AC SUBSTATION GROUNDING DESIGN
A project
Presented to the faculty of the Department of Electrical and Electronic Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Electrical and Electronic Engineering
by
Mamadou Keita
Arnel Q. Molina
SPRING
2013
AC SUBSTATION GROUNDING DESIGN
A Project
by
Mamadou Keita
Arnel Q. Molina
Approved by:
_______________________________________, Committee Chair
Dr. Turan Gonen
__________________
Date
ii
Students: Mamadou Keita
Arnel Q. Molina
I certify that these students have met the requirements for format contained in the University
format manual, and that this project is suitable for shelving in the Library and credit is to be
awarded for the project.
______________________________, Graduate Coordinator
Preetham B. Kumar
Department of Electrical and Electronic Engineering
iii
__________________
Date
DEDICATION
In memory of my dear uncle Bappa Ibrahima, and sister Hadja Conakry,
You will always be my guiding principles.
Mamadou Keita
My heartfelt gratitude to my wife Rhea and our dear children, who have
been patiently supported me during my absence of my responsibilities as
husband and a father.
To my manager at work, who gives me flexibility of time to go back and
forth to school.
I also dedicate this project to Dr. Turan Gonen. His vast knowledge and
professional experience in Power System Engineering is essential in completing
this project. I love his book that we used in one of our references titled
"Electrical Power Transmission System Engineering: Analysis and Designs". It is
rich in technical design.
Above all, I thank my personal Lord and Savior Jesus Christ, who gives me strength
and his grace is always sufficient for me in my weaknesses.
Arnel Q. Molina
iv
ACKNOWLEDGEMENTS
We thank all the teachers and faculty of the department of Electrical and
Electronic Engineering especially Dr. Turan Gonen, Dr. Mohammad
Vaziri, and Dr. Preetham B. Kumar for all the help and guidance
through the years. We are highly indebted to IEEE for their great
resources that helped us in completing the project.
v
Abstract
of
AC SUBSTATION GROUNDING DESIGN
by
Mamadou Keita
Arnel Q. Molina
Statement of problem
This paper presents AC substations grounding system for either conventional
or gas-insulated. The design of grounding systems of substations has the primary
purpose of ensuring the safety and well being of personnel, who may become
electrically coupled to the grounding mats during unbalanced fault conditions (ElDessouky, El-Aziz, & Khamis, 1998), (Phan, 1990). In general, an unbalanced fault
will cause a ground potential rise of the system neutral and any conductive medium
electrically connected to the neutral. The approach of this design is based on the IEEE
Standard 80-2000 which discusses the following subjects safety in grounding,
tolerable body current limit, primary and auxiliary ground electrodes, grounding
enclosure sizing of conductors and materials, soil characteristics, ground resistance,
types of ground faults, installation of connections, pigtails, ground rods, and ground
grid integrity test. In this project, general system structure as well as rules and data
representations are discussed. An illustrative example is presented using 15 kv
vi
medium voltage switchgear for Tri-Met Portland Westside light rail (Thomas & Pham,
1999). The ac substations grounding system design presented in this project can assist
grounding system engineer to obtain a safe grounding system which is one of most
important design aspects of substations.
_______________________________________, Committee Chair
Dr. Turan Gonen
_____________________
Date
vii
TABLE OF CONTENTS
Page
Dedication ........................................................................................................................ iv
Acknowledgments............................................................................................................. v
List of Tables .................................................................................................................. xii
List of Figures ................................................................................................................xiii
Chapter
1. INTRODUCTION, DESCRIPTION OF PROBLEMS, PROJECT LIMITATIONS
AND GROUNDING TERMINOLOGIES ....................................................................... 1
1.1 Introduction ............................................................................................................. 1
1.2 Problems’ Description ............................................................................................. 1
1.3 Project Limitations .................................................................................................. 2
1.4 Grounding Terminologies ....................................................................................... 3
2. THEORY AND COMPUTATIONAL PROCEDURES, AND HUMAN FACTOR
OF SUBSTATION GROUNDING .................................................................................. 8
2.1 Safety in Grounding ................................................................................................ 8
2.2 Conditions of Danger ............................................................................................ 10
2.3 Range of Tolerable Current ................................................................................... 11
viii
2.4 Effects of Frequency, Duration, and Magnitude ................................................... 11
2.5 Shock and Current Path Through the Body (Gonen, 2009) .................................. 13
2.6 Reclosing ............................................................................................................... 17
2.6.1 Accidental Circuit Equivalents ....................................................................... 18
2.6.2 Typical Shock Situations ................................................................................ 24
2.6.3 Typical Shock Situations for Gas-Insulated Substations, (GIS)..................... 28
2.6.4 Effect of Sustained Ground Currents.............................................................. 30
3. SUBSTATION GROUNDING DESIGN PARAMETERS ....................................... 31
3.1 Introduction ........................................................................................................... 31
3.2 Design Considerations........................................................................................... 31
3.2.1 Importance and Benefit of the Ground Grid ................................................... 31
3.2.2 Conceptual Analysis ....................................................................................... 33
3.2.3 Non Ideal Design Situations ........................................................................... 34
3.2.4 Grid’s Connections ......................................................................................... 35
3.3 Gas Insulated Substation Feature .......................................................................... 36
3.3.1 Gas Installed-Substation Enclosures .............................................................. 37
3.3.2 Special Aspects of GIS Grounding ................................................................. 37
3.3.3 Touch Voltage in Gas Insulated Substation ................................................... 38
ix
3.4 Conductors and Connectors .................................................................................. 41
3.4.1 Conductors ...................................................................................................... 42
3.4.2 The Sizing Factors of Conductors .................................................................. 43
3.4.2.1 Symmetrical Currents .................................................................................. 43
3.4.2.2 Asymmetrical Currents ................................................................................ 45
3.4.2.3 Additional Factors in Conductor Sizing: ..................................................... 46
3.4.2.4 Connectors Selection ................................................................................... 47
3.5 Soil in Substation Grounding ................................................................................ 47
3.5.1 Outside Effect on Soil Characteristics ............................................................ 48
3.5.2 Surface Layer Material ................................................................................... 50
3.5.3 Soil Resistivity Measurement and its Interpretation....................................... 51
3.6 Ground Resistance and Maximum Grid Current .................................................. 57
3.6.1 Simplified Calculation of Ground Resistance .................................................... 57
3.6.2 Schwarz’s Equations .......................................................................................... 59
3.6.3 Ways to Lower Soil Resistivity.......................................................................... 61
3.6.3.1 Soil Treatment ............................................................................................. 61
3.6.3.2 Concrete-Encased Electrodes ...................................................................... 62
3.6.4 Maximum Grid Current ...................................................................................... 66
x
4. DESIGN OF SUBSTATION GROUNDING SYSTEM ............................................ 75
4.1 Design Criteria ...................................................................................................... 75
4.1.1 Critical Parameters ......................................................................................... 76
4.2 Design Procedure .................................................................................................. 76
4.3 Maximum Step and Mesh Voltages ...................................................................... 77
4.3.1 Mesh Voltages (Em) ........................................................................................ 78
4.3.2 Step Voltages (Es) ........................................................................................... 81
5. APPLICATION OF SUBSTATION GROUNDING DESIGN ................................. 82
5.1 Introduction ........................................................................................................... 82
5.2 Initial Design of Hillsboro Central Substation ...................................................... 83
5.3 Modified Design of Hillsboro Central Substation ................................................ 92
6. CONCLUSION ........................................................................................................... 96
Appendix ......................................................................................................................... 98
Work Cited .................................................................................................................... 114
xi
LIST OF TABLES
Tables
Page
2.1 Effect of Frequency, Duration and Magnitude ........................................................... 12
2.2 Resistivity of Different Soils (Gonen, 2007) .............................................................. 16
3.1 Material Constants ...................................................................................................... 44
3.2 Typical Values of Df ................................................................................................... 46
3.3 Effect of Moisture Content on Soil Resistivity ........................................................... 49
3.4 Resistivity of Different Soils ...................................................................................... 52
3.5 Typical Grid Resistances ............................................................................................ 59
5.1 Input Data for the Grounding System Design............................................................. 83
xii
LIST OF FIGURES
Figures
Page
2.1 Equipotential countours of a typical grounding grid with and without ground rods .. 10
2.2 Exposure to touch voltage .......................................................................................... 19
2.3 Impedance to touch voltage ........................................................................................ 20
2.4 Touch voltage circuit .................................................................................................. 21
2.5 Exposure to step voltage ............................................................................................. 22
2.6 Step voltage circuit ..................................................................................................... 22
2.7 Basic shock situations ................................................................................................. 26
2.8 Typical situation of extended transferred potential .................................................... 27
2.9 Typical metal-to-metal touch situation in GIS............................................................ 27
2.10 Touch voltage limits for metal-to-metal contact and a typical range of enclosure
voltages to ground .................................................................................................... 29
3.1 Typical faults in GIS ................................................................................................... 41
3.2 Soil model ................................................................................................................... 48
3.3 Effects of moisture, temperature, and salt upon soil resistivity .................................. 50
3.4 Wenner four-pin method ............................................................................................. 53
3.5 Circuit diagram for three-pin or driven-ground rod method ....................................... 55
3.6 Short-time current loading capacity of concrete-encased ground electrodes ............. 64
3.7 Grid with encased vertical electrodes ......................................................................... 65
xiii
3.8 Fault within local substation; local neutral grounded ................................................. 69
3.9 Fault within local substation; local neutral grounded at remote location ................... 70
3.10 Fault in substation; system grounded at local substation and also at other points .... 70
3.11 Typical current division for a fault on high side of distribution substation .............. 71
4.1 Design procedure block diagram ................................................................................ 77
5.1 Cs versus hs................................................................................................................. 87
5.2 Square grid with 26 rods ............................................................................................. 88
5.3 Square grid with 38 rod............................................................................................... 93
5.4 Example of grid layout................................................................................................ 94
xiv
1
Chapter 1 - INTRODUCTION, DESCRIPTION OF PROBLEMS, PROJECT
LIMITATIONS AND GROUNDING TERMINOLOGIES
1.1 Introduction
This project’s materials and design concept are almost entirely derived from the
IEEE standard 80-2000. In all types of high voltage substation, is necessary to install a
system for effectively connecting all metallic structures and non-energized parts of the
power system equipment together and to the earth in order to limit to safe values any
potential differences between them. This system is generally referred to as the
“Grounding System” (Phan, 1990).
1.2 Problems’ Description
The potential differences might be the result of lightning discharges, ground
currents caused by fault conditions, switching or in-rush currents caused by normal
system operations. The passage of these currents through the soil and metallic
conductors causes high voltages which can be dangerous to human life, and can cause
damage, and malfunction of, system equipment.
The grounding system provides a means to safely discharge lightning strokes to
earth, reduces step and touch potentials to safe levels and confines dangerous soil
currents to inaccessible areas. It also allows the detection of ground fault currents by
protective relaying systems, provides low impedance paths through the earth for load
2
currents, and provides a common ground reference which assists in the coordination of
insulation throughout the system(Thomas & Pham, 1999), (Phan, 1990).
