II. Numerical modeling - Lightning Research Laboratory (UF)

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Distribution of Currents in the Lightning Protective System of a Residential Building—Part II: Numerical Modeling Lin Li and Vladimir A. Rakov, Fellow, IEEE

Abstract—The distribution of lightning current in the lightning protective system (LPS) of a test residential building was experimentally studied in 2004 and 2005 at Camp Blanding, FL. Lightning was initiated using a rocket-and-wire technique and its current was injected into the LPS. Results are presented in the companion paper. The current distribution is modeled here using a model based on the lumped circuit theory in the frequency domain. The injected lightning current is represented in the model by an ideal current source. The effect of electromagnetic field radiated by the lightning channel is also accounted in the model (for one of the configurations tested). In field calculations, the lightning channel and the wire connecting the rocket launcher and the test house are modeled as vertical and horizontal electric dipoles above lossy ground. The discrete complex images method is used to calculate the electromagnetic field radiated by the electric dipoles. The time-domain current waveforms are obtained by means of the inverse Fourier transform. The calculated currents in the LPS are compared with those measured. Index Terms—Grounding, lightning electromagnetic field, lightning protective system (LPS), lumped circuit model.

I. INTRODUCTION HEN a protected residential building is struck by lightning, the lightning current flows through the lightning protective system (LPS) of the building. The total current is of the order of several to tens of kiloamperes and contains frequencies up to some megahertz. Part of it flows into the ground through the grounding system of the house, while some current enters the electrical circuit neutral and flows to remote grounds of the system. The overall division of the lightning current is influenced by many factors, including the number and positions of down conductors, the grounding system of the building, parameters of the soil, the remote grounding systems, and the impedance of the neutral. Another, often unrecognized factor, is the electromagnetic coupling between the lightning channel and the LPS, which can significantly change the distribution of currents in the system for some configurations. It is important

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Manuscript received August 7, 2007; revised December 20, 2007. This work was supported in part by the National Natural Science Foundation of China under Grant 50577019, in part by the Natural Science Foundation of Hebei, China under Grant E2005000561, and by the National Science Foundation under Grant ATM-0346164. Paper no. TPWRD-00488-2007. L. Li is with the School of Electrical Engineering, North China Electric Power University, Baoding, Hebei, 071003, China (e-mail: [email protected]). V. A. Rakov is with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2008.923075

to study the distribution of lightning current in the LPS for the development of adequate protection of buildings and evaluation of lightning electromagnetic environment inside the building. In 2004 and 2005, two practical LPS configurations have been tested at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, FL (see [1] and the companion paper). This paper presents an attempt to model current divisions observed in these latter experiments. For the modeling of lightning current distribution, methods based on the electromagnetic-field theory usually employ the electric-field integral equation in the frequency or time domain for thin-wire structures and the method of moment for solving the equation [2], [3]. The methods are suited for considering the overall electromagnetic environment around the LPS. However, large computing resources are required. Some researchers studied the lightning performance of LPS of buildings and transmission lines by means of the Electromagnetic Transient Program (EMTP) [4]. In [5], the transmission-line equations were solved in the time domain to calculate the induced voltage in a tall building struck by lightning. The simple images theory was employed in calculating the magnetic field of lightning channel. In [6] and [7], the aerial and buried conductors of the LPS of buildings were modeled by equivalent networks with, respectively, lumped and distributed parameters in the frequency domain. Ionization of soil was taken into account by means of a nonlinear current-dependent model of ground rods [7]. Various methods, in the time or frequency domain, have been developed for calculation of electromagnetic fields of lightning return strokes [8], [9]. Typically, the lightning channel is assumed to be a straight vertical line, and its height is assumed to be 5 to 7 km. An analytical time-domain formula can be obtained based on an electric dipole model under the assumption of infinite ground conductivity [8]–[10]. The ground effects on the horizontal electric-field component are calculated, making use of the concept of surface impedance of the ground or another approximate formula [14], [15]. Sommerfeld developed the general formulation for the electromagnetic field of a horizontal or vertical electric dipole above or within the lossy ground, which contains an infinite integral of special functions [16]. The direct numerical evaluation of the integral is usually time-consuming because of the oscillating and slowly decaying behavior of the kernel function and the special function. The Norton’s approximation for the integral has a good precision for a relatively high soil conductivity of 0.01 S/m [17], and its accuracy was further analyzed for different

