IEEE TRANSACTTONS ON BlOMEDICALEh'GI"G,
1 IO5
VOL. 42, NO. 11. N O W E R 1995
Transmission-Line Electric Field Induction in
Humans Using Charge Simulation Method
Mazen Abdel-Salam, Fellow, IEEE, and Hassan Mohamed Abdallah, Senior Member, IEEE
Absfrmt-This paper is simed at determining the distribution
of the fields, induced charges, and currents on a human body
standing in the high elechic fields produced by high voltage
overhead t r a n s m n lines. This method of analysis is based
on the charge simulation technique. This will serve to explain
the biological studies of possible long-term expasure effects to
f'
1::
: ' ' :' -0 5
H
electric fields.
0
1 ,,,,,,, ,,,,,!,,/,,,,,,,,,,,R/
I. INTRODUCTION
HE calculation of the electric fields around three-phase
overhead transmission lines has been discussed thoroughly [I]. The electric field at the ground level is, practically
speaking, uniform and vertical to the ground plane. Underneath
the conductors of 525-kV lines, the maximum electric field
at the ground plane is about 9 kV/m [2]. The corresponding
maximum field values beneath the conductors of 275 kV and
132 kV lines are about 6 kV/m and 2 kV/m, respectively, with
still lower values for lower voltage distribution lines [3]. In
the presence of a human body beneath the line conductors,
the electric field is highly perturbed with an enhancement of
the field strength by a factor that may reach eight or even
more [4]. The induced currents in a human body due to such
enhanced fields may exceed the safe limits [2].
In the vicinity of ac power lines, a 60-cycle electric field
exists in the space between the energized conductors and
ground. Linemen engaged in maintaining these lines work in
this field. For a man insulated from the ground, the body will
acquire a potential depending upon his position in the field
and the field strength. Accordingly, a displacement current
enters one side of the body, flows through it, and lines of force
emanate from the other side to ground. Under these conditions,
he will assume a potential other than ground and receive a
small disturbing shock with the associated short-circuit current
when he touches a grounded object.
A simplified derivation of the induced charge on an ungrounded body undemeath ac power lines was proposed [2].
The induced charge was found to depend on the unperturbed
electric field and the properties of the human body, including
height above ground and body capacitance to ground. The
derivation is based on the assumption that the body will
T
Manuscript received January 20, 1994: revised July 24. 1995.
M. Abdel-Salam is with the Electrical Engineering Department, Assiut
University, Assiut, Egypt.
H. M. Abdallah is with the Biomedical Technology Department, King Saud
University, Riyadh 11421, Saudi Arabia.
IEEE Log Number 9414809.
Simulation l i n e charge
x x n Contour p o i n t
Fig. 1. Equivalent stressed plate-to-ground plane arrangement.
not significantly alter the charges on the transmission line
conductors. A rough estimation of the short-circuit current
was also proposed [2] which was found proportional to the
body's potential and capacitance to ground. Again, the body
was considered to have a negligible effect on the source of
the electric field and the surface charge on the transmission
line conductors.
The object of this paper is to present a method for determining not only the power-frequency field and charge at the
surface of a human body underneath high voltage overhead
lines, but also the induced currents in the body.
11. METHOD OF ANALYSIS
A. Assumptions
1) The electric field at the ground level undemeath the
overhead transmission line is practically uniform and directed
vertically to the ground plane. Therefore, the field between a
stressed horizontal metal plate and the ground plane is considered analogous to the ground-level electric field produced
by the overhead transmission lines. In this way, the stressed
plate replaces the line conductors.
2) The large conductivity and the large relative equivalent
dielectric constant of the human body, about 0.1 S/m and about
1OOOOO respectively [4], cause the extemal power-frequency
electric field near the human body to be perpendicular to
the surface [4]. This is why the human body is treated as
a conducting body.
B. Model
For energized transmission line, the surface charge on the
stressed plate is simulated by a set of 2NI unknown infinite
0018-9294/95$04.00 0 1995 IEEE
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[EEE TRANSACTlONS O N BIOMEDICAL ENGINEERING. VOL. 42, NO. 11. NOYEMBER 1995
t'
IL
Also,the field components E,., and E=,at the contour point
i are the vectorial sum of the field contributions from all the
simulationcharges Qj,j = 1, . . . ,2N1+ N2, and are expressed
as [61
+t
line charges extending along the line length (Fig. 1). The
human body is modeled by a sphere for the head, a thin
cylinder for the neck, a thick cylinder for the waist/mtch, and
another thick cylinder, but of lesser radius, for the legs (Fig. 2).