The grounding system is also utilized to shield control cables and other low
voltage wiring from the effects of electromagnetic interference (EMI) and capacitive
coupling by tending to reduce the voltages across the grid, assists in minimizing
voltages between different points along, and between, the low voltage cables used for
controls, communications, and auxiliary power.
1.3 Project Limitations
The most obvious limitation of this project is space since Hillsboro Central
station of the Tri-Met Portland Westside Light Rail is in the middle of the town, where
real state comes with high price and not all the properties owners would agree to sell.
Since space is limited, conductors with better conductivity could have been chosen
instead of the copper-clad steel wire of 30% conductivity. Another limiting factor is the
fault current. It would have been very beneficial if the total fault current could be
reduced which would decrease the ground potential rise and all gradients in proportion.
But, it is almost unrealistic to reduce the total the fault current and if done at the
expense of greater fault clearing time, the danger may be increased rather than
diminished (IEEE- Standards Board, 2000).
3
1.4 Grounding Terminologies
All the definitions in this project are sourced from IEEE standard 80-2000.
DC offset:Difference between the symmetrical current wave and the actual current wave
during a power system transient condition. Mathematically, the actual fault current can
be broken into two parts, a symmetrical alternating component and a unidirectional (dc)
component. The unidirectional component can be of either polarity, but will not change
polarity, and will decrease at some predetermined rate.
decrement factor: An adjustment factor used in conjunction with the symmetrical
ground fault current parameter in safety-oriented grounding calculations. It determines
the rms equivalent of the asymmetrical current wave for a given fault duration, tf,
accounting for the effect of initial dc offset and its attenuation during the fault.
enclosure currents: Currents that result from the voltages induced in the metallic
enclosure by the current(s) flowing in the enclosed conductor(s).
fault current division factor: A factor representing the inverse of a ratio of the
symmetrical fault current to that portion of the current that flows between the grounding
grid and surrounding earth.
NOTE—In reality, the current division factor would change during the fault duration,
based on the varying decay rates of the fault contributions and the sequence of
interrupting device operations. However, for the purposes of calculating the design
value of maximum grid current and symmetrical grid current per definitions of
symmetrical
4
grid current and maximum grid current, the ratio is assumed constant during the entire
duration of a given fault.
gas-insulated substation: A compact, multicomponent assembly, enclosed in a
grounded metallic housing in which the primary insulating medium is a gas, and that
normally consists of buses, switchgear, and associated equipment (subassemblies).
ground: A conducting connection, whether intentional or accidental, by which an
electric circuit or equipment is connected to the earth or to some conducting body of
relatively large extent that serves in place of the earth.
grounded: A system, circuit, or apparatus provided with a ground(s) for the purposes of
establishing a ground return circuit and for maintaining its potential at approximately
the potential of earth.
ground current: A current flowing into or out of the earth or its equivalent serving as a
ground.
ground electrode: A conductor imbedded in the earth and used for collecting ground
current from or dissipating ground current into the earth.
ground mat: A solid metallic plate or a system of closely spaced bare conductors that
are connected to and often placed in shallow depths above a ground grid or elsewhere at
the earth’s surface, in order to obtain an extra protective measure minimizing the danger
of the exposure to high step or touch voltages in a critical operating area or places that
are frequently used by people. Grounded metal gratings, placed on or above the soil
surface, or wire mesh placed directly under the surface material, are common forms of a
ground mat.
5
ground potential rise (GPR): The maximum electrical potential that a substation
grounding grid may attain relative to a distant grounding point assumed to be at the
potential of remote earth. This voltage, GPR, is equal to the maximum grid current
times the grid resistance.
NOTE—Under normal conditions, the grounded electrical equipment operates at near
zero ground potential. That is, the potential of a grounded neutral conductor is nearly
identical to the potential of remote earth. During a ground fault the portion of fault
current that is conducted by a substation grounding grid into the earth causes the rise of
the grid potential with respect to remote earth.
ground return circuit: A circuit in which the earth or an equivalent conducting body is
utilized to complete the circuit and allow current circulation from or to its current
source.
ground return circuit: A circuit in which the earth or an equivalent conducting body is
utilized to complete the circuit and allow current circulation from or to its current
source.
grounding grid: A system of horizontal ground electrodes that consists of a number of
interconnected, bare conductors buried in the earth, providing a common ground for
electrical devices or metallic structures, usually in one specific location.
NOTE—Grids buried horizontally near the earth’s surface are also effective in
controlling the surface potential gradients. A typical grid usually is supplemented by a
number of ground rods and may be further connected to auxiliary ground electrodes to
lower its resistance with respect to remote earth.
6
grounding system: Comprises all interconnected grounding facilities in a specific area.
maximum grid current: A design value of the maximum grid current.
mesh voltage: The maximum touch voltage within a mesh of a ground grid.
metal-to-metal touch voltage: The difference in potential between metallic objects or
structures within the substation site that may be bridged by direct hand-to-hand or handto-feet contact.
NOTE—The metal-to-metal touch voltage between metallic objects or structures
bonded to the ground grid is assumed to be negligible in conventional substations.
However, the metal-to-metal touch voltage between metallic objects or structures
bonded to the ground grid and metallic objects internal to the substation site, such as an
isolated fence, but not bonded to the ground grid may be substantial. In the case of a
gas-insulated substation (GIS), the metal-to-metal touch voltage between metallic
objects or structures bonded to the ground grid may be substantial because of internal
faults or induced currents in the enclosures.
In a conventional substation, the worst touch voltage is usually found to be the potential
difference between a hand and the feet at a point of maximum reach distance. However,
in the case of a metal-to-metal contact from hand-to-hand or from hand-to-feet, both
situations should be investigated for the possible worst reach conditions.
step voltage: The difference in surface potential experienced by a person bridging a
distance of 1 m with the feet without contacting any grounded object.
subtransient reactance: Reactance of a generator at the initiation of a fault. This
reactance is used in calculations of the initial symmetrical fault current. The current
7
continuously decreases, but it is assumed to be steady at this value as a first step, lasting
approximately 0.05 s after an applied fault.
surface material: A material installed over the soil consisting of, but not limited to, rock
or crushed stone, asphalt, or man-made materials. The surfacing material, depending on
the resistivity of the material, may significantly impact the body current for touch and
step voltages involving the person’s feet.
symmetrical grid current: That portion of the symmetrical ground fault current that
flows between the grounding grid and surrounding earth.
symmetrical ground fault current: The maximum ms value of symmetrical fault current
after the instant of a ground fault initiation. As such, it represents the rms value of the
symmetrical component in the first half-cycle of a current wave that develops after the
instant of fault at time zero.
touch voltage: The potential difference between the ground potential rise (GPR) and the
surface potential at the point where a person is standing while at the same time having a
hand in contact with a grounded structure.
X/R ratio: Ratio of the system reactance to resistance. It is indicative of the rate of
decay of any dc offset. A large X/R ratio corresponds to a large time constant and a slow
rate of decay.
8
Chapter 2 - THEORY AND COMPUTATIONAL PROCEDURES, AND HUMAN
FACTOR OF SUBSTATION GROUNDING
2.1 Safety in Grounding
Substation grounding system is concern with two main objectives:

To lay pathways for the electric currents to disseminate through the earth
under normal and fault conditions while maintaining equipment working
conditions and the continuity of service. It is called the intentional
ground and consists of ground electrodes concealed beneath the earth’s
surface.

To provide a safe mean for a person on the vicinity of grounded
facilities is not exposed to the danger of critical electric shock. This is
referred to as accidental ground which is temporary and happens when
an individual is exposed to a potential gradient in a grounded area.
Because an object is grounded doesn’t necessarily mean that it is safe to touch as
stated in the following passage from IEEE standard 80-2000,
“A low substation ground resistance is not, in itself, a guarantee of safety. There
is no simple relation between the resistance of the ground system as a whole and
the maximum shock current to which a person might be exposed. Therefore, a
substation of relatively low ground resistance may be dangerous, while another
substation with very high resistance may be safe or can be made safe by careful
design.”
9
A low substation ground resistance is not, in itself, a guarantee of safety. There
is no simple relation between the resistance of the ground system as a whole and the
maximum shock current to which a person might be exposed. Therefore, a substation of
relatively low ground resistance may be dangerous, while another substation with very
high resistance may be safe or can be made safe by careful design. For instance, if a
substation is supplied from an overhead line with no shield or neutral wire, a low grid
resistance is important. Most or all of the total ground fault current enters the earth
causing an often steep rise of the local ground potential as shown in Figure 2.1(a)
(IEEE- Standards Board, 2000). If a shield wire, neutral wire, gas-insulated bus, or
underground cable feeder, etc., is used, a part of the fault current returns through this
metallic path directly to the source. Since this metallic link provides a low impedance
parallel path to the return circuit, the rise of local ground potential is ultimately of lesser
magnitude as shown in Figure 2.1(b) (IEEE- Standards Board, 2000). In either case, the
effect of that portion of fault current that enters the earth within the substation area
should be further analyzed. If the geometry, location of ground electrodes, local soil
characteristics, and other factors contribute to an excessive potential gradient at the
earth’s surface, the grounding system may be inadequate despite its capacity to carry the
fault current in magnitudes and durations permitted by protective relays (IEEEStandards Board, 2000).
10
Ie
IF
IF
IF
IF
+
I F = IG
I F = IG
Rg
Ie
IG
IG
IG
Ie
Rg
IG
(a)
(b)
Figure 2.1 Equipotential countours of a typical grounding grid with and without
Ground rods
2.2 Conditions of Danger
Potential gradients are produced and within around a substation with the flow of
current to earth during typical ground fault conditions. A well designed ground system
can prevent the maximum potential gradient developed during ground fault conditions
to cause considerable harm to a person in the substation area.
There are situations cited in the IEEE standard 80-2000 as conditions that lead to
accidental electric shock listed below:
a) Relatively high fault current to ground in relation to the area of ground system
and its resistance to remote earth.
b ) Soil resistivity and distribution of ground currents such that high potential
gradients may occur at points at the earth’s surface.
11
c) Presence of an individual at such a point, time, and position that the body is
bridging two points of high potential difference.
d) Absence of sufficient contact resistance or other series resistance to limit
current through the body to a safe value under circumstances a) through c).
e) Duration of the fault and body contact, and hence, of the flow of current
through a human body for a sufficient time to cause harm at the given current intensity.
2.3 Range of Tolerable Current
The effect of conduction of electric current on human body parts depends on the
duration, magnitude, and frequency of this current. The body resistance considered is
usually between two extremities, either from one hand to both feet of from one foot to
the other one. The most critical part of the body exposed to electric shock is the heart.
Currents of higher magnitudes can cause the heart to stop muscular contraction, a
condition called "ventricular fibrillation (EDSA Micro Corporation, 2008).
