the influence of the slope angle of the ocean–land mixed propagation path on the lightning...

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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY 1

The Influence of the Slope Angle of the OceanLandMixed Propagation Path on the Lightning

Electromagnetic FieldsJavad Paknahad, Student Member, IEEE, Keyhan Sheshyekani, Senior Member, IEEE,

Mohsen Hamzeh, Member, IEEE, Dongshuai Li, and Farhad Rachidi, Fellow, IEEE

AbstractIn this paper, lightning electromagnetic fields in thepresence of an oceanland mixed propagation path having dif-ferent configurations are evaluated using a finite-element-basedfull-wave approach. The simulations are conducted consideringlightning strikes to ground and to the ocean. The lightning elec-tromagnetic fields are obtained for observation points inside theground and on the ground surface. The landocean interface isrepresented by a linearly increasing ocean depth characterized bythe slope angle. Different sets of simulation results show that theelectric field components (vertical and horizontal) in the immedi-ate vicinity of the interface can be affected by the interface slopeangle. The obtained results also show that, for observation pointslocated beyond 50 m or so from the ocean, the effect of the slopeangle of the oceanland interface on the lightning electromagneticfields can be disregarded.

Index TermsFinite element method, lightning electromagneticfields, oceanland mixed propagation path.

I. INTRODUCTION

ACCURATE evaluation of lightning electromagnetic fieldshas been the subject of many investigations over the pastdecades (e.g., [1]). In most of the works, as a common practice,the ground has been assumed to be a homogeneous lossy or idealmedium [1][7]. However, this assumption is rather unrealisticin the sense that the ground is usually composed of differenthorizontal or vertical layers. In addition, the electric parame-ters of the soil might exhibit a frequency dependence property.Thus, extensive studies have been recently conducted to takeinto account the effect of soil multilayer structure (see [8][26])as well as the soil dispersive properties (see [27][31]) in thecalculation of lightning electromagnetic fields and their induceddisturbances on overhead lines and buried cables.

Concerning the effect of a vertically stratified ground -also called mixed propagation path - although a few workshave addressed this problem, none of them has considered the

Manuscript received January 15, 2015; revised April 7, 2015; accepted May16, 2015.

J. Paknahad, K. Sheshyekani, and M. Hamzeh are with the Electrical Engi-neering Department, Shahid Beheshti University, Tehran 19839-63113, Iran(e-mail: [email protected]; [email protected]; [email protected]).

D. Li is with the Nanjing University of Information Science and Technology,Nanjing 210044, China (e-mail: [email protected]).

F. Rachidi is with the Ecole Polytechnique Federale de Lausanne, Lausanne1015, Switzerland (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TEMC.2015.2435894

inclined nature of the oceanland interface, namely the oceandepth quasi-linearly increasing with distance from the shore-line. It is noted that early works studying the wave propagationalong a vertically stratified ground are mainly those presentedby Millington [32], Suda [33], and Bremmer [34]. Recently,the concept of attenuation function presented by Wait (see [35]and [36]), has been used by Shoory et al. [9] for the evaluationof lightning electromagnetic fields over a mixed propagationpath showing that the Waits formula is able to reproduce thelightning electromagnetic fields for distant observation points.In another attempt, Zhang et al. [10][12] have managed touse a modified version of CoorayRubinstein formula for theevaluation of lighting electromagnetic fields above a smoothoceanland mixed path. The accuracy of the method is, however,limited to conductivities ranging from 0.01 to 0.001 S/m whenthe fields propagate from the ocean surface to the land section[13]. More recently, a finite-difference time-domain (FDTD)approach has been used to evaluate the validation of time do-main method the effect of a horizontally and vertically strat-ified ground on the lightning induced voltages [14][16] andelectromagnetic fields [17]. In [18] and [19], the lightning elec-tromagnetic fields have been computed over the ground takinginto account the ground roughness. Also, different approachesfor the calculation of lightning electromagnetic fields above ahorizontally stratified ground have been presented in [20][22].Additionally, the finite element method (FEM) has also beenadopted for the evaluation of lightning electromagnetic fieldsin the presence of either a horizontally stratified ground [23],[24], or a vertically stratified ground [25], [26]. However, to thebest of the authors knowledge and as already mentioned, thereis no attempt in the literature to take into account the inclinedoceanland interface in the evaluation of lightning electromag-netic fields. Therefore, more investigations are required to modelthe oceanland interface with a more accurate representation,especially for observation points in the vicinity of the interface.

