Substation Grounding
Substation Grounding
Substation Grounding
Richard P. Keil
Commonwealth  Associates,  Inc.
11.1 Reasons for Substation Grounding System................... 11-1
11.2 Accidental Ground Circuit ............................................. 11-2
Conditions 
.
Permissible  Body Current  Limits 
.
Importance of  High-Speed Fault Clearing 
.
Tolerable Voltages
11.3 Design Criteria................................................................. 11-8
Actual  Touch and  Step Voltages 
. 
Soil  Resistivity 
.
Grid Resistance 
. 
Grid Current 
. 
Use of  the  Design
Equations 
. 
Selection of  Conductors 
. 
Selection
of  Connections 
. 
Grounding  of  Substation Fence 
.
Other Design Considerations
11.1   Reasons for Substation Grounding System
The substation grounding system is an essential part of the overall electrical system. The proper
grounding of a substation is important for the following two reasons:
1. It provides a means of dissipating electric current into the earth without exceeding the operating
limits of the equipment.
2. It provides a safe environment to protect personnel in the vicinity of grounded facilities from the
dangers of electric shock under fault conditions.
The grounding system includes all of the interconnected grounding facilities in the substation area,
including the ground grid, overhead ground wires, neutral conductors, underground cables, founda-
tions, deep well, etc. The ground grid consists of horizontal interconnected bare conductors (mat) and
ground rods. The design of the ground grid to control voltage levels to safe values should consider the
total grounding system to provide a safe system at an economical cost.
The following information is mainly concerned with personnel safety. The information regarding the
grounding system resistance, grid current, and ground potential rise can also be used to determine if the
operating limits of the equipment will be exceeded.
Safe grounding requires the interaction of two grounding systems:
1. Intentional ground, consisting of grounding systems buried at some depth below the earths
surface
2. Accidental ground, temporarily established by a person exposed to a potential gradient in the
vicinity of a grounded facility
It is often assumed that any grounded object can be safely touched. A low substation ground resistance is
not, in itself, a guarantee of safety. There is no simple relation between the resistance of the grounding
system as a whole and the maximum shock current to which a person might be exposed. A substation
 2006 by Taylor & Francis Group, LLC.
with  relatively  low  ground  resistance  might  be  dangerous,  while  another  substation  with  very  high
ground  resistance  might  be safe  or could be  made  safe  by careful  design.
There are many parameters that have an effect on the voltages in and around the substation area. Since
voltages  are  site-dependent,  it  is  impossible  to  design  one  grounding  system  that  is  acceptable  for  all
locations. The grid current, fault duration, soil resistivity, surface material, and the size and shape of the
grid  all  have  a  substantial  effect  on  the  voltages  in  and  around  the  substation  area.  If  the  geometry,
location  of  ground  electrodes,  local  soil  characteristics,  and  other  factors  contribute  to  an  excessive
potential  gradient  at  the  earth  surface,  the  grounding  system  may  be  inadequate  from  a  safety  aspect
despite its capacity to carry the fault current in magnitudes and durations permitted by protective relays.
During typical ground fault conditions, unless proper precautions are taken in design, the maximum
potential  gradients  along  the  earth  surface may  be  of  sufcient  magnitude  to  endanger  a  person  in  the
area. Moreover, hazardous voltages may develop between grounded structures or equipment frames and
the  nearby earth.
The  circumstances  that  make  human  electric  shock  accidents  possible  are:
.
Relatively  high  fault  current  to  ground  in  relation  to  the  area  of  the  grounding  system  and  its
resistance to  remote  earth.
.
Soil resistivity and distribution of ground currents such that high potential gradients may occur
at  points  at  the  earth  surface.
.
Presence  of  a  person  at  such  a  point,  time,  and  position  that  the  body  is  bridging  two  points  of
high potential  difference.
.
Absence of sufcient contact resistance or other series resistance to limit current through the body
to  a  safe  value  under  the  above  circumstances.
.
Duration of the fault and body contact and, hence, of the ow of current through a human body
for  a  sufcient  time  to  cause  harm  at  the  given  current intensity.
Relative  infrequency  of  accidents  is  largely  due  to  the  low  probability  of  coincidence  of  the  above
unfavorable  conditions.
To  provide  a  safe  condition  for  personnel  within  and  around  the  substation  area,  the  grounding
system design limits the potential difference a person can come in contact with to safe levels. IEEE Std.
80,  IEEE  Guide  for  Safety  in  AC  Substation  Grounding  [1],  provides  general  information  about
substation grounding and the specic design equations necessary to design a safe substation grounding
system.  The  following  discussion  is  a  brief  description  of the  information  presented  in  IEEE  Std.  80.
The  guides  design  is  based  on  the  permissible  body  current  when  a  person  becomes  part  of  an
accidental  ground circuit.  Permissible  body current will not cause  ventricular brillation,  i.e.,  stoppage
of the heart. The design methodology limits the voltages that produce the permissible body current to a
safe  level.
11.2  Accidental Ground Circuit
11.2.1  Conditions
There  are  two  conditions  that  a  person within  or  around  the  substation  can  experience  that  can  cause
them  to  become  part  of  the  ground  circuit.  One  of  these  conditions,  touch  voltage,  is  illustrated  in
Figs.  11.1  and  11.2.  The  other  condition,  step  voltage,  is  illustrated  in  Figs.  11.3  and  11.4.  Figure  11.1
shows the fault current being discharged to the earth by the substation grounding system and a person
touching a grounded metallic structure, H. Figure 11.2 shows the Thevenin equivalent for the persons
feet in parallel, Z
Th
, in series with the body resistance, R
B
. V
Th
is the voltage between terminal H and F
when the person is not present. I
B
is the body current. When Z
Th
is equal to the resistance of two feet in
parallel, the touch voltage is
E
touch
  I
B
(R
B
Z
Th
) (11:1)
 2006 by Taylor & Francis Group, LLC.
Z (system)
U
I
f
I
g
H
F
Station grid
R
B
I
B
FIGURE 11.1 Exposure to touch voltage.
V
Th
V
Th
 = touch voltage
R
B
 = body resistance Z
Th
Terminal F
Terminal H
Z
Th
 = R
f
2
FIGURE 11.2 Touch-voltage circuit.
Z (system)
U
I
f
I
B
F
1
F
2
I
g
Station grid
FIGURE 11.3 Exposure to step voltage.
V
Th
V
Th
 = step voltage
R
B
 = body resistance Z
Th
Terminal F
2
Terminal F
1
Z
Th
 = 2R
f
FIGURE 11.4 Step-voltage circuit.
 2006 by Taylor & Francis Group, LLC.
Figures 11.3 and 11.4 show the conditions for step voltage. Z
Th 
is the Thevenin equivalent impedance for
the persons feet in series and in series with the body. Based on the Thevenin equivalent impedance, the
step  voltage  is
E
step 
 I
B
( R
B 
 Z
Th
)  (11:2)
The  resistance  of the  foot  in  ohms  is  represented  by a  metal  circular  plate  of  radius  b  in meters  on  the
surface of homogeneous  earth  of  resistivity r  (V-m)  and  is  equal  to
R
f 
r
4b 
(11:3)
Assuming  b   0:08,  R
f 
 3r  (11:4)
