SYSTEM EARTHING

Chapter

1
SYSTEM EARTHING
1. EARTHING REQUIREMENTS

It is a statutory obligation in most countries, as well as a technical requirement, that all

parts of an electric power system shall have an effective connection to earth (or to
ground in American parlance). This implies that each electrically separate part of a
system, which is magnetically coupled to other parts at the transformation points, must
be separately earthed. In the words of the definition contained in the 1937 Electricity
Supply Regulations, which still holds good, ‘A connection to earth means connected with
the general mass of earth in such a manner as to ensure at all times an immediate and
safe discharge of energy’. The purpose of earth connections in different parts of a system
differs, but generally one or more of the following is fulfilled:
a) Zero phase-sequence protection. The earth connection must provide a path of
low impedance and adequate thermal capacity for earth fault (zero sequence)
current so that protective relays may operate satisfactorily.
b) Equipment or protective earthing. This is to ensure the safety of the public and
of the personnel who operate electrical equipment.
c) Limitation of earth potential differences. This is to avoid injury or death to
persons or to animals who are more susceptible to electric shock than human
beings.
d) Lightning and over voltage protection. This conducts to earth charges due to
lightning and protects equipment from over-voltage by means of surge arresters
to which the earth connection is made.
On any transmission or distribution system, these requirements are satisfied by both
system earths and equipment earths. There must also be adequate bonding of the
connections throughout the earthing system to ensure that currents to earth of the
highest magnitude may be carried without fusing of joints or of the earth conductor itself
and without appreciable voltage drop.
Ch.#1

1
2. MEANS OF EARTHING

System earthing may be direct, by a connection straight to earth, or indirect with a resistor or
reactor connected in the earth lead. In either case the earth connection is made to the system
neutral (star point) where this exists or, on a true 3-phase system, by establishing an artificial
star point. The various means are shown in Fig. 1 and the application of these means to an
entire system is shown by Fig. 2. Generators normally have their star point earthed directly
or through a resistance which limits zero sequence current, due to an earth fault, to between
10 and 25 per cent of the 3-phase fault current; the lower figure is determined by the
minimum current required to operate earth fault protection relays and the upper figure by
the cost of the resistor as decided by the energy loss in the time that the maximum fault
current may continue to flow. Generator earthing on the British system is either by resistor of
300 A rating or by high resistance provided by a transformer with a grid resistor across the
secondary which limits the current to about 10 to 15 A. This applies to all larger sets, say 60
MW and above, which are connected through transformers to the 132, 275 or 400 KV
systems, but the now obsolescent direct connected generator would have its earthing related
to the rest of the 33 or 11 KV system which would in practice mean a resistor to carry 300
to 500 A. European continental practice favors higher values of generator earthing
resistance, even resonant-circuit earthing to give a minimum fault current, therefore causing
the least possible damage for faults within the generator itself. Power transformers are a
means of establishing a system earth connection where a star-connected winding is available,
particularly with main transmission lines where delta-star- and star-delta- connected main
transformers or star-connected auto-transformers normally have the sending-end and
receiving-end earth connections made at the star points (Fig. 2). A delta-connected tertiary
winding on such transformers, for connecting to a synchronous compensator does not affect
nor is affected by the earth connection. Where no star-point exists, as on a secondary
transmission system supplied by a delta-connected transformer at 66KV or below, it is
necessary to establish a star-point by means of an earthing transformer (Fig. I (h) and (j)).
The only duty of such a transformer is to pass zero phase-sequence current in the event of
an earth fault on the system, accordingly its size and cost must be kept to the minimum. It
may be connected star-delta, with the delta-connected secondary winding on open- circuit,
or alternatively with both the primary and the secondary windings of a one-to-one ratio
transformer, interconnected to form an inter-star connection; this latter is generally a more
economical construction except where an additional winding is provided to supply the
substation auxiliary load.
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2
Fig-1 Methods of system earthing. (a) to (d) are consumer’s voltage systems and (e) to 0) are
medium and high voltage systems. Arrows indicate direction of power flow.
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3
 Fig. 2 Schematic Diagram of Earthing on a system from generator to consumers

On main transmission lines where the earth resistivity is normal, the tower footings usually
provide an adequate low-resistance earth, although earth electrodes may be provided for
special towers, but in addition a tower may be connected to adjacent towers by means of an
earth wire or wires carried on the highest point or points of the towers. The earth wire,
when present, not only provides lightning protection but, in the event of a fault to earth, it
provides a path to the nearest system earth for zero phase-sequence currents additional to
that provided by the earth electrodes and the earth itself (Fig. 3 (b)). This assists earth fault
protection where earth resistivity is high or variable. Terminal towers are connected to the
earthing systems at the substations at either end of the line. This provides better earthing
than the individual tower earths and, for lines with an overhead earth wire, gives the best
protection against lightning. Medium voltage lines (33 KV and below) of wood pole
Ch.#1

construction are to one of two specifications, the difference being mainly in the earthing and

4
bonding requirements. One construction specifies a continuous earth wire with bonding and
earthing at intermediate poles while the other does not specie an earth wire and only requires
bonding and earthing at poles which carry transformers, hand-operated switchgear or cable
take-off, in fact the provision of equipment earths where the equipment itself may be
dangerous if it becomes faulty. Such a line is sometimes referred to as an ‘unearthed line’ and
is able to withstand high impulse voltages due to lightning and is relatively free of trouble
due to temporary earthing of the line conductors by birds, etc. It relies in fact on the
insulation resistance of the wood or concrete pole to minimize the fault current at ground
level.
Low or consumer voltage lines of 3-phase, four-wire construction have the neutral or
earthed conductor carried continuously from pole to pole. This provides a safeguard against
a broken line conductor remaining undetected since, in falling, it is likely to make contact
with the neutral conductor and thus operated protective equipment. Leakage across an
insulator is protected against by bonding the supporting metalwork of insulators together
and to the neutral conductor. In the case of metal poles, the insulator-supporting framework
is insulated from the pole. A pole which is used as a support for both HV and LV lines, as
for instance the terminating pole of a HV line which carries a transformer, has a special
earthing requirement which is that the earth of the high-voltage system must be kept
separate from the low voltage system earth and neutral. This means, in effect, that the
earthing of the transformer tank and its supporting structure should be at the base of the
pole carrying the transformer and the neutral of the LV system should be separately earthed
at the first pole away on the LV line. The reason for this may be seen from Fig. 4 where, in
the event of the consumer earth being of lower resistance than the common earth on the
HV/LV pole, a flash-over is liable to occur in the consumer’s installation.

Fig. 3 Earth fault on an overhead line showing the paths of the fault current; (a) with no earth wire,
(b) with continuous earth wire carried on the towers.
Ch.#1

5
A general principle of equipment earthing is that the housings of all current- carrying parts
must be bonded together by copper wire or strip conductors of adequate thermal capacity so
that no reliance is placed on glands, bolts, racks, worm screws, wheels nor any supporting
metalwork to conduct fault current in the event of an internal fault in the equipment.
Transformer tanks, frames of machines and other large equipment have at least one earthing
terminal which must be provided with locknut or other anti-vibration device. For outdoor
equipment which is manually operated, the best protection which may be afforded the
operator is the provision of an earth-mat, bonded to the equipment at the point where a
man must stand to operate it. In the event of a fault to earth, the equipment and the earth-
mat, which is usually a copper tape mesh buried just below the earth surface, reach almost
the same potential so that an operator, in contact with the equipment and with earth in the
vicinity of the mat has no voltage across the body.