Within this context, this paper focuses on the evaluation ofthe effect of an oceanland interface on the lightning radiatedelectromagnetic fields inside the ground and on the ground sur-face. The analysis is carried out by making use of the COMSOLMultiphysics software which is based on the FEM solutions ofMaxwells equations.

This paper is organized as follows. In Section II, we presentbriefly the full wave finite element modeling for the calculationof lightning electromagnetic fields. In Section III, the effectof the oceanland interface on the lightning electromagnetic

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2 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY

Fig. 1. Geometry for the calculation of lightning electromagnetic fields in thepresence of an oceanland mixed propagation path. (a) Land strike (side view).(b) Land strike (top view). (c) Ocean strike (side view).

fields is discussed. Finally, general conclusions are presented inSection IV.

II. ANALYSIS METHOD AND ADOPTED MODELS

The geometry of the problem is shown in Fig. 1. We con-sider a vertical lightning return stroke channel in the vicinityof an oceanland interface. The analysis of this problem usingCOMSOL Multiphysics involves the modeling of: 1) lightningreturn stroke channel, and 2) the mixed propagation path in-cluding the ocean and the land. Details about modeling of thisproblem can be found in [23][26]. In our simulations, the airis considered to be lossless (i.e., = 0, r = 1), while the landand the ocean are respectively characterized by conductivity andrelative permittivity of (l = 0.001 S/m, rl = 10) and (o =4 S/m, ro = 30). The lightning return stroke is modeled by us-ing the transmission line with exponential decay (MTLE) model

TABLE IHEIDLERS PARAMETERS FOR TYPICAL SUBSEQUENT RETURN STROKES

Parameters I0 1(kA)

1 1(s)

1 2(s)

n1 I0 2(kA)

2 1(s)

2 2(s)

n2

Typicalsubsequentreturn strokecurrent

10.7 0.25 2.5 2 6.5 2.1 230 2

Fig. 2. Horizontal component of the electric field (Er ) at a depth of 1 m insidethe ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke currenttypical of subsequent strokes (land strike and normal incidence).

with a current height decay constant of = 2000 m and assum-ing a return stroke speed of v = 1.5 108 m/s (see [37] and[38]). According to the MTLE model, the current distributionalong the channel is expressed as

i (z, t) = i(0, t z

v

).e z (1)

where i(z, t) is the channel current at height z, while v denotes thereturn stroke speed, and is the current height decay constant.

As for the lightning channel-base current, we use a wave-shape typical of subsequent return strokes represented using asum of two Heidlers functions whose parameters are given inTable I [39].

In COMSOL, natural Neumann conditions are used in thesoilair and in the soil layer interfaces, while the natural Dirich-let conditions are imposed on the solution domain as the ex-ternal boundary condition [29]. To apply the finite elementapproach to open region problems such as lightning electro-magnetic field studies, an artificial boundary is introduced in


PAKNAHAD et al.: INFLUENCE OF THE SLOPE ANGLE OF THE OCEANLAND MIXED PROPAGATION PATH ON THE LIGHTNING 3

Fig. 3. Vertical component of the electric field (Ez ) at a depth of 1 m insidethe ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke currenttypical of subsequent strokes (land strike and normal incidence).

order to confine the region of analysis and to limit the numberof unknowns to a manageable size. For this purpose, the scatter-ing boundary condition available in the RF module of COMSOLis used in order to prevent the waves from being reflected by theboundaries [40].

Regarding the modeling specifications, the simulations areconducted on an Intel i7 PC with 64-GB RAM. A system oflinear equations is obtained using 185 613 mesh elements. Forthe calculation of electromagnetic fields, we used a 2-D finiteelement modeling which takes about 30 s and could be consid-ered as an applicable choice for the assessment of the lightningelectromagnetic fields.

III. EFFECT OF THE INCLINED OCEAN-LAND INTERFACEON THE LIGHTNING ELECTROMAGNETIC FIELDS

With reference to Fig. 1, we aim at evaluating the lightningradiated electromagnetic fields for two different angles of inci-dence 1 = 90 (henceforth referred to as normal incidence)and 2 < 1 , (henceforth referred to as oblique incidence)onto the oceanland interface. For both normal and obliqueincidences, results are obtained at two observation points: oneinside the ground and the other on the ground surface. Assuming(x, y, z) = (0, 0, 0) m as the coordinates for the lightning strokelocation in Fig. 1(b), for normal incidence the coordinates of theobservation point on the ground surface is (0, 200, 0) m whilethe coordinates for the observation point inside the ground is(0, 200, 1). Similarly, for the case of oblique incidence, thecoordinates of the observation point on the ground surface is

Fig. 4. Azimuthal component of the magnetic field (H ) at a depth of 1 minside the ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return strokecurrent typical of subsequent strokes (land strike and normal incidence).

