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Electric Power Systems Research 73 (2005) 197–204

Electromagnetic compatibility analysis in buildings affected by lightning strike A.M.A. Bakera , M.S. Alama,∗ , M. Tanriovena , H.B. Ahmadb a

Department of Electrical and Computer Engineering, University of South Alabama, Mobile, AL 36688-0002, USA b Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 80990 JB, Malaysia Received 30 March 2004; accepted 16 August 2004 Available online 18 November 2004

Abstract In this paper, we present the electromagnetic compatibility (EMC) analysis of a telecommunication building struck by a direct lightning stroke based on a simulation model. For this purpose, the resulting magnetic and electric fields have been determined as a function of time considering potential points where lightning is expected to strike. These potential points correspond to places where highly susceptible equipment is installed in the telecommunication building. For illustration purposes, electromagnetic interference inside a telecommunication building is calculated using the newly proposed three-dimensional cell model and finite difference discretization technique. Some illustrations are presented to point out the advantages of the proposed electromagnetic interference prediction model used during the design of the electrical and electronic installations by considering the lightning effects. Finally, examples of electric and magnetic fields inside the building as well as lightning-induced over voltages due to side return stroke were given at various distances in the simulation results. © 2004 Elsevier B.V. All rights reserved. Keywords: Electromagnetic compatibility; Lightning strike; Finite difference technique; Wave propagation theory; Dipole and image method

1. Introduction The evaluation of the effects of lightning strike has been a special concern in our modern society due to the use of highly susceptible equipment, such as electronic devices and systems, for a wide variety of applications. Lightning flash between cloud and ground generates transient electromagnetic fields, which can result in extremely high voltages induced in the vicinity of lightning strike. When a building is struck by lightning, the resulting current and voltage transients can cause effects that can be dangerous from various points of view. The current that flows in the columns and beams of a building produces electromagnetic fields which couples with the components of electrical and electronic systems and may result in material damage, malfunction of equipment, and al∗

Corresponding author. Tel.: +1 205 348 9777; fax: +1 205 348 6959. E-mail address: [email protected] (M.S. Alam).

0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2004.08.004

teration of information. When lightning strikes to or near a building, it causes the local earth potential to rise to dangerously high level. As a result, all equipment within the building is subjected to the same high earth potential. Other surrounding buildings, even the neighboring ones, will be at a much lower potential. Often these two or more earth locations having drastically different potentials, and the equipment referenced to them, are linked by a power line or data communications line causing the difference in potential to be shared between the line and the equipment at each end. The potential across the components of these equipments is referenced as a resistively coupled transient over voltage. The geometry of this coupling is shown in Fig. 1. Thus, from the electromagnetic compatibility (EMC) point of view, it is very important to analyze the behavior of buildings, especially telecommunication buildings, when they are struck by lightning in order to determine the best solution for the lightning protection system and for the layout

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Fig. 1. Geometry of resistively coupled transients.

Fig. 2. Postulated lightning channel current waveform to calculate EM fields.

as of equipment. Various studies have been carried out to evaluate lightning-induced electromagnetic pulse effects inside the building [1]. Several techniques have been developed to compute these fields and their effects. Bessi et al. [2] used a numerical modeling based method, which computes over voltages and over currents conducting to the equipment. Some of the researchers such as Pieoricci and Pomponi [3] studied lightning effects experimentally. In reference [3], a lightning current is injected to the telecommunication tower to simulate the effects of lightning on the building. In this paper, we proposed a finite difference discretization based numerical technique, which calculates the electromagnetic fields as well as over voltages due to lightning stroke on the basis of a novel three-dimensional cell model and wave propagation theory. One of the main goals herein is to improve the aspects related to the EMC level of all electrical and electronic systems to ensure minimal damage due to direct lightning effects.

2. Analytical modeling One of the most important problems related to EMC analysis is the evaluation of the electromagnetic environment around a structure when struck by direct lightning. In this work, we propose to develop an electromagnetic field calculation methodology in the interior of a lightning protection system during a lightning strike. The proposed scheme uses a three-dimensional cell model, which represents the finite number of elementary units in the protection system conductors, lightning model and electromagnetic field model.

2.1. Lightning model The lightning strike is simulated by an ideal unidirectional current source injected at the striking point without taking into account the lightning channel. For mathematical convenience, the current wave shape has been expressed by the sum of two simple ramp functions. In this study, a simple triangular current pulse is used as shown in Fig. 2. The current propagates at constant velocity in an upright channel from the ground with damping and can be expressed

Ip for 0 < t ≤ tf · t, tf i= Ip · (t − te ), for tf < t ≤ te tf − te

(1)

This model that can be used for predicting the physical characteristics of the lightning strike with primary emphasis on the remote electric and magnetic fields to the channel current. This approach provides the closest approximation and is obtained by assuming a spatial and temporal form for the channel current and then uses these current components to calculate the remote fields. The current waveform is constrained to agree with the properties of lightning currents measured at ground level and by the available data on the measured electric and magnetic fields. In this paper, this approach has been adopted for the calculation of electromagnetic fields because this type of model better relates the theoretical data with the experimental one. 2.2. Cell model The objective of the present work is to carry out a discretization technique in space and time domains to calculate the distribution in a lightning protection system and the flux density of electromagnetic fields inside the protected volume. For this purpose, we developed a three-dimensional model of an element or a cell, where the central node corresponds to a junction of transmission lines, forming an impedance discontinuity in each line as shown in Fig. 3. This model represents a unit cell, which can be chosen by dividing the considered building into cells, where the length is chosen to be much smaller than the minimum wavelength of the transient wave. The response of the aforementioned cell to incident voltage pulses and the current distribution was determined by the using transmission line and wave propagation theory [4,5]. Then, an infinitesimal time-varying dipole and image method were used to calculate the contribution of each of the reflected and incident currents of the element corresponding to the electric and magnetic fields. The total electric and magnetic fields as a function of time at any point of the space can then be determined by utilizing the principle of superposition, after subdividing the protection system conductors into a finite number of elementary units. The proposed three-dimensional elements or cells represent these elementary units. The pro-

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199

Fig. 4. Geometry of a straight vertical lightning channel of height H used to calculate the EM field at a point above a perfectly conducting ground.

