Introduction:
The grounding system is an essential element
for the electrical system security and it is required to:
 Allow for protective devices activation
when there is an insulation fault.
 Equalize the potential of conductive
parts that can be accessed simultaneously, with the potential
in the surrounding soil in order to prevent people from
being exposed to hazardous voltages.
 Allow the lightning strike energy to
be safely dissipated.
 Reduce electromagnetic interferences.
Due to the fact that it is a system designed
to guarantee safety, its effectiveness should be verified.
The diffusion resistance value is the parameter normally considered
to be the most relevant one to test grounding system quality
and its capacity to carry out its function properly. But the
correct measurement of this parameter needs to fulfill several
requirements, which will be analyzed in this issue.
Physical nature of the earth resistance:
The understanding of the earth resistance
physical nature will help us evaluate the conditions to be
fulfilled in order to get its correct measurement.
According to its definition, resistors
have two terminals and its resistance is defined as the quotient
of the voltage applied on those terminals and the current
circulating between them as a consequence of that voltage.
The value of the resistance (eq. 1)
depends on the type of material (resistivity) and its physical
dimensions (area and length of the resistive element), as
it is shown in figure 1.
Only one of the terminals is evident in
the earth resistance. In order to find the second terminal
we should recourse to its definition: Earth Resistance is
the resistance existing between the electrically accessible
part of a buried electrode and another point of the earth,
which is far away (Figure 2).
The idea is that outside the earth volume
next to a buried electrode, through which a current is injected,
all the planet volume is equipotential related to that current.
Any point of that equipotential volume (Figure
3) can be considered as the second electrode of the earth
resistance.
In order to justify the previous statement,
we will closely analyze the resistance geometry in the area
surrounding the buried electrode, which, in the following
example, is supposed to be hemispherical (Figure
4).
The current being injected in the earth
through the buried electrode goes out from it in all directions,
with a uniform density (supposing the ground is electrically
homogeneous), and it must later go through the various layers
illustrated in figure 4. Each layer
offers a resistance to the passing current, which is proportional
to the ground resistivity and to the layer thickness (resistance
length in Figure 1), and inversely
proportional to the layer's area, according to eq.1.
Then, the total resistance is the sum of many small resistances
in series. The thickness is arbitrarily defined as thin enough
so as to consider both surfaces of the layer as of the same
area (requirement necessary to apply eq.
1).
Really, the thickness is infinitesimal
and the sum of the resistances is an integral as shown in
eq. 2, where r0 is the radius of the
buried hemisphere.
In order to allow an easier physical visualization
of the phenomenon, we could imagine the structure of an onion,
made up of a great number of very thin layers, each of which
represents one of the resistances of the series.
The important concept to be observed
is that, since the ground resistivity was supposed to be homogeneous
and the thickness of all the layers is the same, the only
element that is modified (it increases) as we go away from
the electrode is the surface of the layer. In figure
4, it can be observed that surface S3 is much bigger than
the surface S1. When the surface increases, the resistance
decreases in the same proportion and therefore the contribution
made by the remote layers to the total resistance tends to
be insignificant.
Calculations for the case of an hemispherical
electrode show that in the nearest region, up to a distance
equivalent to 10 times the electrode radius, the 90% of the
total resistance is concentrated. In other words, the contribution
made to the resistance by the layers located outside this
area, is not significant. And as there is no resistance, there
is no fallofpotential either. Consequently, outside the
region closest to the electrode (called resistance area),
all the ground is at the same potential.
Measurement method:
In order to measure the resistance, we
need to apply a voltage among its terminals that causes the
circulation of a current through it. One of the terminals
is the earth system accessible contact E. The second one,
according to the definition, is any other point of the earth
that is really far away from the first. In order to carry
out the measurement, we should hammer an auxiliary electrode
H at that point. The second electrode will inevitably have
its own earth resistance and resistance area.
If we look at figure
5, we will see that:
 Our objective is to measure electrode
E earth resistance. However, if a conventional resistance
measurement between points E and H is carried out by measuring
the voltage and the circulating current, the sum of the
earth resistance of both electrodes will be obtained and
not the earth resistance of electrode E. The difference
may be very significant since due to its very own condition
of auxiliary electrode the H dimensions are very small in
comparison with E, so its contribution to the total resistance
may be very important, introducing a considerable error.