2.4 Effects of Frequency, Duration, and Magnitude
Effects can range from a barely perceptible tingle to severe burns and immediate
cardiac arrest. Although it is not known the exact injuries that result from any given
amperage, the following Table 2.1(OSHA) demonstrates this general relationship for a
60 cycle, hand-to-foot shock of one second's duration:
12
Current level,
Probable Effect on Human Body
mA
Perception level. Slight tingling sensation in the hands or
1
fingertips. Still dangerous under certain conditions.
1-6
Slight shock felt; not painful but disturbing. Average
individual can let go. However, strong involuntary reactions to
shocks in this range may lead to injuries. Dalziel’s classic
experiment with 28 women and 134 men provides data
indicating an average let-go current of 10.5mA for women and
16mA for men, 6mA and 9mA as the respective threshold
values.
6 to 16
Painful shock, begin to lose muscular control. Commonly
referred to as freezing current or "let go" range [am1]. These
effects are not permanent and disappear when the current is
interrupted, unless the contraction is very severe and breathing
is stopped for minutes rather than seconds.
17 to 99
Extreme pain, respiratory arrest, severe muscular contractions
or inhibition of respiration. Individual cannot let go. A person
trained in cardiopulmonary resuscitation should administer
CPR until the victim can be treated at a medical facility [am1].
Death is possible.
100 to 2000
Ventricular fibrillation (unever, uncoordinated pumping of the
heart). Muscular contraction and nerve damage begins to
occur. Death is likely.
> 2000
Cardiac arrest, internal organ damage, and severe burns. Death
is probable
Table 2.1Effect of Frequency, Duration and Magnitude
13
2.5 Shock and Current Path Through the Body (Gonen, 2009)
In grounding design the main consideration is the threshold value. Below is an
equation provided by IEEE Std. 80-2000 to find the nonfibrillating current of magnitude
IB at durations ranging from 0.03 to 3.0 seconds is related to the energy absorbed by the
𝑆𝐵 = (𝐼𝐵 )2 × 𝑡𝑠
body.
(2.1)
where:
IB is the rms magnitude of the current through the body in A
tS is the duration of the current exposure in s
SB is the empirical constant related to the electric shock energy tolerated by a
certain percent of a given population
For 99.5% of population, the 60 Hz minimum required body current, IB leading to
possible fatality through ventricular fibrillation can be expressed as
𝐼𝐵 =
𝐼𝐵 =
0.116
√𝑡 𝑠
0.157
√𝑡 𝑠
𝐴 for 50 kg body weight
(2.2a)
𝐴 for 70 kg body weight
(2.2b)
where ts is in seconds in the range from approximately 8.3 ms to 5 ms.
Experiments have shown that the body can tolerate much more current flowing from
one leg to the other than it can when current flows from one hand to the legs. Treating
the foot as a circular plate electrode gives an approximate resistance of 3𝜌s, where 𝜌s is
the soil resistivity in Ω/meters. The resistance of the body itself is usually about 23 kΩ
hand-to-hand or 1.1kΩ hand-to-foot. But IEEE Std. 80-2000 recommends the use of
14
1kΩ as a reasonable approximation for body resistance. Therefore, the total branch
resistance for hand-to-foot currents can be expressed as
𝑅𝐸 = 1000 + 1.5𝜌𝑠 Ω
for touch voltage
(2.3a)
for step voltage
(2.3b)
and, for foot-to-foot currents,
𝑅𝐸 = 1000 + 6𝜌𝑠 Ω
If the surface of the soil is covered with a layer of crushed rock or some other highresistivity material, its resistivity should be used in equations 2.2 and 2.3. Thus, for a
person with body weight of 50 or 70kg, the maximum allowable or tolerable touch
voltages can be expressed as
𝑉𝑡𝑜𝑢𝑐ℎ50 = (1000 + 1.5𝐶𝑠 ∙ 𝜌𝑠 )
0.116
𝑉𝑡𝑜𝑢𝑐ℎ70 = (1000 + 1.5𝐶𝑠 ∙ 𝜌𝑠 )
0.157
√𝑡 𝑠
𝑉 for 50kg body weight
(2.4a)
and
√𝑡 𝑠
𝑉 for 70kg body weight
(2.4b)
Note that the above equations are applicable only in the event that no protective surface
layer is used. Hence for the metal-to-metal touch in V, equation 2.4a and b become
𝑉𝑛𝑜𝑛−𝑡𝑜𝑢𝑐ℎ50 =
116
√𝑡 𝑠
𝑉
for 50kg body weight
(2.4c)
𝑉
for 70kg body weight
(2.4d)
and
𝑉𝑛𝑜𝑛−𝑡𝑜𝑢𝑐ℎ70 =
157
√𝑡 𝑠
The maximum allowable or tolerable step voltages, for a person with body weight of
50kg or 70kg, are given respectively, as
15
𝑉𝑆𝑡𝑒𝑝50 = (1000 + 6𝜌𝑠 )
0.116
√𝑡 𝑠
𝑉 for 50kg body weight (2.5a)
and
𝑉𝑆𝑡𝑒𝑝70 = (1000 + 6𝜌𝑠 )
0.157
√𝑡 𝑠
𝑉 for 70kg body weight (2.5b)
Again, the above equations are applicable only in the event that no protection
surface layer is used. For metal-to-metal, use 𝜌s = 0. There are more detailed
applications described in IEEE Std. 80-2000. Also, it is important to note that in using
the above equations, it is assumed that they are applicable to 99.5% of the population
but of course there are always exceptions.
Also, the touch voltage limit can be expressed as
𝑉𝑡𝑜𝑢𝑐ℎ = (𝑅𝐵 +
𝑅𝑓
2
∙ 𝐼𝐵 )
(2.6)
where:
RB is the resistance of the human body in Ω,
Rf is ground resistance of the one foot (with presence of the substation
grounding system ignored in Ω, IB is the rms magnitude of the current
through the body in A.
16
Ground Type
Resistivity, 𝜌s
Seawater
.01 - 1.0
Wet organic soil
10
Moist soil (average earth)
100
Dry soil
1000
Bedrock
104
Pure slate
107
Sandstone
109
Crushed rock
1.5 x 108
Table 2.2 Resistivity of Different Soils (Gonen, 2007)
As an example, suppose a human body is part of a 60 Hz electric power circuit
for about 0.49s and that the soil type is average earth. Based on the IEEE Std. 80-2000,
determine the following (Gonen, 2009):
a) Tolerable touch potential,
b) Tolerable step potential,
c) Tolerable (or limit) touch voltage for metal-to-metal contact if the person is
50kg,
d) Tolerable (or limit) touch voltage for metal-to-metal contact if the person is
70kg,
Solution:
a) Using equation (2.4a),
17
𝑉𝑡𝑜𝑢𝑐ℎ50 = (1000 + 1.5𝐶𝑠 ∙ 𝜌𝑠 )
0.116
𝑉𝑡𝑜𝑢𝑐ℎ50 = (1000 + 1.5 × 100)
√𝑡𝑠
0.116
√𝑡𝑠
𝑉
= 191 𝑉
b) Using equation (2.5a),
𝑉𝑆𝑡𝑒𝑝50 = (1000 + 6𝜌𝑠 )
0.116
√𝑡𝑠
𝑉𝑆𝑡𝑒𝑝50 = (1000 + 6 × 100)
𝑉
0.116
√0.49
= 265 𝑉
c) Since 𝜌s = 0, for 50kg body weight
𝑉𝑛𝑜𝑛−𝑡𝑜𝑢𝑐ℎ50 =
116
√𝑡𝑠
𝑉=
116
√0.49
= 165.7 𝑉
for 50 kg body weight
d) Since 𝜌s = 0,
𝑉𝑛𝑜𝑛−𝑡𝑜𝑢𝑐ℎ70 =
157
√𝑡𝑠
𝑉=
157
√0.49
= 224.3 𝑉for 70kg body weight
2.6 Reclosing
Reclosure after a ground fault is common in modern operating practice. In such
circumstances, a person might be subjected to the first shock without permanent injury.
Next, a single instantaneous automatic reclosure could result in a second shock, initiated
within less than 0.33 s from the start of the first. It is this second shock, occurring after
a relatively short interval of time before the person has recovered, that might cause a
serious accident. With manual reclosure, the possibility of exposure to a second shock is
reduced because the reclosing time interval may be substantially greater.
18
The cumulative effect of two or more closely spaced shocks has not been thoroughly
evaluated, but a reasonable allowance can be made by using the sum of individual
shock durations as the time of a single exposure.
2.6.1 Accidental Circuit Equivalents
Using the value of tolerable body current established by either Equation 2.5a or
Equation 2.5b and the appropriate circuit constants, it is possible to determine the
tolerable voltage between any two points of contact.
The following notations are used for the accidental circuit equivalent shown in Figure
2.2 (IEEE- Standards Board, 2000):
where:
IB is the body current (body is part of the accidental circuit) in A,
RA is the total effective resistance of the accidental circuit in Ω,
VA is the total effective voltage of the accidental circuit (touch or step) in V.
19
Z(system)
U
If
Ig
Ib
F
`
Station Grid
Figure 2.2 Exposure to touch voltage
Ib is the body current (body is part of the accidental circuit) in A
RA is the total effective resistance of the accidental circuit in Ω
VA is the total effective voltage of the accidental circuit (touch or step) in V
The tolerable body current, IB, defined by Equation 2.5a or Equation 2.5b, is
used to define the tolerable total effective voltage of the accidental circuit (touch or step
voltage): the tolerable total effective voltage of the accidental circuit is that voltage that
will cause the flow of a body current, Ib, equal to the tolerable body current, IB.
Figure 2.2 shows the fault current If being discharged to the ground by the grounding
system of the substation and a person touching a grounded metallic structure at H.
Various impedances in the circuit are shown in Figure 2.3 (IEEE- Standards Board,
2000). Terminal H is a point in the system at the same potential as the grid into which
the fault current flows and terminal F is the small area on the surface of the earth that is
20
in contact with the person’s two feet. The current, Ib flows from H through the body of
the person to the ground at F. The Thevenin theorem allows us to represent this two
terminal (H, F) network of Figure 2.3 bythe circuit shown in Figure 2.4 (IEEEStandards Board, 2000).