The surface charge on the human is simulated by another set of
Nz unknown ring charges. Images of the simulation charges
with respect to the ground plane are considered. Symmetry
about the Z-axis reduces the number of unknown charges to
N I Nz.
+
where E, is the normal component of the electric field
calculated at the boundary point, and E, is the permittivity
of free space. E, is equal to the total field at the boundary
point on the human body in light of the fact that the human
is treated as a conducting body.
At the boundary point, the induced current density J , normal
to the surface and just inside the boundary, is expressed as
J = wu = we,E,
C. Boundary Conditions
Contour points are chosen on the stressed plate and on the
human body to satisfy the pertinent boundary conditions:
1) The potential calculated at the contour points chosen on
the stressed plate is equal to the applied voltage V.
2) The potential calculated at the contour points chosen on
the human body is equal to: a) the unknown induced
voltage for an insulated body, orb) zero for a grounded
body.
3) The sum of the charges simulating the human is equal
to zero for the insulated (ungrounded) body only.
D. Describing Equations
The potential 4%at contour point z is the sum of the
potential contributionsfrom all the simulationcharges Q3,j =
1 , . . ,2N1 Nz, and is expressed as [5], [61
+
(6)
where w is the angular frequency of the voltage applied to the
stressed plate representing the transmission line conductors.
The induced current Ik just inside the boundary of a part
of the body, say kth, is obtained by integrating J over the
surface area SI, of this part
(7)
On the other hand, the current density distribution inside the
body depends on the material constants assigned to the human
organs filling the volume of the body.
E.
su,.jaceElectric ~ ~ l d ,
Charge, and Induced Current
Satisfaction of the boundary points at the chosen contour
points using (1) results in a set of equations whose solution
4c =
Ps,3Q3
( l ) determines the charges simulating the body as well as the
3=1
induced potential on the insulated body. Once the simulation
charges are determined, the electric field, the induced charge,
where Ps,l is the potential coefficient of the charge Q3 and current at the surface of the human body are determined
calculated at the zth contour point (Appendix I).
using (2t(7).
2N1+N2
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11M
ABDEL-SALAM AND ABDALLAH: TRANSMISSION-LINEUEClwC FIELD INDUCI'ION IN HUMANS
TABLE I
FlELD ENHANCWNT
FACTORAND CHARGE DENSITY ALONG HUMAN BODY
Position
(Eo =10 kV/m)
top of hcad
0.716
middle of ncck
0.424
middle of waisr/crotch
2.1
AYE
I
ZL 3 m
CON0
3:
I 'r
n m m
AYE COND
Z2.2m
HEIGHTS
P'
7777777777777,
(b)
(a)
0.186
Fig. 3. (a) 362- and (h) 550-kV overhead transmission-line configurations.
middle of legs
0.106
1.2
TABLE 11
INDUCED CURRENTS IN GROLINDED
AND INSULATED HUMAN BODIES
Induced Nmnui (uA)
middle of raist/crotch
Position
top of head
I
21
I
18
middle of neck
middle of waistlmtch
a
middle of lcgs
157
io
20
40
M
BO
70
BO
Dlstance x from tronsmlsslon-line center, m
(a)
III. NUMERICAL
DATA
The height of the stressed plate H over the ground plane
is five times the height of the human body h to make sure
that the field at the stressed plate remains unperturbed with
the presence of the human body. The width 2 0 of the plate is
long enough to make sure that the plate edge effect is minor
at the position of the body, so D is chosen equal to H.
Typical values [2] for the human body dimensions are 9 cm
for the head radius, 6 cm for the neck radius, 20 cm for the
waistkrotch radius, and 15 cm for the leg radius (Fig. 2). The
length of the neck = 6 cm, the length of the waist/crotch =
60 cm, and the length of the legs = 90 cm, for a person of
175 cm height.
Gmcnded p a l UndaMwl m-wline
4 8 0
I
I - middle of leaf
- middle of wonnt/crotch
0
10
20
M
40
50
60
Distance x from transmission-line
70
EO
center, m
(h)
Fig. 4. Induced current in a grounded human as dependent on his position
underneath (a) a 362-kVtransmission line and (b) a 550kV transmission line.
N. RESULTS AND DISCUSSION
Table I gives the field enhancement factor and the charge
density values along the body of a grounded human standing
in an unperturbed field E,. The enhancement factor at the top
of the head agreed well with the values reported before [3].
Table II gives the induced current distributionin the body of
a person standing in a 60-Hzunperturbed field E, (= IO kV/m)
for grounded and insulated bodies. The body is insulated by
shoes of 2-cm thickness.