Fig. 4 Fault current distribution with a common earth for high voltage equipment and low
voltage neutral. Earthing resistance Rc causes a rise in voltage at A which may be sufficient
to cause a flashover in the consumer’s main switch.

3. NEUTRAL SYSTEMS
3.1 Insulated Neutral System
An alternator stator winding or transformer secondary winding with unearthed star-point is
shown in figure 5.
Under healthy, balanced conditions, the star-point will be at earth potential even though it is
not connected to earth. When a ground fault occurs on one line, as shown, the fault current
is limited by the line to earth capacitances, one of which is shorted out by the itself. Thus the
fault current (If) is the phasor sum of.

These currents lead their respective line voltages as shown, and leads VR by 90O.
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 Fig. 5
At the instant of arc extinction (i.e. when If waveform passes through zero), the point B is
therefore either at + max, phase voltage to earth or at - max. phase voltage to earth. Taking
the instant when B is at + max. VPH to earth, then N is at earth potential, and R and W will
each be at 0.5 max. VPH to earth.
Since the potential of B to earth is a maximum, the arc will be immediately restruck. This
instantaneously earths B. so that N is then at max VPH to earth and R and W are each at - 1.5
max. VPH to earth. Thus, at the instant of re-strike, R and W have their potentials with
respect to earth suddenly changed from -0.5 max. VPH to - 1.5 max. VPH. This happens each
time the lf waveform passes through zero and causes a succession of voltage surges to be
generated into the system.
Furthermore, all line insulation must be capable of withstanding 1.5 max. V PH instead of
max. VPH to earth.

3.2 Advantages of Earthing the Neutral

• The star-point is always at earth potential so that when an earth fault occurs on one
line, the potential difference between the healthy lines and earth cannot exceed max.
VPH. Also graded insulation can be used on the line end turns of transformers.
• Simple protective systems based on the detection of earth leakage currents can be
used.
• An arcing ground fault cannot occur.
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7
3.3 Disadvantages of Earthing the Neutral
• The earth fault current is very much heavier than in an insulated neutral system
because in the latter the fault current is limited by the line to earth capacitances.
• Earth connections must be made at all vulnerable points in the system. This is at grid
substations and consumer substations as well as at generating stations and
consumers’ premises.
• In an earthed neutral system, an earth fault must be isolated immediately because of
the heavy fault current. In an insulated neutral system immediate isolation is not
essential although it is desirable, since the voltage surges generated by arcing ground
faults may be three or four times normal voltage.
Above 33 KV line, the cost of transformer insulation is an important part of the total cost of
a system. Therefore significant economies can be made by earthing the neutral, so that
graded insulation may be used. Also, above 33 KV, the line impedance is usually high
enough to limit earth fault currents to a reasonable value without using a resistance or
reactor in the earth connection.
In general, therefore, high voltage transmission systems have their star-points solidly earthed
and system
3.4 Methods of Earthing
• Solid copper connection to buried earth electrode.
• Connection to earth through a resistor of a few ohms.
• Connection to earth through an un-tuned reactor.
• Connection to earth through a tuned reactor (called an arc suppression coil or
Peterson coil).
• If the supply system has no star-point, an artificial one can be created by means of
the special earthing transformer shown in figure 6.

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8
3.4.1 Solid Earthing
In solid earthing a direct metallic connection is made from the neutral of the system to one
or more earth electrodes. The earth electrodes may be of plates, rods or pipes buried in the
ground.

Fig. 7
Fig. 7 shows a three phase system with its neutral solidly earthed and with a ground fault at F
in phase B.
The phasor diagram of the voltage and currents are as shown in fig. 8
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 Fig. 8

Considering fault at F in phase B, the current in phase B consists of:

a) (ir + iy), the vector sum of which is equal to icf This flows from faulty phase B to earth.
b) Faulty current If provided by the power source.
By analyzing the fault current with the help of symmetrical components we get:

3VBN 3VPH
If = =
Z1 + Z 2 + Z 0 Z1 + Z 2 + Z 0

Where: Vph phase voltage

Z1, Z2 and Z0 are positive, negative and zero sequence impedances.

Advantages of Solid Earthing

• The neutral point is always at earth potential under all operating conditions and as
such the voltage of any conductor with respect to earth will never exceed the normal
phase voltage of the system. It results in saving of cost as we have to provide
insulation not beyond phase voltage.
• The heavy fault current I nullifies the effect of capacitive current icf so no arcing
phenomena or over voltage occurs.
• Lightning arresters for solidly earthed system can be employed.
Disadvantages
• The increased ground fault current produces more conductor burning, more burning
of circuit breaker contacts and influences greatly the neighboring communication
circuits.
Uses
This system can be used at voltage levels below 2.2 KV and above 33 Ky.

3.4.2 Resistance Earthing

The disadvantages of solid grounding i.e. heavy ground fault currents can be reduced by
inserting a current limiting device between the neutral of the system and earth. One of the
current limiting device is resistance - metallic or liquid. Now a days liquid resistors are mostly
used because of the following advantages.
Though the metallic resistors have the advantages that these do not alter with time and
practically de not require any maintenance but these are slightly inductive.
Liquid resistors are free from the above disadvantages.
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 Fig. 9

Fig. 10
Figures 9 and 10 indicate a fault at F in phase B and vector representation of voltages and
currents. The three currents at F are If, IBR. The current If lags behind the phase voltage by
an angle which depends upon the value of resistance of the resistor R and reactance of the
system up to point of fault. Icf is the resultant of IBR and I and IBY (IBR and IBY lead VR and
VY by 90°). It may be noted that if the value of R is made very high then it amounts to
ungrounded system and if the value of resistance R is made very low then it practically
amounts to solid earthing.
So it is a general practice to choose the value of resistor such that fault current If does not
exceed the full rating of the largest transformer or generator.
VL
Resistance of resistor R =
3I
Where: VL — Line voltage in Kv.
I Full load current of largest generator or transformer in kilo amperes
R - Resistance in ohms.
There is another formula, given by Peterson for finding the value of resistance of
resistor R.

K
i.e. R =
C R + CY + C B
Ch.#1

Where: CR, CY and C8 are the capacities of each phase to earth.

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 K -varies between I to 2.5.
Advantages
• It facilitates the use of discriminative protective gear and minimizes the hazards of
arcing grounds.
• It improves the stability of the system.

Disadvantages
• Loss of power occurs in resistance and sometimes it becomes difficult to dissipate
energy from resistance to atmosphere.
• It adds to the cost of resistor and fi.ill rating of lightning arresters have to be used.
Uses
It is used on a system operating at voltage between 2.2 KV to 33 KV and the total capacity
of source should be more than 5 MVA.