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distances, ground conductivities, and frequencies in [11]. A modified image method was used to calculate the lightning-radiated electromagnetic field in which the mirror image of a real source was multiplied by a correction factor [12]. The correction factor is related to the angular frequency, the permittivities of the air and soil, and the conductivity of soil. A quasiimage method was developed in [13] for the calculation of lightning electromagnetic fields at very close distances based on Taylor series expansion. The Sommerfeld integrals can be evaluated numerically if the kernel function is approximated by a series of exponential functions with different complex coefficients. This technique is called the discrete complex image method (DCIM) [18]–[22] which is used in the microwave techniques area. An effective method to obtain the complex series of exponential functions is the matrix pencil method (MPM) [23], [24]. In this paper, the distribution of lightning currents is calculated in the LPS of a test residential building at the International Center for Lightning Research and Testing (ICLRT). Two different configurations of LPS tested in 2004 and 2005 (see [1] and the companion paper) are considered. The model is based on the lumped-circuit theory in the frequency domain, with measured lightning current used as an input current source. The lumped circuit model is employed here to see if it is suitable for studying the LPS response to direct lightning strikes. The effect of electromagnetic field of the lightning channel on the distribution of currents in the LPS for the configuration tested in 2004 is taken into account. The lightning channel, including the wire connecting the rocket launcher and the test house, is modeled as a number of vertical and horizontal electric dipoles above lossy ground. DCIM is used to calculate the electromagnetic field radiated by the electric dipoles in the frequency domain. The modified transmission-line model of lightning return stroke is used. The Fourier and inverse Fourier transform techniques are used to convert the results between the time domain and the frequency domain. The magnetic vector potentials of all electric dipoles are vectorially added in the time domain. The electromagnetic field is additionally calculated by means of image theory under the assumption of infinite ground conductivity. The calculated lightning currents in the LPS for the two cases (lossy ground and perfectly conducting ground) are compared with those measured. No attempt is made here to improve the match via adjustment of model parameters. II. METHODOLOGY A. Lumped Circuit Model and Its Parameters For lightning analysis in the frequency domain, the maximum frequency is thought to be less than 10 MHz. According to the sampling theorem, the maximum frequency here is set to 20 MHz. Although the corresponding wavelengths are comparable with the dimensions of the house, we assume that the lumped circuit model be still valid, because the higher frequency components in the lightning current (above a few megahertz or so) are expected to be very small. The grounding resistances of buried vertical or horizontal conductors can be estimated by means of the approximate for-

mulae given in [25]. For a vertical ground rod, the grounding resistance is (1) where and are the length and radius of the rod, respectively, and is the conductivity of the soil. The combined grounding resistance of two parallel vertical ground rods of the same length if both of them are buried with their separated by the distance tops being flush with the surface of the ground is (2) The second term in (2) represents the mutual influence between these two ground rods. This influence can be viewed as mutual grounding resistance between the two rods [26] (3) For a horizontal wire of radius buried at depth , the grounding resistance is (4) where is the length of the wire. The mutual inductance between two thin cylindrical conductors (bare or insulated) can be calculated as (5) where is the permeability of air, and are the axes of the two conductors, and is the distance between and . Formula (5) can be also used to calculate the self-inductance of a thin cylindrical conductor, assuming that is its axis and is a line on its surface. The self-capacitance of a horizontal or vertical grounding electrode can be estimated as [27] (6) where is the permittivity of the soil. The effect of the air–earth interface has been considered in the calculation of resistance . For the sake of simplicity, the mutual capacitances between conductors are neglected. Every conductor in the LPS or electrical system is modeled as a circuit branch, and the parameters of circuit elements are calculated using the aforementioned formulae. As an example, the model of a single vertical ground rod is shown in Fig. 1, where L, C, and R are, respectively, the self-inductance, self-capacitance, and grounding resistance. The internal resistance of the ground rod is neglected because it is much smaller than its grounding resistance. The asterisks represent the fact that there are mutual inductances and mutual resistances between this branch and other branches. An electric network is built in the frequency domain based on the lumped circuit parameters of LPS and electrical system, and the lightning current measured at the injection

