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ANALYSIS OF GROUNDING PRACTICES
IN UNIFORM LAYER SOIL
BY
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MO HAM ED SHAHRTMANBIN MOHAME* YUNUS
DATE RECEIVED :
ACCESSION NO :
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A Dissertation Submitted In Partial Fulfillment of the Requirements
for the Degree of Master of Electrical Engineering,
College of Graduate Studies
Universiti Tenaga Nasional
DECEMBER 2008
CHAPTER 1
INTRODUCTION
1.1
System Grounding
1.1.1
Overview
Grounding of an electrical system is a task that is faced by most engineers who look into
planning, designing or modifying electrical distribution system. The quality and the
performance o f grounding systems are a major concern in today4s power system design.
Grounding is important in our effort to increase the reliability o f the supply service, as it
helps to prevent excessive voltage peaks during disturbances and also provides a
measure of protection against lightning.
Most o f the electric power systems are grounded (connected to ground by means o f
ground-embedded electrodes) for a number o f reasons:
a) To assure correct operation o f electrical devices
b) To provide safety during normal or fault conditions
c) To stabilize the voltage during transient conditions and therefore to minimize
the probability o f a flashover during transient
d) To dissipate lightning strokes
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In general, a structure is called grounded if it is electrically connected to groundembedded metallic structures. The ground-embedded metallic structures will be called
the grounding system and provide a conducting path o f electricity to ground.
Ideally, the potential o f the neutral o f an electrical o f a three phase system should be the
same as that o f the ground. In this case, human beings and animal are safe whenever
they touch metallic structures connected to the system neutrals. Unfortunately, the
impedance o f the grounding system to ground is always a finite number. Thus the
potential o f grounded structures may becomes different than potential at various point
on ground during abnormal operation. Abnormal operation includes highly unbalanced
operating condition or fault conditions.
Grounding o f either a system or equipment involves the provision o f a connection to the
general mass o f ground. This connection should have resistances not greater than the
design value and should be capable o f carrying the expected maximum fault current. It
is therefore necessary to consider the various factors which affect the resistance to
ground and the fault current capacity o f the buried conductor, designated as the ground
electrode. These include the size and shape o f the ground electrode and soil in which the
electrode is buried. It is also necessary to give consideration to current density at the
surface o f the ground electrode and the ground potentials in its vicinity.
1.1.2
Definition
For the purpose o f this dissertation, the following terms and definitions will be used.
1. Effectively grounded: Grounded through a sufficiently low impedance such that for
all system conditions the ratio o f zero-sequence reactance to positive-sequence
reactance
(XoIX\) is positive and not greater than 3, and the ratio o f zero-sequence
resistance to positive-sequence reactance (Ro/X{) is positive and not greater than 1 [1].
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2. Ground: A conducting connection, whether intentional or accidental, between an
electrical circuit or equipment and the ground, or to some other body that serves in place
o f the ground [1].
3. Grounded: Connected to ground or to an extended conducting body that serves
instead o f the ground, whether the connection is intentional or accidental [1].
4. Grounded system: A system in which at least one conductor or point (usually the
middle wire or neutral point o f transformer or generator windings) is intentionally
grounded, either solidly or through an impedance [1].
5. Grounding system: A system that consists o f all interconnected grounding
connections in a specific power system and is defined by its isolation from adjacent
grounding systems. The isolation is provided by transformer primary and secondary
windings that are coupled only by magnetic means. Thus, the system boundary is
defined by the lack o f a physical connection that is either metallic or through a
significantly high impedance [1],
1.2
Description of the Problem
Grounding is an important part o f electric power system installation. If the system is
not properly designed, human or animal will be exposed to shock hazards. The doubts
that engineer have includes:
a) What are the grounding systems available in Malaysia?
b) What are the reasonable assumptions for the effective grounding technique in
uniform layer soil?
c) What is the relationship between the grounding techniques and the grounding
resistance?
d) What are the factors contributing to the grounding resistance?
In BS 7430 (Code o f Practice for Earthing), there are a few grounding techniques that
are proposed for electrical installation. With the rapid increase o f electrical load in
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recent years, in order to protect the electrical equipment especially the electronic part,
decreasing the grounding resistance o f the grounding system is very important to the
premises, building and also for the power generating stations.
Therefore, in this dissertation, the analysis will focus on the performance o f a few
grounding technique that had been discussed in the BS 7430 (Code o f Practice for
Earthing) for uniform soil layer [2].
1.3
Research Objectives
The intention o f this dissertation is to assist the engineer in making decisions on the
subject by presenting basic reasons for grounding and by reviewing general practices
and methods o f system grounding. Therefore, with respect to the above problem, the
objective o f this dissertation is to analyze:
a) The grounding technique systems in Malaysia
b) The relationship between the grounding techniques to the grounding resistance
c) The factors which affect the output ground resistance
1.4
Scope of Analysis/ Description of Analysis
The scope o f this dissertation is limited to finding the effective grounding techniques
that are available in Malaysia and to analyse them in order to determine the technique
that will give the lowest value o f resistance. This dissertation will analyse the
performances o f all the grounding technique by computing the ground resistance.
This dissertation will focus on the analysis performed on a soil with resistance o f 100
fim (Clayey sands, poorly graded sand-clay mixtures) [1]. The analysis results for soil
resistance o f 50 Qm (Silty or clayey fine sand with slight plasticity) [1] and 1000 Qm
(well graded gravel, gravel sand mixture, little or no fines) [1] are shown in the
Appendix B and Appendix C.
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The analysis will concentrate on the uniform layer soil was done for various technique
as Single Ground Rod, Two Ground Rod, Four Point Star, Six Point Star, Ring of Wire,
Horizontal Round Plate and Vertical Round Plate. All analysis were carried out using
MATLAB.