3.4.3 Reactance Earthing

Reactance earthing means earthing through an impedance predominantly reactive.
A system is said to be reactance earthed if the ratio of zero sequence component of
reactance of the apparatus connected and positive sequence component of reactance i.e.
X0
exceeds 3 but is less than the value required for resonant earthing.
X1

3.4.4 Arc Suppression Coils (Peterson Coil)

The advantage of a free neutral can be obtained by joining the neutral of a 3 phase supply
system to earth through special reactor known as an arc suppression coil or a Peterson coil,
the effect of which is to prevent unbalanced capacitance currents entering an earth fault, and
so producing the dangerous intermittent arcing. The diagrams 11 and 12 indicate the
connections of an arc suppression coil X to the neutral of a 3 phase transformer supplying
through three lines, R, Y, and B. Let there be a fault at F in phase B. The voltages to earth of
lines R and Y become equal to the line voltage of the supply, and the capacitance currents
from these lines to earth are equivalent to those that would flow in two similar condensers
CR and CY. The resultant of the currents in these two condensers is 90 O lagging on the
resultant of two voltages R to B and Y to B. The voltage to earth of neutral is the same as
the neutral to B voltage and owing to thus voltage a current will flow through X to earth 90O
lagging on this neutral to B voltage which is in phase with the resultant of R to B and Y to B
voltages.
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12
 Fig. 11

Fig 12

In practice the arcing current may be not exactly zero due to the Fact that the Petersen coil
has a little resistance. Also tappings will be necessary so that the value of L can be altered
when the length of the line is altered.

The resultant capacitance current from lines R and Y and the current flowing from the
neutral through X are respectively 90o leading and 90° lagging on the same voltage: their
directions are therefore opposite at every instant, so that, if the ohmic value of the reactance
of X is correctly adjusted, the two currents will be equal, and will cancel to zero, and no
current will enter the system at the fault on B line. In effect the capacitive currents from the
unearthed lines return to the source of supply through the arc suppression coil x.

The resultant capacity current is 3 times the normal charging current of one phase.
Ch.#1

13
 I CF = 3I BR
3 VL 3 3VPh 3VPh 3  Vph
I BR = = = = =
XL Xc Xc Xc
3xLine T = 3  line to neutral Ch arg ing

Where: V1 - Line voltage.

Xc - Capacitance from line to neutral.
V ph
Fault current I f = where XL - is the inductance of coil.
XL
As described earlier that Icf is neutralized with If
I CF = I F
3V ph V ph 1 1
or = or XL = → L=
XL XC 3C 3 2 C
The current rating of the coil is given by

3VPh
I=
XC

An arc suppression coil is constructed like an oil immersed transformer and consists of a
winding on an iron core provided with a number of taps, so that its ohmic resistance can be
adjusted or tuned to such a value that the current it passes in earth fault conditions
corresponds to the resultant unbalanced capacitance current of the system in which it is
used. The arcing suppression coil may be rated either for short time duty of about 5 minutes,
or so that it will carry its rated current continuously. A short time rated coil is equipped with
an automatic circuit breaker, which by the action of a relay responsive to the neutral to earth
voltage, short circuits the coil after the lapse of definite time lag, and so connects the neutral
of the system directly to earth. A short time rated coil allows the clearing of intermittent
faults, without interruption of the supply. Sustained faults are removed by the disconnection
of the faulty section by the ordinary gear. A continuously rated coil allows a fault to remain
in the system till it is located and removed.
An arc suppression coil is usually provided with an auxiliary winding for energizing a relay to
operated the short circuiting device of a short time rated coil, or a graphic instrument for
recording the number and duration of faults on the system.
3.4 Peterson Coil
Suppose that an arcing ground fault occurs on one line as shown in Fig. 12.
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 Fig 12
The Fault connects the Petersen coil across the blue phase winding causing a current If to
flow through the coil. Assuming that the coil has negligible resistance.
IL must lag lB by 90O as shown. If IL numerically equal to IF by tuning the reactor
appropriately then the arcing current is the phasor sum of If and IL is zero at all instants.
Let the appropriate inductance of the Peterson coil be LH then:
VLine
IL = 3
LA

Now I F = 3I CBR or 3I CBr  A

VLine
But I CBR =
1
C
VLine
Therefore L = 3VLine • L =
3L

1 X
And L = H or X L = 
3 C
2
3

Example .1
A 230 KV, 3 phase, 50 c/s, 200 Km transmission line has a capacitance to earth of 0.02
µF/Km per phase. Calculate the inductance and Solution:
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 1
L=
3 C 2

1
=
3  (2f ) 2  C
1
=
3  3.13  (3.14  50) 2  (200  0.02  10 −6 )
1
=
3  314  (200  0.02  10 −6 )
2

10 6
= = 0.8455henrys
3  98586  4
230
V ph ( 3  10 3 )
IF = =
XL XL
230 10 3
= 
3 2  50  0.845
230 10 3
=  = 50 Amperes
3 314  0.845
230
Rating = 50  = 6640 KVA
3

Example.2
A 132 KV, 3 phase, 50 c/s transmission line 200 Km long consists of three conductors of
effective diameter 20.00 mm arranged in a vertical plane with 4 m spacing and regularly
transposed. Find the inductance and KVA rating of the arc suppresser coil in the system.
Solution:
Capacitance between phase to neutral or earth
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4. Earth Resistivity and the Earth Gradient
Earth resistivity, as normally stated in ohm-meter or ohm-cm (1 .m = 100.cm), varies
widely between different types of soil and is particularly affected by the moisture content.
This is because conduction in soil is mainly of an electrolytic nature so that a high moisture
content, in excess say of 20 per cent by weight, is required to give the minimum resistivity of
a range. Ranges of approximate values for the various types of soil are shown in Table 1.
Made-up ground is indeterminated and ground containing soluble salts, acid or alkali, will
have resistivity which varies widely with the amount and the type of the chemical content.
Soil resistivity rises sharply when the moisture content falls below about 22 per cent by
weight so it is essential to bury current-carrying electrodes at such a depth that the
surrounding soil is not affected by seasonal variations, particularly drying out during dry
weather. In temperate climes, the variation in moisture content of the soil with seasonal
changes occurs mainly at the surface, within a depth of 1 meter; below this depth the
Ch.#1

moisture content and resistivity do not change to a marked degree. An earth electrode or

17
mat should therefore be driven or buried deep enough to be permanently in contact with
moist earth, but where this is not possible or, as in the case of a large earth-mat, too costly, a
well-distributed system of vertical rods, driven to a sufficient depth and bonded to the earth
grid, will usually suffice.

Table I
Type of Soil Resistivity -m
Clay and loam 10-16
Sandy clay 80-200
Marsh peat 150-300
Sand 130-500
Rock and chalk any value up to I o
The minimum specific resistivity for clay/loam of 100-m is the value at 20° C. Increase of
temperature may show a slight decrease in resistivity provided local drying-out at the
electrode surface does not occur.

However, decrease in temperature of the same soil to - 5° C shows a very rapid rise in soil
resistivity to 50 -m and at -20°C the same soil has a resistivity of 500 -m. This is a further
reason for placing earth electrodes at a sufficient depth since, as with moisture variation, this
will avoid an increase in resistivity due to frost penetration of the earth.