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. LI AND RAKOV: DISTRIBUTION OF CURRENTS IN THE LIGHTNING PROTECTIVE SYSTEM OF A RESIDENTIAL BUILDING—PART II

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is the fist kind Bessel function of order zero, is the where length of dipole, and the kernel function and other variables are given by

Fig. 1. Circuit model of a vertical ground rod.

where and are the wave numbers of the air and soil, respectively, and is the integral variable. For a horizontal electric dipole, also shown in Fig. 2, which lies along the direction at height over the lossy ground, the and vertical components of magnitudes of horizontal magnetic vector potential are, respectively

Fig. 2. Vertical and horizontal electric dipoles above ground.

is the fist kind Bessel function of order one, where length of dipole, and the kernel functions G and T are

point is modeled as an ideal current source. For the configurations tested in 2004 and 2005, the numbers of circuit nodes are, respectively, 12 and 16. The node voltage equations are solved for every sampling frequency in order to obtain the responses of the circuit models. The Fourier and inverse Fourier transform techniques are used to calculate the current distribution in the LPS (7) is one of where is the time, is the angular frequency, is the transfer the time-domain responses of circuit, and function in the frequency domain. and are Fourier and is the inverse Fourier transforms, respectively, and lightning current measured at the injection point. In the following sections B and C, we describe the method to calculate the electromotive force induced by the lightning electromagnetic field in the LPS configuration tested in 2004. This electromotive force is included as a lumped voltage source in the circuit model. B. Magnetic Vector Potential of an Electric Dipole Above Lossy Ground

(9) is the

In the case of lossy ground, the MPM is used to approximate each kernel function F, G, and T as the sum of exponential functions with different complex coefficients. As an example, function F can be approximated as [24] (10) and is the number of complex expowhere nential functions. Inserting (10) into (8), we obtain

(11) The Sommerfeld identity is

Both vertical and horizontal dipoles will be considered here. For a vertical electric dipole over a flat, homogeneous lossy ground shown in Fig. 2, the magnetic vector potential above the ground level can be expressed in the frequency domain as [28]

(8)

(12) where into

. Utilizing (12), we can transform (11)

(13)



where . The first term in (13) represents the magnetic vector potential of an electric dipole in free space. The second term in (13) can be viewed as the sum of conimages of the dipole, which are called “distributions from crete complex images,” with being the complex amplitudes of images and being the positions of images. This method of evaluation of Sommerfeld integrals is referred to as the DCIM. In a similar manner, we can approximate the horizontal comof the magnetic vector potential in (9). For the verponent of the magnetic vector potential in (9), tical component the method is similar but only the differential of the Sommerfeld identity is needed. The partial derivative of the Sommerfeld identity (12) with respect to variable is (14) If ground conductivity approaches infinity, the kernel functions , , and in (8) and (9) will approach 1, , and in (9) is equal to zero. 0, respectively. In this latter case, in (8) and in (9) can be reduced to Utilizing (12), (15) (16) . As expected, formulae (15) and where (16) are consistent with the classical image theory. C. Electromotive Force Induced in LPS by Electromagnetic Field of Lightning Return Stroke In the triggered lightning testing considered here, negative charge was effectively transported to ground. Therefore, the conventional current of the lightning return stroke flows from ground through the LPS of the test house to the injection point on the roof of the house and then, via the connecting wire and tower launcher to the lightning channel. The total lightning current is measured at the injection point. In order to calculate the electromagnetic field (magnetic vector potential) produced by the lightning channel and connecting wire, the channel and wire were divided into many small segments. The upward propagation speed of the return m/s. Based on this propagation stroke front was set at 1.0 speed and the 0.5 s sampling time step, the length of each small segment of the channel and wire is set to 5 m. Each small section of the channel is modeled as a vertical electric dipole. The connecting wire is represented by five horizontal and vertical electric dipoles. The electromagnetic field of each electric dipole is first calculated in the frequency domain. The frequency points are chosen according to the sampling theorem. The time-domain field is obtained by means of the inverse Fourier transform technique. The modified transmission-line model with exponential decay [29] was used to calculate the currents in the time domain at the different segments (electric dipoles) along the channel. The currents are converted into frequency domain by the Fourier transform. The magnetic vector potential of every electric dipole is calculated by using (8) or (9), then it