Fig. 3. The proposed three-dimensional model of an element or a cell.

posed scheme is suitable for the evaluation of energy and interference levels, which occurs during a lightning strike. 2.3. EM ﬁeld modeling The mathematical modeling for radiation in a linear, homogeneous, isotropic, and time invariant medium is given by Maxwell’s equations, which can be written in time domain as ¯ =ρ ∇¯ · E ε ¯ ·B ¯ =0 ∇ ¯ (2) ¯ = − ∂B ∇¯ × E ∂t ¯ ∇¯ × B ¯ = µ0 J¯ + 1 ∂E v2c ∂t ¯ represents the electric field, B ¯ the magnetic field, where E vc the velocity of light, J¯ the current density, ρ the electric charge density, and µ0 and ε0 are the permeability and permittivity of free space, respectively. The solutions to the Maxwell’s equations for the electric and magnetic fields in terms of retarded scalar and vector potentials are ¯ ¯ = −∇¯ · φ ∂A E (3) ∂t ¯ ¯ = ∇¯ × A, B (4) ¯ where A(r, t) is the vector magnetic potential and φ(r,t) is the ¯ t) and φ(r,t) can be easily deterscalar electric potential. A(r, mined from a current element. Once the vector magnetic and scalar electric potentials are determined, the EM fields can be calculated using Eqs. (3) and (4). The geometry used for calculating the electric and magnetic fields at a point above a perfectly conducting ground due to a straight vertical lightning channel is shown in Fig. 4. It is obvious that only at close distances (within 3 km) from the lightning channel, the horizontal electric field (HEF) at few meters above the ground

can be calculated with reasonable accuracy by assuming that the ground is a perfectly conducting media. The effect of a perfectly conducting ground can be included in the expressions of E and B fields by considering an image dipole at the same distance beneath the ground plane as shown in Fig. 4. The image dipole fields are defined as [6] dz 3r(z + z) t R ¯ dE = − i −z, t − dt 4πε0 vc R 5 0 3r(z + z ) R + i −z, t − c vc R 4

r(z + z ) ∂i(−z, t − R /vc ) + a¯ r ∂t v2c R 3 2(z + z )2 − r 2 t R + i −z, t − dt vc R 5 0 2(z + z ) − r 2 R + i −z, t − vc vc R 4

r2 ∂i(−z, t − R /vc ) − a¯ z (5) ∂t v2c R 3 r R ¯ = − µ0 dz dB i −z, t − 4π vc R 3

r ∂i(z, t − R /vc ) + (6) a¯ ϕ , ∂t vc R 2 and, the analytical expressions for the vertical and horizontal electric fields in a rectangular system are defined as 2(z − z)2 − r 2 t dz R ¯z = dE dt i z, t − 4πε0 vc R5 0 2(z − z)2 − r 2 R i z, t − vc vc R4

r2 ∂i(z, t − R/vc ) − 2 3 a¯ z ∂t vc R

+

(7)

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¯H = dE

dEz

3r(z − z) t R dt i z, t − vc R5 0 3(z − z) R + i z, t − vc vc R 4

r(z − z) ∂i(z, t − R/vc ) + 2 3 (cos θ a¯ x + sin θ a¯ y ) ∂t vc R (8)

dz 4πε0

dz =− 4πε0

2(z + z )2 − r 2

R dt i −z, t − vc 0

dz 4πε0

3r(z + z )

(9)

t

×(cos θ a¯ x + sin θ a¯ y )

(11)

∂ ∂ V (y, t) + L · i(y, t) = Ey (y, t) ∂y ∂t

(12)

3.1. Finite-difference numerical technique

R i −z, t − dt vc R 5 0 3r(z + z ) R + i −z, t − vc vc R 4

r(z + z ) ∂i(−z, t − R /vc ) + ∂t v2c R 3

¯H dE =−

∂ ∂ i(y, t) + C · V (y, t) = 0 ∂y ∂t

3. Algorithm development

t

R 5 R 2(z + z )2 − r 2 i −z, t − + vc vc R 4

r2 ∂i(−z, t − R/vc ) − az ∂t v2c R 3

to it’s inherent capacity to include both horizontal and vertical components of the electric field as shown in Eqs. (11) and (12).

(10)

In the Eqs. (5)–(10), a¯ x , a¯ y , and a¯ z are unit vectors in the ¯z rectangular coordinate system (refer to Fig. 4), and dE ¯ and dEH the vertical and horizontal components of elec¯ z and dH ¯ z are the vertric field, respectively. Similarly, dE tical and horizontal components of theimage dipole electric

fields, and cosθ = x/r, sinθ = y/r, R = x2 + y2 + (z − z )2 , and r = x2 + y2 are geometric factors. In the Eqs. (5)–(10), the vertical and horizontal components of electric fields contain three components – the integral of channel current representing the electrostatic component, derivative of channel current representing the radiation component, and channel current only representing the induction component. However, the magnetic field has only induction and radiation components. 2.4. Induced voltage modeling The calculation of lightning-induced over voltages (LIOVs) are based on the transmission line approximation, which means that the transverse dimension of the line considered is much smaller than the minimum significant wavelength, and that the response of the line to the lightning electromagnetic field is quasi-transverse electromagnetic. In this case, we utilized the Agrawal coupling model [7] to calculate the induced surges in telecommunication buildings, due

The finite-difference numerical method is particularly suitable for solving transient problems. Moreover, it is quite versatile due to the availability of present computer technology for solving computationally intensive practical problems. In the finite-difference method, continuous space-time partial differential equations are replaced with a system of algebraic equations. These equations can be readily implemented and solved in a digital computer. Furthermore, an iterative scheme can be implemented without requiring to the solution of large matrices, which results in significant savings in computer time. More recently, the development of parallel processors further enhanced the efficiency of the finite difference methods, which can be approximated in many ways [6]. For example, the forward, backward and central differences can be expressed as ∂φ(r, t) φ(r, t + = ∂t

t) − φ(r, t) t

φ(r, t) − φ(r, t − ∂φ(r, t) = t ∂t φ (r, t + ∂φ(r, t) = ∂t

(13)

t)

t/2) − φ(r, t − t

(14) t/2)

,

(15)

where the incremental time interval t is a very small number. Although the finite difference method provides the best approximation, in this study, approximations represented by Eqs. (13) and (14) are used for convenience in solving the differential coupling equations corresponding to lightninginduced over voltages. 3.2. Numerical solution of EM ﬁeld In this study, a detailed computer simulation program has been developed to obtain the numerical solution for the analytical expressions of the electric (E) and magnetic (B) fields. The basic procedure for solving any physical problem is through the development of an algorithm that resolves the problem into a number of arithmetic and logical expressions. In this paper, an algorithm has been developed to solve the vertical and horizontal components of the electric and magnetic fields. The development procedure of the algorithm for solving the electric and magnetic fields is almost the same.