Fig. 5. Horizontal electric field at a depth of 1 m inside the ground, dl = 1 m.Slope angle = 30o . Return stroke current typical of subsequent strokes (landstrike and normal incidence). Results obtained using FEM and FDTD methods.

(100, 200, 0) m while the coordinates for the observation pointinside the ground is (100, 200, 1) m. In our simulations, theoceanland interface is characterized by its slope angle (i.e., in Fig. 1). It is assumed that the ocean depth increases linearlywith distance from the land. We calculate the electromagneticfields for different distances between the observation point andthe oceanland interface (i.e., dl in Fig. 1).

We consider both lightning strikes to ground (referred toas land strike) and to ocean (referred to as ocean strike).For each considered case, we simulate the horizontal and ver-tical components of the electric field (i.e., Er , Ez ) and the az-imuthal component of the magnetic field (i.e., H ), for differentdistances between the observation point and the oceanland in-terface, namely dl = 1, 5 and 50 m.

This study is especially important for the evaluation oflightning-induced voltages on overhead transmission lines andinduced currents on buried cables located near the sea or ocean.In fact, according to this study, the electromagnetic fields



Fig. 6. Horizontal component of the electric field (Er ) at a depth of 1 m insidethe ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke currenttypical of subsequent strokes (land strike and oblique incidence).

Fig. 7. Vertical component of the electric field (Ez ) at a depth of 1 m insidethe ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke currenttypical of subsequent strokes (land strike and oblique incidence).

Fig. 8. Azimuthal component of the magnetic field (H ) at a depth of 1 minside the ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return strokecurrent typical of subsequent strokes (land strike and oblique incidence).

used in the LEMP-to-line coupling models can be properlymodified when needed for the calculation of lightning-inducedvoltages/currents on the ocean-side transmission lines andcables [41].

A. Land Strike: Electromagnetic Fields Inside the GroundFigs. 2 to 4 show, respectively, the horizontal electric field,

the vertical electric field and the azimuthal magnetic field atobservation point P1 at a depth of 1 m inside the ground for thecase of normal incidence, considering a land strike (see Fig. 1).Simulations were carried out for different interface slopes ( =30, 45, 60, 75 and 90). Note that a slope of = 90o (verticalinterface) corresponds to a vertical interface, as considered inall previous studies.

Examining these figures, the following remarks can be made:1) The vertical and horizontal components of the electric

field are noticeably affected by the oceanland interfaceslope when the observation point is close to the interface(i.e., dl = 5 m or so). As expected, this effect is muchmore pronounced when the observation point gets closerto the shoreline (i.e., dl = 1 m).

2) As the observation point gets far away from the ocean,the effect of the oceanland interface slope becomes neg-ligible. Starting from a distance of dl = 50 m [see Figs.2(c) and 3(c)], the effect of oceanland interface slopebecomes negligible.



Fig. 9. Horizontal component of the electric field (Er ) at the ground surface.(a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke current typical ofsubsequent strokes (land strike and normal incidence).

Fig. 10. Vertical component of the electric field (Ez ) at the ground surface.(a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke current typical ofsubsequent strokes (land strike and normal incidence).

Fig. 11. Azimuthal component of the magnetic field (H ) at the groundsurface. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke currenttypical of subsequent strokes (land strike and normal incidence).

3) From Fig. 4, it is seen that the azimuthal component ofthe magnetic field is slightly affected by the oceanlandinterface slope for an observation point very close to theoceanland interface (i.e., dl = 1 m or so).

4) For observation points in the immediate vicinity of theinterface (dl = 1 m or dl = 5 m), the peak values of thehorizontal and vertical electric field components increasewith decreasing the slope angle.