Fig. 3. Relative positions of the test house, tower launcher, and connecting wire. Q and P are current injection points in 2004 and 2005, respectively.

is converted into time domain by the convolution and inverse Fourier transform. The magnetic vector potentials of all electric dipoles are vectorially added in the time domain. The resultant time-domain magnetic vector potential of the lightning channel is converted into the frequency domain by the Fourier transform. The induced voltage (emf) in the main loop formed by the LPS above-ground conductors for the configuration tested in 2004 is calculated in the frequency domain as (17) where

is the magnetic vector potential. III. RELATIVE POSITION OF THE TEST HOUSE AND TOWER LAUNCHER

The LPS configurations of the test house at ICLRT can be found in the companion paper. Relative positions of the test house and tower launcher are shown in Fig. 3. The distance between the central point of the test house and the launcher is roughly 27 m. The height of the tower launcher is 11 m. In 2004, the lightning current injection point was point Q and in 2005, it was point P, which are the positions of two air terminals on the roof of the test house. The connecting wire between the test house and the tower is modeled as two straight lines and (see Fig. 3). The longer one is divided into four uniform segments, and all of these segments as well as segment are approximated as stairs, which are represented by horizontal and vertical electric dipoles. This representation procedure is used in DCIM to calculate magnetic vector potentials and then the induced voltage in the loop formed by the above ground conductors of LPS for the configuration tested in 2004.


Fig. 4. Calculated and measured waveforms for magnetic coupling is neglected.

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Fig. 5. Calculated and measured waveforms for i magnetic coupling is neglected.

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(stroke 0521-1). ElectroFig. 6. Calculated and measured waveforms for magnetic coupling is neglected.

i

(stroke 0521-1). Electro-


IV. RESULTS



Fig. 8. Calculated and measured waveforms for magnetic coupling is neglected.


A. 2005 Configuration: Lumped Circuit Model Without Electromagnetic Coupling Between Lightning Channel and LPS (stroke 0521-1) The LPS of the test house tested in 2005 is modeled here as a lumped circuit in the frequency domain. The measured current of the lightning return stroke at the injection point is modeled as an ideal current source. The time-domain current is transferred to the frequency domain by using the fast Fourier transform (FFT). Electromagnetic coupling between the lightning channel and LPS is disregarded in this section. The responses at different nodes and branches are calculated in the frequency domain. Then, the inverse Fourier transform is applied to obtain the corresponding time-domain responses. The experimental data for the return stroke labeled 0521-1, having a peak current of 6.8 kA, are used in this section. In the experiment, the insulation of the buried 600-V power-supply cable, whose neutral connected point D at the test house to the remote ground rod, was damaged by electrical breakdown (not known during which lightning flash). Currents measured at the two ends (points D and G) of the power cable neutral were not the same, with the difference between these two currents being likely due to current leaking into ground at the breakdown points. In order to account for this leakage current, we employed an ideal current source connected between point D and the reference ground in the circuit model, which accounts for the difference between the current measured at point D and that at point G. Calculated and measured currents in the LPS and electrical system neutral of the test house are shown in Figs. 4–8.

i

Currents , , , , and in these figures correspond, respectively, to the currents in the four down conductors A, A1, B, B1, and at point D in the power cable neutral (see companion paper). It can be seen that the calculated currents agree fairly well with the measured ones. The results show that the lumped circuit approach is applicable to the LPS configuration tested in 2005. Note that the initial (prior to peak) portion of waveforms shown in Figs. 4–8 (also in Figs. 9–17) is influenced by numerical errors discussed in Section V-A and is to be ignored. Fairly good agreement between calculated and measured waveforms in Figs. 4–8 implies that the LPS configuration tested in 2005 is not significantly affected by the electromagnetic coupling between the lightning channel and LPS. For



Fig. 9. Calculated and measured waveforms for i and measured waveform for the current at injection point (stroke 0401-3). Electromagnetic coupling is neglected.



Fig. 13. Calculated electromotive force induced in the above ground part of LPS tested in 2004 (stroke 0401-3).

Fig. 14. Calculated and measured waveforms for i (stroke 0401-3). Electromagnetic coupling between the lightning channel and the LPS is included in the model.