The  Thevenin  equivalent  impedance for  two feet  in parallel  in the  touch voltage,  E
touch
,  equation  is
Z
Th 
R
f
2
   1:5r  (11:5)
The  Thevenin  equivalent  impedance for  two feet  in series  in the  step  voltage, E
step
,  equation  is
Z
Th 
 2R
f 
 6r  (11:6)
The  above  equations  assume  uniform  soil  resistivity.  In  a  substation,  a  thin  layer  of  high-resistivity
material  is  often  spread  over  the  earth  surface  to  introduce  a  high-resistance  contact  between  the
soil  and  the  feet,  reducing  the  body  current.  The  surface  layer  derating  factor,  C
s
,  increases  the  foot
resistance  and  depends  on  the  relative  values  of  the  resistivity  of  the  soil,  the  surface  material,  and  the
thickness  of the  surface  material.
The  following  equations  give  the  ground resistance of  the  foot  on  the  surface  material:
R
f 
r
s
4b
_   _
C
s 
(11:7)
C
s 
 1 
16b
r
s
1
n 1
K 
n 
R
m(2 nhs ) 
(11:8)
K  
r r
s
r r
s
(11:9)
where
C
s 
surface layer derating  factor
K  reection  factor  between  different  material  resistivities
r
s 
surface material  resistivity  in V-m
r  resistivity of the  earth  beneath  the  surface  material  in V-m
h
s 
is  the  thickness  of the  surface  material  in m
b  is  the  radius  of the  circular  metallic disc  representing the  foot  in  m
R
m(2nhs)
is the mutual ground resistance between the two similar, parallel, coaxial plates, separated
by a distance (2nh
s
), in an innite medium of resistivity  r
s
in  V-m.
A series of C
s 
curves has been developed based on Eq. (11.8) and b  0.08 m, and is shown in Fig. 11.5.
 2006 by Taylor & Francis Group, LLC.
The following empirical equation by Sverak [2], and later modied, gives the value of C
s
. The values of
C
s
obtained using Eq. (11.10) are within 5% of the values obtained with the analytical method [3]:
C
s
  1 
0:09 1 
  r
r
s
_   _
2h
s
0:09
(11:10)
11.2.2   Permissible Body Current Limits
The duration, magnitude, and frequency of the current affect the human body as the current
passes through it. The most dangerous impact on the body is a heart condition known as ventri-
cular brillation, a stoppage of the heart resulting in immediate loss of blood circulation. Humans
are very susceptible to the effects of electric currents at 50 and 60 Hz. The most common physio-
logical effects as the current increases are perception, muscular contraction, unconsciousness,
brillation, respiratory nerve blockage, and burning [4]. The threshold of perception, the detection of
a slight tingling sensation, is generally recognized as 1 mA. The let-go current, the ability to control the
muscles and release the source of current, is recognized as between 1 and 6 mA. The loss of muscular
control may be caused by 925 mA, making it impossible to release the source of current. At slightly
higher currents, breathing may become very difcult, caused by the muscular contractions of
the chest muscles. Although very painful, these levels of current do not cause permanent damage
to the body. In a range of 60100 mA, ventricular brillation occurs. Ventricular brillation can be a
fatal electric shock. The only way to restore the normal heartbeat is through another controlled
electric shock, called debrillation. Larger currents will inict nerve damage and burning, causing
other life-threatening conditions.
The substation grounding system design should limit the electric current ow through
the body to a value below the brillation current. Dalziel [5] published a paper introducing an equation
0.95
0
0
0.1
0.2
0.3
0.4
0.5
C
s
0.6
0.7
0.8
0.9
k = 0.1
k = 0.95
1
0.02   0.04   0.06   0.08   0.1   0.12  0.14   0.16   0.18   0.2   0.22   0.24   0.26 0.28   0.3
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
k =
h
s
FIGURE 11.5   C
s
vs. h
s
.
 2006 by Taylor & Francis Group, LLC.
relating  the  ow  of  current  through  the  body  for  a  specic  time  that  statistically  99.5%  of  the  popu-
lation  could  survive  before  the  onset  of  brillation.  This  equation  determines  the  allowable  body
current:
I
B 
t
s
p  (11:11)
where
I
B
rms  magnitude  of  the  current through the  body,  A
t
s
duration  of  the  current  exposure,  sec
k
S
B
p
S
B 
empirical  constant  related  to  the  electric  shock  energy  tolerated  by  a  certain  percent  of  a
given  population
Dalziel found the value of k  0.116 for persons weighing approximately 50 kg (110 lb) or k  0.157 for a
body  weight of  70  kg  (154  lb) [6].  Based  on  a  50-kg  weight,  the  tolerable  body current  is
I
B 
0:116
t
s
p  (11:12)
The  equation  is  based  on  tests  limited  to values  of  time  in  the  range  of  0.033.0  sec.  It is  not  valid  for
other values of time. Other researchers have suggested other limits [7]. Their results have been similar to
Dalziels  for  the  range  of  0.033.0  sec.
11.2.3  Importance of High-Speed Fault Clearing
Considering the signicance of fault duration both in terms of Eq. (11.11) and implicitly as an accident-
exposure factor,  high-speed  clearing  of ground faults  is  advantageous  for  two reasons:
1.  Probability of exposure to electric shock is greatly reduced by fast fault clearing time, in contrast
to  situations  in which  fault  currents  could persist  for  several  minutes  or  possibly  hours.
2.  Both tests and experience show that the chance of severe injury or death is greatly reduced if the
duration  of a  current ow  through  the  body  is  very  brief.
The allowed current value may therefore be based on the clearing time of primary protective devices, or
that  of the  backup  protection.  A good  case  could be  made  for  using  the  primary clearing  time  because
of  the  low  combined  probability  that  relay  malfunctions  will  coincide  with  all  other  adverse  factors
necessary for an accident. It is more conservative to choose the backup relay clearing times in Eq. (11.11),
because  it  assures  a  greater safety  margin.
An  additional  incentive  to  use  switching  times  less  than  0.5  sec  results  from  the  research  done  by
Biegelmeier  and  Lee  [7].  Their  research  provides  evidence  that  a  human  heart  becomes  increasingly
susceptible  to  ventricular  brillation  when  the  time  of  exposure  to  current  is  approaching  the  heartbeat
period, but that the danger is much smaller if the time of exposure to current is in the region of 0.060.3 sec.
In reality, high ground gradients from faults are usually infrequent, and shocks from this cause are
even more uncommon. Furthermore, both events are often of very short duration. Thus, it would not be
practical to design against shocks that are merely painful and cause no serious injury, i.e., for currents
below the brillation threshold.
11.2.4   Tolerable Voltages
Figures  11.6  and  11.7  show  the  ve voltages  a  person  can  be  exposed  to  in a  substation.  The  following
denitions describe the voltages:
Ground  potential  rise  (GPR): The maximum electrical potential that a substation grounding grid
may attain relative to a distant grounding point assumed to be at the potential of remote earth. GPR is
 2006 by Taylor & Francis Group, LLC.
the product of the magnitude of the grid current, the portion of the fault current conducted to earth
by the grounding system, and the ground grid resistance.
Mesh voltage: The maximum touch voltage within a mesh of a ground grid.
Metal-to-metal   touch  voltage: The difference in potential between metallic objects or structures
within the substation site that can be bridged by direct hand-to-hand or hand-to-feet contact.
REMOTE
EARTH
E
mm
E
m
SURFACE
POTENTIAL
PROFILE
T
R
A
N
S
F
E
R
E
D
V
O
L
T
A
G
E
M
E
S
H
 