The effect of the oceanland slope angle on the lightningelectromagnetic fields can be explained as follows: The oceancan be represented by a conductive body with a tip that becomessharper when the slope angle decreases. This effect results inan enhancement of the electric field in its immediate vicinity.Obviously, the electric field enhancement is more significantfor a smaller slope angle (sharper tip). To confirm the obtainedresults, we compared our FEM simulations with results obtainedusing an independent computer code presented in [10], whichis based on the FDTD method. The results for the horizontalelectric field for an observation point at a depth of 1 m insidethe ground and for dl = 1 m and = 30 [corresponding toFig. 2(a)] is shown in Fig. 5. It can be seen that the FEM resultsare in very good agreement with their FDTD counterparts.

For the case of oblique incidence, we calculated the samecomponents of the lightning electromagnetic fields at a depthof 1 m inside the ground for the same distances between theobservation point and the oceanland interface (see Figs. 68). It can be seen from the simulation results that the lightningelectromagnetic fields inside the ground are affected by the slope



Fig. 12. Azimuthal component of the magnetic field (H ) at the groundsurface with dl = 1 m. Return stroke current typical of subsequent strokes(land strike and oblique incidence).

Fig. 13. Horizontal component of the electric field (Er ) at a depth of 1 minside the ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return strokecurrent typical of subsequent strokes (ocean strike and normal incidence).

angle of the oceanland interface in a way similar to the case ofa normal strike.

B. Land Strike: Electromagnetic Fields on the Ground SurfaceIn this section, we study the effect of the oceanland interface

on the lightning electromagnetic fields at an observation pointlocated on the ground surface for normal incidence. The threecomponents of the lightning electromagnetic fields are plottedin Figs. 911. From these figures, the following conclusions canbe drawn:

1) As it can be seen from Fig. 9, the horizontal componentof the electric field is noticeably affected by the oceanland interface slope when the observation point is closeto the interface (i.e., dl = 5 m or so). The amplitude of

Fig. 14. Vertical component of the electric field (Ez ) at a depth of 1 m insidethe ground. (a) dl = 1 m, (b) dl = 5 m and (c) dl = 50 m. Return stroke currenttypical of subsequent strokes (ocean strike and normal incidence).

this component shows a decreasing trend as a function ofslope angle.

2) The vertical electric field (see Fig. 10) and the azimuthalmagnetic field (see Fig. 11) at the ground surface arenot affected by the oceanland interface so that the ef-fect of oceanland interface slope could be reasonablydisregarded for these components, regardless of the dis-tance of the observation point to the interface.

For the case of oblique incidence, the radial and verticalelectric fields on the ground surface (not shown here) appear tobe affected by the oceanland interface slope in a way similarto the case of normal incidence. The azimuthal magnetic fieldon the ground surface associated with an oblique land strike asshown in Fig. 12 is only slightly affected by the oceanlandinterface slope when the observation point is very close to theocean.

C. Ocean Strike: Electromagnetic Fields Inside the LandIn this section, we consider the case of a lightning strike to the

ocean. The electromagnetic fields were evaluated at the sameobservation points on the land side, at a distance of 200 m fromthe lightning channel. The geometry of the problem is shownin Fig. 1(c). The electromagnetic fields obtained for the caseof normal incidence at the observation point 1 m inside the



Fig. 15. Azimuthal component of the magnetic field (H ) at a depth of 1 minside the ground. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return strokecurrent typical of subsequent strokes (ocean strike and normal incidence).

ground. Results are reported in Figs. 1315. From these figures,the following conclusions can be drawn:

1) The horizontal electric field is markedly affected by theoceanland interface slope only for observation pointsclose to the interface (i.e., dl = 5 m or so). The minimumpeak value for the horizontal electric field occurs for avertical oceanland interface with = 90o (see Fig. 13).

2) The vertical electric field can be significantly affected bythe oceanland interface slope only when the observationpoint is located in the close vicinity of the shoreline (i.e.,dl = 5 m or so) as seen from Fig. 14(a) and (b). In thiscase, similar to the case of land strike, with decreasingthe slope angle, the vertical electric field increases. Inthis case, the minimum peak value is obtained for thevertical oceanland interface (see Fig. 14). As can be seenfrom Fig. 14(a), the slope of the interface may changethe polarity of the vertical E-field: negative for a verticalinterface, and becoming positive for smaller slope angles(75 and smaller).

3) As seen from Fig. 15, the effect of an inclined oceanlandinterface on the azimuthal component of the magneticfield is negligible for all considered slope angles.