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The algorithm required to calculate the vertical electric field (VEF) provides an overall idea about the steps involved in the field calculations. Once the expressions for the electric and magnetic fields of a short channel section and its image are formulated, the fields at point P(r, θ, z ) due to the dipole at point (0, 0, z ) are found from the sum of the fields contributed by the dipole and the image dipole section of the lightning channel. The fields for the whole channel can be found by integrating the dipole fields over the channel. Therefore, the total dipole-induced electric fields for the whole channel can be expressed as H ¯ ¯ z + dE ¯ H ) dz E= (dE (16) ¯ = B

0

H

dBdz

(17)

0

Similarly, the total image dipole-induced electric fields for the whole channel are H ¯ = E (dEz + dEH ) dz (18) ¯ = B

0

H

dB dz.

(22) and (23) can be solved for voltage and current for every incremental time at any point as follows V [i, j + 1] = −

I[i, j + 1] = −

t {I[i, j] − I[i − 1, j]} + V [i, j] C y

t Ey [i, j + 1] + Ey [i, j] + I[i, j] L 2

+

¯ tot = E ¯ +E ¯ E

(20)

¯ tot = B ¯ +B ¯ B

(21)

Using Eqs. (24) and (25), and the boundary conditions reported in reference [7], the scattered voltages and line currents at the left and right ends of the channel can be calculated using the following set of four equations 1 t V m [1, j + 1] V [1, j + 1] = − − V [2, j + 1] + kk1 L y R0

t Ey [1, j + 1] + Ey [1, j] + + I[1, j] 2 L (26)

I[1, j + 1] = −

V [1, j + 1] + V m [1, j + 1] R0

(27)

1 t V [i + 1, j + 1] = − − V [i, j + 1] kk2 L y −

Note that there is no field at point P(r, θ, z ) until the time t = R0 /vc , where R0 represents a distance shown in Fig. 4 and vc is the velocity of light.

V m [i + 1, j + 1] Rl

t Ey [i, j + 1] + Ey [i, j] + + I[i, j] L 2

(28)

3.3. Algorithm for calculation of LIOV on a cell This algorithm involves step-by-step development of a detailed computer software package to calculate LIOV and over currents, using finite difference equations (in conjunction with the calculation of vertical and horizontal component of electric fields). In this technique, the finite difference representation of the Agrawal coupling model [7] are used. Therefore, Eqs. (11) and (12) and can be rewritten, respectively, as (22)

V [i + 1, j + 1] − V [i, j + 1] I[i, j + 1] − I[i, j] +L y t Ey [i, j + 1] + Ey [i, j] , 2

(25)

(19)

Therefore, the total electric and magnetic fields corresponds to the sum of dipole field and image dipole field, and are given as

=

(24)

t {V [i + 1, j + 1] − V [i, j + 1]} L y

0

I[i, j] − I[i − 1, j] V (i, j + 1 − V )[i, j] +C =0 y t

201

(23)

where i denotes incremental position, j denotes incremental time, and Ey [i, j] represents the horizontal electric field. Eqs.

I[i, j + 1] = −

V [i + 1, j + 1] + V m [i + 1, j + 1] , Rl

(29)

where Vm [i, j] are incident voltages, and kk1 and kk2 are constants determined from kk1 = 1/r0 + t/L y and kk2 = 1/rl + t/L y, respectively. Thus, the induced voltage at any point can be calculated as Vind = V (y, t) + V m (y, t)

(30)

Now Eqs. (24)–(30) are the complete expressions for the LIOV calculation at any point. The software package was developed using C++ to calculate the lightning-induced over voltages and over currents. Calculation of voltages and currents are done in the main program while the subprograms are used by the main program for the calculation of horizontal and vertical components of electric fields. The following assumptions were made in the development of the algorithm:

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• The cell consists of 16 equal size segments, • The positive values of horizontal electric field and currents are directed from the left to the right of the cell; • The vertical electric field is positively directed towards the ground; • LIOVs are positive from the ground to telecommunication subscriber lines (TSL); and • The position-increment strictly maintains the condition y ≥ Vp t, where Vp is the velocity of propagation along the TSL.

4. Simulation results The radiated electric and magnetic fields from a lightning channel present different behaviors depending upon different parametric conditions of return stroke. As mentioned earlier, the electric field has two components – the vertical and horizontal components. Each of the vertical and horizontal electric fields consists of three terms: electrostatic, induction, and radiation terms. On the other hand, the magnetic field has only horizontal component, which possesses induction and radiation field terms. This research highlights the change in electric and magnetic fields due to different parametric effects of the return stroke. This analysis is based on the following assumed conditions: • The lightning channel is straight and located vertically at a distance of 4 km. • A triangular pulse current with tf = 2.5 s, te = 25 s, and Ip = 10 kA moves with a velocity of 100 m/s from ground and terminates in the cloud. • The lightning channel is assumed as a lossless transmission line terminating in its characteristic impedance to exclude the reflection of channel current.

Fig. 6. Induced voltages at the right end of a 1 km for the side return strokes occur at different distances 0.5, 1, and 1.5 km to the left.

the rise time of 7.75, 11.5, and 14.75 s for the SRS occurring at 0.5, 1, and 1.5 km, respectively (refer to Fig. 5). The rise time is defined as the time taken by the LIOV to reach their peak values from the zero value. On the other hand, the peak values of LIOV to the right are 773, 364, and 230 V with respect to the rise times of 5.25, 4.89, and 4.75 s for the above strikes, respectively (refer to Fig. 6). The LIOV due to front side stroke (FRS) occurring at 0.5, 1, and 1.5 km along the perpendicular bisector of the cell are shown in Fig. 7, where the peak values are 2370, 852, and 442 V with their respective rise times of 7.25, 7.75, and 7.75 s. The results show that LIOV vary inversely with the distance. For the SRS, the distance ratio 1:2:3 produces approximate peak LIOV ratio of 3:2:1. However, for FRS, the peak LIOV ratio is approximately 6:2:1. It means that FRS produces worst case in terms of peak values. The change in front time shows that steepness of LIOV is distance dependent for the case of SRS. The LIOV at the right are steeper than that of the left because of the effect of the radiation field term of vertical electric field. The FRS has no significant effect on steepness. Comparing the side and front return strokes, it is found that the first case produces higher steepness of induced voltages.

