical electric field radiated by lightning strike to tall object on the perfectly conducting ground and FDS, respectively, and d is the horizontal distance between the observation point and lightning channel, W (0,d,t) is the inverse Fourier transformation of the attenuation function W (0,d,jω) in frequency domain [26] W (0,d,jω)=1 j πp exp ( p) erfc (j p) (5) P = jωd 2c Δ2 (6) Δ= k 0 k ( 1 k2 0 k 2 ) 1/2 (7) k = k 0 (ε j60σλ 0 ) 1/2 (8) k 0 = ω (μ 0 ε 0 ) 1/2 (9) where erfc is the complementary error function,d is the observed distance, ω is the angular frequency, c is the light speed, j = 1. ε 0 and μ 0 are the dielectric constant and magnetic permeability of free space, respectively. σ and ε are the conductivity and dielectric parameters of FDS, and λ 0 is the wave length in free space. Δ is the effective impedance of FDS, k and k 0 is wave number in free space and FDS, respectively. In the following analysis, we will employ the FDS model presented by Portela [48], which is based on his own measurements for the electrical parameters of five different types of soil in the frequency range of 100 Hz to 2 MHz: ( π )] σ = σ 0 +Δ i [cot ( ) α 2 α ω 2π 10 6 (10) ( ) α ω ε = Δ i 2π 10 6 ω α 1 (11) where σ 0 is the earth conductivity measured at 100 Hz, and is supposed to be equal to that measured at low frequency (here, we name it as low-frequency conductivity, LFC). α is an adjustable parameter model of the soil, and Δ i is the value of ωε at 1 MHz Fig. 2. (a) Frequency-dependent conductivity (FDS) with constant conductivity values measured at 100 Hz (LFC) σ 0 =0.01, and S/m, respectively and (b) frequency-dependent permittivity. (ω is the angular frequency). Generally, the parameters α and Δ i depend on the soil model. Here, as done in [41], we adopted the median values α =0.706 and Δ i =11.71 ms/m. The characters of frequency-dependent conductivity and permittivity can be seen in Fig. 2 III. RESULTS AND ANALYSIS Figs. 3 5 show the propagation effect of FDS on the vertical electric fields radiated by subsequent lightning strike to 50-m and 300-m-tall objects, respectively, and RT ranges from 0.2 to 2 μs (ρ b =1.0 and ρ t = 0.5) ρ b =1.0. The computation for our simulation (when a PC with Intel(R) Core(TM) i CPU was used) was about 4 min for every result [e.g., red and dashed line in Fig. 3(a) (the subsequent lightning with RT of 0.2 μs strike to 300-m-tall objects)], and the memory required was about 300 MB. It is seen from comparison that the presence of tall object causes more than one field peak, corresponding to sharply rise or decline of lightning current waveforms (see Fig. 1). For strike to tall objects, on the one hand tall objects will increase the far initial vertical field peak and on the other hand the corresponding

4 ZHANG et al.: EFFECT OF FREQUENCY-DEPENDENT SOIL ON THE PROPAGATION OF ELECTROMAGNETIC FIELDS 115 Fig. 3. Effect of FDS on the vertical electric fields radiated by subsequent lightning strike to flat ground (black line), 50-m (blue line) and 300-m tall objects (red line), respectively, and RT ranges from 0.2 to 2 μs. Solid lines represent the case of LFC and dashed lines represent that of FDS. field attenuation will become more than that strike to flat ground, due to the intensification of lightning higher-frequency contents. First, from Figs. 3 and 4, it is seen that with the decrease of LFC, the propagation effect of FDS on the far vertical electric field becomes more obvious. For example, for LFC of σ 0 =0.01 S/m (see Fig. 3), the simulated results for the cases with constant electric parameters are similar to that of FDS. However, for extremely poor parameters of σ 0 = S/m (see Fig. 4), we have to consider the effect of FDS, and the field attenuation along FDS is much less than that for the soil with LFC, and the corresponding field peak for FDS may reach as much as 2.5 times of that case with LFC for strike to a 300-m-tall object. Second, the presence of 300-m-tall object obviously increases the initial field peak, and for the 50-m-tall object, the effect of tall objects can be approximately ignored in most cases, except for a much more initial field peak in Figs. 3(a) and 4(a); however, the initial field peak has higher-frequency contents and it quickly attenuates [see Figs. 3 (b) and 4(b)]. Above all, when LFC is 0.01 S/m, the effect of FDS can be ignored for object heights ranging from 50 to 300 m in most