Since earth resistivity measurements are normally made with small currents, it is important to
ascertain that larger currents, such as those which may occur during a system earth fault, do
not alter the resistivity value. This is so provided the earth current due to a fault is of
sufficiently short duration, but if it persists for more than a second, the heat generated due
to the contact resistance between the electrode and the ground may dry out the earth in the
vicinity of the electrode, causing a rise in earth resistance due to a reduction in moisture
content. Excessive drying out of the soil around an electrode may leave an air-space as a
result of earth shrinkage, giving defective earth contact. This is however only likely to occur
with a fault current of long duration and is, in any case, only dangerous on low-voltage
systems since, with high voltage, spark-over occurs which does not lead to appreciable
increase in earth resistance. A very large earth current may also give rise to a voltage
gradient, which exceeds the breakdown value of the earth adjacent to the electrode, which
depends on the nature of the soil but is of the order of some KV per cm. If this value is
exceeded, arcs will start at the electrode surface, effectively increasing the size of the
electrode and reducing the voltage gradient to a value which the earth can withstand. The
number of electrodes to be used for a given fault current and duration depends on tile
thermal capacity of earth rods which is further considered in the following section.
A voltage gradient in the earth occurs when current from an electrode flows through the
earth resistance. It is theoretically infinite at the surface of the electrode and decreases to
Ch.#1

zero at an infinite distance from the electrode.

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Practically, a danger exists to persons or large animals, particularly the latter due to their
greater sensitivity and the greater distance apart of their legs, if the potential difference at the
ground surface is sufficient to pass a dangerous current across the body from leg to leg. This
potential difference, known as the step voltage, because it is the voltage which a man would
receive across the body by taking a 1-meter step in a radial direction from the earth
electrode, depends on the current density at the step, the resistivity of the soil and the depth
of the electrode for rod pipe electrodes. It has been shown that if the electrode is situated at
a greater depth than 1 meter, the voltage difference at the surface is very small. It is therefore
a necessary precaution that earth connections on overhead lines, whether an equipment or
system earth, should be by means of an insulated conductor, from some point well out of
reach of man or animal, to the actual electrode whose top should be at least 0.5 meter, but
preferably deeper, below ground level.

5. EARTH ELECTRODES AND NETWORKS

The simplest earth electrodes for the calculation of potential gradient, voltage above remote
earth and earth resistance are the hemisphere at the earth surface and the sphere buried at a
sufficient depth to minimize the discontinuity of the surface. Although these electrodes are
seldom used in practice, the equations derived for them form the basis of those for the more
usual rod or plate electrodes. For the hemisphere (Fig. 13) of radius r from which a total
current I spreads out radially into the earth, the current density through a concentric
hemisphere of radius x is

I
i=
2X 2

and the potential gradient at distance x is obtained from the voltage drop across the
hemispherical shell of thickness dx,
pIdx
Voltage drop = pi dx =
2X 2

pI
Potential gradient e x =
2X 2

The voltage from the surface of the hemisphere to a point at the distance x is the line
integral of the potential gradient from r to x,

pI dx pI  1 1 
V X =  edx =  = −
2 X 22 2  r x 
Ch.#1

VX is in volts for i in A/m2 and p in ohm-m.

19
 Fig. 13 The hemispherical earth electrode

The potentials at the surface of the hemisphere and at a distance x, with reference to remote
earth potential, are respectively,

The resistance R at the electrode surface is

This assumes perfect contact between electrode and earth but additional contact resistance is
normally small and is ignored in practice. An indication of the order or earth resistance is
that for a hemispherical electrode of radius 0.5 m, embedded in clay-loam of the minimum
resistivity (p= 10 -m);

rising to a value of say 95 ohm for sandy loam of higher resistivity. As the curves of Fig. 14
show, this resistance is distributed over the entire hemisphere to an infinite radial distance,
but in practice the greater part of it is concentrated in the vicinity of the electrode. This fact
is of importance in determining the step voltage, which human or animal could receive in the
vicinity of an electrode. 1f for example, a faulty transmission tower is considered which
delivers 100 A to earth and assuming a hemispherical electrode as above and an earth
resistivity of 50 -m, the potential gradient at a distance of 0.5 m from the electrode surface
is
50  100
Ch.#1

e= = 800 / m
2  (0,5 + 0.5) 2

20
a high value which is likely to result in a fatal step voltage near the electrode.
For the spherical electrode with an insulated lead, buried at depth h, where h is very great,
the area of equipotential surface is twice that of the hemisphere so the values of eqns. (1.1)
to (1.4) are all halved giving:
pI
Potentialg radient e x =
4X 2

Fig. 14 Values of potential E and potential gradient e (broken line) for a hemispherical
electrode of radius r = 05m, earth resistivity of 10 -m, dissipating a current of 1A to earth.
potentials at the surface of the sphere and at distance x respectively

With h finite but still large compared to r, the non-uniformity due to the earth surface may
be eliminated by considering identical and equal current flowing from an image electrode at a
distance h above the earth surface (Fig. 15). The electric-field strength at a point P1 in the
area is then due to the superposition of the electric fields of the two electrodes so that the
potential at point P1, distant x and x respectively from the center of the electrode and its
image in Fig. 15 is

For a point at the surface of the electrode x becomes rand x’ becomes 2h approximately so
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21
Whence the resistance at the electrode surface is increased

Potential and gradient at the earth surface at point P2, distant x from the point vertically
above the center of the sphere, is

Fig. 15 Spherical atmosphere and its image for a calculation of resistance, potential
difference; eqns. (10.7) to (JO.10)

The potential at the earth surface vertically above the center of the sphere
(x=0) is

So the difference in potential between the surface of the sphere and the earth surface
vertically above it is
Ch.#1

22
Figure 16 shows the potential around a buried spherical electrode based on eqns. (15) to
(16). The maximum potential gradient evidently occurs between (x0.5) and (x=1.0) and is in
fact independent of x and dependent only on the depth of the sphere, being given by

Fig. 16 Variation of potential at point P, in Fig. 10.7 due to a spherical electrode.

E, is the potential vertically above the centre of the electrode

The potential at the earth surface, vertically above the center of the sphere, is lower the
greater the buried depth. However, the difference of potential between this area of earth
surface and the metal structure which is connected to the electrode increases with depth, so
a man standing on the surface and in contact with the structure receives a higher voltage
across the body. An increase in depth of an electrode is thus no protection against contact
Ch.#1

23
with a structure connected to it but, from eqn (18), increase in depth reduces the maximum
potential gradient and therefore gives lower step voltages away from the structure.
In practice earth electrodes are normally of rod or pipe in which the length is great
compared with the diameter. An approximation to a rod of length L and diameter d, driven
vertically into the earth, is to divide it into a large number (n) of nearly spherical elements in
contact, each passing a current I/n into the earth and having a mutual distance, equal to the
sphere/rod diameter, of I/n. This gives an earth resistance,

The method of calculation is however approximate and a more accurate practical formula is

Whether the factor be taken as 4 or 3 is of little significance, as is the shape of the rod (lid)
since it forms only the argument of the logarithm. What is important is the length (I) since
the earth resistance is nearly inversely proportional to it. Rods or pipes should be spaced a
distance apart at least equal to their length plus the depth of the top below the earth surface
thus a 2-meter rod driven 1 meter below the surface should not be closer than 3 meters to a
similar rod in parallel with it.
The potential at the earth surface at the earth surface at a distance x from the rod has the
approximate expression

and the gradient on the earth surface is

For large values of x the gradient approximates to the expression for the hemispherical
electrode (eqn. 1.2) and for distances short compared with the rod length

where i is current per unit length,

Ch.#1

24
giving a potential at the rod surface of

therefore

from which Fig. 17 has been drawn, for p=10-m and i=1 A/m. Cast-iron pipes of 10 cm or
greater diameter are used in special circumstances and hot galvanized mild steel pipes of up
to 5 cm diameter may be used where low cost is necessary, such as in temporary installations.
But since they cannot be driven, the cost is greater than rods and the resistance higher than
that obtainable with plates for equivalent amount of excavation.