V
O
L
T
A
G
E
T
O
U
C
H
 
V
O
L
T
A
G
E
S
T
E
P
 
V
O
L
T
A
G
E
M
E
T
A
L
-
T
O
-
M
E
T
A
L
T
O
U
C
H
 
V
O
L
T
A
G
E
E
t
E
s
REMOTE
EARTH
1
METER
E
trrd
 ~ GPR
~
FIGURE 11.6 Basic shock situations.
CONDUCTING PATH
BETWEEN SUBSTATIONS
I
F
E
trrd
STATION 2
SURFACE POTENTIAL PROFILE
ZERO POTENTIAL
STATION 1
GPR STATION 1
GPR STATION 2
FIGURE 11.7 Typical situation of external transferred potential.
 2006 by Taylor & Francis Group, LLC.
Note: The metal-to-metal touch voltage between metallic objects or structures bonded to the ground grid is
assumed to be negligible in conventional substations. However, the metal-to-metal touch voltage between
metallic  objects  or  structures  bonded  to  the  ground  grid  and  metallic  objects  inside  the  substation  site
but  not  bonded  to  the  ground  grid,  such  as  an  isolated  fence,  may  be  substantial.  In  the  case  of
gas-insulated substations, the metal-to-metal touch voltage between metallic objects or structures bonded
to the ground grid may be substantial because of internal faults or induced currents in the enclosures.
Step  voltage:  The  difference in  surface potential  experienced  by  a  person  bridging  a  distance  of  1  m
with  the  feet  without  contacting  any other  grounded object.
Touch voltage: The potential difference between the GPR and the surface potential at the point where
a  person  is  standing  while  at  the  same  time  having  a  hand in  contact  with  a  grounded  structure.
Transfer red  voltage: A  special case  of  the  touch voltage  where a voltage is  transferred  into  or out  of
the substation, from or to a remote point external to the substation site. The maximum voltage of any
accidental circuit must not exceed the limit that would produce a current ow through the body that
could cause  brillation.
Assuming the more conservative body weight of 50 kg to determine the permissible body current and
a  body  resistance of  1000  V,  the  tolerable  touch voltage  is
E
touch50 
 (1000  1:5C
s 
r
s
)
0:116
t
s
p  (11:13)
and  the  tolerable  step  voltage  is
E
step50 
 (1000  6C
s 
r
s
)
0:116
t
s
p  (11:14)
where
E
step
step  voltage,  V
E
touch 
touch voltage, V
C
s 
determined  from Fig.  11.5  or Eq.  (11.10)
r
s 
resistivity of  the  surface material,  V-m
t
s 
duration  of  shock  current,  sec
Since the only resistance for the metal-to-metal touch voltage is the body resistance, the voltage limit is
E
mm-touch50 
116
t
s
p  (11:15)
The shock duration is usually assumed to be equal to the fault duration. If re-closing of a circuit is planned,
the fault duration time should be the sum of the individual faults and used as the shock duration time t
s
.
11.3  Design Criteria
The  design  criteria  for  a  substation  grounding  system  are to  limit  the  actual  step  and  mesh voltages  to
levels below the tolerable touch and step voltages as determined by Eqs. (11.13) and (11.14). The worst-
case  touch voltage,  as  shown  in  Fig.  11.6,  is  the  mesh voltage.
11.3.1  Actual Touch and Step Voltages
The  following  discusses  the  methodology  to  determine  the  actual  touch  and  step  voltages.
11.3.1.1  Mesh Voltage (E
m 
)
The  actual  mesh  voltage,  E
m 
(maximum  touch  voltage),  is  the  product  of  the  soil  resistivity,  r;  the
geometrical factor based on the conguration of the grid, K
m
; a correction factor, K
i
, which accounts for
 2006 by Taylor & Francis Group, LLC.
some of the errors introduced by the assumptions made in deriving K
m
; and the average current per unit
of effective buried length of the conductor that makes up the grounding system (I
G
=L
M
):
E
m
 