The Thevenin voltage VTh is the voltage between terminals H and F when the
person is not present. The Thevenin impedance ZTh is the impedance of the system as
seen from points H and F with voltage sources of the system short circuited. The current
Ib through the body of a person coming in contact with H and F is given by
𝐼𝐵 =
𝑉𝑇ℎ
(2.7)
𝑍𝑇ℎ +𝑅𝐵
Terminal H
Z sys
Terminal F
Grid
Rm
Rg
Rf /2
True Ground
Figure 2.3 Impedance to touch voltage
21
Terminal H
VTh
ZTh
R B = Body Resistance
VTh = Touch voltage
ZTh = Rf /2
Terminal F
Figure 2.4 Touch voltage circuit
Figure 2.5 (IEEE- Standards Board, 2000) shows the fault current If being
discharged to the ground by the grounding system of the substation. The current, Ib,
flows from one foot F1 through the body of the person to the other foot, F2. Terminals
F1 and F2 are the areas on the surface of the earth that are in contact with the two feet,
respectively. The Thevenin theorem allows us to represent this two-terminal (F1, F2)
network in Figure 2.6 (IEEE- Standards Board, 2000). The Thevenin voltage VTh is the
voltage between terminals F1 and F2 when the person is not present. The Thevenin
impedance ZTh is the impedance of the system as seen from the terminals F1 and F2 with
the voltage sources of the system short circuited. The current Ib through the body of a
person is given by Equation 2.7. The Thevenin equivalent impedance, ZTh is computable
with a number of methods.
22
Z(system)
U
If
Ig
Ib
F1 F2
`
Station Grid
Figure 2.5 Exposure to step voltage
Terminal H
VTh
ZTh
R B = Body Resistance
Terminal F
VTh = Step voltage
Figure 2.6 Step voltage circuit
In this guide, the following conservative formulas for the Thevenin equivalent
impedance are used.
For touch voltage accidental circuit
23
𝑅𝑓
𝑍𝑇ℎ =
(2.8)
2
And for the step voltage accidental circuit
𝑍𝑇ℎ = 2𝑅𝑓
(2.9)
where:
Rf is the ground resistance of one foot (with presence of the substation
grounding system ignored) in Ω,
For the purpose of circuit analysis, the human foot is usually represented as a
conducting metallic disc and the contact resistance of shoes, socks, etc., is neglected.
The ground resistance in ohms of a metallic disc of radius b(m) on the surface of a
homogeneous earth of resistivity 𝜌 (Ω.m) is given by Laurent
𝑅𝑓 =
𝜌
4𝑏
(2.10)
Traditionally, the metallic disc representing the foot is taken as a circular plate with a
radius of 0.08 m. With only slight approximation, equations for ZTh can be obtained in
numerical form and expressed in terms of 𝜌 as follows:
For touch voltage accidental circuit
𝑍𝑇ℎ = 1.5𝜌
And for step voltage accidental circuit
(2.11)
24
𝑍𝑇ℎ = 6.0𝜌
(2.12)
Equation 2.11 and Equation 2.12 are conservative in the sense that they underestimate
the Thevenin equivalent impedance and, therefore, will result in higher body currents.
The permissible total equivalent voltage (i.e., tolerable touch and step voltage), using
Equation 2.11 and Equation 2.12, is
𝐸𝑡𝑜𝑢𝑐ℎ = 𝐼𝐸 (𝑅𝐸 + 1.5 ∙ 𝜌)
(2.13)
and
𝐸𝑠𝑡𝑒𝑝 = 𝐼𝐵 (𝑅𝐵 + 6.0 ∙ 𝜌)
(2.14)
2.6.2 Typical Shock Situations
Figure 2.7 (IEEE- Standards Board, 2000) and Figure 2.8 (IEEE- Standards
Board, 2000) show five basic situations involving a person and grounded facilities
during a fault. For a foot-to-foot contact, the accidental circuit equivalent is that of
Figure 2.5, and its driving voltage U is equal to Es or Vs (step voltage). For the three
examples of hand-to-feet contact Figure 2.7 applies, and U is equal to Et or Vt (touch
voltage), Em or Vm (mesh voltage), or Etrrd or Vtrrd (transferred voltage), respectively.
The accidental circuit involving metal-to-metal contact, either hand-to-hand or hand-tofeet, is shown in Figure 2.9 (IEEE- Standards Board, 2000) where U is equal to the
metal-to-metal touch voltage, Emm or Vmm.
During a fault, the earth conducts currents that emanate from the grid and other
25
permanent ground electrodes buried below the earth’s surface. The resulting potential
gradients have a primary effect on the value of U.
In the case of conventional substations, the typical case of metal-to-metal touch voltage
occurs when metallic objects or structures within the substation site are not bonded to
the ground grid. Objects such as pipes, rails, or fences that are located within or near the
substation ground grid area, and not bonded to the ground grid, meet this criteria.
Substantial metal-to-metal touch voltages may be present when a person standing on or
touching a grounded object or structure comes into contact with a metallic object or
structure within the substation site that is not bonded to the ground grid. Calculation of
the actual metal-to-metal touch voltage is complex. In practice, hazards resulting from
metal-to-metal contact may best be avoided by bonding potential danger points to the
substation grid.
Typically, the case of transferred voltage occurs when a person standing within
the substation area touches a conductor grounded at a remote point, or a person standing
at a remote point touches a conductor connected to the substation grounding grid.
During fault conditions, the resulting potential to ground may equal or exceed the full
GPR of a grounding grid discharging the fault current, rather than the fraction of this
total voltage encountered in the ordinary touch contact situations in Figure 2.8. In fact,
as discussed in Clause 17, the transferred voltage may exceed the sum of the GPRs of
both substations, due to induced volt- ages on communication circuits, static or neutral
wires, pipes, etc. It is impractical, and often impossible, to design a ground grid based
26
on the touch voltage caused by the external transferred voltages. Hazards from these
external transferred voltages are best avoided by using isolating or neutralizing devices
and by treating and clearly labeling these circuits, pipes, etc., as being equivalent to
energized lines (Schaerer, 2011).
ME
UC
TO
E
AG
LT
VO
E
AG
LT
VO
E
AG
LT
VO
SH
H
EP
ST
L
TA
ME E
O- TAG
L-T VOL
TA
ME U C H
TO
1
Et
METER
Emm
Em
SURFACE
POTENTIAL
PROFILE
Etrrd ≈ GPR
Es
REMOTE EARTH
REMOTE EARTH
Figure 2.7 Basic Shock Situations
27
IF
C o n d u c tin g p a th
b e tw e e n s u b s ta tio n s
S u b s ta tio n 2
S u b s ta tio n 1
G P R S T A T IO N 1
E
trrd
S u rfa c e P o te n tia l P ro file
Z e ro P o te n tia l
G P R S T A T IO N 2
Figure 2.8 Typical situation of extended transferred potential
E to (A 1 – A 2 )
E to (A – B )
A1
A2
A
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
B
X
X
X
X
Figure 2.9 Typical metal-to-metal touch situation in GIS
28
2.6.3 Typical shock situations for Gas-Insulated Substations, (GIS)
In the grounding analysis of GIS, the touch voltage considerations present
several unique problems. Unlike conventional facilities, the GIS equipment features a
metal sheath enclosing gas-insulated switchgear and inner high-voltage buses. Each bus
is completely contained within its enclosure and the enclosures are grounded. Because a
voltage is induced in the outer sheath whenever a current flows in the coaxial busbar,
certain parts of the enclosure might be at different potentials with respect to the
substation ground. To evaluate the maximum voltage occurring on the bus enclosure
during a fault, it is necessary to determine the inductance of the outer sheath to ground,
the inductance of the inner conductor, and the mutual inductances for a given phase
configuration of individual buses.
A person touching the outer sheath of a GIS might be exposed to voltages
resulting from two basic fault conditions:
a) An internal fault within the gas-insulated bus system, such as a flashover between
the bus conductor and the inner wall of the enclosure.
b) A fault external to the GIS in which a fault current flows through the GIS bus and
induces currents in the enclosures.
Because the person may stand on a grounded metal grating and the accidental
circuit may involve a hand-to- hand and hand-to-feet current path, the analysis of GIS
grounding necessitates consideration of metal-to- metal touch voltage in Figure 2.9.
29
Figure 2.10 Touch voltage limits for metal-to-metal contact and a typical range of
enclosure voltages to ground
Most GIS manufacturers consider the enclosure properly designed and
adequately grounded if the potential difference between individual enclosures, and the
potential difference between an enclosure and other grounded structures, does not
exceed 65–130 V during a fault. The metal-to-metal touch voltage equations, equation
2.4c and equation 2.4d, reveal that this voltage range corresponds to fault times ranging
from 0.8 s to 3.2 s if a 50 kg criterion is used, and ranging from 1.46 s to 5.8 s for the
assumption of a 70 kg body. This relationship is, however, better perceived in the
graphical form of Figure 2.10 (IEEE- Standards Board, 2000), which also helps to grasp
the related problem of sufficient safety margins.
The fault conditions and the corresponding circuit equivalents for determining or
verifying the critical safety design parameters of GIS grounding is detailed in Clause
30
10.
2.6.4 Effect of Sustained Ground Gurrents
After the safe step and touch voltage limits are established, the grounding
system, can then be designed based on the available fault current and overall clearing
time. The designer should also consider sustained low- level (below setting of
protective relays) fault magnitudes that may be above the let-go current threshold. Some
sustained faults above the let-go current, but below the fibrillation threshold, may cause
asphyxiation from prolonged contraction of the chest muscles. However, it would not be
practical to design against lesser shocks that are painful, but cause no permanent injury.
31
Chapter 3 – SUBSTATION GROUNDING DESIGN PARAMETERS
3.1 Introduction
This section details the principal design considerations of substation grounding
system, and the special considerations for the gas insulated substation or GIS. The
process of conductors and connectors’ selection, the soil characteristics, structure, and
model selection are described. And to end the chapter, the ground resistance is
evaluated with the steps to determine the maximum grid current is explained.
3.2 Design Considerations
The basic function of a grounding system is to limit the effect of ground
potential gradients to such voltage and current levels that will not endanger the safety of
personnel and equipment under normal and fault conditions while maintaining service
continuity (Phan, 1990), (Thomas & Pham, 1999). As indicated in section 9.2 of the
IEEE standard 80-2000, the prevailing concept that represents the practice of most
utilities both in the United States and in other countries in grounding system design rely
on the system of ground electrodes in the form of a grid of horizontally buried
conductors, supplemented by a number of vertical ground rods connected to the grid.
3.2.1 Importance and Benefit of the Ground Grid
There are benefits in using combined vertical rods and horizontal conductors
system in substation grounding system which makes a safe substation for people and the
32
equipment. A single electrode is by itself inadequate in providing a safe grounding
system, but when several electrodes are connected to each other and to all equipment
neutrals, frames, and structures that are to be grounded, the result is grid arrangement of
ground electrodes. This network alone may represent an excellent grounding system, if
the connecting links happen to be buried in a soil having good conductivity.