Fig.17. Variation of potential with distance for a rod electrode of length 3 m, diameter
3cm and dissipating a current of IA per metre of rod-length. E, is the potential
at the rod surface.

Plates, either flat or ribbed, have the advantage of greater current dissipation where
excavation is necessary and rods cannot be driven. A circular plate electrode of radius r,
buried at a depth h, in either horizontal or vertical plane (Fig. 18), with the connection
insulated, has the approximate resistance
Ch.#1

25
This empirical equation gives results which differ little from measured values and in practice
it is sufficient to take

and

and apply interpolation for medium depths. A square plate is comparable with a circular
plate with a radius of 0.6 times the side, or a plate 1 meter square buried at a depth of 1
meter has a resistance of 0.25p, a value close to that for a 4 meter rod.

Rectilinear electrodes buried horizontally may be either of round rod or flat strip for which
the approximate earth resistance are:

Or

where I is length, d is rod diameter, w is strip width and h depth at which the electrode is
buried, all dimensions being in meters. Rods and strips, if laid parallel, should not be closer
than 2.5 meters since the less the distance apart, the smaller the advantage in reducing
resistance value. Large substations require an earthed area which may consist or rod
electrodes, driven at regular intervals, connected below the surface by rectilinear rod or strip
to which each rod electrode is bonded, the whole forming a grid which saturates a
corresponding area of earth and is almost equivalent to a solid plate buried at the same
depth. An approximate estimate of earth resistance is therefore given by eqn. (22) and a
more accurate estimate by considering the total length of buried conductor in the area.
Ch.#1

26
6. EARTHLING AND BONDING OF EQUIPMENT AND

CABLES

The equipment earth is the means of connecting the outer casing or supporting structures of
all live equipment to the main body of earth and, in the event of an earth fault within the
equipment, it may have to carry the full phase short-circuit current. Equipment earthing is
essential for the safety of operating personnel, but particularly so on overhead line
distribution systems. In underground distribution networks all live equipment is metalclad
and earthed, the cables with their sheaths and sometimes armour, the switchgear and the
transformers, but this is not so on overhead systems without a continuous earth wire, that is
the majority of distribution networks below 33 KV. In this case the resistance of the earth
return path for fault current may be high, and a dangerous voltage may exist on faulty
equipment unless an additional parallel return path is provided by the equipment earth.
Bonding is the term for connections made between the outer casing and supporting
structures of all live equipment, and to the earth electrode, in order to provide a low
resistance path for leakage current to the equipment earth and back through the main body
of earth to the system earth. This ensures adequate current to operate the protective
equipment and reduces the magnitude and duration of dangerous voltages. Bonding
conductors must be as short as possible and so arranged that any fault current is diverted to
them instead of flowing indiscriminately through housings and support frames, since these
normally have bolted connections in their construction where local heating and sparking
might occur.
Bonding conductors and their joints must have adequate thermal capacity for the estimated
fault current and its duration. This latter is normally taken as 3 seconds, the same as the
short-circuit time rating of switchgear and current transformers.
4 cm by 5 mm (1/5 in by 3/16in) copper strip:
Main earth or common bonding bars in major substations.
Individual equipment bonding for main structures in outdoor substations at 33 KV and
above.
HV cable bonding where cable size are larger than 120 mm2.

Transformer tank bonding above 500 KVA.

Common bonding systems in substations where the fault level is above 75 MVA at 6.6 and
150 MVA at 11 KV.
Neutral bus-bar bonding on LV boards above 500 KVA.
2.5 cm by 3 mm (1 in b 1/8 in) copper strip:
Bonding in small distribution substations where fault levels are less than 75 MVA at 6.6 and
150 MVA at 11 KV or where the HV cables are 120 mm2 or less.
Transformer tank bonding below 500 KVA.
HV and LV cable bonding, 70 mm2 or below.
Ch.#1

LV disconnecting boxes, pillars, kiosks and auxiliary equipment in all substations.

27
Danger points in equipment earthing which need special attention are equipment operating
handles such as that for a section switch on an overhead line.
The danger here is that an earth fault may occur while the operator is opening or closing the
switch, either due to insulator failure on line or switch, or to the opening n error or an
energized circuit resulting in an arc to the structure. In either case the steelwork of the tower,
or the switch- operating mechanism, even if separately earthed, may be raised to a sufficient
voltage above earth to give a dangerous step or touch voltage. If the operating handle is
within an extensive substation earth-grid area, step voltage should be within safe limits as
elsewhere within the station perimeter, but for an isolated switch on an overhead line further
protection is necessary. This may consist of an insulating handle or, more effectively, the
bonding of the switch handle and associated mechanism to a separate earth-mat, buried
horizontally as near the earth surface as is practicable, at a position immediately below that at
which the operator must stand, while the tower steelwork, cross-arms, etc., is separately
earthed. If an earth fault occurs which raises the steelwork voltage above earth, the voltage
between an operator’s hand and feet will be negligible since they are virtually connected
through a low-resistance bond. Even this does not always ensure sufficient protection and a
portable steel mat which may be spread on the earth and bonded to the switch handle may
prove to be necessary.
Metallic cable sheaths, unless effectively earthed and bonded, may attain a dangerous voltage
due to sheath to insulation failure, charges due to electrostatic induction and the flow of
sheath current or to the voltage rise, under fault conditions, of the station earth to which the
sheaths are connected. With cables that are lead-covered and armoured, the armouring must
be adequately bonded to the lead sheath at the point where connection to earth is made. The
reason is to ensure that under fault condition there is no voltage difference between
armouring and sheath which would cause arcing and subsequent petting of the lead. At
junction points between lines and cable, the cable sheath or sheaths in, the case of three
cables in trefoil must be bonded together and to the earth of the tower or pole. The base of
the sealing bell, which is bolted directly to the supporting structure, must be bonded to the
gland or plumbed to the lead sheath and connected to the tower or to the earth wire of the
pole. For a pole-mounted transformer the bonding and earthing of the transformer tank and
supporting structure must be quite separate from the earth of the low- voltage line neutral;
the reason for this has already been shown by Fig. 4. Why this precaution is necessary with
pole transformer and not with other types of substation is the difficulty of obtaining
economically in rural areas a satisfactory low-resistance earth at all seasons.
Lightning arresters or surge diverters must be provided with as short and direct a path to
earth as is possible by bonding the bases of the three arresters to a separate earth electrode
situated at the base of the supporting structure. This electrode may however be paralleled
with the main substation earth grid where this is practicable. If the arresters are mounted on
a steel structure, this may provide a lower resistance path than copper strip, in which case
the three arresters and the earth electrode are bonded to it.
The advantage of fitting lightning arresters as close as possible to the equipment to be
protected has led to them being fitted on the top of transformer tanks where an earth
terminal or copper-plated earth pad should be provided for connection to the arresters, in
addition to the normal earth terminal at the base of the tank. This is an advantage as the
transformer tank provides better conductivity than a separate earth connection.
Ch.#1