5 116 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 57, NO. 1, FEBRUARY 2015 Fig. 4. Similar to Fig. 3, but for a LFC of σ o = S/m. cases. When LFC is S/m, the effect of FDS becomes very obvious and has to be considered. However, for LFC of S/m, FDS increases the field peak value about within 20% [see Fig. 5(a)]. In Figs. 3 5, we study the effect of FDS on the propagation of vertical electric fields radiated by subsequent lightning strike to tall objects. It is further found that the effect of tall objects on the field propagation decreases with the increase of lightning RT. When RT is higher than 5 h/c (h is the object height and c is the light speed), the case for strike to tall objects is about close to that for strike to flat ground at distances from 10 to 100 km; however, the field waveform RT for strike to tall object is shorter than that for the flat ground because of less field attenuation for FDS (see Figs. 6 and 7). IV. CONCLUSION In this paper we have studied the propagation effect of the FDS on the vertical electric fields radiated by subsequent lightning strike to tall objects. When the LFC measured at 100 Hz

6 ZHANG et al.: EFFECT OF FREQUENCY-DEPENDENT SOIL ON THE PROPAGATION OF ELECTROMAGNETIC FIELDS 117 Fig. 5. Similar to Fig. 4, but for LFC of σ o =0.001 S/m and at the observed distance of 100 km from the lightning channel. is equal or greater than 0.01 S/m, the effect of FDS can be ignored. However, when LFC is S/m, the corresponding field peak for FDS may reach as much as 2.5 times of that earth with LFC for strike to a 300-m-tall object. Also, only when the strike object height is approximately higher than 50 m, the effect of tall objects may be considered in most cases. In fact, for the subsequent lightning flashes strike to flat ground, the effect of FDS on the far vertical field can be ignored. However, when the subsequent lightning flashes strike tall objects, the transient processes along the object result in more high-frequency components; therefore, the effect of FDS becomes more obvious, Fig. 6. Lightning-radiated field on the ground surface at distances ranging from 10 to 100 km from the lightning channel both for strike to flat ground (black line) and 50-m-tall object (red line), respectively. Solid lines represent the case of LFC and dashed lines represent that case of FDS.