4.1. Effects of strike distance on LIOV 4.2. Effect of VEF and HEF on LIOV Strike distance dependency of LIOV due to side return stroke (SRS) occurring at 0.5, 1, and 1.5 km along the left extension of a 1 km for left and right end voltages are shown in Figs. 5 and 6, respectively. The peak values of LIOV in the left are calculated for 1079, 514, and 327 V with respect to

Voltage induced due to horizontal and vertical electric fields in a 1.8 km over the telecommunication building during front return stroke at 0.5 km from the mid point is shown in

Fig. 5. Induced voltages at the left end of a 1 km for side return strokes occur at different distances 0.5, 1, and 1.5 km to the left.

Fig. 7. Induced voltages at the left end of a 1 km the line for front return stroke occur at 0.5, 1, and 1.5 km from the midpoint and along the perpendicular bisector of the line.

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Fig. 8. Contribution of horizontal and vertical electric fields on induced voltages in a 1.8 km during FRS at 0.5 km.

Fig. 8. Side return stroke at 0.5, 1, and 5 km from the left end of the telecommunication building are shown in Figs. 9–11, respectively. The dotted line indicates the contribution of horizontal electric field in producing induced over voltages on subscriber line while the vertical electric field is set to zero. The dotted–dashed line indicates the contribution of vertical electric field while the horizontal electric field is set to zero. Finally, the solid line indicates the contribution of both fields. During the front return stroke, the horizontal electric field is dominant over vertical electric field in contributing to LIOV (refer to Fig. 8). However, during side return stroke, the vertical electric field contribution becomes dominant over horizontal electric field on induced voltages (refer to Fig. 9). The effect of horizontal electric field becomes insignificant

Fig. 11. Contribution of horizontal and vertical electric fields on LIOV on a 1.8 km TB during SRS at 5 km.

when compared to the vertical electric field if the strike distance increases (refer to Figs. 10 and 11). 4.3. Effects of strike locations on LIOV The different strike locations for the lightning return strokes and the corresponding LIOV at the left termination of a 1-km TSL are shown in Fig. 12. The numerical values obtained from the analysis indicate that the peak LIOV due to SRS at 0.5 km are 1067, 1602, 2370, 1664, and 773 V with corresponding rise time of 6, 6.25, 7.25, 6.5, and 5.25 s. It is evident from Fig. 12 that the wave shapes of LIOV are different depending upon the strike locations. The front return strokes produce higher peak values of LIOV compared to the side return strokes. On the other hand, LIOV due to SRS are steeper than that of front return stroke. The behavior of the electromagnetic field has been analyzed by considering the maximum value and front steepness of the field waveform and different lighting strike points. The magnetic flux density, and the horizontal and vertical electric fields as a function of time (s) at point (8, 0, −7 m) due to the current distribution in the structure, are depicted in Figs. 13–15, respectively. The waveforms of the horizontal and vertical electric fields at the

Fig. 9. Contribution of horizontal and vertical electric fields on induced voltages in a 1.8 km during SRS at 0.5 km.

Fig. 10. Contribution of horizontal and vertical electric fields on LIOV on a 1.8 km TB during SRS at 1 km.

Fig. 12. Induced voltages at the left end of a 1-km TSL for different strike locations. Strike points are at 0.5 km from the nearest point of the line when it is placed on ground and the distance between two consecutive front strikes is 250 m.

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the former is about 6 s, the latter’s peak-reaching time is around 4 s.

5. Conclusion

Fig. 13. Magnetic field B(T) as a function of time (s) at point (8, 0, −7 m).

A new three-dimensional numerical model based on the transmission line and wave propagation theory for calculating the current distribution in a structure, which is struck by direct lightning, is presented. The proposed technique utilizes the infinitesimal time-varying dipole theory while the method of images is used to calculate the electromagnetic field around it. With this model, the EMC analysis has been carried out and the results are presented. It is shown that the proposed methodology is simple but it is a suitable numerical method for electromagnetic compatibility studies. The salient features of the proposed technique are: • It is a fast and direct method from computational point of view, • It is possible to represent many building configurations by appropriate composition of the elementary cell, and • The electromagnetic field can be predicted, which helps the designer to make the best decisions during an EMC study when many parameters are involved.

Fig. 14. Horizontal electric field Er (T) as a function of time (s) at point (8, 0, −7 m).

Fig. 15. Vertical electric field Ey (T) as a function of time (s) at point (8, 0, −7 m).

point (8, 0, −7 m) exhibit a rise and decay characteristic similar to that of lightning current. While peak-reaching time of

References [1] M. Bandienelli, F. Bessi, S. Chitti, M. Infantino, R. Pomponi, Numerical modeling for LEMP effect evaluation inside a telecommunication exchange, IEEE Trans. Electromag. Compatibility 38 (3) (1996) 265–273. [2] B.F. Bessi, S. Chitti, R. Pomponi, LEMP effects in telecommunication Center, in: 10th Zurich Symp. Tech. Exhibit, EMC, March, 1993. [3] I.M. Pieoricci, R. Pomponi, Simulated LEMP effects inside a telecommunication exchange: field test results, in: 11th Zurich Symp. Tech. Exhibit, EMC, March, 1995. [4] C.A.F. Sartori, J.R. Cardoso, Evaluation of electromagnetic environment around a structure during a lightning stroke, in: Proceedings of the 1994 International Symposium on EMC, Rome, Italy, 1994, pp. 746–749. [5] P.B. Johns, R.L. Beurle, Numerical modeling of 2-dimensional scattering problems using a transmission line matrix, in: Proceedings of IEE, vol. 118, no. 9, September, 1971, pp. 1203–1208. [6] M. Rubinstein, M.A. Uman, Transient electric and magnetic fields associated with establishing a finite electrostatic dipole, IEEE Trans. Electromag. Compatibility 33 (1991) 312–320. [7] A.M. Ramli, Measurement of lightning induced surges on telecommunication subscriber cables in Malaysia, MEE Thesis, September 1998.