rK
m
K
i
I
G
L
M
(11:16)
The geometrical factor K
m
[2] is as follows:
K
m
 
1
2p
ln
  D
2
16hd
(D 2h)
2
8Dd
  
h
4d
_   _
K
ii
K
h
ln
8
p(2n 1)
_   _ _   _
(11:17)
For grids with ground rods along the perimeter, or for grids with ground rods in the grid corners, as well
as both along the perimeter and throughout the grid area, K
ii
1. For grids with no ground rods or grids
with only a few ground rods, none located in the corners or on the perimeter,
K
ii
 
1
(2n)
2
n
(11:18)
K
h
 
1 
h
h
0
  h
0
  1 m (grid reference depth) (11:19)
Using four grid-shaped components [8], the effective number of parallel conductors, n, in a given grid
can be made applicable to both rectangular and irregularly shaped grids that represent the number of
parallel conductors of an equivalent rectangular grid:
n  n
a
n
b
n
c
n
d
(11:20)
where
n
a
 
2L
C
L
p
(11:21)
n
b
1 for square grids
n
c
1 for square and rectangular grids
n
d
1 for square, rectangular, and L-shaped grids
Otherwise,
n
b
L
p
4
A
p
(11:22)
n
c
L
x
L
y
A
_   _0:7A
Lx Ly
(11:23)
n
d
D
m
L
2
x
 L
2
y
_ (11:24)
 2006 by Taylor & Francis Group, LLC.
where
L
C
total  length  of  the  conductor in  the  horizontal  grid,  m
L
p
peripheral  length  of  the  grid,  m
A  area of  the  grid,  m
2
L
x
maximum  length  of  the  grid  in  the  x  direction,  m
L
y
maximum  length  of  the  grid  in  the  y direction,  m
D
m 
maximum  distance  between  any  two  points  on  the  grid,  m
D  spacing  between  parallel  conductors,  m
h  depth  of the  ground  grid  conductors,  m
d  diameter of the  grid  conductor,  m
I
G
maximum  grid  current,  A
The  irregularity  factor,  K
i
,  used in  conjunction with  the  above-dened  n, is
K
i 
 0:644  0:148n  (11:25)
For grids with no ground rods, or grids with only a few ground rods scattered throughout the grid, but
none  located  in  the  corners  or  along  the  perimeter of  the  grid,  the  effective buried  length,  L
M
, is
L
M 
 L
C 
 L
R 
(11:26)
where
L
R 
 total  length  of all  ground  rods,  m
For grids with ground rods in the corners, as well as along the perimeter and throughout the grid, the
effective buried  length, L
M
, is
L
M 
 L
C 
  1:55  1:22
  L
r
L
2
x 
 L
2
y
_
_
_
_
_
_
_
_
_
_
_ L
R 
(11:27)
where
L
r 
 length  of each  ground  rod, m
11.3.1.1.1  Geomet r ical  Factor  K
m
The equation for K
m 
has variables of D, the spacing between the conductors; n, the number of conductors;
d, the diameter of the conductors; and h, the depth of the grid. Each variable has a different impact on K
m
.
Figure 11.8 shows how the distance between conductors affects K
m
. For this example, changing the spacing
from 10  to  40 m  only changes K
m 
from  0.89  to  1.27.  The  greatest  change  takes place  for  relatively  small
spacings.  The  closer  the  spacing,  the  smaller  K
m 
is.  Figure  11.9  shows  that  as  the  number  of conductors
increases and  the  spacing  and  depth  remain constant,  K
m 
decreases  rapidly.  The  diameter of the  ground
conductor as shown in Fig. 11.10 has very little effect on K
m
. Doubling the diameter of the conductor from
0.1 m(2=0) to  0.2 m  (500 kcmil) reduces K
m 
by  approximately  12%. D  and  n  are  certainly dependent  on
each other for a specic area of grid. The more conductors are installed, the smaller the distance between
the  conductors.  Physically,  there  is  a  limit  on  how  close  conductors  can  be  installed  and  should  be  a
design  consideration. Changing  the  depth as  shown  in  Fig.  11.11  also  has  very  little inuence  on K
m
for
practical depths.
11.3.1.2   Step Voltage (E
s
)
The maximumstep voltage is assumed to occur over a distance of 1 m, beginning at and extending outside
of the perimeter conductor at the angle bisecting the most extreme corner of the grid. The step-voltage
 2006 by Taylor & Francis Group, LLC.
values are obtained as a product of the soil resistivity  r, the geometrical factor K
s
, the corrective factor K
i
,
and the average current per unit of buried length of grounding system conductor (I
G
=L
S
):
E
s
 
rK
s
K
i
I
G
L
S
(11:28)
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Ddistance between conductors (m)
K
 