D. Ocean Strike: Electromagnetic Fields on theGround Surface

In the final set of simulations, we evaluate the effect of oceanland interface slope on lightning electromagnetic fields evalu-ated on the ground surface for the case of a lightning strike to the

Fig. 16. Horizontal component of the electric field (Er ) at the ground surface.(a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke current typical ofsubsequent strokes (ocean strike and normal incidence).

ocean (for normal incidence). The obtained results for differentcomponents of the lightning electromagnetic fields are reportedin Figs. 1618. Examining these figures, the following remarkscan be made:

1) The horizontal component of the electric field is markedlyaffected by the oceanland interface slope for observationpoints close to the interface. Similar to the case of a landstrike, as the slope angle increases, the horizontal electricfield decreases so that the minimum peak value is obtainedfor a vertical oceanland interface (i.e., = 90).

2) The vertical electric field and the azimuthal magnetic fieldcomponents are not affected by the oceanland interfaceslope, for all considered distances between the observationpoint and the oceanland interface (see Figs. 17 and 18).

IV. CONCLUSIONIn this paper, we used the COMSOL Multiphysics for the eval-

uation of lightning electromagnetic fields in the presence of anoceanland mixed propagation path having different configura-tions. Unlike previous studies in which the interface was consid-ered as vertical, the inclined nature of the oceanland interfacewas considered in the evaluation of lightning electromagneticfields. Simulations were conducted considering lightning strikesto the ground and to the ocean. The lightning electromagneticfields were obtained for observation points inside the groundand on the ground surface. From the simulations conducted forthe case of a land strike for both normal and oblique incidences,it was found that:



Fig. 17. Vertical component of the electric field (Ez ) at the ground surface.(a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke current typical ofsubsequent strokes (ocean strike and normal incidence).

1) For underground observation points when they are in theimmediate vicinity of the ocean (i.e., 5 m or so), the hori-zontal and vertical electric fields are markedly affected bythe oceanland interface slope.

2) The underground azimuthal magnetic field is found to beslightly affected by the interface slope and only when theobservation point is very close to the interface (i.e., 1 mor so).

3) For an observation point on the ground surface, the hori-zontal electric field is found to be markedly affected by theoceanland slope angle, while the vertical electric field isnot affected by the oceanland slope angle.

4) The azimuthal magnetic field on the ground surface isfound to be very slightly affected by the interface, only forthe case of an oblique incidence and when the observationpoint is very close to the oceanland interface (i.e., 1 mor so).

Qualitatively, similar results have been obtained for the caseof a strike to the ocean for which it was found that the elec-tric field components can be affected by the oceanland inter-face slope, only for observation points located in the immediatevicinity of the shoreline. In particular, it was found that theslope of the interface may change the polarity of the verticalE-field. The obtained results show that, for observation pointslocated far from the ocean (i.e., beyond 50 m or so), the effect ofthe oceanland interface slope on the lightning electromagneticfields becomes negligible.

Fig. 18. Azimuthal component of the magnetic field (H ) at the groundsurface. (a) dl = 1 m, (b) dl = 5 m, (c) dl = 50 m. Return stroke currenttypical of subsequent strokes (ocean strike and normal incidence).

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers fortheir useful and constructive comments.

REFERENCES[1] V. A. Rakov and F. Rachidi, Overview of recent progress in lightning

research and lightning protection, IEEE Trans. Electromagn. Compat.,vol. 51, no. 3, pp. 428442, Aug. 2009.

[2] R. Thottappillil, Computation of electromagnetic fields from lightningdischarge, in The Lightning Flash. London, U.K.: IEEE Press, 2003.

[3] V. Cooray, Horizontal electric field above and underground producedby lightning flashes, IEEE Trans. Electromagn. Compat., vol. 52, no. 4,pp. 936943, Nov. 2010.

[4] V. Cooray, Some considerations on the CoorayRubinstein formulationused in deriving the horizontal electric field of lightning return strokes overfinitely conducting ground, IEEE Trans. Electromagn. Compat., vol. 44,no. 4, pp. 560566, Dec. 2002.

[5] M. J. Master and M. A. Uman, Transient electric and magnetic fieldsassociated with establishing a finite electrostatic dipole, Amer. J. Phys.,vol. 51, pp. 118126, 1983.

[6] M. Rubinstein and M. A. Uman, Methods for calculating the electromag-netic fields from a known source distribution: Application to lightning,IEEE Trans. Electromagn. Compat., vol. 31, no. 2, pp. 183189, May1989.