Ground rods are very handy in cases where the magnitude of the current dissipated
into the earth is high since it is seldom impossible to install a grid with resistance so low
as to assure that the rise of a ground potential will not generate surface gradients unsafe
for human contact. This hazard can only be locally eliminated by control of the
potentials through the entire area. Sufficiently long ground rods will stabilize the
performance of horizontal grid conductors which are most effective in reducing the
danger of high step and touch voltages on the earth’s surface, provided that the grid is
installed in a shallow depth [usually 0.3-0.5 m below grade (IEEE- Standards Board,
2000). This is very significant for many installations since freezing or drying of upper
soil layers could vary the soil resistivity with seasons, but the resistivity of lower soil
layers remains nearly stable. For some gas insulated substations (GIS) and space-limited
installations where two-layer or multilayer soil is encountered, rods penetrating the
lower resistivity soil are far more effective in dissipating fault currents. The verticals
rods will considerably moderate the steep increase of the surface gradient near the
peripheral meshes if they are installed primarily along the grid perimeter in high-to-low
or uniform soil.
33
3.2.2 Conceptual Analysis
It is important to note before diving into the design the aspect of the substation
grounding that most grounding systems utilize two groups of ground electrodes. One
specially designed for grounding purposes which include grounding grids, counterpoise
conductors, ground rods and ground wells. And the secondary called auxiliary ground
electrodes are underground metal structures installed for purposes other than grounding.
The main starting point of a grid system design starts with the site visit to inspect
the substation layout plan showing all the major equipment and structures. This help to
establish the basic ideas and concepts of the design. In the IEEE standard 80-2000, the
following points are sited to serve as guidelines for starting a typical grounding grid
design:
a) The perimeter of the area as much as practical should be surrounded by a
continuous conductor loop. The conductors within the loop should be laid in
parallel lines along the structures or rows of equipment to provide for short
ground connections.
b) Copper 4/0 bare conductors buried 0.3-0.5 m below grade, spaced 3-7 m apart in
a grid pattern may be included for a typical grid system design. Ground rods
should be installed at major equipment and in multilayer or high resistivity soils;
it be might be useful to use longer rods or rods installed at additional junction
points.
34
c) The grid system should be extended over the entire substation switchyard and
beyond the fence line is possible. And the ratio of the sides of the grid meshes
usually is from 1:1 to 1:3 unless a precise analysis warrants more extreme
values.
3.2.3 Non Ideal Design Situations
Special solutions are needed for some areas where the soil resistivity is rather
high or the substation space is at a premium in which cases it may not be possible to
achieve low impedance grounding system by spreading the grid electrodes over a large
area. Some of these situations may be encountered in many GIS installations and
industrial substations which occupy only a fraction of the land area used for
conventional equipment making the control of the surface gradients difficult.
To overcome these constrains, the following remedies are given in the IEEE
standard 80-2000:
a) connection(s) of remote ground grid(s) and adjacent grounding facilities system
utilizing separate installations in buildings, underground vaults, etc. A careful
consideration should be given to the use of remote ground electrodes of
transferred potentials, surge arrester locations and other critical points.
b) Use of deep-driven ground rods and drilled ground wells.
c) The soil should be treated with various additives in conjunction with ground
rods and interconnected conductors.
35
d) Wire mats should be used in combination with surface material to equalize the
gradient field near the surface.
e) Connection of static wires and neutrals to the ground should be used if feasible
to lower the overall resistance of a ground system. Frequently with careful
evaluation metallic objects are used on the site that qualify for and can serve as
auxiliary ground electrodes, or as ground ties to other systems.
f) A satellite grid may be used nearby if feasible with the deposit of low resistivity
material of sufficient volume. This satellite grid, when sufficiently connected to
the main grid, will lower the overall resistance. Thus, the ground potential rise
of the grounding grid.
3.2.4 Grid’s Connections
The connectors between the following materials should be made of conductors
of adequate ampacity and mechanical strength: all ground electrodes, all above-ground
conductive metal parts that might accidentally become energized such as gas-insulated
switchgear, all fault current sources and where appropriate, machine neutrals and power
circuits. Metal parts that have become energized should be bonded together with
conductive metal parts that might be at a different potential.
All accessible ground leads should be inspected periodically, soldered
connections should be avoided because of the possibility of failure under high fault
currents, and also paint films that might otherwise introduce a highly resistive
connection should be removed. Suitable joint compound should be applied or other
36
effective means. Equal division of currents should not be assumed between multiple
ground leads at cross-connections or similar junction points. Facilities that supply or
carry a high current should be connected to the grid with more than one ground leads
run in opposite directions to eliminate common mode failure.
3.3 Gas Insulated Substation Feature
The same low-impedance grounding and magnitude of ground fault current required
for conventional substations are required for gas insulated-substations. But GIS
installation occupies 10-25% less land area than required for conventional equipment
which makes it difficult to obtain adequate grounding solely by conventional methods.
Thus, particular attention should be given to the bonding of the metallic enclosures of
the GIS assembly to ensure induced currents of significant magnitude are confined to
specific paths.
The following transients may have to be considered in in some cases in the overall
grounding design of gas insulated-substations because of their compact nature and short
distances: electrical breakdown in the insulating gas either across the contacts of
switching device during operation or in a fault that generates very high frequency
transients that can couple onto the grounding system. These transients may cause high
magnitude, short duration ground rise and are also the source of electromagnetic
interference or EMI.
37
3.3.1 Gas Installed-Substation Enclosures
The bus enclosure impedance which governs the circulation of induced currents
determines its shielding effectiveness. The magnitude and direction of the enclosure
current is influenced by the size of the enclosure and the phase spacing between the
buses, as well as by the method of interconnecting the enclosures since each phase has
its own enclosure. There are two types of enclosures continuous and non-continuous
which is not currently used by the industry. The continuous-type enclosures provide a
return
path to induced currents to ensure effective external shielding of the field internal to the
enclosure, but under asymmetrical faults, the DC component causes an external voltage
drop due to enclosure resistance.
The best solution to minimize hazardous touch and step voltages within the GIS
area is through frequent bonding and grounding of GIS enclosures. The use of
conductive platforms (ground mats) that are connected to GIS structures and ground are
additional measures to minimize hazardous touch and step voltages within the GIS area.
3.3.2 Special Aspects of GIS Grounding
Most of the times there have to be collaboration between the gas installed
substation manufacturer and user since the manufacturer defines what constitutes the
main ground bus of the GIS and specifies what is required of the user for connecting the
GIS assembly to the substation ground. If the main ground bus consists of system of
interconnections between the GIS components and structures, and no separate bus bar is
38
furnished, ample documentation is necessary to assure that none of the proposed
connections from the main ground bus to the grounding grid will not interfere with the
required enclosure current path or any other operational feature of the GIS design.
Information on the sources of fault current and the expected magnitudes and durations
is provided by the user who should assist the GIS manufacturer in reviewing all
proposed grounding provisions to assure proper interfacing with existing structures.
Special attention should be paid to those portions of the GIS grounding system
that include discontinuities, or where the design requires an abrupt change in the pattern
of ground electrodes the earth path of ground currents is strongly affected by the
relative position of conductive objects in the ground. To prevent circulating currents in
the circuit breaker and transformer tank steel, special care is needed in the proximity of
discontinuities in enclosure grounding paths at the transformer connections to GIS and
at the interface points to conventional switchgear. Excessive currents should be
prevented from being induced into adjacent frames, structures, or reinforcing steel, and
prevent the establishment of current loops via other substation equipment, such as
transformers or separate switchgear.
3.3.3 Touch Voltage in Gas Insulated Substation
Gas insulated substation user have to establish that the entire installation is safe
since the GIS manufacturer generally designs the equipment to meet the constructions
standard established by the user. In the design of the GIS, the circulating currents
generated in the enclosures during a fault should also be taken into account, where these
39
currents will circulate, and to what degree both the user and the manufacturer prefer
these currents to circulate. This is against the general wisdom that a large ground
connection equals a good grounding practice.
In the continuous enclosure design, the enclosure currents include some
structural members of the GIS frame and the enclosures themselves. Hence because of
the size of some of the structures that are comparable to that of the grounding straps that
connect the GIS assembly to a ground grid, the following questions need to be asked as
stated in section 10.8 of the IEEE standard 80-2000
a) If the currents divide and flow via all available metallic paths, what ratio is to
be expected between the currents circulating within the GIS assembly and those
circulating via a ground connection?
b) How much current circulating via a ground connection loop is too much?
c) Should the GIS be designed to be safe if no circulating current would circulate
via ground connection?
d) And finally, how much ground is needed for the best balance between
operational and safety related requirements?
To this day, there no one answer that fit all, some manufacturers prefer to
supply a special ground bus as part of the GIS package with indicated ground
connections points; while others let the user complete the grounding.
The fault current of concern range from hundreds to thousands of amperes, the
goal is to limit the body current to some value in a milliampere range. It should be
40
assumed that the existing full potential difference prior to a contact would not change
while forcing the current through an alternate path including the human body. Then the
case of a person touching the GIS sheath metal can be reduced to the problem of finding
the voltage drop between two points of contact along one or between two enclosures
and a common ground. Only a minor modification of the application criterion of
equations 2.5a and 2.5b is required in order to take into account the maximum inductive
voltage drop occurring within the GIS assembly for the hand-to-feet contact made by a
person standing a nonmetallic surface.
The touch voltage criterion for GIS is:
2
√𝐸𝑡2 + 𝐸𝑡𝑜
𝑚𝑎𝑥 < 𝐸𝑡𝑜𝑢𝑐ℎ
(3.1)
𝐸𝑡 is the maximum touch voltage, as determined for the point underneath a person’s feet
′
𝐸𝑡𝑜
𝑚𝑎𝑥 is the (predominantly inductive) maximum value of metal-to-metal voltage
difference on and between GIS enclosures, or between these enclosures and the
supporting structures, including any horizontal or vertical members for which the GIS
assembly is designed.
In reality as shown in Figure 3.1, a multiplicity of return paths and considerable
cross-coupling occurs which makes it sometimes difficult the calculation of
longitudinally induced currents and for some remote external faults outright unpractical
(IEEE- Standards Board, 2000).
41
C
A
B
I1
R
(A) INTERNAL FAULT
(B) CLOSE EXTERNAL FAULT
(C) REMOTE EXTERNAL FAULT
Figure 3.1 Typical faults in GIS
3.4 Conductors and Connectors
The materials conductors and connectors are made of and their selection is of
great importance in substation grounding. Conductors and connectors have to be strong
enough to withstand maximum allowable temperature limit and mechanical forces
caused by the electromagnetic forces of the maximum fault current regardless of the
fault duration or the adverse temperature. They must be corrosion resistant and have
good current carrying capacity. And they should have an excellent electrical
conductivity so they will not contribute substantially to local voltage differences.
42
3.4.1 Conductors
A common material used in substation grounding is copper. Copper conductors
have very good electrical conductivity and the advantage of being resistant to most
underground corrosion because they are cathodic with respect to most other metals that
are likely to be buried in the vicinity (IEEE- Standards Board, 2000).
Where theft is a problem, copper-clad steel is used most the time for
underground rods and occasionally for grounding grids. The use of copper and to a
lesser degree copper-clad steel with adequate size assures that the integrity of the
underground network will be maintained for years provided the soil conditions are not
corrosive.
