-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
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
0018-9375 2015 IEEE. Personal use is permitted, but
republication/redistribution requires IEEE permission.See
http://www.ieee.org/publications
standards/publications/rights/index.html for more information.
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
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
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
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
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
4 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY
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.
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
PAKNAHAD et al.: INFLUENCE OF THE SLOPE ANGLE OF THE OCEANLAND
MIXED PROPAGATION PATH ON THE LIGHTNING 5
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
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
6 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY
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
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
PAKNAHAD et al.: INFLUENCE OF THE SLOPE ANGLE OF THE OCEANLAND
MIXED PROPAGATION PATH ON THE LIGHTNING 7
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:
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
8 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY
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.
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
PAKNAHAD et al.: INFLUENCE OF THE SLOPE ANGLE OF THE OCEANLAND
MIXED PROPAGATION PATH ON THE LIGHTNING 9
[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.
-
This article has been accepted for inclusion in a future issue
of this journal. Content is final as presented, with the exception
of pagination.
10 IEEE TRANSACTIONS ON 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.