m
K
m
FIGURE 11.8   K
m
vs. D.
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Nnumber of conductors
K
m
K
m
FIGURE 11.9   K
m
vs. N.
 2006 by Taylor & Francis Group, LLC.
For  the  usual burial  depth of  0.25  < h  <  2.5 m  [2],  K
s 
is  dened as
K
s 
1
p
1
2h 
1
D  h 
1
D
_
1  0:5
n 2
_
_   _
(11:29)
and K
i 
as  dened  in Eq.  (11.25).
0.45
0.55
0.65
0.75
0.85
0.95
0
.
0
1
0
.
0
2
0
.
0
3
0
.
0
4
0
.
0
5
0
.
0
6
0
.
0
7
0
.
0
8
0
.
0
9
0
.
1
ddiameter of cable (m)
K
m
K
m
FIGURE 11.10   K
m
vs. d.
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0.25   0.5   0.75   1   2   3   4   5   6   7
hdepth of grid conductors (m)
K
m
K
m
FIGURE 11.11   K
m
vs. h.
 2006 by Taylor & Francis Group, LLC.
For  grids  with  or  without  ground  rods,  the  effective buried conductor  length,  L
S
,  is  dened  as
L
S 
 0:75L
C 
 0:85L
R 
(11:30)
11.3.1.2.1  Geomet r ical  Factor  K
s
The equation  for  K
s 
also has variables D,  n,  d, and  h. K
s 
is not  affected  much by either  the  distance,  D,
between or the number, n, of conductors as can be seen in Figs. 11.12 and 11.13. This is reasonable since
the step voltage lies outside the grid itself. The inuence of each conductor as it moves from the edge is
reduced. On the other hand, the depth of burial has a drastic affect on K
s
. The deeper the conductor is
buried, the lower the value of K
s 
as shown in Fig. 11.14. This is reasonable since there is a voltage drop as
the  current passes  through  the  soil  reducing  the  voltage  at  the  surface.
11.3.1.3  Evaluation of the Actual Touch- and Step-Voltage Equations
0.3000
0.3500
0.4000
0.4500
0.5000
0.5500
0.6000
0.6500
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Ddistance (m)
K
s
K
s
FIGURE 11.12   K
s
vs. D.
0.3400
0.3450
0.3500
0.3550
0.3600
0.3650
0.3700
0.3750
0.3800
0.3850
2 3 4 5 6 8 10 12 14 16 18 20 22 24 26 28
Nnumber of conductors
K
s
K
s
FIGURE 11.13   K
s
vs. N.
 2006 by Taylor & Francis Group, LLC.
It is essential to determine the soil resistivity and maximumgrid currents to design a substation ground-
ing system. The touch and step voltages are directly proportional to these values. Overly conservative
values of soil resistivity and grid current will increase the cost dramatically. Underestimating them may
cause the design to be unsafe.
11.3.2   Soil Resistivity
Soil resistivity investigations are necessary to determine the soil structure. There are a number of tables
in the literature showing the ranges of resistivity based on soil types (clay, loam, sand, shale, etc.) [911].
These tables give only very rough estimates. The soil resistivity can change dramatically with changes in
moisture, temperature, and chemical content. To determine the soil resistivity of a particular site, soil
resistivity measurements need to be taken. Soil resistivity can vary both horizontally and vertically,
making it necessary to take more than one set of measurements. A number of measuring techniques are
described in detail in Ref. [12]. The most widely used test for determining soil resistivity data was
developed by Wenner and is called either the Wenner or four-pin method. Using four pins or electrodes
driven into the earth along a straight line at equal distances of  a, to a depth of  b, current is passed
through the outer pins while a voltage reading is taken with the two inside pins. Based on the resistance,
R, as determined by the voltage and current, the apparent resistivity can be calculated using the
following equation, assuming b is small compared with a:
r
a
  2paR (11:31)
where it is assumed the apparent resistivity,   r
a
, at depth a is given by the equation.
Interpretation of the apparent soil resistivity based on eld measurements is difcult. Uniform and
two-layer soil models are the most commonly used soil resistivity models. The objective of the soil
model is to provide a good approximation of the actual soil conditions. Interpretation can be done
either manually or by the use of computer analysis. There are commercially available computer
programs that take the soil data and mathematically calculate the soil resistivity and give a condence
level based on the test. Sunde [10] developed a graphical method to interpret the test results.
The equations in IEEE Std. 80 require a uniform soil resistivity. Engineering judgment is required to
interpret the soil resistivity measurements to determine the value of the soil resistivity,   r, to use in the
equations. IEEE Std. 80 presents equations to calculate the apparent soil resistivity based on eld
measurements as well as examples of Sundes graphical method. Although the graphical method and
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5
hdepth of grid conductors (m)
K
s
K
s
FIGURE 11.14   K
s
vs. h.
 2006 by Taylor & Francis Group, LLC.
equations are estimates, they provide the engineer with guidelines of the uniform soil resistivity to use in
the  ground grid  design.
11.3.3  Grid Resistance
The  grid  resistance,  i.e.,  the  resistance  of  the  ground  grid  to  remote  earth  without  other  metallic
conductors  connected,  can  be  calculated  based  on  the  following  Sverak  [2]  equation:
R
g 
 r
1
L
T
20A
p  1 
1
1  h
20=A
_
_   _ _   _
(11:32)
where
R
g 
substation  ground  resistance,  V
r  soil  resistivity,  V-m
A  area  occupied by  the  ground grid,  m
2
h  depth  of the  grid,  m
L
T 
total  buried  length  of  conductors,  m
11.3.3.1  Resistance
The  resistance of the  grid  is  mainly determined  by  the  resistivity  and the  area of the  site.  Adding  more
conductors or changing the depth of the grid does little to lower the resistance. The effect of ground rods
depends  on  the  location  and  depth  of  the  ground  rod  with  respect  to  the  soil  resistivity.  The  effects  of
ground  rods  on  the  resistance  can  be  substantial,  although  it  is  sometimes  difcult  to  determine  the
effects. In uniform soil, it is difcult to determine if the addition of more conductors or the addition of
ground rods will affect the overall resistance the most. In most cases though, the addition of ground rods
has a greater impact because the ground rods discharge current into the earth more efciently than the
grid conductors. Assuming a two-layer soil model with a lower resistivity soil in the lower layer, ground
rods can have a substantial impact on the resistance of the grid. The more the ground rods penetrate into
the lower resistivity soil, the more the rods will reduce the grid resistance [2426]. These rods also add
stability since the variations in soil resistivity due to moisture and temperature are minimized  at lower
depths.  The  effects  of  moisture  and  temperature  on  the  soil  resistivity  can  be  quite  dramatic.  Ground
rods placed on the outside of the grid have a greater impact than those placed in the interior of the grid
because  of  current  density.
The  importance  of  the  lower  ground  grid  resistance  is  reected  in  the  GPR  and  actual  touch
and  step  voltages.  Lowering  the  resistance  of  the  grid  normally  reduces  the  GPR,  although
not necessarily proportionally. Lowering the resistance may somewhat increase the grid current because
the  change  is  the  current  split  between  all  the  ground  current  return  paths.  Another  way  to  decrease
the  resistance  is  to  install  counterpoises.  This,  in  effect,  results  in  adding  area  to  the  grid.  Although
IEEE-80 equations cannot take into account these various methods to decrease the resistance, it is
important for the engineer to understand there are methods that can be used to lower the resistance of a
ground grid.
The following graphs show the effects of the area, number of conductors, and depth for a simple
square  grid  with  no  ground  rods.  Figure  11.15  shows  conclusively  that  the  area  has  a  great  inuence
on the resistance. The length was not kept constant in the example since more conductor length is
needed to cover the area. The number of conductors is related to the change in length and very little
decrease in resistance takes place when the number of conductors is increased in a constant area.
This can be seen by comparing the resistance of a constant area as the number of conductors increases.
Since the amount of material is related to the number of conductors, adding more material does not
inuence the resistance very much.
 2006 by Taylor & Francis Group, LLC.
Figure 11.16 shows the effects of varying the depth of burial of the grid. The area for this example is
900 m
2
. The depth is varied from 0.5 to 2.5 m and the number of conductors from 4 to 10. As can be
seen from Fig. 11.16, there is very little change in the resistance even if the depth is increased by a factor
of 5 and the number of conductors is changed from 4 to 10.
11.3.4   Grid Current
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
2.000
4 5 6 7 8 9 10
NNumber of conductors
R
e
s
i
s
t
a
n
c
e
Area = 900 m
2
Area = 1800 m
2
Area = 2700 m
2
Area = 3600 m
2
FIGURE 11.15 Resistance vs. N.
1.400
1.500
1.600
1.700
1.800
1.900
0.5 1 1.5 2 2.5
 Burial depth (m)
R
g
g
r
i
d
 