Aluminum is used less often for ground grids because aluminum may corrode in
certain soils. A corroded aluminum material is nonconductive for all practical
grounding purposes. Also, it may be a problem under certain conditions the gradual
corrosion caused by alternating currents. Hence, caution and care should be applied in
using aluminum in substation grounding. However unlike steel or other materials,
aluminum is anodic to many metals and would sacrifice itself to protect other materials
against corrosion in the presence of an electrolyte. Thus, high purity electric conductor
grades are recommended instead of alloys if aluminum is used.
The use of steel materials for ground grid and rods requires attention be paid to
the corrosion factor. In a typical steel grounding systems, the combination of cathodic
protection and the use of galvanized or corrosion resistant steel are applied.
43
There other considerations cited on pages 40 – 41 of IEEE standard 80-2000
details.
3.4.2 The Sizing Factors of Conductors
3.4.2.1 Symmetrical Currents
Symmetrical current here means there is no dc offset in the fault current. From
equations 3.2 through 3.4, it can be obtained the required conductor size as function of
conductor current, or the short time temperature rise in a ground conductor. The
ampacity of any conductor for which the material constants are known, or can be
deduced by calculation is evaluated by these equations. Material constants of the most
commonly used materials are listed in Table 3.1(IEEE- Standards Board, 2000).
𝑇𝐶𝐴𝑃.10−4
𝐼 = 𝐴𝑚𝑚2 √(
𝑡𝑐 𝛼𝑟 𝜌𝑟
𝐾 +𝑇
) 𝑙𝑛 ( 𝐾𝑜 +𝑇𝑚 )
𝑜
(3.2)
𝑎
Please go the variables section for the definition of the above variables.
For conductors whose size are given in kcmils (mm2 x 1.974 = kcmils), equation (m2)
becomes.
𝑇𝐶𝐴𝑃
𝐼 = 5.07. 𝐴𝑘𝑐𝑚𝑖𝑙 √(𝑡
𝑐 𝛼𝑟 𝜌𝑟
𝐾 +𝑇
) 𝑙𝑛 ( 𝐾𝑜 +𝑇𝑚)
𝑜
𝑎
(3.3)
A more simplified version of the conductor size as a function of the conductor current is
given below.
𝐴𝑘𝑐𝑚𝑖𝑙 = 𝐼. 𝐾𝑓 √𝑡𝑐
(3.4)
44
Tma(C)
Material
Conductivity (%)
Kf
Copper, annealed soft-drawn
100.0
1083
7.00
Copper, commercial hard-drawn
97.0
1084
7.06
Copper, commercial hard-drawn
97.0
250
11.78
Copper-clad steel wire
40.0
1084
10.45
Copper-clad steel wire
30.0
1084
12.06
Copper-clad steel rod
20.0
1084
14.64
Aluminum EC Grade
61.0
657
12.12
Aluminum 5005 Alloy
53.5
652
12.41
Aluminum 6201 Alloy
52.5
654
12.47
Aluminum-clad steel wire
20.3
657
17.20
Steel 1020
10.8
1510
15.95
Stainless clad steel rod
9.8
1400
14.92
Zinc-coated steel rod
8.6
419
28.96
Stainless steel 304
2.4
1400
30.05
Table 3.1 Material Constants
It important note that the actual conductor size is usually larger than the base
fusing, so the conductor has enough strength to withstand any expected mechanical and
corrosive abuse in the design life span of the install grounding. The design engineer
should give the conductor a high conductance enough to prevent any possible dangerous
voltage drop during a fault, and safety should be applied to the grounding system.
45
3.4.2.2 Asymmetrical Currents
Asymmetry current contrary to the symmetry current, the dc offset is accounted
for in the calculations of the fault current. The effect of the dc offsets can be neglected
if the duration of the current is greater than or equal to 1 s or X/R ratio at the fault
location is less than 5. The equivalent value of the symmetrical current IF, representing
the effective value of an asymmetrical current integrated over the fault duration tc, can
be found as a function of X/R by using the decrement factor Df, which should be
applied before equations 3.2 through 3.4.
𝐼𝐹 = 𝐼𝑓 × 𝐷𝑓
(3.5)
Assuming that the ac component does not decay with time and stays constant at
it initial subtransient value, the resulting value of IF is always larger than If because of
the decrement factor which values are given in Table 3.2 (IEEE- Standards Board,
2000).
𝑇𝑎
𝐷𝑓 = √1 + 𝑇 (1 − 𝑒
𝑓
−2𝑡𝑓
𝑇𝑎
)
(3.6)
46
Fault duration, tf
Decrement factor, Df
Cycles 60
Seconds
X/R =
Hz
X/R = 10
X/R = 20
X/R = 30
40
0.5
1.576
1.648
1.675
1.688
3
1.232
1.378
1.462
1.515
6
1.125
1.232
1.316
1.378
0.20
12
1.064
1.125
1.181
1.232
0.30
18
1.043
1.085
1.125
1.163
0.40
24
1.033
1.064
1.095
1.125
0.50
30
1.026
1.052
1.077
1.101
45
1.018
1.035
1.052
1.068
60
1.013
1.026
1.039
1.052
0.00833
0.05
0.10
0.75
1.00
Table 3.2 Typical Values of Df
3.4.2.3 Additional Factors in Conductor Sizing:
Precaution should be taken to ensure that the temperature of any conductor and
connection in the grounding installation does not pose a danger to the substation. The
environment should be examined for possible corrosion exposure. The practical
47
requirements on mechanical reliability will set the minimum conductor size, but even
though this might be correct in light of local conditions, the need for conservatism
deserves consideration.
3.4.2.4 Connectors Selection
As stated in section 11.4 of IEEE std 80-2000, all connections made in a
grounding network above and below the ground should be evaluated to meet the same
general requirements of the conductor used, i.e. electrical conductivity, corrosion
resistance, current carrying capacity, and mechanical strength. The connectors should
be massive enough to ride through a temperature rise below that of the conductor and to
withstand the effect of heating.
3.5 Soil in Substation Grounding
Soils behave most of the time both as conductor of resistance, r, and as a
dielectric. The charging current is negligible in comparison to the leakage current
except for high- frequency and steep-front waves penetrating a very resistive soil
material, and the earth can be represented by a pure resistance. Figure 3.2 is a circuit
that represents the behavior of a ground electrode buried in soil and can be used to
evaluate it (IEEE- Standards Board, 2000).
An investigation in the soil has to be conducted at the substation site to
determine the soil composition and degree of homogeneity, and the information on the
presence of various layers and the nature of soil material, helping to figure out the range
of the site resistivity.
48
C
r1
C
r2
C
r3
C
r4
Figure 3.2 Soil model
3.5.1 Outside Effect on Soil Characteristics
When the voltage gradient exceeds certain critical value, the soil resistivity is
affected. This value is the range of several kilovolts per centimeter and varies with the
soil material, but once exceeded, arcs would develop at the electrode surface and
progress into the earth until when the gradients are reduced to values that the soil
material can withstand. The gradient should always be assumed to be below the critical
range since substation grounding system is normally designed to comply with far more
stringent criteria of step and touch voltage limits.
Current flowing from electrodes into the surrounding soil effects on soil
resistivity depends on its magnitude and duration. But the thermal characteristics and
the moisture content of the soil will determine if the current will cause significant
drying and thus increase the effective soil resistivity. Thus, it is stated in IEEE standard
80-2000 that the current density is to be kept below 200 A/m2 for 1 s.
The resistivity of most soils rises inversely with its moisture content of because
electrical conduction in soils is electrolytic. There is sharp increase in the soil resistivity
whenever its moisture content fall below 15% of the soil weight as illustrated by Table
49
3.2, but as can be seeing by the Figure 3.3 curve 2 the moisture has little effect on the
soil resistivity after it exceeds 22% of the soil content (Gonen, 2007), (IEEE- Standards
Board, 2000). It should also be noted that the soil moisture content depends on the grain
size, compactness, and variability of the grain sizes (IEEE- Standards Board, 2000).
Effect of Moisture content on Soil Resistivity
Resistivity (Ω − 𝑚)
Moisture Content
(wt %)
Top Soil
Sandy Loam
0
>109
>109
2.5
250,000
15,000
5
165,000
43,000
10
53,000
18,500
15
19,000
10,500
20
12,000
6300
30
6400
4200
Table 3.3 Effect of Moisture Content on Soil Resistivity
50
Figure 3.3 Effects of moisture, temperature, and salt upon soil resistivity
Temperature has a little effect on soil resistivity if it is above 0 oC, but it effect
increase significantly once it falls below the freezing 0 oC refer to Figure 3.3 curve 3.
The soil resistance may considerably be affected by the composition and the
amount of soluble salts, acids, or alkali present in it. Please see Figure 3.2 curve 1.
3.5.2 Surface Layer Material
Surfaces are very useful in protecting the moisture content in the soil during
long dry season, thus keeping the soil resistance in check. Gravel is the most surface
material used and it is usually about 3 – 6 inches depth. Surface materials are very
51
instrumental in reducing shock currents, and the range of resistivity values for the
surface material layer depends on many factors such as the kinds of stone, size,
condition of stone, amount and type of moisture content, atmospheric contamination,
etc. From the Table 3.3, surface material subjected to sea spray may have substantially
lower resistivity than surface material utilized in arid environments.
3.5.3 Soil Resistivity Measurement and its Interpretation
Soil resistivity test should be conducted on multiple locations at the substation
site since estimates based on soil classification yield only a rough approximation. It is
very seldom to find a substation site with uniform soil resistivity over the entire area,
and to a considerable depth. There are several layers in a typical soil, and each layer has
different resistivity. The resistivity test should be made to determine if there are
significant variations in soil resistivity with depth, and more test should done where the
variations are large. Table 3.4 gives typical values for various ground types (Gonen,
2009), (Gonen, 2007).
52
Resistivity of Different Soils
Ground Type
Resistivity, 𝜌𝑠
Seawater
0.01-1.0
Wet organic soil
10
Moist soil (average earth)
100
Dry soil
1000
Bedrock
104
Pure slate
107
Sandstone
109
Crushed rock
1.5x108
Table 3.4 Resistivity of Different Soils
An increased range of probe spacing should be used in places where the
resistivity varies appreciably in order to obtain an estimate of the resistivity of deeper
layers. Please see IEEE standard 81-1983 for measurement technique. Figure 3.4 shows
the Wenner four-pin method which is the most commonly technique used. To some it,
four probes are driven into the earth along a straight line, at equal distance a to a depth
b. the voltage between the two inner (potential) electrodes is then measured and divided
by the current between the two outer (current) electrodes to give a value of resistance R
(Gonen, 2007), (Gonen, 2009).