28
7. MEASUREMENT OF EARTH ELECTRODE RESISTANCE
AND EARTH LOOP IMPEDANCE
To assess the safety of electrical installations the measurement of dissipation resistance of
their earthing system is necessary, whether it be a single electrode or an earth electrode
system such as the earthing installation of a substation. In distribution, the measurement of
the earth loop impedance of consumer installations is called for by the Regulations for the
Electrical Equipment of Buildings of the I.E.E. The three basic methods which are available
and with which more or less sophisticated equipment may be used are:
a) the fall of potential method or alternating current injection;
b) the three point or triangulation method;
c) the ratio method.
In the fall of potential or current injection method, which is the most general and commonly
used, a transformer supplies current to the electrode under test and via the earth to an
auxiliary electrode which, as a rough guide, should be at least 50 m apart (Fig. 19). The
current injected is measured, also the fall in potential from the electrode under test to a third
electrode situated roughly midway between the other two. If a high resistance voltmeter is
used, the resistance of the third electrode is negligible by comparison so a single rod
electrode is sufficient. Voltage

Fig 19 Measurement of the dissipation resistance of an earth electrode by the fall of potential or current
injection method

readings should be taken with the potential electrode moved say 5 m nearer and further away
from the test electrode; there should be no appreciable difference in these readings, but if
there is, it is an indication that the auxiliary and test electrodes are too close together.
Accuracy depends on passing a large current so the auxiliary electrode must be substantial,
particularly if the test electrode is a relatively low resistance substation earth. One power
authority specifies 6.5 mm diameter rods, 75 cm long, which can be driven and withdrawn
with hand tools, used in groups of 10, spaced 1 m apart and connected by a flexible cord. As
many groups as necessary are used to give the required current depending on the soil
resistivity and the dissipation resistance of the electrode under test. Further precautions
Ch.#1

29
which should be taken are to separate or place at right angles the leads carrying the injected
current and those connected to the voltmeter, to minimize induced voltages. Electrolytic
potentials are eliminated by connecting a blocking capacitor in the potential circuit and, in
the case of a station-earth system, the point of connection to the system is changed to check
that no appreciable change in the voltage reading results.
In spite of precautions and the use of a large injected current, inaccuracy in the potential
measurement may occur due to coupling between the current and potential measuring
circuits, electrolytic potentials and potentials due to large stray currents of fundamental or
harmonic frequency. An earth- testing ohm-meter eliminates some of these errors and has
the advantage of being a single easily portable instrument, independent of external power
supply. The instrument operates on reversed direct current, with commutators on the hand-
generator shaft which reverse the direction of current in both the control coil and the
deflecting coil synchronously. It thus measures resistance only and is less susceptible to stray
earth currents. While the standard earth-testing ohmmeter suffices for measuring the
resistance of less than 0.3 ohm may be expected but a geophysical earth- testing ohmmeter,
which is a modification of the standard instrument used for geophysical surveying, does have
a sufficiently low-reading range. Several other methods have been devised to minimize errors
and to avoid the expense and inconvenience of a large test current, one of which uses 30Hz
frequency current supplied by a battery-powered motor generator. A valve voltmeter
preceded by an amplifier, tuned to accept the 30 Hz voltage and reject stray 50 Hz voltages,
measures the drop of potential due to electrode resistance.
Another method recognizes that the effect of stray currents is mainly to produce sinusoidal
potentials of fundamental frequency which remain fairly constant in magnitude and phase
and can therefore be measured without the test current flowing. Figure 20 (a) is a typical
phasor diagram for an electrode resistance measurement, taking the various effects of
induction (Vi) and stray potential (Vs) into account and (b) is the circuit of a simple form of
alternating current potentiometer which may be used. The method is sensitive and accurate
in difficult situations where large stray potentials exist.
The three-point method is suitable for the measurement of higher values of electrode
resistance such as tower footings or single isolated equipment earths.
Fall of potential is measured as before giving three measurements, with the unknown
electrode X and two auxiliary electrodes A and B taken two at a time in series: If a constant
voltage is applied to each pair of electrodes in turn, the three current readings give three
values of resistance, that of each pair of electrodes in series:
V
R1 = = RX + RA
I XA
V
R2 = = R X + RB
I XB
V
R3 = = R X + RC
I XC
Ch.#1

30
Whence
1
RX = ( R1 + R2 + R3 )
2
To obtain reasonable accuracy, it is necessary to use auxiliary electrodes whose resistance is
of the same order of magnitude as that of the unknown. The ratio method measures the
series resistance of the unknown resistance and an auxiliary electrode by means of a
Wheatstone bridge. A slide-wire potentiometer is shunted across these two electrodes and
the galvanometer is connected between the sliding contact and a second auxiliary electrode.
In this way the ratio of the resistance of the electrode under test, to the total resistance of
the two electrodes in series, is found and the ohmic value obtained by multiplying this ratio
by the value obtained in the first measurement. A portable self-contained instrument makes
use of this method and has the advantage that only small test currents are used and a single
small auxiliary electrode required. The method is, however, insufficiently accurate to measure
the low resistances of large electrode systems.
The measurement of potential gradient on the earth surface uses the same circuit as Fig. 19
and requires readings of voltage with distance from the electrode under test. Using a high-
resistance voltmeter, a short probe is sufficient to give good contact with moist earth but the
voltage measured depends on the current flowing.
By measuring this current It and the resistance Rt of the test electrode, the total voltage to
infinity ItRt = E0 is known. This is taken as one per-unit and marked on the voltage/distance
graph of Fig. 16 or 17. For a fault to earth at the test electrode, one per-unit voltage will be
the phase to neutral system voltage so the voltage scale of the gradient curve is fixed
accordingly.