r
e
s
i
s
t
a
n
c
e
N = 4
N = 5
N = 6
N = 8
N = 10
Area = 900 m
2
FIGURE 11.16 Resistance vs. depth.
 2006 by Taylor & Francis Group, LLC.
The maximum grid current must be determined, since it is this current that will produce the greatest
GPR and the largest local surface potential gradients in and around the substation area. It is the ow of
the current from the ground grid system to remote earth that determines the GPR.
There are many types of faults that can occur on an electrical system. Therefore, it is difcult to
determine what condition will produce the maximum fault current. In practice, single-line-to-ground
and line-to-line-to-ground faults will produce the maximum grid current. Figures 11.17 through 11.19
show the maximum grid current, I
G
, for various fault locations and system congurations.
Overhead ground wires, neutral conductors, and directly buried pipes and cables conduct a portion of
the ground fault current away from the substation ground grid and need to be considered when
FAULT
GROUNDED
STATION
STRUCTURE
I
F
I
F
I
F
I
F
; I
G
 = 0
FIGURE 11.17 Fault within local substation, local neutral grounded.
FAULT
I
GROUNDED
STATION
STRUCTURE
I
F
i
1
  i
2
  i
n
I
G
 = i =  I
F
FIGURE 11.18 Fault within local substation, neutral grounded at remote location.
I
F
 = I
F
1
 + I
F
2
I
G
 = I
F
  I
F1
I
F2
I
F
I
F1
I
F1
I
F2
I
G
FAULT
GROUNDED
STATION
STRUCTURE
OTHER
SYSTEM
GROUNDS
FIGURE 11.19 Fault in substation, system grounded at local station and also at other points.
 2006 by Taylor & Francis Group, LLC.
determining the maximum grid current. The effect of these other current paths in parallel with the
ground grid is difcult to determine because of the complexities and uncertainties in the current ow.
11.3.4.1   Current Division Consideration
There are many papers that discuss the effects of overhead static wires, neutrals, cables, and other ground
paths. As shown in Fig. 11.20, the process of computing the current division consists of deriving an
equivalent model of the current paths and solving the equivalent circuit to determine what part of the
total current ows into the earth and through other ground paths. Endrenyi [13], Sebo [14], Verma and
Mukhedkar [15], and Garrett [16] provide approaches to determine the current ows in different
current paths for overhead circuits. Dawalibi [17] provides algorithms for deriving simple equations
to solve for the currents in the grid and in each tower while Meliopoulos [18] introduces an equivalent
conductor to represent the earth using Carsons equations. Sebo [19], Nahman [20], and Sobral [21]
provide approaches to determine the current ow when substations are cable fed. Each method can
provide insight into the effects of the other current paths on the grid current.
Computer programs are available to determine the split between the various current paths. There are
many papers available to determine the effective impedance of a static wire as seen from the fault point.
The fault current division factor, or split factor, represents the inverse of a ratio of the symmetrical
fault current to that portion of the current that ows between the grounding grid and the surround-
ing earth.
S
f
 