It is quite clear that the induced current values increase
along the length of the body, starting from the head downwards
to the legs. Moreover, the induced currents for the grounded
body are larger than those for the insulated body. This is in
agreement with previous findings [2].
Underneath transmission-line configurations (Fig. 3) the
electric field changes from point to point [7] and the induced
current in the human body changes accordingly. Figs. 4 and
5 show the induced current distribution through the body
of grounded and insulated persons underneath the threephase transmission line configurations of Fig. 3. The body
is insulated by shoes of 2-cm thickness. The induced current
follows the pattern of the electric field distribution underneath
the transmission line [7].
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lEEE TRANSACTIONS ON BIOMEDICAL ENGl"G,
1108
VOL. 42, NO. 11. NOVEMBER 1995
Fig. 6. Ring charge in r-z coordinates.
Distance x from transmission-line center, m
where
(a)
+
f f 2 = d(ra +
a1 = J(ra
.
.
+
=
=
-
,o---- ,'
.
0 ,
0
a.(
ffl
a2
.
.....
IO
+ + z,)2
- Zj)2
2m2 =-
.. top of hsod
,--.
.\
,
Tj)2
a.(
ml = -
-- middle of neck
I
+
2
m
- middle of laps
- middls of xdst/uobh
=20-
Tj)2
20
\
*.
-_.. .,-- - _ _ _
..., ...,
--..--I7.z.: :.::.=.7.z,-",z"I
40
50
v--.E-.
60
and T(m) is the complete elliptic integral of the first kind [SI
and E is the permittivity of air.
r)
70
BO
Dlstance x from transmlsslon-line center, m
(bt
B. Infinite Line Charge
me
Fig. 5. (a) Induced current in an insulated human as dependent on his p s i - di tnet , , , ,
coefficient P , , ~calculated at the ith point
tion undemeath (a) a 362-kV transmission line and (b) a 550-kVuansmission
of coordinates ( T ~zi)
, for a line charge located at ( r j ,zj) and
line.
its image is expressed as
V. CONCLUSION
A method is proposed for determining the distribution of
the elecmc fields, induced charges, and currents in a human
body standing in high elecmc fields produced by high-voltage
overhead transmission lines. This method is based on the
charge simulation technique. The calculated field enhancement
factor at the top of the head of the human agreed well
with those reported before. The calculated induced current in
grounded and insulated humans conform with those reported
earlier.
APPENDIX I
PO^^ c o m c m Pi,j
A. Ring Charge
With reference to Fig. 6, the field coefficients fYt,> and
for
a ring charge of radius rj located at z = z j and its image
are expressed as
fz,,, calculated at the ith point p of coordinates (ri,2;)
A. Ring Charge
With reference to Fig. 6, the potential coefficient Pi,*calcu, for a ring charge
lated at the ith point pof coordinates ( T ~z,)
of radius r, located at z = z, and its image is expressed as
fP,,)
=-
(T; -
+
r,? (z1 - zj)2)r(ml) - P 3 3 m l )
4::
- (7: - T-: + (2;+ z,)2)r(m2) - P;r(mz)
QZPZZ
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ABDFLSALAM AND ABDALLAH: TRANSMISSION-LINZELECIXlC FWLD INDUCITON IN HUMANS
where
1109
Mpzen Abdel-Salam (SM78-F‘93),
and r(m)is
kind
PI.
B. Infinite Line Charge
me field c.ficients fr,,, and fz,,,
at the ith
mint
. .V Of COOrdinateS (T;.- , z ; ) for a line charge located at
( ~ jzj)
, and its image are expressed as
\
.I
1
(Tt
-
(Ti
- Tj)
(Ti - T j ) 2
(2;
+ +
(21
-
- T3)
i.(
(Ti - T j ) 2
2j)2
- “3)
I
I
+ 23)
+ (.i + % j ) 2
’
(12)
(I3)
ACKNOWLEDGMENT
The authorswish to
employers
for the support they received during the progress of the
work. The authors also wish to thank the reviewers for their
comments which enhanced the clarity of the paper.
was horn in
Egypt. He received the BSc. degree in 1967, the
M.Sc. degree in 1970, and the Ph.D. degree in 1973,
all in electrical engineering from the University of
Cairo, Egypt.