Fig. 15. Calculated and measured waveforms for i (stroke 0401-3). Electromagnetic coupling between the lightning channel and the LPS is included in the model. Fig. 11. Calculated and measured waveforms for i magnetic coupling is neglected.


this and other reasons, we did not perform calculations with electromagnetic coupling included for the LPS configuration tested in 2005. B. 2004 Configuration: Lumped Circuit Model Without Electromagnetic Coupling Between Lightning Channel and LPS (Stroke 0401-3)



The experimental data for return stroke 0401-3 having a peak current of 11 kA are used in this section. The current measured at point G (in the remote ground rod) was corrupted, because of arcing from the instrumentation box to the grounded power cable from a different experiment. Calculated and measured currents are shown in Figs. 9–12. The measured current at the injection point is additionally




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using (17). This induced voltage was represented as an ideal, lumped voltage source in the circuit model. The electromotive force waveforms calculated for lossy ground and perfect ground cases are shown in Fig. 13. The calculated current waveforms for lossy ground and perfect ground are compared with the measured current waveforms in Figs. 14–17. It can be seen from Figs. 14–17 that the peak values of calculated currents , , and coincide with the measured values, although there are still larger discrepancies in the tails of the waveforms. There is also large disagreement between the calculated and the measured waveform of current , whether electromagnetic coupling is included or not. The reasons for these discrepancies are presently unknown. The lumped circuit model, whether with or without electromagnetic coupling between the lightning channel and the LPS, does not allow one to faithfully reproduce all of the features of measured waveforms for the configuration tested in 2004. Comparing Figs. 9–12 with Figs. 14–17, one can infer that the electromagnetic coupling does play a significant role in the distribution of lightning currents in the LPS tested in 2004. The modeling results provide one possible explanation of the experimental fact that more higher-frequency components are contained in currents , , and than in the current at the injection point. Further, the electromagnetic coupling between the lightning channel and the LPS appears to be responsible for the peak value of current being larger than the peak value of the injected current, and for the oscillations in the waveforms of and . V. ANALYSIS AND DISCUSSION

shown in Fig. 9. It can be seen that there are large discrepancies between the calculated and measured currents. In the lumped circuit model, current at the injection point and , as required should be equal to the sum of currents by Kirchhoff’s current law. Also, the waveshapes of currents and should be similar to that of current at the injection point. However, this is not the case in the experimental data. It can be noted from Fig. 9 that the measured peak value of current is larger than the peak value of the injected current. The are sharper measured waveforms for currents , , and near the peak than the current waveform measured at the injection point, and there are oscillations in the measured waveforms and . These features show that more higher-frequency of components are contained in currents , , and than in the current at the injection point. One possible reason for the discrepancies between calculated and measured waveforms is our disregard in this section for electromagnetic coupling between the lightning channel and LPS. We will examine this factor in Section IV-C. Another possible reason for these discrepancies is the electromagnetic coupling to the measuring circuit in 2004. C. 2004 Configuration: Lumped Circuit Model With Electromagnetic Coupling Between Lightning Channel and LPS (stroke 0401-3) The voltage (emf) induced in the LPS by the electromagnetic coupling between lightning channel and the above ground part of LPS tested in 2004 was calculated in the frequency domain

A. Errors The approximate formulae are used to calculate the circuit parameters, such as the resistances, inductances, and capacitances of ground rods. Due to different assumptions used to arrive to each approximation, those parameters may be inconsistent with each other to a different degree. This inconsistency would introduce errors in the calculations. Although the calculation of induced voltage waveform in Fig. 13 is not related to circuit parameters, there is a large error (mismatch) at the initial stage of waveform. Therefore, the errors (not an offset) prior to the peak of waveforms in Figs. 4–17 are not related to circuit parameters. These errors are probably caused by the numerical convolution used in the calculation of circuit responses. Peak values and tail portions at the waveforms are not materially affected by these errors. For the lightning pulses having a nonzero constant component, an inherent systematic error exists when the FFT–IFFT algorithm is used to obtain the transient responses, such as the induced voltages on the transmission lines [30]. A theorem for this problem was introduced in [30]. According to the theorem, the error depends not only on the shape of the lightning pulse but also on the transfer function. From Figs. 10 and 15, it can be noted that there are large errors in the tail part of the waveforms of current , regardless of whether the influence of the electromagnetic field of the lightning channel is considered or not. When the electromagnetic coupling effect is included in the model, the oscillations appear near the peaks of calculated waveforms of currents