 The concept of "far away" previously
used without making greater precisions is now clarified.
In fact, it can be considered that the auxiliary electrode
H is sufficiently far away from the earth system which resistance
is being measured when its respective resistance areas do
not overlap. In such a case, all the volume that is outside
the resistance areas is, very approximately, at the same
potential, which makes it possible to develop the following
measurement method.
FallofPotential Method
A third electrode S is used in order
to avoid the error introduced by the earth resistance of electrode
H, The S rod is hammered at any point outside the E and H
influence zones, giving as a result a geometry similar to
the one shown in Figure 6.
This arrangement is known as FallofPotential
Method and it is the most commonly used for the earth resistance
measurement in small or medium dimension systems, in which
the separation of the resistance areas is obtained with reasonable
distances between electrodes. The current circulates through
the earth system E and the auxiliary electrode H, and the
voltage is measured between E and the third electrode S. This
voltage is the fall of potential that the test current produces
in the earth system resistance, Rx, which in this way can
be measured without being affected by the earth resistance
of the H rod.
The 62% rule
Many publications that make reference
to the FallofPotential Method indicate that, in order to
obtain a correct measurement, the three electrodes must be
well aligned and the distance between E and S must be the
61.8% of the distance between E and H (figure
7). This concept comes from a careful mathematical development
for the particular case of an hemispherical electrode, published
by Dr. G. F. Tagg (Note. 1) in 1964.
Nevertheless, this configuration is not
easily applied in the real life. The first problem to be faced
is that real earth systems have complex geometries and it
is difficult to assimilate them with an hemisphere in order
to precisely determine its center, from which distances can
be measured accurately enough. Besides, in urban areas it
is difficult to find places where the rods can be hammered,
and it is rare for those available places to coincide in their
position with the 62% rule requirements (alignment and distances
relationship).
Fortunately, by using the same calculations
of the previously mentioned paper we can derive another geometry,
which is easier to apply. Consider the segment joining E with
H and the straight line that intersects that segment at its
middle point and that is perpendicular to the mentioned segment.
By placing the electrode at any point lying on the straight
line the measured value of the resistance will fall between
0.85 and 0.95 of the true value of the earth resistance of
the electrode. Then, multiplying the measured value by 1.11
the correct earth resistance value is obtained, with an error
lower than ±5%. It is also observed that as the voltage electrode
goes far away from the segment EH, the area where the measured
value is within the indicated range of tolerance becomes wider,
making the method to be more tolerant to changes in the position
of the voltage electrode in both directions. In Figure
8, if the electrode S is hammered at any point outside
the gray areas, the error will be lower than ±5% when applying
this procedure that we will call "The 1.11 rule".
Perhaps the expected error caused by the
suggested method may appear to be too high. In order to evaluate
this point, we will cite again the same Dr. Tagg´s paper:
"...bearing in mind that a high degree of accuracy is not
necessary. Errors of 510% [in the measurement of earth resistance]
can be tolerated... This is because an earth resistance can
vary with changes in climate or temperature, and, as such
changes may be considerable, there is no point in striving
after a high degree of accuracy."
"Recipe" for the 1.11 rule
 Being D the greatest dimension of the
grounding system which resistance is to be measured, an
auxiliary rod H should be hammered into the soil at a distance
greater than 5D. If the grounding system approximates to
a rectangle, then D is its diagonal (Figure
9).
 Imagine the segment EH that joins the
center of the grounding system E with the auxiliary rod
H. At the middle point of that segment, draw an imaginary
straight line perpendicular to the segment.
 Hammer the auxiliary rod S (potential
electrode) at any point that lies on that imaginary straight
line, far away from the EH segment.
 Measure the earth resistance using
an "earth tester" and multiply the obtained value, by 1.11,
in order to get the grounding resistance real value.
 Take into account that this method
is very tolerant to variations in the potential rod position.
That's why you should worry neither for determining with
real accuracy the middle point position of the segment nor
for the imaginary straightline perpendicularity. These
values are merely indicative, and the measured value does
not significantly modify itself based on those values as
long as the lateral withdrawal of the potential ground rod
is large (greater than 4D).