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Electromagnetic compatibility analysis in buildings affected by lightning strike A.M.A. Bakera , M.S. Alama,∗ , M. Tanriovena , H.B. Ahmadb a

Department of Electrical and Computer Engineering, University of South Alabama, Mobile, AL 36688-0002, USA b Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 80990 JB, Malaysia Received 30 March 2004; accepted 16 August 2004 Available online 18 November 2004

Abstract In this paper, we present the electromagnetic compatibility (EMC) analysis of a telecommunication building struck by a direct lightning stroke based on a simulation model. For this purpose, the resulting magnetic and electric fields have been determined as a function of time considering potential points where lightning is expected to strike. These potential points correspond to places where highly susceptible equipment is installed in the telecommunication building. For illustration purposes, electromagnetic interference inside a telecommunication building is calculated using the newly proposed three-dimensional cell model and finite difference discretization technique. Some illustrations are presented to point out the advantages of the proposed electromagnetic interference prediction model used during the design of the electrical and electronic installations by considering the lightning effects. Finally, examples of electric and magnetic fields inside the building as well as lightning-induced over voltages due to side return stroke were given at various distances in the simulation results. © 2004 Elsevier B.V. All rights reserved. Keywords: Electromagnetic compatibility; Lightning strike; Finite difference technique; Wave propagation theory; Dipole and image method

1. Introduction The evaluation of the effects of lightning strike has been a special concern in our modern society due to the use of highly susceptible equipment, such as electronic devices and systems, for a wide variety of applications. Lightning flash between cloud and ground generates transient electromagnetic fields, which can result in extremely high voltages induced in the vicinity of lightning strike. When a building is struck by lightning, the resulting current and voltage transients can cause effects that can be dangerous from various points of view. The current that flows in the columns and beams of a building produces electromagnetic fields which couples with the components of electrical and electronic systems and may result in material damage, malfunction of equipment, and al∗

Corresponding author. Tel.: +1 205 348 9777; fax: +1 205 348 6959. E-mail address: [email protected] (M.S. Alam).

0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2004.08.004

teration of information. When lightning strikes to or near a building, it causes the local earth potential to rise to dangerously high level. As a result, all equipment within the building is subjected to the same high earth potential. Other surrounding buildings, even the neighboring ones, will be at a much lower potential. Often these two or more earth locations having drastically different potentials, and the equipment referenced to them, are linked by a power line or data communications line causing the difference in potential to be shared between the line and the equipment at each end. The potential across the components of these equipments is referenced as a resistively coupled transient over voltage. The geometry of this coupling is shown in Fig. 1. Thus, from the electromagnetic compatibility (EMC) point of view, it is very important to analyze the behavior of buildings, especially telecommunication buildings, when they are struck by lightning in order to determine the best solution for the lightning protection system and for the layout

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Fig. 1. Geometry of resistively coupled transients.

Fig. 2. Postulated lightning channel current waveform to calculate EM fields.

as of equipment. Various studies have been carried out to evaluate lightning-induced electromagnetic pulse effects inside the building [1]. Several techniques have been developed to compute these fields and their effects. Bessi et al. [2] used a numerical modeling based method, which computes over voltages and over currents conducting to the equipment. Some of the researchers such as Pieoricci and Pomponi [3] studied lightning effects experimentally. In reference [3], a lightning current is injected to the telecommunication tower to simulate the effects of lightning on the building. In this paper, we proposed a finite difference discretization based numerical technique, which calculates the electromagnetic fields as well as over voltages due to lightning stroke on the basis of a novel three-dimensional cell model and wave propagation theory. One of the main goals herein is to improve the aspects related to the EMC level of all electrical and electronic systems to ensure minimal damage due to direct lightning effects.

2. Analytical modeling One of the most important problems related to EMC analysis is the evaluation of the electromagnetic environment around a structure when struck by direct lightning. In this work, we propose to develop an electromagnetic field calculation methodology in the interior of a lightning protection system during a lightning strike. The proposed scheme uses a three-dimensional cell model, which represents the finite number of elementary units in the protection system conductors, lightning model and electromagnetic field model.

2.1. Lightning model The lightning strike is simulated by an ideal unidirectional current source injected at the striking point without taking into account the lightning channel. For mathematical convenience, the current wave shape has been expressed by the sum of two simple ramp functions. In this study, a simple triangular current pulse is used as shown in Fig. 2. The current propagates at constant velocity in an upright channel from the ground with damping and can be expressed

Ip for 0 < t ≤ tf · t, tf i= Ip · (t − te ), for tf < t ≤ te tf − te

(1)

This model that can be used for predicting the physical characteristics of the lightning strike with primary emphasis on the remote electric and magnetic fields to the channel current. This approach provides the closest approximation and is obtained by assuming a spatial and temporal form for the channel current and then uses these current components to calculate the remote fields. The current waveform is constrained to agree with the properties of lightning currents measured at ground level and by the available data on the measured electric and magnetic fields. In this paper, this approach has been adopted for the calculation of electromagnetic fields because this type of model better relates the theoretical data with the experimental one. 2.2. Cell model The objective of the present work is to carry out a discretization technique in space and time domains to calculate the distribution in a lightning protection system and the flux density of electromagnetic fields inside the protected volume. For this purpose, we developed a three-dimensional model of an element or a cell, where the central node corresponds to a junction of transmission lines, forming an impedance discontinuity in each line as shown in Fig. 3. This model represents a unit cell, which can be chosen by dividing the considered building into cells, where the length is chosen to be much smaller than the minimum wavelength of the transient wave. The response of the aforementioned cell to incident voltage pulses and the current distribution was determined by the using transmission line and wave propagation theory [4,5]. Then, an infinitesimal time-varying dipole and image method were used to calculate the contribution of each of the reflected and incident currents of the element corresponding to the electric and magnetic fields. The total electric and magnetic fields as a function of time at any point of the space can then be determined by utilizing the principle of superposition, after subdividing the protection system conductors into a finite number of elementary units. The proposed three-dimensional elements or cells represent these elementary units. The pro-

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199

Fig. 4. Geometry of a straight vertical lightning channel of height H used to calculate the EM field at a point above a perfectly conducting ground.