1.5
Summary of Chapters
In Chapter 2, the grounding systems were discussed. The discussion concentrated on the
hemispherical electrode at the surface o f ground, two hemisphere embedded on the
surface o f the ground and sphere buried in ground. The discussions on the current flow
for the three techniques were discussed.
In Chapter 3, the characteristic o f grounding performance were discussed. The factors
that contribute to the ground resistance such as electrode pattern and soil resistivity, p
were explained in this chapter. The skin effect phenomena which affect the distribution
o f electric current were also discussed.
The connection to ground which includes the grounding resistance, recommended
values for grounding system and the technique o f measuring resistance to ground will
be covered in Chapter 4.
Chapter 5 is dedicated to the method analysis o f grounding practice by using MATLAB
program to find the best grounding practice for ground system and the effect o f
grounding performance. This chapter will also discuss the results.
Chapter 6 of this dissertation will conclude the techniques for grounding system design
for the low voltage system.
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CHAPTER 2
INTRODUCTION TO GROUNDING SYSTEMS
2.1
Hemispherical Electrode at the Surface of Ground
The simplest grounding system from the analysis point o f view is a hemispherical
electrode embedded or buried in soil or ground o f resistivity, p as shown in Figure
2.1(a). The center o f the hemispherical electrode is located on the surface o f the ground.
Assume that the potential o f the hemisphere is V. For this example, the electric current
will flow at the surface o f the electrode to the ground. Because o f the symmetry, the
flow o f the electric which illustrates a sphere embedded in an infinite medium o f
resistivity, p a s shown in Figure 2.1(b) [3].
When an electrical current is injected into the ground via the grounding system, the
current is directly dependent on the resistivity o f the soil or ground. Due to the effect o f
current flowing through this resistance, the electrical potential o f the grounding system
and all metallic structures connected to it will also rise. In other words, the flow o f the
current will be such that the equipotential surfaces generated will be concentric spherical
surfaces.
The resistivity above the surface is similar to below the surface because o f similarity in
humidity. However, as the depth below the surface increases, there is a possibility that
the resistivity will vary. In this dissertation we assume that the resistivity above the
surface is same as below the surface for the ease o f analysis.
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air
7777777777777777777777777777777777777\
0
y//////////////////////////^//////M
re sistiv ity = p
(a) Actual system
(b) Equivalent system for analysis purposes
Figure 2.1 Hemispherical electrode embedded in ground [3]
(a) Actual system (b) Equivalent system for analysis purposes
If total current, / flows from surface o f the hemisphere into ground (Figure 2.1(a)), the
total current which is two times / will flow from the sphere into ground (Figure 2.1(b)).
The current density, J(r) at a point located r distance from the center o f the electrode
will be:
2i —
j ( r ) = ------ r
4w
amperes/m2
r>a
................................(2.1)
where:
a = the radius o f the hemisphere and
r = unit vector in the radial direction.
Using Ohm’s law, the electric field intensity at a point located r distance from the center
o f the hemisphere will be:
E(r) = pJ(r) r
r>a
........................................ (2.2)
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The potential o f the hemisphere with respect to a point x located at a distance r = rj from
the center o f the hemisphere will be given by equation below:
.(2.3)
V(rx)= J J (r )p d r
r-a
Upon substitution and evaluation o f the integral, we have:
V(rl) = £ i
2 n va
.(2.4)
j
The potential o f the sphere with respect to remote ground, Vx , is obtained by letting
r, —>oo .
Voo =
pi
2m
.(2.5)
The potential on the surface o f the ground along a line passing through the center o f the
hemisphere is illustrated in Figure 2.2. The resistance o f the hemisphere to remote
ground is:
R = -V
I
P
.(2.6)
2im.
Figure 2.2 Potential distribution on the surface of the ground generated
by a hemisphere [3]
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2.2
Two Hemisphere Embedded on the Surface of the Ground
The second configuration technique o f the grounding system are the two hemispheres
embedded parallel on the surface o f ground as shown in Figure 2.3(a) where an electric
current source is connected between the two hemisphere, which will cause total electric
current, I to flow through the ground. For analysis purposes, it can be assumed that the
presence o f one hemisphere does not effect the current distribution on the surface o f the
other hemisphere where the current distribution o f two parallel rod do not overlap each
other. This assumption is valid assuming that the distance between the two hemisphere
is much larger than their radius (d > r ) [3],
The solution for this case is obtained by superposition. Specifically, the electric current
density J ( x , y ) at a point ( x . y ) , illustrated in Figure 2.3(a) is:
J(x, y ) = - — j f \ —
4^r2
Anrx
where :
r2
amperes/m2
.......................... (2.7)
ri,r2 = the distances
r \ , n - unit vectors
The first term is the contribution to the electric current density from the first hemisphere
and the second term is the contribution from the second hemisphere. Similarly, the
electric field intensity E(x,y) is computed as:
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-
21
-
E ( x ,y ) = p ----- - r \ - p ---- —
l n
4^,
volts/meter
4w 2
The voltage between the electrodes is computed from:
V = § E ( x, y )d r
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............................. (2.8)
Selecting an integration path along the line AB and carrying out the integration yields:
r .
V =p
1
2k
ax
1.
\
1 , 1
■+ ------D - a 2 a2 D - a x
•(2.9)
If the both hemispheres are identical (i.e aj = ai), then the equation o f F becomes:
V =p n
1
1
a
D -a
.(2.10)
The resistance between the two hemispheres becomes:
I
P_ ____1_ "
n Ka D - a y
.(2.11)
The lines o f flow o f electric current are illustrated in Figure 2.3(b).
(a)
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