I
g
3I
0
(11:33)
where
S
f
fault current division factor
I
g
rms symmetrical grid current, A
I
0
zero-sequence fault current, A
REMOTE
SOURCE
(12)
(12)
1492
(1492)
444
I
G
 = 1048   I
G 
= 742   I
G
 = 99
338
338 448 99
DISTRIBUTION
SUBSTATION
LOAD
SUBSTATION
A
B
C
A(73)
B(103)
C(70)
FIGURE 11.20 Typical current division for a fault on higher side of distribution substation.
 2006 by Taylor & Francis Group, LLC.
The process of computing the split factor, S
f
, consists of deriving an equivalent representation of the
overhead ground wires, neutrals, etc., connected to the grid and then solving the equivalent to determine
what fraction of the total fault current ows between the grid and earth, and what fraction ows through
the ground wires or neutrals. S
f
is dependent on many parameters, some of which are:
1. Location of the fault
2. Magnitude of substation ground grid resistance
3. Buried pipes and cables in the vicinity of or directly connected to the substation ground system
4. Overhead ground wires, neutrals, or other ground return paths
Because of S
f
, the symmetrical grid current I
g
and maximum grid current I
G
are closely related to the
location of the fault. If the additional ground paths of items 3 and 4 above are neglected, the current
division ratio (based on remote vs. local current contributions) can be computed using traditional
symmetrical components. However, the current   I
g
computed using such a method may be overly
pessimistic, even if the future system expansion is taken into consideration.
IEEE Std. 80 presents a series of curves based on computer simulations for various values of ground
grid resistance and system conditions to determine the grid current. These split-current curves can be
used to determine the maximum grid current. Using the maximum grid current instead of the
maximum fault current will reduce the overall cost of the ground grid system.
11.3.5   Use of the Design Equations
The design equations above are limited to a uniform soil resistivity, equal grid spacing, specic buried
depths, and relatively simple geometric layouts of the grid system. The basic requirements for a safe
design have not changed through the various revisions of the guide from 1961 to the 2000 edition.
The equations in IEEE-80 have changed over the years and will continue to change as better approximate
techniques are developed.
It may be necessary to use more sophisticated computer techniques to design a substation ground
grid system for nonuniform soils or complex geometric layouts. Commercially available computer
programs can be used to optimize the layout and provide for unequal grid spacing and maximum
grid current based on the actual system conguration, including overhead wires, neutral conductors,
underground facilities, etc. Computer programs can also handle special problems associated with fences,
interconnected substation grounding systems at power plants, customer substations, and other unique
situations.
11.3.6   Selection of Conductors
11.3.6.1   Materials
Each element of the grounding system, including grid conductors, connections, connecting leads, and
all primary electrodes, should be designed so that for the expected design life of the installation, the
element will:
1. have sufcient conductivity, so that it will not contribute substantially to local voltage
differences;
2. resist fusing and mechanical deterioration under the most adverse combination of a fault current
magnitude and duration;
3. be mechanically reliable and rugged to a high degree; and
4. be able to maintain its function even when exposed to corrosion or physical abuse.
Copper is a common material used for grounding. Copper conductors, in addition to their high conduct-
ivity, have the advantage of being resistant to most underground corrosion because copper is cathodic with
respect to most other metals that are likely to be buried in the vicinity. Copper-clad steel is usually used for
 2006 by Taylor & Francis Group, LLC.
ground rods and occasionally for grid conductors, especially where theft is a problem. Use of copper, or to a
lesser  degree  copper-clad  steel,  therefore  assures  that  the  integrity  of  an  underground  network  will  be
maintained  for  years,  so  long  as  the  conductors  are  of  an  adequate  size  and  not  damaged  and  the  soil
conditions are not corrosive to the material used. Aluminum is used for ground grids less frequently. Though
at rst glance the use of aluminum would be a natural choice for GIS equipment with enclosures made of
aluminum or aluminum alloys, there are several disadvantages to consider:
.
Aluminum can corrode in certain soils. The layer of corroded aluminum material is nonconduc-
tive for  all practical  grounding  purposes.
.
Gradual corrosion caused by alternating currents can also be a problem under certain conditions.
Thus, aluminum should be used only after full investigation of all circumstances, despite the fact that,
like  steel,  it  would  alleviate  the  problem  of  contributing  to  the  corrosion  of  other  buried  objects.
However, it is anodic to many other metals, including steel and, if interconnected to one of these metals
in  the  presence  of  an  electrolyte,  the  aluminum  will  sacrice  itself  to  protect  the  other  metal.  If
aluminum  is  used,  the  high-purity  electric-conductor  grades  are  recommended  as  being  more  suitable
than  most  alloys.  Steel  can  be  used  for  ground  grid  conductors  and  rods.  Of  course,  such  a  design
requires that attention be paid to the corrosion of the steel. Use of galvanized or corrosion-resistant steel,
in  combination with  cathodic  protection,  is  typical  for  steel  grounding  systems.
A grid of copper or copper-clad steel forms a galvanic cell with buried steel structures, pipes, and any
of the lead-based alloys that might be present in cable sheaths. This galvanic cell can hasten corrosion of
the latter. Tinning the copper has been tried by some utilities because tinning reduces the cell potential
with respect to steel and zinc by about 50% and practically eliminates this potential with respect to lead
(tin  being  slightly  sacricial  to  lead).  The  disadvantage  of  using  tinned  copper  conductor  is  that  it
accelerates and concentrates the natural corrosion, caused by the chemicals in the soil, of copper in any
small  bare  area. Other often-used  methods  are as  follows:
.
Insulation of the sacricial metal surfaces with a coating such as plastic tape, asphalt compound,
or  both.
.
Routing  of  buried metal elements  so  that any copper-based  conductor  will cross  water  pipelines
or  similar  objects  made  of  other  uncoated  metals  as  nearly  as  possible  at  right  angles,  and  then
applying an insulated coating to one metal or the other where they are in proximity. The insulated
coating  is  usually  applied  to  the  pipe.
.
Cathodic  protection  using  sacricial  anodes  or  impressed  current systems.
.
Use  of nonmetallic  pipes  and  conduits.
11.3.6.2  Conductor Sizing Factors
Conductor  sizing  factors  include  the  symmetrical  currents,  asymmetrical  currents,  limitation  of  tem-
peratures  to  values  that  will  not  cause  harm  to  other  equipment,  mechanical  reliability,  exposure  to
corrosive environments, and future growth causing higher grounding-system currents. The following
provides information concerning symmetrical and asymmetrical currents.
11.3.6.3   Symmetrical Currents
The short-time temperature rise in a ground conductor, or the required conductor size as a function of
conductor current, can be obtained from Eqs. (11.34) and (11.35), which are taken from the derivation
by Sverak [22]. These equations evaluate the ampacity of any conductor for which the material constants
are known. Equations (11.34) and (11.35) are derived for symmetrical currents (with no dc offset).
I  A
mm
2
TCAP  10
4
t
c
a
r
r
r
_   _
ln
  K
0
T
m
K
0
T
a
_   _
(11:34)
 2006 by Taylor & Francis Group, LLC.
where
I  rms  current, kA
A
mm
2  conductor cross  section,  mm
2
T
m 
maximum  allowable  temperature,  8C
T
a 
ambient  temperature,  8C
T
r 
reference temperature for  material  constants,  8C
a
0 
thermal  coefcient  of resistivity  at  0  1  C, 1=8C
a
r 
thermal  coefcient  of resistivity  at  reference temperature T
r
, 1=8C
r
r 
resistivity of the  ground  conductor  at  reference temperature  T
r
, mV-cm
K
0 
1=a
0 
or  (1=a
r
)  T
r
,  8C
t
c 
duration  of  current,  sec
TCAP  thermal  capacity  per  unit  volume,  J=(cm
3 
 8C)
Note that a
r 
and r
r 
are both to  be found  at the  same reference temperature of T
r 
8C .  If  the conductor
size  is  given  in  kcmils  (mm
2 
  1.974  kcmils),  Eq.  (11.34)  becomes
I  5:07  10
3
A
kcmil
TCAP
t
c
a
r
r
r
_   _
ln
  K
0
T
m
K
0
T
a
_   _
(11:35)
11.3.6.4   Asymmetrical Currents: Decrement Factor
In cases where accounting for a possible dc offset component in the fault current is desired, an
equivalent value of the symmetrical current, I
F
, representing the rms value of an asymmetrical current
integrated over the entire fault duration,   t
c
, can be determined as a function of   X=R by using the
decrement factor D
f
, Eq. (11.37), prior to the application of Eqs. (11.34) and (11.35):
I
F
  I
f
  D
f
(11:36)
D
f
 