Ch.#1

31
FIG. 2.0 Measurement of electrode dissipation resistance by alternating current
potentiometer. (a) is phasor diagram of the voltages; V, and V.. are voltages measured with
the injected earth current OFF and ON respectively and V, is the required voltage for
estimating the earth resistance. (b) is the measurement circuit

8. CONSUMER INSTALLATION EARTHING AND

PROTECTIVE MULTIPLE EARTHING

While the responsibility for the earthing of an installation is that the consumer, supply
authorities have generally attempted to ensure safety by providing earthing facilities which
comply with current earthing regulations. The earliest method of earthing was to connect the
consumer’s earth conductivity conductor to an earth electrode on the consumer’s premises,
consisting of a driven rod, buried plate or metallic water-pipe, most frequently the latter.
Such direct earthing may be entirely unsafe, due to the fact that neither supply authority nor
consumer are obliged to make a periodic check of the electrode, and the use of plastic mains
by water authorities is likely to make it less effective in the future. The fact that the I.E.E.
Ch.#1

Regulations for the Electrical Equipment of Buildings (14th ed.) does not accept the use of

32
water or gas pipes, either jointly or separately, as the sole earthing electrode makes it
incumbent on the supply authority to make alternatives to the direct earthing on the
consumer’s premises available; such alternatives are cable-sheath earthing, continuous earth-
wire, earth leakage circuit-breakers and protective multiple earthing.
Cable-sheath earthing is common in urban areas where the method of distribution is by
underground cable of paper-insulated lead-covered type and where the service mains and
main cable have plumbed joints. The consumer’s continuity earth is then connected directly
to the lead sheath of the cable, providing a low impedance path back to the supply
transformer where the lead sheath is earthed to the same earth electrode as the system
neutral. This method of earthing is reliable and effective, giving loop impedances as low as
0.5 ohm, so that a prospective fault current of say 500 A is possible, which ensures speedy
operation of the fuse on the affected circuit in the consumer’s installation. The plumbed
joint is, however, the highest standard of jointing and the most costly so that it has given
way to joint boxes with mechanical clamps which do not provide a sufficient]y reliable low-
resistance contact between different parts of the cable sheath to permit it to be used as an
earth conductor. But where plumbed joints exist throughout, cable sheath earthing is an
economical arrangement since the Lead sheath serves its primary purpose of preventing the
ingress of moisture to the paper insulation of the cable so that its use as an earth conductor
is a bonus.
Continuous earth-wire provision was used extensively in rural areas where earth electrode
resistance is high. A separate continuous earth-wire was run as the lowest conductor on the
poles, below the phase and neutral conductors, and the consumer continuity earths all
connected to it to provide a low impedance path for earth-fault currents back to the supply
transformer. The only risk involved in this otherwise satisfactory arrangement is the
breakage of the earth-wire, which could possibly remain undetected for some time since
there are no monitoring facilities. This and the extra capital cost of the fifth wire in each
distributor limited the system to short distributors with a high consumer density, if the
earthing cost per consumer were to be economic. Eventually the development of the
protective multiple earthing system made the provision of a separate earth conductor
unnecessary so this system is likely to be obsolescent or used only in cases of special
difficulty. Figure 21 shows the path for earth-fault current; (a) for a single-phase consumer
installation with an earth electrode and (b) for the same installation with either the cable-
sheath or the continuous earth-wire system of earthing. In the former case the prospective
fault current is limited by the impedance of one line plus the earth-electrode resistances of
both the consumer and the substation earths in series, while in the latter no earth-electrode
resistance is involved.
The earth leakage circuit-breaker has the advantage over the more common fuse link that a
return path of low impedance, which is required to carry the heavy fault current needed to
blow a fuse, is not necessary. Instead of fuses in the main and sub-circuits of the consumer’s
installation a miniature circuit-breaker is inserted, the operating coil of which trips the
circuit-breaker when a predetermined level of earth leakage current is reached. The trip coil
Ch.#1

is either of high resistance (voltage operated) or of low resistance (current operated),

33
connected between the frame of the equipment to be protected and the supply neutral or the
consumer’s earth electrode. This may provide a relatively high resistance earth since a rated
tripping current of 0.5 A is usual and breakers with tripping current down to 25 mA are
available. Against the advantage of operation on a small earth-fault current must be set the
extra cost of the circuit-breaker and the fact that it normally protects only against an earth
fault and that additional overcurrent devices, or a more costly circuit-breaker with both earth
leakage and overcurrent tripping facilities, are needed to protect against both phase-to-
neutral and phase-to-phase faults.
Protective Multiple Earthing (P.M.E.) or M.E.N. (Multiple Earthing of the Neutral) has been
made possible by the relaxation of the restrictions regarding the earthing of the neutral of a
3-phase, four-wire supply. Originally earthing was permitted at one point only in the UK and
the initial conditions to multiple earthing were too stringent to encourage the general
adoption of the system. However, in 1965 general approval was given and, since then,
M.E.N. systems have grown rapidly. In this system, Fig. 21 (c), where the neutral provides
the return path of low impedance for earth-fault currents, there are two sources of danger,
an open-circuited neutral connection and a rise in voltage of the neutral due to a local phase
to-earth fault. These dangers are mitigated by two requirements, firstly that the neutral shall
be earthed not only at the supply end but also at the far end of the distributor, and secondly
that all metalwork within a consumer’s premises shall be bonded together and to the neutral.
The former requirement ensures that, in the event of a broken neutral conductor, both parts
remain effectively earthed and the latter that in the event of a voltage rise of the neutral,
possible theoretically up to the phase voltage of the system, all metal in a consumer’s
premises is at the same potential so that it is not possible for a person to make contact both
with the neutral and with the whole body of earth. This neglects the apparently dangerous
possibility of contact outside the equipotential cage of metalwork, such as to damp stone
floors, etc., but, although special precautions may need to be taken in certain industrial and
commercial premises, there is no evidence of danger to the public from the system. It is
evident, however, that the neutral bonding in the consumer’s premises must be thorough,
preferably done by the supply authority although the consumer and not the authority is
responsible for the cost. Ch.#1

34
Fig. 21 Paths of fault current for n earth fault in consumer’s installation: (a) with earth
electrode on consumer’s premises, (b) with, consumer’s continuity earth connected to supply
authorities earth wire or cable sheath and (c) with protective multiple earthing

It is probable that extensive adoption of M.E.N. in distribution results in a lowering of the

overall neutral to earth resistance by interconnection of the neutrals on previously separate
distribution systems, by the fortuitous earth at each consumer’s premises and by the
connection to the neutral of the metalwork of street-lighting standards. This lowering of the
neutral-to- earth resistance leads directly to a corresponding reduction in the possible voltage
rise which might occur on the metalwork in a consumer’s premises and has apparently made
the theoretical safety hazard negligible.
The advantages of P.M.E. are that it is possible for a supply authority to provide to all
consumers a safe and efficient system of earthing at a lower cost than by any other means. It
also leads to the adoption on underground distribution systems of new designs of cable
which save as much as 20 per cent on the material by providing three shaped cores in the
cable with a concentric neutral conductor consisting of a wave-wound wire sheath which
Ch.#1

facilitates jointing. This has resulted in systems where cable and installation costs have been

35
reduced by a quarter, giving a future annual saving to electricity supply authorities in the UK
of some £2 to £3 million.