and , this feature being consistent with the measured waveforms. On the other hand, the tail part of the waveform is not affected significantly by electromagnetic coupling, because the lightning current contains less higher- frequency components at that stage. Therefore, the large errors in the tail part of calculated current waveforms are likely due to approximate circuit parameters, model assumptions, or other factors, such as insulation breakdown along the buried cable. The electromagnetic coupling to the measuring circuits in 2004 could also have influenced some of the measured currents (see the companion paper). B. Lightning Protective System It appears that the distribution of currents in the LPS tested in 2004 is significantly influenced by the electromagnetic field of lightning channel and connecting wire, but not in the LPS tested in 2005. Comparing the LPS configurations tested in 2004 and 2005, one can observe that the conductors of LPS tested in 2004 (two down conductors) were arranged to form only one main loop, but the conductors of LPS tested in 2005 (four down conductors interconnected by a buried loop conductor) formed a cage. It is likely that the electromagnetic coupling between the lightning channel and the different loops of the LPS tested in 2005 tended to cancel each other. Further, the induced effects depend not only on the configuration of the LPS but also on the relative positions of the test house and the tower launcher, orientation of the lead conductor, and the current injection point (see companion paper). VI. CONCLUSION We numerically modeled the distribution of lightning currents in the lightning protective system of a test house at the International Center for Lightning Research and Testing at Camp Blanding, FL, for the LPS configurations tested in 2004 and 2005. The model is based on the lumped circuit theory and is formulated in the frequency domain. The electromagnetic coupling between the lightning channel and the LPS is taken into account for the configuration tested in 2004, using the complex images method. Both lossy and perfectly conducting ground cases were considered. The calculated lightning currents in the LPS are compared with the measured ones. For the LPS configuration tested in 2005, a fairly good agreement was observed without including the electromagnetic coupling. For the LPS configuration tested in 2004, the agreement was not good, but was somewhat improved by including the electromagnetic coupling and lossy ground effects. ACKNOWLEDGMENT The authors would like to thank G. Maslowski, N. Theethayi, J. Schoene, J. Jerauld, R. Olsen, and A. Nag for helpful discussions. This work was performed when the first author was a visiting scholar at the University of Florida from August 2006 to July 2007. REFERENCES [1] B. A. DeCarlo, V. A. Rakov, J. Jerauld, G. H. Schnetzer, J. Schoene, M. A. Uman, K. J. Rambo, V. Kodali, D. M. Jordan, G. Maxwell, S. Humeniuk, and M. Morgan, “Triggered-lightning testing of the protective system of a residential building: 2004 and 2005 results,” in Proc. 28th Int. Conf Lightning Protection, Kanazawa, Japan, 2006, pp. 628–633.

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Lin Li received the Ph.D. degree in electrical engineering from the North China Electric Power University, Hebei, China, in 1997. Currently, he is a Professor with the School of Electrical Engineering at North China Electric Power University, Hebei, where he has been since 2001. His main research interests are in the fields of electromagnetic compatibility and electromagnetic-field theory and application.

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Vladimir A. Rakov (SM’96–F’03) received the M.S. and Ph.D. degrees in electrical engineering from the Tomsk Polytechnic University, Tomsk, Russia, in 1977 and 1983, respectively. From 1977 to 1979, he was an Assistant Professor of electrical engineering at Tomsk Polytechnic University. In 1978, he became involved in lightning research at the High Voltage Research Institute, where from 1984 to 1994, he was Director of the Lightning Research Laboratory. Currently, he is a Professor in the Department of Electrical and Computer Engineering, University of Florida, Gainesville, and Codirector of the International Center for Lightning Research and Testing (ICLRT). He is the author or coauthor of one book, ten book chapters, over 30 patents, and more than 400 papers and technical reports on various aspects of lightning, with over 140 papers being published in reviewed journals. Dr. Rakov is the Chairman of the Technical Committee on Lightning of the Biennial International Zurich Symposium on Electromagnetic Compatibility and Former Chairman of the AGU Committee on Atmospheric and Space Electricity (CASE). He is a Fellow of AMS and IET and a member of AGU, SAE, and ASEE.