1 
T
a
t
f
1 e
2t
f
Ta
_ _
(11:37)
where
t
f
is the time duration of fault in sec
T
a
is the dc offset time constant in sec [T
a
X=(vR); for 60 Hz, T
a
X=(120pR)]
The resulting value of   I
F
is always larger than  I
f
because the decrement factor is based on a very
conservative assumption that the ac component does not decay with time but remains constant at its
initial subtransient value.
The decrement factor is dependent on both the system X=R ratio at the fault location for a given fault
type and the duration of the fault. The decrement factor is larger for higher  X=R ratios and shorter
fault durations. The effects of the dc offset are negligible if the X=R ratio is less than ve and the duration
of the fault is greater than 1 sec.
11.3.7   Selection of Connections
All connections made in a grounding network above and below ground should be evaluated to meet the
same general requirements of the conductor used, namely electrical conductivity, corrosion resistance,
current-carrying capacity, and mechanical strength. These connections should be massive enough to
maintain a temperature rise below that of the conductor and to withstand the effect of heating, be strong
 2006 by Taylor & Francis Group, LLC.
enough to withstand the mechanical forces caused by the electromagnetic forces of maximum expected
fault currents, and be able to resist corrosion for the intended life of the installation.
IEEE Std. 837 (Qualifying Permanent Connections Used in Substation Grounding) [23] provides
detailed information on the application and testing of permanent connections for use in substation
grounding. Grounding connections that pass IEEE Std. 837 for a particular conductor size, range, and
material should satisfy all the criteria outlined above for that same conductor size, range, and material.
11.3.8   Grounding of Substation Fence
Fence grounding is of major importance, since the fence is usually accessible to the general public,
children, and adults. The substation grounding system design should be such that the touch potential
on the fence is within the calculated tolerable limit of touch potential. Step potential is usually not
a concern at the fence perimeter, but this should be checked to verify that a problem does not exist.
There are various ways to ground the substation fence. The fence can be within and attached to the
ground grid, outside and attached to the ground grid, outside and not attached to the ground grid,
or separately grounded such as through the fence post. IEEE Std. 80 provides a very detailed analysis of
the different grounding situations. There are many safety considerations associated with the different
fence grounding options.
11.3.9   Other Design Considerations
There are other elements of substation grounding system design which have not been discussed here.
These elements include the renement of the design, effects of directly buried pipes and cables, special
areas of concern including control and power cable grounding, surge arrester grounding, transferred
potentials, and installation considerations.
References
1. Institute of Electrical and Electronics Engineers, IEEE Guide for Safety in AC Substation Grounding,
IEEE Std. 80-2000, IEEE, Piscataway, NJ, 2000.
2. Sverak, J.G., Simplied analysis of electrical gradients above a ground grid: part Ihow good is the
present IEEE method? IEEE Trans. Power Appar. Syst., 103, 725, 1984.
3. Thapar, B., Gerez, V., and Kejriwal, H., Reduction factor for the ground resistance of the foot in
substation yards, IEEE Trans. Power Delivery, 9, 360368, 1994.
4. Dalziel, C.F. and Lee, W.R., Lethal electric currents, IEEE Spectrum, 4450, February 1969.
5. Dalziel, C.F., Threshold 60-cycle brillating currents, AIEE Trans. Power Appar. Syst., 79, 667673,
1960.
6. Dalziel, C.F. and Lee, R.W., Reevaluation of lethal electric currents,   IEEE  Trans.   Ind.   Gen.   Appl.,
4, 467476, 1968.
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