9. SUBSTATION EARTHING

The requirements for substation earthing are to dissipate to the earth a large amount current,
of the order of thousands of amperes, without heating and consequent drying-out of the
earth in the neighborhood of an earth electrode, and secondly to control the potential
gradient over the whole substation area and beyond so that step-and-touch voltages nowhere
exceed a safe value. In a substation of any size, no single earth electrode will suffice to
dissipate the fault current so several such electrodes spaced over the substation area would
be required, interconnected below the earth surface by horizontal conductors and connected
to switchgear frames, equipment casings, system neutrals and tower footings. Such an earth
grid, as it is in effect, is itself an excellent earthing system so that a multiple electrode system
may prove to be very little better, as regards earth resistance and current dissipation, than is
the buried connecting network itself. The earth grid or mesh electrode, covering as it does
the whole substation area, provides control of local potentials throughout the area so that
dangerous step-and-touch voltages do not occur. These may be prevented by reducing the
spacing of conductors in the buried grid until a suitable distribution of voltage over the area
is achieved. The mesh electrode is normally constructed of rectangular strip, copper of
minimum size 2.5 cm by 3 mm or steel 5 cm by 5 mm, of length not exceeding 100 m,
beyond which consideration of impedance at 50 Hz indicates that no appreciable reduction
is dissipation resistance would occur. Since the efficient design of earth electrodes requires
them to have the largest possible surface for a given amount of material, the long flat strip is
most suitable and is easily jointed to similar strips at right angles to form a mesh which may
vary from a minimum of two strips and two cross-members around the perimeter of the site
to a theoretical maximum of a solid plate covering the whole area (Fig. 22).
The dissipation resistance or earth resistance (R) of such a mesh electrode buried in
homogeneous soil is given with sufficient accuracy by the Laurent and Niemann equation,

p p
R= +
4r L
This assumes that the voltage of the mesh electrode above the general body of earth has two
pI pI
components, due to the mesh regarded as a buried plate and due to the total
4r L
length of buried conductor where
p = average earth resistivity, -m
r = radius of a circular plate having the same area A as the mesh electrode

= ( A /  )m
Ch.#1

36
 L = total length of buried conductor in the mesh excluding cross connectors, m.

Alternatively, it may be considered that the second term recognizes that the resistance of the
mesh is more than that of a solid plate of the same area, the difference decreasing as the
length of conductor increases, becoming zero when L is infinite and the solid plate condition
is reached. In arid regions the subsoil may have appreciably lower resistivity p s than topsoil
at the earth ‘surface pt; in this case both values of resistivity are used in eqn. , the buried
plate term uses ps and pt is used for the local voltage drop term giving. For large-mesh
electrodes, even if pt rises considerably, say 10 times, due to seasonal drying out of the earth
surface, the total resistance change is not great owing to the large value of L, but for smaller
substations it may be of importance. Where the subsoil resistivity is the greater, the first term
of the equation may become sufficiently large to make the local voltage drop term negligible.
The buried conductors are then likely to saturate the earth surface so that only an increase in
the area of the mesh will lead to any considerable reduction in the dissipation resistance.
A rough calculation of the length of buried conductor in a mesh electrode of given area may
be made by keeping the various voltages at the earth surface within specified limits. The
three voltages are:
Vstep the step voltage over a horizontal distance of one meter,
Vtouch here defined as the voltage between a structure earthed to the mesh and
a point on the earth surface one meter away,
Vmech a special case of touch voltage being the voltage from an earthed structure to a point
on the earth surface at the center of a rectangular formed by the mesh conductors.

Fig. 22 Values of the product of the coefficient Km and KI for square mesh electrodes with
Ch.#1

different meshes

37
Laurent has given the approximate values for the usual ranges of conductor size, buried
depth and spacing of mesh conductors for French practice as
V step= 0.1-0.15 pi
Vtouch= 0.6-0.8 pi
Vmesh= pi
Where i is current flowing to earth, per meter of buried conductor. Touch voltage rather
than step voltage is taken as the basis of calculation since step voltage involves the resistance
to earth of two feet in series, rather than in parallel for touch voltage, thus limiting the body
current for the former. Assuming body resistance constant, ventricular fibrillation may be
prevented by keeping the total energy (joule) absorbed by the body during a shock to below
a given value. Tests in the time range 0.03s to 3s, by a number of workers in several
countries have led to the conclusions by Daiziel that this threshold of energy, which will only
cause fibrillation in half of I per cent of a large group of normal men is
I2bt= 0.027

where Ib is the current (rms) through the body and t the time (second) or

0.165
Ib =
t

The above expression shows the virtue of fast fault clearance in raising the figure for safe
body current. Taking p as resistivity of earth near the surface, it has been determined that the
resistance of the two feet in series (step contact) is approximately 6p t ohm and of two feet in
parallel (touch contact) approximately 1.5pt ohm. Body and skin resistance varies widely,
from 500 to 3000 ohm, but a value of 1000 ohm is reasonable considering the improbability
that all the factors which contribute to shock severity would have their most adverse values
at a particular instant. Hence

Taking the value of for Emesh in place of Etouch since for most mesh electrodes it is likely to
be the greater

or

An estimation of L from this expression assumes idealized conditions such as uniform soil
Ch.#1

resistivity, a symmetrical mesh electrode composed of squares of uniform side and constant

38
current to earth per unit length of mesh conductor. The latter condition is not fulfilled even
with a square mesh since the current which flows is higher for conductors at the sides than
at the center of the mesh electrode and higher yet at the corners. Since the voltage gradients
vary accordingly, any reasonably accurate estimate of Emesh must take account of the
position of a given rectangle in the mesh as well as the number, spacing, dimensions and
depth of burial of the mesh conductors. This leads to the use of two coefficients in the
expression for Emesh,

Where Km is a coefficient which takes into account the effect of number, n, spacing, D,
diameter, d, and depth of burial, h, of the grid conductors. It is given by

the number of factors in parentheses in the second term above being two less than the
number of parallel conductors in the mesh, excluding cross- connectors.
Ki is an irregularity correction factor to allow for non-uniformity of the current to earth
from different parts of the mesh. It conforms closely for rectangular symmetrical mesh
electrodes to an empirical relation,
Ki = 0.65 +0.1 72n
Where n is the number of parallel mesh conductors.
Use of the above expression for Emesh permits a closer estimate of L in order to keep the
mesh voltage within safe limits, and a determination of the coefficients for each rectangle in
the mesh will show whether the mesh voltage is likely to be exceeded at any point.
The value of the Km Ki product as determined experimentally by Koch are shown by Fig.
22 for rectangular meshes having 2, 3, 5 and 9 parallel conductors in one direction, but the
same tests show that a value as high as 2.25 is possible for the same rectangle with an
irregular spacing of the mesh conductors. However, the extent to which differences of
potential occur between different parts of the mesh electrode itself, under fault conditions,
also depends on the points of connection of machines equipment and system neutrals, from
which an earth fault current may flow to the mesh conductors. As such equipment will
normally be earthed in the central part of the mesh rather than at the periphery, with
consequent rise in voltage at these points, the general tendency for the earth current per
meter of mesh conductor to be greater with the outer conductors will to some extent be
compensated. The area of the substation itself may be made safer by the use of a surface
layer of crushed rock which has a much higher resistivity than soil even when wet. Special
care may be required with perimeter fencing which must be connected throughout to the
mesh electrode and with railway track which, being earthed within the substation area, may
convey the mesh electrode potential to a distance where it might give a dangerous touch
voltage to earth.
Ch.#1

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APPENDIX
Formulas for Calculation of Resistances to Ground*
(Approximate formulas including effects of images. Dimensions must be in centimeters
when resistivity is in ohm-centimeters.)

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* H.B. Dwight, Calculation of Resistance to Ground, Electrical Engineering, vol. 55, p. 1319,
Ch.#1

December 1936.

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