In 1%7, he was with the Academy of Science
and Technology, Cairo, as a Research Assistant. In
1973, he joined the faculty of Electrical Engineering
at Assiut University, Egypt, as an Assistant Professor, and in October 1977, he became an Asmiate
Professor. Dnrine the academic vem of 1977-1979,
he was an Alexander-van-Humholdt Feliow in the El&trical Engineering
Depmmnt, Technical University of Munich, Germany, and the Electrical
Engineering Department, University of Liverpool. England. In September
1979, he began work as a Researcher with General Electric Company,
Pittsfield. MA. In J”-+
1982, he xioined Assiut University as a R&ssor
of Electrical Power Engineering. Dm&g the academic years of 1982-1984,
he was a Professor in the Department of Electrical Engineering, University
of Jordan, Amman. During the academic years of 1984-1986, he was a
Visiting Full Rofessor in the Department of Electrical Engineering, Michigan
Technological University, Houghton. From 199%1994, he was a Professor
of Elech’ic Power E n g i n d g in the Department of Electrical Engineering
at King Fahd University of Petrolwm and Minerals, Dhahran, Saudi Arabia.
He had obtained research fellowships at the Military Technical University of
Hambnrg, Germany, in 1984, at the University of Leeds, U.K., in 1988, at
Kaiserslautem University, Germany in 1989, and at Michigan Technological
University in 1990. He is currently a Professor of Electric Power Engineering,
Assiut University. His rescareh activities include corona studies, digital
calculation of electric fields, investigations of high-voltage phenomena, lowvoltage distribution networks, and control of electrical machines. He is a
ceauthor of High Voltage Engineering--Theory and Practice (New York
Marcel Dekker, 1990).
Dr. Abdel-Salam was the Founderl&mnker of the Middle East Power
System Conference (MEPCON) that washeld in Bgypt, January 1989. He is
a Member of the Electrostatic Pmeesses Committee of the IEEE Industrial
Applications Society. He received the Egyptian National Prize in 1987 for
contributions to applied electrostatics and in 1993 for contributions to highvoltages applications in industry. He is a Fellow of the Institution of Electrical
En&&-London,
England.
REFERENCES
M. Abdel-Salam and M. T. El-Mohands, “Electric field around parallel
dc and multi-Dhase ac transmission lines.” IEEE Tram. Elm. Imul.. vol.
28, pp. 114<1152. 1990.
121 EPRI, ‘Transmission line reference book 345 kV and ahave,” USA,
1983. Dn. 365-369.
r31 B. I. Maddock, I. C. Male, and W. T. Noms, “50 Hz elechic and
magnetic fields near power “ission
circuits and so“ associated
exposure and health studies,” in Pmc. Inr. Con$ Elect. M a p . Fields
Med. Bid., London, U.K., 1985, pp. 112-116.
[41 T. Matsumoto, “Measurement for human exposure to AC elecnic fields,”
in P m . Int. Symp. HVEng., Braunschweig, Germany, Aug. 1987. paper
a? 3.*.1
_..,.‘
[SI M. Abdel-Salam, “High voltage engineering theory and practice,” in
Electric Fie&, M . Khalifa, Ed. New York:Marcel D e k , 1990, pp.
30-36.
[6] H. Singer, H. Steinhigler, and P.Weiss, “A charge simulation methods
for the calculation of high voltage fields.’’ IEEE Trans. Power Applicat.
Sysf., vol. PAS-93, pp. 3660-3668, 1974.
[7] lEEE Tutorial Course, ‘The elecUostatic and elecUomagnetic effects of
ac transmission lines,” 79 EH0145-3-PwQ 1979.
[SI P. Silvester, Modem Ekcrmmagnetic Fields. Englewood Cliffs, N I
Prentice-Hall, 1968, Appendices.
Ha~sanMohsmed AbdPIlah (M’83SM83) was
ham in Egypt on November 28, 1943. He received
the B.Sc. degree in 1966, and the MSc. degree
in 1970 in electrical engineering from.Assiut University. Assiut, Egypt. He joined the University of
Southampton as a Ph.D. student in 1972. and he
received the Ph.D. degree in electrical engineering
in 1978.
In 1966, he was with Assiut University as a
Demonstrator in the Electrical Engineering Depanment of Assiut Universitv. From December 1978 to
September lW9, he worked as a Research Officer with the School of Electrical
Engineering, University of Bath,Bath, U.K. From January 1980 to November
1983, he served as an Assistant Professor with the Electrical Engineering
Department of Assiut University. From December 1983 to September 1984,
he was an Associate Professor with the Electrical Engineering Department
of Rochester Institute of Technology, Rochester, NY.From September 1984
to September 1988, he was an Associate Professor with the Electrical
Engineering Department of Bahrain University, Bahrain.Currently, he is an
Associate Professor with the Biomedical Technology Department, King Sand
University, Riyadh, Saudi Arabia.
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