53
I
V
b
a
a
a
Figure 3.4 Wenner four-pin method
Then,
𝜌𝑎 =
4𝜋𝑎𝑅
(3.7)
2𝑎
𝑎
1+
−
2
2
2
√𝑎 +4𝑏
√𝑎 +𝑏2
Ifb is small compared to a, as is the case of probes penetrating the ground only a short
distance, equation 3.7 can be reduced to 3.8f
𝜌𝑎 = 4𝜋𝑎𝑅
(3.8)
Most of the current penetrates deeper soils for large spacing, but the current tends to
flow near the surface for the small probe spacing. Thus, it is acceptable to assume that
the
resistivity measured for a given probe spacing a represents the apparent resistivity of the
soil to a depth of a when soil layer resistivity contrasts are not excessive.
54
The driven-rod method is another method of measuring soil resistivity as seen in
Figure 3.5 below described in IEEE standard 81-1983 (Gonen, 2007), (Gonen, 2009). Lr
of the driven-rod located in the soil to be tested is varied in this method, and the other
two rods, known as reference rods are driven to a shallow depth in a straight line. The
location of the voltage rod is varied between the test rod and the current rod.
Alternately, the voltage rod may be placed on the side opposite the current rod. The
apparent resistivity is given by
𝜌𝑎 =
2𝜋𝐿𝑟 𝑅
(3.9)
8𝐿
ln( 𝑑𝑟 )−1
Wenner four-pin or the driven-rod three-pin methods provide information needed to
develop a soil model. Wenner four-pin method is the commonly used because the soil
resistivity data for deeper layers is obtained without driving the test pins to those layers;
no heavy equipment is needed to perform the test with four-pin and the results are not
affected by the means used to get the data. In the contrary, the driven-rod three-pin
method has an advantage of determining to what depth the ground rods can be driven
into the soil. The downside of the driven-rod method is that most of the time, it loses
contact with the soil due to the vibration and the large diameter couplers resulting in
higher measured resistivity when testing. Thus, a ground grid designed with these high
resistance values would be too conservative.
The information on the moisture content of the soil at the time of measurement
and the temperature data should be included in the resistivity measurement records.
55
Should also be recorded all data available on known buried conductive objects in the
area studied. Reading made by the methods described can be invalidated if the buried
conductive objects in contact with the soil are close enough to alter the test current flow
pattern. The remedy in such case is to take readings in a short distance outside the grid,
with the probes so placed as to minimize the effect of the grid on the current flow
pattern.
I
V
E
P
C
Ground
Level
Lr
D
Figure 3.5 Circuit diagram for three-pin or driven-ground rod method
The most difficult part of the measurement program is the interpretation of
apparent resistivity obtained in the field since the main objective is to develop a soil
model that is a good approximation of the actual soil. It is worth noting that soil
resistivity varies laterally and with respect to depth depending on the soil stratification.
Due to varying weather conditions, seasonal variations may occur in soil resistivity. The
perfect match of the actual soil is unlikely but an approximation of the soil conditions if
feasible.
56
The two most commonly used soil resistivity models are the uniform and twolayer. Most soil structures can be approximated by the two-layer soil model while
complex soil conditions should be approximated by multilayer soil models. Uniform
soil model should be used only in instances where there is trivial variation in apparent
resistivity (homogeneous soil conditions) which is very rare.
3.5.3.1 Uniform Soil Model
When there are slight variations in the measurement of apparent resistivity of
different soils layers, uniform soil model can be used. Uniform soil model can also be
used whenever there is no access to two-layer or multilayer measurement tools even
though some inaccuracies have to be assumed in that case. The uniform soil resistivity
may be obtained after all the measurements have been taken by taking an arithmetic
average of the measured apparent resistivity data as in equation (3.10)
𝜌𝑎(𝑎𝑣1) =
𝜌𝑎(1) +𝜌𝑎(2) +𝜌𝑎(3) +⋯+𝜌𝑎(𝑛)
𝑛
(3.10)
As noted before, most soils structures are two-layer or multi-layer, thus will not
meet the criteria of equation 3.10. But because the step and touch voltage equations
formulated with the uniform soil models, the authors of the IEEE standard 80-2000
made the attempt to develop an equation for the apparent resistivity for the uniform soil
models. Equation 3.11 is another method to calculate the soil apparent resistivity, but
should be used with caution since many assumptions were made in deriving it.
𝜌𝑎(𝑎𝑣2) =
𝜌𝑎(𝑚𝑎𝑥) +𝜌𝑎(𝑚𝑖𝑛)
2
(3.11)
57
3.5.3.2 Two-Layer Soil Model
An upper layer soil of a finite depth above a lower layer of infinite depth can
represent the two-layer soil model, and the change in resistivity at the boundaries of soil
layer can be represented by a reflection factor K and is defined by equation 3.12
𝐾=
𝜌2 −𝜌1
𝜌1 +𝜌2
(3.12)
Since the accurate representation of a grounding system is neither technically not
feasible nor economically justifiable, the representation of a ground electrode based on
an equivalent two-layer earth model is sufficient enough for designing a safe grounding
system.
3.5.3.3 Multi-Layer Soil Model
Multi-layer soil model is used in highly non-uniform soil conditions and in cases
where the two-layer soil model is not feasible. Computer programs and graphical
methods are required to technically interpret highly non-uniform soil resistivity.
3.6 Ground Resistance and Maximum Grid Current
3.6.1 Simplified Calculation of Ground Resistance
Providing low resistance to remote earth is the quality of excellent grounding
system to minimize the ground potential rise. The resistance is about 1Ω or less for large
substations and most transmission, and 1Ω to 5Ω for small distribution substations
depending on the local conditions.
58
The first steps in determining the size and basic layout of a grounding system
are the estimation of the total resistance to remote earth. The area to be occupied by the
grounding system, which is usually known in the early design stage, is the primary
backbone of the resistance. A minimum of the substation grounding system resistance
in uniform soil can be estimated by means of the formula of circular metal plate at zero
depth is the first approximation.
𝜌
𝜋
𝑅𝑔 = √
4 𝐴
(3.13)
By adding a second term to equation 3.13, an upper limit of the substation ground
resistance can be obtained.
𝜌
𝜋
𝜌
𝑅𝑔 = √ +
4 𝐴
𝐿
(3.14)
𝑇
For grid rod combination in uniform soil, a combined length of horizontal conductors
and ground rods will yield a slightly conservative estimate of LT, because ground rods
usually are more effective on a per unit length basis as stated in section 14.2 of IEEE
standard 80-2000. The fact that the resistance of any actual grounding system that
consists of a number of conductors is higher than that of a solid metallic plate is
recognized by the second term. When the condition of a solid plate is reached, the
difference will decrease with the increasing length of buried conductors and will
approach 0 for infinite LT. Equation 3.14 has been expanded by Sverak to take into
account the effect of grid depth
59
𝑅𝑔 = 𝜌 [
1
𝐿𝑇
+
1
√
(1 +
20𝐴
1
1+ℎ√20⁄𝐴
)]
(3.15)
Table 3.5 below contains the comparison of the calculated and actual measured
resistance for five different substations using equation 3.14 (IEEE- Standards Board,
2000).
Parameter
Sub1
Sub2
Sub3
Sub4
Sub5
texture
Sand and
Sandy
Sand and
Sand and
Soil and
gravel
loam
clay
gravel
clay
Resistivity(Ω. 𝑚)
2000
800
200
1300
28.0
Grid area(𝑓𝑡 2 )
15159
60939
18849
15759
61479
Buried length(ft)
3120
9500
1775
3820
3000
Rg (calculated Ω)
25.7
4.97
2.55
16.15
0.19
Rg (measured Ω)
39.0
4.10
3.65
18.20
0.21
Table 3.5 Typical Grid Resistances
3.6.2 Schwarz’s Equations
The equations to determine the total resistance of a grounding system in a homogeneous
soil consisting of horizontal (grid) and vertical (rods) electrodes is developed by
Schwarz. Schwarz introduced an equation for the mutual ground resistance Rm between
60
the grid and rod bed, and his equations extended accepted equations for a straight
horizontal wire to represent the ground resistance, R1, of a grid consisting of
crisscrossing conductors, and a sphere embedded in the earth to represent ground rods,
R2.
𝑅𝑔 =
2
𝑅1 𝑅2 −𝑅𝑚
𝑅1 +𝑅2 −2𝑅𝑚
(3.16)
Equation 3.16, which is the combine resistance of the grid, rods, and mutual ground
resistance, represents the total system resistance, Rg, developed by Schwarz from the
equation introduced by Sunde and R𝑢̈ denberg.
Ground Resistance of the grid
𝑅1 =
𝜌
𝜋𝐿𝑐
[ln
2𝐿𝑐
𝑎′
+
𝑘1 .𝐿𝑐
√𝐴
− 𝑘2 ]
(3.17)
Ground Resistance of the rod bed
𝑅2 =
𝜌
2𝜋𝑛𝑅 𝐿𝑅
[ln
4𝐿𝑅
𝑏
−1+
2𝑘1 .𝐿𝑟
√𝐴
(√𝑛𝑅 − 1)2 ]
And for the mutual ground resistance between the and the rod bed
𝑅𝑚 =
𝜌
𝜋𝐿𝑐
[ln
2𝐿𝑐
𝐿𝑟
+
𝑘1 .𝐿𝑐
√𝐴
− 𝑘2 + 1]
(3.19)
(3.18)
61
The combined ground resistance of the grid and the rod bed will be lower than
the resistance of either component alone, but still higher than that of a parallel
combination.
The constants k1 and k2 were added to Schwarz’s equations since the first publication in
1954 to account for the equations in two-layer soil (IEEE- Standards Board, 2000).
3.6.3 Ways to Lower Soil Resistivity
3.6.3.1 Soil Treatment
Adding more grid conductors or ground rods doesn’t often lead to desired
reduction in ground resistance. To achieve further reduction in ground resistance, the
diameter of the electrode is increased by modifying the soil surrounding the electrode.
Advantage is taken to the fact that the inner shell of soil closest to the electrode
normally comprises the bulk of ground resistance to remote earth. As stated in IEEE
standard 80-2000, the following chemicals are used to treat the soil around the
electrodes.
Sodium chloride, magnesium, and copper sulfates, or calcium chloride can be
used to increase the conductivity of the soil immediately surrounding an electrode.
Bentonite, a natural clay containing the mineral montmorillionite, is noncorrosive,
stable, and has a resistivity of 2.5 Ω.m at 300% moisture. Bentonite uses water to obtain
and maintain its characteristic, thus it not advised to use bentonite in very dry
environment because it may shrink away from the electrode, producing the adverse
result of reducing the resistivity. Chemical-type electrodes consist of copper tube filled
62
with a salt, and ground enhancement materials, some with a resistivity of less than 0.12
Ω. m are some of the means used to treat the soil around the electrode.
The use of some of the chemicals sited above might not be permitted by federal,
state, or local authorities because of possible leaching to surrounding areas.