[7] V. Cooray, Lightning-induced overvoltages in power lines: Validity ofvarious approximations made in overvoltage calculations, in Proc. 22ndInt. Conf. Lightning Protection, Sep. 1994, pp. 1923.

[8] M. Rubinstein, An approximate formula for the calculation of the hori-zontal electric field from lightning at close, intermediate, and long range,IEEE Trans. Electromagn. Compat., vol. 38, no. 3, pp. 531535, Aug.1996.



[9] A. Shoory, A. Mimouni, F. Rachidi, V. Cooray, and M. Rubinstein,On the accuracy of approximate techniques for the evaluation of light-ning electromagnetic fields along a mixed propagation path, Radio Sci.,vol. 46, no. 2, pp. RS2001-1RS2001-8, 2011.

[10] Q. Zhang, D. Li, X. Tang, and Z. Wang, Lightning-radiated horizon-tal electric field over a rough- and ocean-land mixed propagation path,IEEE Trans. Electromagn. Compat., vol. 55, no. 4, pp. 733737, Aug.2013.

[11] Q. Zhang, X. Jing, J. Yang, D. Li, and X. Tang, Numerical simulation ofthe lightning electromagnetic fields along a rough and ocean-land mixedpropagation path, J. Geophys. Res., vol. 117, pp. D20304-1D20304-7,2012.

[12] Q. Zhang, D. Li, Y. Zhang, J. Gao, and Z. Wang, On the accuracy ofWaits formula along a mixed propagation path within 1 km from thelightning channel, IEEE Trans. Electromag. Compat., vol. 54, no. 5,pp. 16, Oct. 2012.

[13] Q. Zhang, D. Li, Y. Fan, Y. Zhang, and J. Gao, Examination of theCoorayRubinstein (C-R) formula for a mixed propagation path by usingFDTD, J. Geophys. Res., vol. 117, pp. D15309-1D15309-7, 2012.

[14] Q. Zhang, X. Tang, J. Gao, L. Zhang, and D. Li, The Influence of thehorizontally stratified conducting ground on the lightning-induced volt-ages, IEEE Trans. Electromagn. Compat., vol. 56, no. 2, pp. 435443,Apr. 2014.

[15] Q. Zhang, L. Zhang, X. Tang, and J. Gao, An approximate formula forestimating the peak value of lightning-induced overvoltage consideringthe stratified conducting ground, IEEE Trans. Electromagn. Compat.,vol. 29, no. 2, pp. 884889, Mar. 2014.

[16] Q. Zhang, X. Tang, W. Hou, and L. Zhang, 3-D FDTD simula-tion of the lightning-induced waves on overhead lines considering thevertically stratified ground, IEEE Trans. Electromagn. Compat., doi:10.1109/TEMC.2015.2420653, in press 2015.

[17] Q. Zhang, L. Zhang, H. Wenhao, and S. Jianfeng, Validation of the ap-proximate time-domain method for the lightning-horizontal electric fieldat the surface of two-layer earth by using FDTD, IEEE Trans. Electro-magn. Compat., vol. 56, no. 5, pp. 11211128, Sep. 2014.

[18] D. Li, Q. Zhang, W. Zhenhui, and L. Tao, Computation of lightninghorizontal field over the two-dimensional rough ground by using the threedimensional FDTD, IEEE Trans. Electromagn. Compat., vol. 56, no. 1,pp. 143148, Feb. 2014.

[19] D. Li, Q. Zhang, T. Liu, and Z. Wang, Validation of the Cooray-Rubinstein(C-R) formula for a rough ground surface by using three-dimensional (3-D) FDTD, J. Geophys. Res., vol. 118, pp. 749754, Nov. 2013.

[20] J. O. S. Paulino, C. F. Barbosa, and W. C. Boaventura, Lightning-inducedcurrent in a cable buried in the first layer of a two-layer ground, IEEETrans. Electromagn. Compat., vol. 56, no. 4, pp. 956963, Aug. 2014.

[21] C. F. Barbosa, J. O. S. Paulino, and W. C. Boaventura, A time-domainmethod for the horizontal electric field calculation at the surface of two-layer earth due to lightning, IEEE Trans. Electromagn. Compat., vol. 55,no. 2, pp. 371377, Apr. 2013.

[22] A. Shoory, F. Rachidi, F. Delfino, R. Procopio, and M. Rossi, Light-ning electromagnetic radiation over a stratified conducting groundPart 2: Validity of simplified approaches, J. Geophys. Res., vol. 116,pp. D11115-1D11115-10, 2011.