Fig. 3. The proposed three-dimensional model of an element or a cell.

posed scheme is suitable for the evaluation of energy and interference levels, which occurs during a lightning strike. 2.3. EM ﬁeld modeling The mathematical modeling for radiation in a linear, homogeneous, isotropic, and time invariant medium is given by Maxwell’s equations, which can be written in time domain as ¯ =ρ ∇¯ · E ε ¯ ·B ¯ =0 ∇ ¯ (2) ¯ = − ∂B ∇¯ × E ∂t ¯ ∇¯ × B ¯ = µ0 J¯ + 1 ∂E v2c ∂t ¯ represents the electric field, B ¯ the magnetic field, where E vc the velocity of light, J¯ the current density, ρ the electric charge density, and µ0 and ε0 are the permeability and permittivity of free space, respectively. The solutions to the Maxwell’s equations for the electric and magnetic fields in terms of retarded scalar and vector potentials are ¯ ¯ = −∇¯ · φ ∂A E (3) ∂t ¯ ¯ = ∇¯ × A, B (4) ¯ where A(r, t) is the vector magnetic potential and φ(r,t) is the ¯ t) and φ(r,t) can be easily deterscalar electric potential. A(r, mined from a current element. Once the vector magnetic and scalar electric potentials are determined, the EM fields can be calculated using Eqs. (3) and (4). The geometry used for calculating the electric and magnetic fields at a point above a perfectly conducting ground due to a straight vertical lightning channel is shown in Fig. 4. It is obvious that only at close distances (within 3 km) from the lightning channel, the horizontal electric field (HEF) at few meters above the ground

can be calculated with reasonable accuracy by assuming that the ground is a perfectly conducting media. The effect of a perfectly conducting ground can be included in the expressions of E and B fields by considering an image dipole at the same distance beneath the ground plane as shown in Fig. 4. The image dipole fields are defined as [6] dz 3r(z + z) t R ¯ dE = − i −z, t − dt 4πε0 vc R 5 0 3r(z + z ) R + i −z, t − c vc R 4

r(z + z ) ∂i(−z, t − R /vc ) + a¯ r ∂t v2c R 3 2(z + z )2 − r 2 t R + i −z, t − dt vc R 5 0 2(z + z ) − r 2 R + i −z, t − vc vc R 4

r2 ∂i(−z, t − R /vc ) − a¯ z (5) ∂t v2c R 3 r R ¯ = − µ0 dz dB i −z, t − 4π vc R 3

r ∂i(z, t − R /vc ) + (6) a¯ ϕ , ∂t vc R 2 and, the analytical expressions for the vertical and horizontal electric fields in a rectangular system are defined as 2(z − z)2 − r 2 t dz R ¯z = dE dt i z, t − 4πε0 vc R5 0 2(z − z)2 − r 2 R i z, t − vc vc R4

r2 ∂i(z, t − R/vc ) − 2 3 a¯ z ∂t vc R

+

(7)

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¯H = dE

dEz

3r(z − z) t R dt i z, t − vc R5 0 3(z − z) R + i z, t − vc vc R 4

r(z − z) ∂i(z, t − R/vc ) + 2 3 (cos θ a¯ x + sin θ a¯ y ) ∂t vc R (8)

dz 4πε0

dz =− 4πε0

2(z + z )2 − r 2

R dt i −z, t − vc 0

dz 4πε0

3r(z + z )

(9)

t

×(cos θ a¯ x + sin θ a¯ y )

(11)

∂ ∂ V (y, t) + L · i(y, t) = Ey (y, t) ∂y ∂t

(12)

3.1. Finite-difference numerical technique

R i −z, t − dt vc R 5 0 3r(z + z ) R + i −z, t − vc vc R 4

r(z + z ) ∂i(−z, t − R /vc ) + ∂t v2c R 3

¯H dE =−

∂ ∂ i(y, t) + C · V (y, t) = 0 ∂y ∂t

3. Algorithm development

t

R 5 R 2(z + z )2 − r 2 i −z, t − + vc vc R 4

r2 ∂i(−z, t − R/vc ) − az ∂t v2c R 3

to it’s inherent capacity to include both horizontal and vertical components of the electric field as shown in Eqs. (11) and (12).

(10)

In the Eqs. (5)–(10), a¯ x , a¯ y , and a¯ z are unit vectors in the ¯z rectangular coordinate system (refer to Fig. 4), and dE ¯ and dEH the vertical and horizontal components of elec¯ z and dH ¯ z are the vertric field, respectively. Similarly, dE tical and horizontal components of theimage dipole electric

fields, and cosθ = x/r, sinθ = y/r, R = x2 + y2 + (z − z )2 , and r = x2 + y2 are geometric factors. In the Eqs. (5)–(10), the vertical and horizontal components of electric fields contain three components – the integral of channel current representing the electrostatic component, derivative of channel current representing the radiation component, and channel current only representing the induction component. However, the magnetic field has only induction and radiation components. 2.4. Induced voltage modeling The calculation of lightning-induced over voltages (LIOVs) are based on the transmission line approximation, which means that the transverse dimension of the line considered is much smaller than the minimum significant wavelength, and that the response of the line to the lightning electromagnetic field is quasi-transverse electromagnetic. In this case, we utilized the Agrawal coupling model [7] to calculate the induced surges in telecommunication buildings, due

The finite-difference numerical method is particularly suitable for solving transient problems. Moreover, it is quite versatile due to the availability of present computer technology for solving computationally intensive practical problems. In the finite-difference method, continuous space-time partial differential equations are replaced with a system of algebraic equations. These equations can be readily implemented and solved in a digital computer. Furthermore, an iterative scheme can be implemented without requiring to the solution of large matrices, which results in significant savings in computer time. More recently, the development of parallel processors further enhanced the efficiency of the finite difference methods, which can be approximated in many ways [6]. For example, the forward, backward and central differences can be expressed as ∂φ(r, t) φ(r, t + = ∂t

t) − φ(r, t) t

φ(r, t) − φ(r, t − ∂φ(r, t) = t ∂t φ (r, t + ∂φ(r, t) = ∂t

(13)

t)

t/2) − φ(r, t − t

(14) t/2)

,

(15)

where the incremental time interval t is a very small number. Although the finite difference method provides the best approximation, in this study, approximations represented by Eqs. (13) and (14) are used for convenience in solving the differential coupling equations corresponding to lightninginduced over voltages. 3.2. Numerical solution of EM ﬁeld In this study, a detailed computer simulation program has been developed to obtain the numerical solution for the analytical expressions of the electric (E) and magnetic (B) fields. The basic procedure for solving any physical problem is through the development of an algorithm that resolves the problem into a number of arithmetic and logical expressions. In this paper, an algorithm has been developed to solve the vertical and horizontal components of the electric and magnetic fields. The development procedure of the algorithm for solving the electric and magnetic fields is almost the same.