7 118 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 57, NO. 1, FEBRUARY 2015 with respect to case where the soil parameters are assumed to be constant. However, our simulated results in this paper are based on the FDS model presented by Portela [48], and different FDS models (e.g., [49] [52]) may result in different results. In fact, as discussed in [41], [53] and [54], the study of FDS is almost a century old, and the measurement of soil parameters is a challenging task, and many measurements of soil electric parameters do not take into account the requirement of causality. Although the model of Portela [48] predicts a less value of potential of the grounding electrode than that of other considered models, it satisfies the Kramers Kronig relationships between the real and imaginary parts of the effective dielectric constant and thus provides a causal result. Therefore, in this paper we have chosen the model of Portela [48], because any solution resulting from the Maxwell s equations must be causal and the soil electrical parameters (permittivity and conductivity) cannot be chosen in an arbitrary manner for a special medium. In a word, although our simulation may be uncertain because of its dependence on the choice of FDS models, it is sure that we should consider the propagation effect of FDS on the far vertical electric fields radiated by subsequent lightning strike to tall objects with heights from 50 to 300 m for very poor conductivity. REFERENCES Fig. 7. Similar to Fig. 6, but for strike to 300-m-tall object. [1] 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, pp , Nov [2] M. A. Uman, D. K. McLain, and E. P. Kride, The electromagnetic radiation from a finite antenna, Am. J. Phys., vol. 43, no. 1, pp , [3] G. Diendorfer, W. Hadrian, and F. Hofbauer, Evaluation of lightning location data employing measurements of direct strikes to a radio object, e&i Elektrotechnik und Informationstechnik, vol. 119, no. 12, pp , [4] G. Diendorfer, Lightning initiated from tall structures A review, in Proc. Int. Symp. Lightning Protection, pp [5] C. Romero, M. Rubinstein, F. Rachidi, M. Paolone, V. A. Rakov, and D. Pavanllo, Some characteristics of positive and bipolar lightning flashes recorded on the Säntis object in 2010 and 2011, in Proc. Int. Conf. Lightning Protection, 2012, doi: /iclp [6] W. Lu, D. Wang, Y. Zhang, and N. Takagi, Two associated upward lightning flashes that produced opposite polarity electric field changes, Geophys. Res. Lett., vol. 36, L05801, 2009, doi.org/ /2008gl [7] W. Lu, L. Chen, Y. Zhang, Y. Ma, Y. Gao, Q. Yin, S. Chen, Z. Huang, and Y. Zhang, Characteristics of unconnected upward leaders initiated from tall structures observed in Guangzhou, J. Geophys. Res., vol. 117, D19211, 2012, doi.org/ /2012jd [8] W. Lu, L. Chen, Y. Ma, V.A. Rakov, Y. Gao, Y. Zhang, Q. Yin, and Y. Zhang, Lightning attachment process involving connection of the downward negative leader to the lateral surface of the upward connecting leader, Geophys. Res. Lett., vol. 40, no. 20, pp , [9] F. Rachidi, V. A. Rakov, C. A. Nucci, and J. L. Bermudez, Effect of vertically extended strike object on the distribution of current along the lightning channel, J. Geophys. Res., vol. 107, no. D23, p. 4699, [10] K. Berger, R. B. Anderson, and H. Kroninger, Parameters of lightning flashes, Electra, vol. 41, pp , [11] A. J. Eriksson, The lightning ground flash An engineering study, Ph.D. dissertation, University of Natal, Pretoria, South Africa, Natl. Electr. Eng. Res. Inst., Pretoria, South Africa, [12] S. Visacro, M. A. O. Schroeder, A. Soares, Jr., L. C. L. Cherchiglia, and V. J. Sousa, Statistical analysis of lightning current parameters: Measurements at Morro do Cachimbo station, J. Geophys. Res., vol. 109, no. D01105, pp. 1 11, 2004.

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9 120 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 57, NO. 1, FEBRUARY 2015 [53] S. Visacro and R. Alipio, Frequency dependence of soil parameters: Experimental results, predicting formula, and influence on the lightning response of grounding electrodes, IEEE Trans. Power Del., vol. 27, no. 2, pp , Apr [54] F. M. Tesche. (2002, Jul.). On the modeling and representation of a lossy earth for transient electromagnetic field calculations. Theoretical Notes. vol [Online]. Available: notes/theoretical.html Tongtong Ji was born in Jiangsu, China, in He received the B.E. degree in lightning protection science and technology from the College of Atmospheric Physics, Nanjing University of Information Science & Technology, Nanjing, China, where he is currently working toward the M.S. degree. His research interests include the numerical methods of lightning electromagnetic field and global lightning activity. Qilin Zhang was born in Gansu, China, in He received the B.S. degree from the Department of Physics, from the Tianshui Normal University, Gansu, China, in 1995, and the M.S. and Ph.D. degrees from the Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou, China, in 2002 and 2007, respectively. In 2007, he joined the College of Atmospheric Physics, Nanjing University of Information Science & Technology, China, where he is currently a Professor. He is the author of more than 60 scientific papers published in journals or international conferences. His research interests include lightning physics and numerical calculation of electromagnetic fields. Wenhao Hou was born in Shanxi, China, in He is currently working toward the B.E. degree in lightning protection science and technology from the College of Atmospheric Physics, Nanjing University of Information Science & Technology, Nanjing, China. His research interests include the computation of lightning electromagnetic fields.