[23] J. Paknahad, K. Sheshyekani, F. Rachidi, and M. Paolone, Lightningelectromagnetic fields and their induced currents on buried cables. Part II:The effect of a horizontally stratified ground, IEEE Trans. Electromagn.Compat., vol. 56, no. 5, pp. 11461154, Oct. 2014.

[24] K. Sheshyekani and J. Paknahad, Lightning electromagnetic fields andtheir induced voltages on overhead lines: The effect of a horizontallystratified ground, IEEE Trans. Power Del., vol. 30, no. 1, pp. 290298,Feb. 2015.

[25] J. Paknahad, K. Sheshyekani, and F. Rachidi, Lightning electromagneticfields and their induced currents on buried cables. Part I: The effect of anocean-land mixed propagation path, IEEE Trans. Electromagn. Compat.,vol. 56, no. 5, pp. 11371145, Oct. 2014.

[26] K. Sheshyekani and J. Paknahad, The effect of an ocean-land mixedpropagation path on the lightning electromagnetic fields and their inducedvoltages on overhead lines, IEEE Trans. Power Del., vol. 30, no. 1,pp. 229236, Feb. 2015.

[27] F. Delfino, R. Procopio, M. Rossi, and F. Rachidi, Influence of frequency-dependent soil electrical parameters on the evaluation of lightning elec-tromagnetic fields in air and underground, J. Geophys. Res., vol. 114,pp. D11113-1D11113-12, 2009.

[28] J. Paknahad, K. Sheshyekani, F. Rachidi, M. Paolone, and A. Mimouni,Evaluation of lightning-induced currents on cables buried in a lossy

dispersive ground, IEEE Trans. Electromagn. Compat., vol. 56, no. 6,pp. 15221529, Dec. 2014.

[29] M. Akbari, K. Sheshyekani, A. Pirayesh, F. Rachidi, M. Paolone,A. Borghetti, and C. A. Nucci, Evaluation of lightning electromag-netic fields and their induced voltages on overhead lines considering thefrequency-dependence of soil electrical parameters, IEEE Trans. Elec-tromagn. Compat., vol. 55, no. 6, pp. 12101219, Dec. 2013.

[30] K. Sheshyekani and M. Akbari, Evaluation of lightning-induced volt-ages on multi-conductor overhead lines located above a lossy dispersiveground, IEEE Trans. Power Del., vol. 29, no. 2, pp. 683690, Apr. 2014.

[31] F. H. Silveira, S. Visacro, R. Alipio, and A. De Conti, Lightning-inducedvoltages over lossy ground: The effect of frequency dependence of elec-trical parameters of soil, IEEE Trans. Electromagn. Compat., vol. 56,no. 5, pp. 11291136, Oct. 2014.

[32] G. Millington, Ground-wave propagation over an inhomogeneous smoothearth, Proc. IEEPart III: Radio Commun. Eng., vol. 96, no. 39,pp. 5364, Jan. 1949.

[33] K. Suda, Field strength calculations-new method for mixed paths, Wire-less Engineer, vol. 31, pp. 249249, 1954.

[34] H. Bremmer, The extension of the Sommerfelds formula for the prop-agation of radio waves over a flat earth, to different conductivities of thesoil, Physica, vol. 20, pp. 441460, 1954.

[35] J. R. Wait and L. Walters, Curves for ground wave propagation overmixed land and sea paths, IEEE Trans. Antennas Propag., vol. 11, no. 1,pp. 3845, Jan. 1963.

[36] J. R. Wait and L. Walters, Correction to curves for ground wave prop-agation over mixed land and sea paths, IEEE Trans. Antennas Propag.,vol. 11, no. 3, pp. 329, May 1963.

[37] C. A. Nucci, C. Mazzetti, F. Rachidi, and M. Ianoz, On lightning returnstroke models for LEMP calculations, in Proc. 19th Int. Conf. LightningProtection, Apr. 1988.

[38] F. Rachidi and C. A. Nucci, On the master, lin, uman, standler andthe modified transmission line lightning return stroke current models, J.Geophys. Res., vol. 95, pp. 2038920394, Nov. 1990.

[39] F. Rachidi, W. Janischewskyj, A. M. Hussein, C. A. Nucci, S. Guerrieri,B. Kordi, and J. S. C. hang, Current and electromagnetic field associatedwith lightning return strokes to tall towers, IEEE Trans. Electromagn.Compat., vol. 43, no. 3, pp. 356367, Aug. 2001.