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The algorithm required to calculate the vertical electric field (VEF) provides an overall idea about the steps involved in the field calculations. Once the expressions for the electric and magnetic fields of a short channel section and its image are formulated, the fields at point P(r, θ, z ) due to the dipole at point (0, 0, z ) are found from the sum of the fields contributed by the dipole and the image dipole section of the lightning channel. The fields for the whole channel can be found by integrating the dipole fields over the channel. Therefore, the total dipole-induced electric fields for the whole channel can be expressed as H ¯ ¯ z + dE ¯ H ) dz E= (dE (16) ¯ = B

0

H

dBdz

(17)

0

Similarly, the total image dipole-induced electric fields for the whole channel are H ¯ = E (dEz + dEH ) dz (18) ¯ = B

0

H

dB dz.

(22) and (23) can be solved for voltage and current for every incremental time at any point as follows V [i, j + 1] = −

I[i, j + 1] = −

t {I[i, j] − I[i − 1, j]} + V [i, j] C y

t Ey [i, j + 1] + Ey [i, j] + I[i, j] L 2

+

¯ tot = E ¯ +E ¯ E

(20)

¯ tot = B ¯ +B ¯ B

(21)

Using Eqs. (24) and (25), and the boundary conditions reported in reference [7], the scattered voltages and line currents at the left and right ends of the channel can be calculated using the following set of four equations 1 t V m [1, j + 1] V [1, j + 1] = − − V [2, j + 1] + kk1 L y R0

t Ey [1, j + 1] + Ey [1, j] + + I[1, j] 2 L (26)

I[1, j + 1] = −

V [1, j + 1] + V m [1, j + 1] R0

(27)

1 t V [i + 1, j + 1] = − − V [i, j + 1] kk2 L y −

Note that there is no field at point P(r, θ, z ) until the time t = R0 /vc , where R0 represents a distance shown in Fig. 4 and vc is the velocity of light.

V m [i + 1, j + 1] Rl

t Ey [i, j + 1] + Ey [i, j] + + I[i, j] L 2

(28)

3.3. Algorithm for calculation of LIOV on a cell This algorithm involves step-by-step development of a detailed computer software package to calculate LIOV and over currents, using finite difference equations (in conjunction with the calculation of vertical and horizontal component of electric fields). In this technique, the finite difference representation of the Agrawal coupling model [7] are used. Therefore, Eqs. (11) and (12) and can be rewritten, respectively, as (22)

V [i + 1, j + 1] − V [i, j + 1] I[i, j + 1] − I[i, j] +L y t Ey [i, j + 1] + Ey [i, j] , 2

(25)

(19)

Therefore, the total electric and magnetic fields corresponds to the sum of dipole field and image dipole field, and are given as

=

(24)

t {V [i + 1, j + 1] − V [i, j + 1]} L y

0

I[i, j] − I[i − 1, j] V (i, j + 1 − V )[i, j] +C =0 y t

201

(23)

where i denotes incremental position, j denotes incremental time, and Ey [i, j] represents the horizontal electric field. Eqs.

I[i, j + 1] = −

V [i + 1, j + 1] + V m [i + 1, j + 1] , Rl

(29)

where Vm [i, j] are incident voltages, and kk1 and kk2 are constants determined from kk1 = 1/r0 + t/L y and kk2 = 1/rl + t/L y, respectively. Thus, the induced voltage at any point can be calculated as Vind = V (y, t) + V m (y, t)

(30)

Now Eqs. (24)–(30) are the complete expressions for the LIOV calculation at any point. The software package was developed using C++ to calculate the lightning-induced over voltages and over currents. Calculation of voltages and currents are done in the main program while the subprograms are used by the main program for the calculation of horizontal and vertical components of electric fields. The following assumptions were made in the development of the algorithm:

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• The cell consists of 16 equal size segments, • The positive values of horizontal electric field and currents are directed from the left to the right of the cell; • The vertical electric field is positively directed towards the ground; • LIOVs are positive from the ground to telecommunication subscriber lines (TSL); and • The position-increment strictly maintains the condition y ≥ Vp t, where Vp is the velocity of propagation along the TSL.

4. Simulation results The radiated electric and magnetic fields from a lightning channel present different behaviors depending upon different parametric conditions of return stroke. As mentioned earlier, the electric field has two components – the vertical and horizontal components. Each of the vertical and horizontal electric fields consists of three terms: electrostatic, induction, and radiation terms. On the other hand, the magnetic field has only horizontal component, which possesses induction and radiation field terms. This research highlights the change in electric and magnetic fields due to different parametric effects of the return stroke. This analysis is based on the following assumed conditions: • The lightning channel is straight and located vertically at a distance of 4 km. • A triangular pulse current with tf = 2.5 s, te = 25 s, and Ip = 10 kA moves with a velocity of 100 m/s from ground and terminates in the cloud. • The lightning channel is assumed as a lossless transmission line terminating in its characteristic impedance to exclude the reflection of channel current.

Fig. 6. Induced voltages at the right end of a 1 km for the side return strokes occur at different distances 0.5, 1, and 1.5 km to the left.

the rise time of 7.75, 11.5, and 14.75 s for the SRS occurring at 0.5, 1, and 1.5 km, respectively (refer to Fig. 5). The rise time is defined as the time taken by the LIOV to reach their peak values from the zero value. On the other hand, the peak values of LIOV to the right are 773, 364, and 230 V with respect to the rise times of 5.25, 4.89, and 4.75 s for the above strikes, respectively (refer to Fig. 6). The LIOV due to front side stroke (FRS) occurring at 0.5, 1, and 1.5 km along the perpendicular bisector of the cell are shown in Fig. 7, where the peak values are 2370, 852, and 442 V with their respective rise times of 7.25, 7.75, and 7.75 s. The results show that LIOV vary inversely with the distance. For the SRS, the distance ratio 1:2:3 produces approximate peak LIOV ratio of 3:2:1. However, for FRS, the peak LIOV ratio is approximately 6:2:1. It means that FRS produces worst case in terms of peak values. The change in front time shows that steepness of LIOV is distance dependent for the case of SRS. The LIOV at the right are steeper than that of the left because of the effect of the radiation field term of vertical electric field. The FRS has no significant effect on steepness. Comparing the side and front return strokes, it is found that the first case produces higher steepness of induced voltages.