A more detailed analytical study of the
development that leads to 1.11 factor rule does not fall within
the scope of this paper, but it can be found in a paper written
by the same author(Note. 2).
Auxiliary electrodes earth resistance
Current and potential auxiliary electrodes
are also earth electrodes, often of small dimensions, and
due to this they can present a fairly high earth resistance
(also depending on the soil resistivity). As it has already
been seen, the 3 electrodes method is a configuration that
makes it possible to eliminate the influence of these resistances
on the measurement. However, earth testers constructive limitations
impose restrictions to the earth resistances maximum value
of the auxiliary ground rods.
Related to current electrodes, the limitation
is imposed by the features of the builtin generator of the
earth tester. A very high resistance of this electrode would
limit the current that the equipment can inject into the soil,
with a subsequent decrease in the measurement sensibility.
Concerning the potential electrode, the
limitation is determined by the voltmeter circuit input impedance
of the earth tester, which must be far greater than the earth
resistance of this auxiliary electrode.
The IEC 615575 standard, specific for
earth testers, determines that the instrument must provide
a correct measurement result with an error lower than ±30%
for any resistance of the auxiliary electrodes of up to 100
x Ra with a maximum of 50kW, being Ra the measured resistance
value. It also requires the instrument to be able to determine
that this condition is fulfilled, in order to avoid an error
of this kind to go unnoticed. Several instruments carry this
out automatically, warning the operator and blocking measurement
when the resistance of any auxiliary electrode is excessive.
If this is not the case, then the measure procedure should
include this checking before each test.
Interferences
When a grounding system resistance of
an energized installation is measured, a significant voltage
of industrial frequency and possible harmonics between the
earth electrode E and the potential electrode S appears due
to the existence of an earth fault current. The same happens
during measurements in soils in which there are spurious currents
circulating, such as it happens in the vicinity of some substations.
These interfering voltages can be much higher than the ones
the equipment should measure. This is because the injected
currents are always small, perhaps a few milliamps, in order
to preserve operators' safety. The greatest challenge that
a good Earth tester faces is to be able to distinguish the
potential drop in earth resistance due to the test current
from the interfering voltages (which may have a substantially
greater magnitude).
This distinction is easier to achieve
if the frequency of the injected current coincides neither
with the industrial frequency nor with any of its harmonics.
This condition is mathematically expressed in
equation 3. Where:
Fg = Frequency of the current injected
by the internal generator
Fi = Industrial frequency (50 Hz or 60
Hz, depending on the country)
N = Any integer greater than zero
Each manufacturer chooses an N value that
he considers to be adequate, from which the equipment operating
frequency results. The 270Hz frequency has the peculiarity
of complying with this condition for N = 4 in the 60 Hz regions,
and at the same time, it is very close to comply with it for
N = 5 in the 50Hz region. Other adequate frequencies following
the same criterion are: 330Hz, 570Hz, 630Hz, 870Hz, 930Hz,
1170Hz, 1230Hz, 1470Hz, 1530Hz, etc.
The separation is carried out using high
selectivity filters. A very adequate configuration is the
synchronous rectifier, in which the same system that generates
the test current controls the switches that rectify the signals
that should be measured. This model is equivalent to a highly
selective and efficient filter, which allows for accurate
measurements even with intense interferences. If the grounding
system behaves as a simple resistance, its value is independent
from the measurement frequency. However, some grounding systems
present a reactive component. In such a case, their behavior
depends on the frequency of the circulating current. For fault
currents the frequency will be low, of about 50 or 60Hz. But,
when it has to dissipate an atmospheric discharge current,
an inductive component may compromise the grounding system
efficiency.
Notes:
 Tagg, G. F.: "Measurement of earthelectrode
resistance with particular reference to earthelectrode
systems covering a large area", PROC. IEE, Vol. III, No.
12, December 1964.
 Manuel J. Leibovich, "Analytical study
of the 1.11 rule for earth resistance measuring.
 The author of the article is Mr. Manuel
Jamie Leibovitch, R&D director of Megabras Industria Electronica
Ltda. Represented by Duncan Instruments Canada Ltd.