[40] COMSOL RF Module Users Guide, COMSOL, Inc., Stockholm, Sweden,May 2011.

[41] A. K. Agrawal, H. J. Price, and S. H. Gurbaxani, Transient responseof multiconductor transmission lines excited by a nonuniform electro-magnetic field, IEEE Trans. Electromagn. Compat., vol. EMC-22, no. 2,pp. 119129, May 1980.

Javad Paknahad (S14) was born in Iran in 1989.He received the B.S. degree in electrical engineer-ing from the Amirkabir University of Technology(Tehran Polytechnique), Tafresh, Iran, in 2011, andthe M.S. degree in electrical engineering from ShahidBeheshti University, Tehran, Iran, in 2013.

He is currently a Research Assistant at the PowerSystem Laboratory, Shahid Beheshti University, anda Researcher at the Power Quality Laboratory, SharifUniversity of Technology, Tehran. His research inter-ests include power system modeling and simulations,

electromagnetic compatibility and application of electromagnetics in powersystem.

Keyhan Sheshyekani (M10SM13) received theB.S. degree in electrical engineering from TehranUniversity, Tehran, Iran, in 2001, and the M.S. andPh.D. degrees in electrical engineering from theAmirkabir University of Technology (Tehran Poly-technique), Tehran, in 2003 and 2008, respectively.

He was with Ecole Polytechnique, Federale deLausanne Lausanne, Switzerland, in September 2007as a Visiting Scientist and later as a Research As-sistant. He is currently an Assistant Professor ofelectrical engineering at Shahid Beheshti University,

Tehran. He was an Invited Professor at the EPFL from June to September 2014.His research interests include power system modeling and simulation, smartgrid, microgrids, and electromagnetic compatibility.



Mohsen Hamzeh (S09M13) was born in Iran in1984. He received the B.Sc. and M.Sc. degrees fromthe University of Tehran, Tehran, Iran, in 2006 and2008, respectively, and the Ph.D. degree from theSharif University of Technology, Tehran, in 2012, allin electrical engineering.

Since 2010, he has been the Senior Research En-gineer at the SGP Company, Tehran. He joined theDepartment of Electrical and Computer Engineering,Shahid Beheshti University, Tehran, in 2013, wherehe is currently an Assistant Professor. His research

interests include distributed generation, microgrid control and applications ofpower electronics in power distribution systems.

Dongshuai Li was born in China in 1987. She re-ceived the B.E. degree in lightning protection sci-ence and technology from the School of AtmosphericPhysics, Nanjing University of Information Scienceand Technology (NUIST), Nanjing, China, in 2010.She is currently working toward the Ph.D. degree atNUIST and is a Visiting Student at Ecole Polytech-nique Federale de Lausanne, Lausanne, Switzerland.

Her research interests include electromagneticfield theory, numerical methods in electromagnetics,global lightning activity and Schumann resonance.

Farhad Rachidi (M93SM02F10) received theM.S. degree in electrical engineering and the Ph.D.degree from the Swiss Federal Institute of Technol-ogy, Lausanne, Switzerland, in 1986 and 1991, re-spectively.

He worked at the Power Systems Laboratory of thesame institute until 1996. In 1997, he joined the Light-ning Research Laboratory, University of Toronto,Canada, and from April 1998 until September 1999,he was with Montena EMC, Switzerland. He is cur-rently a Titular Professor and the Head of the EMC

Laboratory, Swiss Federal Institute of Technology. He served as the Vice-Chairof the European COST Action on the Physics of Lightning Flash and its Effects(20052009), the Chairman of the 2008 European Electromagnetics Interna-tional Symposium (EUROEM), and the President of the International Confer-ence on Lightning Protection (20082014). He is presently the Editor-in-Chiefof the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, and thePresident of the Swiss National Committee of the International Union of Ra-dio Science. He is the author or coauthor of 130 scientific papers publishedin peer-reviewed journals and more than 250 papers presented at internationalconferences.

Dr. Rachidi, in 2005, was the recipient of the IEEE Technical AchievementAward and the CIGRE Technical Committee Award. In 2006, he was awardedthe Blondel Medal from the French Association of Electrical Engineering, Elec-tronics, Information Technology and Communication. In 2014, he was conferredthe title of Honorary Professor of the Xian Jiaotong University in China.

the influence of the slope angle of the ocean–land mixed propagation path on the lightning...

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