4.1. Effects of strike distance on LIOV 4.2. Effect of VEF and HEF on LIOV Strike distance dependency of LIOV due to side return stroke (SRS) occurring at 0.5, 1, and 1.5 km along the left extension of a 1 km for left and right end voltages are shown in Figs. 5 and 6, respectively. The peak values of LIOV in the left are calculated for 1079, 514, and 327 V with respect to

Voltage induced due to horizontal and vertical electric fields in a 1.8 km over the telecommunication building during front return stroke at 0.5 km from the mid point is shown in

Fig. 5. Induced voltages at the left end of a 1 km for side return strokes occur at different distances 0.5, 1, and 1.5 km to the left.

Fig. 7. Induced voltages at the left end of a 1 km the line for front return stroke occur at 0.5, 1, and 1.5 km from the midpoint and along the perpendicular bisector of the line.

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203

Fig. 8. Contribution of horizontal and vertical electric fields on induced voltages in a 1.8 km during FRS at 0.5 km.

Fig. 8. Side return stroke at 0.5, 1, and 5 km from the left end of the telecommunication building are shown in Figs. 9–11, respectively. The dotted line indicates the contribution of horizontal electric field in producing induced over voltages on subscriber line while the vertical electric field is set to zero. The dotted–dashed line indicates the contribution of vertical electric field while the horizontal electric field is set to zero. Finally, the solid line indicates the contribution of both fields. During the front return stroke, the horizontal electric field is dominant over vertical electric field in contributing to LIOV (refer to Fig. 8). However, during side return stroke, the vertical electric field contribution becomes dominant over horizontal electric field on induced voltages (refer to Fig. 9). The effect of horizontal electric field becomes insignificant

Fig. 11. Contribution of horizontal and vertical electric fields on LIOV on a 1.8 km TB during SRS at 5 km.

when compared to the vertical electric field if the strike distance increases (refer to Figs. 10 and 11). 4.3. Effects of strike locations on LIOV The different strike locations for the lightning return strokes and the corresponding LIOV at the left termination of a 1-km TSL are shown in Fig. 12. The numerical values obtained from the analysis indicate that the peak LIOV due to SRS at 0.5 km are 1067, 1602, 2370, 1664, and 773 V with corresponding rise time of 6, 6.25, 7.25, 6.5, and 5.25 s. It is evident from Fig. 12 that the wave shapes of LIOV are different depending upon the strike locations. The front return strokes produce higher peak values of LIOV compared to the side return strokes. On the other hand, LIOV due to SRS are steeper than that of front return stroke. The behavior of the electromagnetic field has been analyzed by considering the maximum value and front steepness of the field waveform and different lighting strike points. The magnetic flux density, and the horizontal and vertical electric fields as a function of time (s) at point (8, 0, −7 m) due to the current distribution in the structure, are depicted in Figs. 13–15, respectively. The waveforms of the horizontal and vertical electric fields at the

Fig. 9. Contribution of horizontal and vertical electric fields on induced voltages in a 1.8 km during SRS at 0.5 km.

Fig. 10. Contribution of horizontal and vertical electric fields on LIOV on a 1.8 km TB during SRS at 1 km.

Fig. 12. Induced voltages at the left end of a 1-km TSL for different strike locations. Strike points are at 0.5 km from the nearest point of the line when it is placed on ground and the distance between two consecutive front strikes is 250 m.

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the former is about 6 s, the latter’s peak-reaching time is around 4 s.

5. Conclusion

Fig. 13. Magnetic field B(T) as a function of time (s) at point (8, 0, −7 m).

A new three-dimensional numerical model based on the transmission line and wave propagation theory for calculating the current distribution in a structure, which is struck by direct lightning, is presented. The proposed technique utilizes the infinitesimal time-varying dipole theory while the method of images is used to calculate the electromagnetic field around it. With this model, the EMC analysis has been carried out and the results are presented. It is shown that the proposed methodology is simple but it is a suitable numerical method for electromagnetic compatibility studies. The salient features of the proposed technique are: • It is a fast and direct method from computational point of view, • It is possible to represent many building configurations by appropriate composition of the elementary cell, and • The electromagnetic field can be predicted, which helps the designer to make the best decisions during an EMC study when many parameters are involved.

Fig. 14. Horizontal electric field Er (T) as a function of time (s) at point (8, 0, −7 m).

Fig. 15. Vertical electric field Ey (T) as a function of time (s) at point (8, 0, −7 m).

point (8, 0, −7 m) exhibit a rise and decay characteristic similar to that of lightning current. While peak-reaching time of

References [1] M. Bandienelli, F. Bessi, S. Chitti, M. Infantino, R. Pomponi, Numerical modeling for LEMP effect evaluation inside a telecommunication exchange, IEEE Trans. Electromag. Compatibility 38 (3) (1996) 265–273. [2] B.F. Bessi, S. Chitti, R. Pomponi, LEMP effects in telecommunication Center, in: 10th Zurich Symp. Tech. Exhibit, EMC, March, 1993. [3] I.M. Pieoricci, R. Pomponi, Simulated LEMP effects inside a telecommunication exchange: field test results, in: 11th Zurich Symp. Tech. Exhibit, EMC, March, 1995. [4] C.A.F. Sartori, J.R. Cardoso, Evaluation of electromagnetic environment around a structure during a lightning stroke, in: Proceedings of the 1994 International Symposium on EMC, Rome, Italy, 1994, pp. 746–749. [5] P.B. Johns, R.L. Beurle, Numerical modeling of 2-dimensional scattering problems using a transmission line matrix, in: Proceedings of IEE, vol. 118, no. 9, September, 1971, pp. 1203–1208. [6] M. Rubinstein, M.A. Uman, Transient electric and magnetic fields associated with establishing a finite electrostatic dipole, IEEE Trans. Electromag. Compatibility 33 (1991) 312–320. [7] A.M. Ramli, Measurement of lightning induced surges on telecommunication subscriber cables in Malaysia, MEE Thesis, September 1998.

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