3.6.3.2 Concrete-Encased Electrodes
Concrete, being hygroscopic, attracts moisture, and a block of concrete buried in
soil behaves as a semiconducting medium with a resistivity of 30-90Ω. m. A wire or
metallic rod encased in concrete has lower resistance than a similar electrode buried
directly in the earth, which make it of particular interest in medium and highly resistive
soils. The concrete encasement reduces the resistivity of the immediate surroundings of
the metal element in much the same way as a chemical treatment of soils. It is worth
noting that the use of concrete is both a blessing and a curse as can be seeing by the
reasons cited below from IEEE standard 80-2000.
a) On the one hand, it is impractical to build foundations for structures where the
inner steel is not electrically connected to the metal of the structure. With the
semiconductive nature of concrete, it is almost impossible to prevent the any
direct metal-to-metal contact even if care were taken with the anchor bolt
placement.
b) On the other hand, a small presence of dc current can cause corrosion of the
rebar material. Even though ac current does not produce corrosion,
63
approximately 0.01% of the ac current becomes rectified at the interface of the
steel bar and concrete.
c) Splitting of concrete may occur either due to the above phenomenon because
corroded steel occupies approximately 2.2 times its original volume, producing
pressures approaching 35 Mpa or the passage of a very high current, which
would vaporize the moisture in the concrete.
Fortunately, 60 V dc is the threshold potential for corrosion below which no
corrosion will occur. The short time current loading capacity, ICE, of concrete-encased
electrodes can be estimated by means of Ollendorff’s formula for an indefinitely
sustainable current 𝐼∞ , adjusted by a 1.4 multiplying factor, or directly from Figure 3.6
(IEEE- Standards Board, 2000).
𝐼𝐶𝐸 = 1.4(𝐼∞ ) =
1.4
𝑅𝑧
√2𝜆𝑔 𝜌(𝑇𝑣 − 𝑇𝑎 )
(3.20)
In practice to prevent damage, the actual current should be less than the value of
ICE determined by the above equation with a reasonable safety margin of 20-25%. Thus,
with proper precautions, the concrete-encased electrodes may be used as auxiliary
ground electrodes.
64
Figure 3.6 Short-time current loading capacity of concrete-encased ground electrodes
Equation for obtaining the ground resistance, RCE-rod, of a vertical rod encased in
concrete used by Fagan and Lee is presented below.
1
𝑅𝐶𝐸−𝑟𝑜𝑑 = 2𝜋𝐿 (𝜌𝑐 [𝑙𝑛(𝐷𝐶 ⁄𝑑 )] + 𝜌[𝑙𝑛(8𝐿𝑟 ⁄𝐷𝐶 ) − 1])
𝑟
(3.21)
Equation 3.21 is related to the commonly used ground rod of length Lr and diameter d,
as follows:
𝜌
𝑅𝑟𝑜𝑑 = 2𝜋𝐿 [𝑙𝑛(8𝐿𝑟 /𝑑) − 1]
𝑟
Then (3.21) can be resolved into:
(3.22)
65
1
𝑅𝐶𝐸−𝑟𝑜𝑑 = 2𝜋𝐿 (𝜌[𝑙𝑛(8𝐿𝑟 ⁄𝐷𝐶 ) − 1] + 𝜌𝑐 [𝑙𝑛(8𝐿𝑟 ⁄𝑑 ) − 1] − 𝜌𝑐 [ln(8𝐿𝑟 /𝐷𝐶 ) − 1])
𝑟
(3.23)
This equation represents a combination of two resistances in series. The latter
term is obtained as a difference of the hypothetical resistance values for a rod in
concrete, if d DC are entered into the single-medium formula equation 3.22, and 𝜌 is
replaced by 𝜌𝑐 .
Such an approach is generally valid for any other electrode having a different shape. For
convenience
𝑅𝑆𝑀 = 𝐹(𝜌, 𝑆0 , 𝐺)
(3.24)
𝑅𝐷𝑀 = 𝐹(𝜌, 𝑆0 , 𝐺) + 𝐹(𝜌, 𝑆𝑖 , 𝐺) − 𝐹(𝜌𝑐 , 𝑆𝑖 , 𝐺)
(3.25)
This form is adaptable to a variety of electrodes, and one possible model of this
type, for which Schwarz’s formula for a rod bed can easily be modified as shown in
Figure 3.7 (IEEE- Standards Board, 2000).
Figure 3.7 Grid with encased vertical electrodes
66
When using concrete-encased electrodes, the following recommendations should
be considered:
a) For a reliable metal-to-metal contact, the anchor bolt and angle stubs should be
connected to the reinforcing steel.
b) Make sure that enough primary ground electrodes will conduct most of the fault
current to reduce the current duty and dc leakage to allowable levels.
c) To reduce the resistance of primary grounding, ground enhancement material
may be used in the areas of high soil resistivity. Augering a 100-250 mm hole
and backfilling it with a soil enhancement material around a ground rod is useful
method to prevent the predominance of auxiliary electrodes in dissipating the
fault current.
3.6.4 Maximum Grid Current
3.6.4.1 Steps to Determine the Largest Fault Current
The largest value of fault current will result in the most hazardous conditions.
But with the existence of many types of faults, it is not an easy task to determine which
fault type and location will result in the greatest flow of current between the ground grid
and
67
surrounding earth because no simple rules applies. Figures 3.8 thru 3.11show maximum
grid current IG for various fault locations and their system configurations (IEEEStandards Board, 2000).
In cases of maximum fault current, the following steps should be taken to
determine the correct design value of maximum grid current IG for use in substation
grounding calculations:
a) Evaluate the type and location of those ground faults that are likely to produce
the greatest flow of current between the grounding grid and surrounding earth,
and hence the greatest GPR and largest local surface potential gradients in the
substation area.
b) Determine, by computation, the fault current division factor Sf for the faults
selected in a), and establish the corresponding values of symmetrical grid
current Ig.
c) For each fault, based on its duration time, tf, determine the value of decrement
factor Df, to allow for the effects of the asymmetry of the fault current wave.
d) Select the largest product Df x Ig, and hence the worst case.
Consideration should be given to the probability of occurrence of the fault in
determining the applicable fault type. Even though multiple simultaneous faults may
result in higher ground current, they should not be considered if their probability of
occurrence is negligible. The recommendation is in practice, to confine the investigation
on single-line-to-ground and line-to-line-to-ground faults.
68
The zero sequence fault current for the case of a single-to-line-to-ground fault is:
𝐸.(𝑅2 +𝑗𝑋2 )
1 +𝑗𝑋1 )[𝑅0 +𝑅2 +3𝑅𝑓 +𝑗(𝑋0 +𝑋2 )]+(𝑅2 +𝑗𝑋2 ).(𝑅0 +3𝑅𝑓 +𝑗𝑋0 )
𝐼0 = (𝑅
(3.27)
The zero sequence fault current for the case of a single-single-to-ground fault is:
𝐼0 =
𝐸
3𝑅𝑓 +𝑅1 +𝑅2 +𝑅0 +𝑗(𝑋1 +𝑋2 +𝑋0 )
(3.28)
The zero sequence fault current for the case of a single-to-ground fault is:
𝐼0 =
𝐸.𝑋2
𝑋1 .(𝑋2 +𝑋0 )+(𝑋2 +𝑋0 )
(3.29)
The zero sequence fault current for the case of a single-to-line-to-ground fault is:
𝐼0 =
𝐸
𝑋1 +𝑋2 +𝑋0
(3.30)
3.6.4.2 Effect of Some Internal and External Elements
The maximum grid current described in section 3.6.4.1 is sufficient in most cases
to derive the maximum grid current IG, by neglecting the system resistance, the
substation ground resistance, and the resistance at the fault. The error introduce in this
situation is small and always on the safe side, even though there may be unusual cases
where the predicted substation ground resistance is so large that it would need to be
included in equations3.25 and 3.28. This poses a hurdle since at this point of the design
69
the substation ground system is not design yet, but the resistance can be estimated from
formulas in sections 3.6.1 and 3.6.2.
For faults within the substation caused by insulation breakdown, it is safe to
assume that the fault resistance zero. On the other hand, for fault outside the substation
area, on a line connected to the substation bus Figure 3.11(IEEE- Standards Board,
2000), it is permissible to use Rf in the ground fault calculations.
A substantial portion of the ground fault current is diverted away from the
substation ground grid when the overhead transmission line ground wires or neutral
conductors are connected to the substation ground. In this case, the overhead ground
wires or neutral conductors should be taken into consideration in the design of the
ground grid, since this will have an increasing effect on the GPR at tower bases, while
lessening it at the substation.
Fault
IF
IF
Grounded
Station
Structure
IF
I F ; IG = 0
Figure 3.8 Fault within local substation; local neutral grounded
70
I
Fault
IF
Grounded
Station
Structure
IF
i1
i2
IG =
in
i = IF
Figure 3.9 Fault within local substation; local neutral grounded at remote location
I = I + I
F F1
F2
IF2
IF2
Fault
IF1
IF
Grounded
Station
Structure
Other
System
Grounds
IF1
I = I –I
G F F1
IG
Figure 3.10 Fault in substation; system grounded at local substation and also at other
points
71
Remote
Source
Distribution
Substation
Load
Substation
ФA(73)
ФA(103)
ФA
ФB
ФC
(12)
(12)
ФC(70)
(1492)
338
448
99
338
1492
444
IG = 1048
IG = 742
IG = 99
Figure 3.11 Typical current division for a fault on high side of distribution substation
3.6.4.3 Worst Fault and Location
The fault that causes the maximum value of IG is the worst fault type for a given
ground system. The worst fault type can be defined as the one resisting in the highest
zero sequence or ground fault current flow into the earth, 3I0, because IG is proportional
to the zero sequence or ground fault current and the current division factor, and because
the current division is almost independent of the fault type. The single-line-to-ground
fault will be the worst fault type if Z1Z0 >𝑍22 at the point of fault. The line-to-line-toground fault will be the worst fault type if Z1Z0 <𝑍22 at the point of fault. In the rare case
where Z2 is assumed equal to Z1, the above comparisons reduce to Z0 >𝑍22 , and Z0 <𝑍22 ,
respectively.
72
Z1, Z2, Z0 are defined as:
Z1 = R1 + jX1
(3.31)
Z2 = R2 + jX2
(3.32)
Z0 = R0 + jX0
(3.33)
There are several considerations involving in the location producing the
maximum grid current IG. The worst fault location can be on either high voltage or low
voltage side, inside the substation or outside on the line, away from the substation. For a
fault to be located inside the substation, it has to be related to a metallic structure that is
electrically connected to the substation grounding grid via negligible impedance. Since
there are no universal rules for the determination of the worst fault location, there are
some related discussions to some of the possible locations in section 5.8on page 78 in
the IEEE standard 80-2000 for more information.
3.6.4.4 Effect of Asymmetry
Asymmetrical current must be taken into account when designing a substation
grounding system, and the decrement factor, Df, will be derived to take into account the
effect of the dc current offset. The subtransient, transient and steady-state ac
components, and the dc offset current component are included in the asymmetrical fault
current study. It is worth noting that the subtransient and transient ac components and
the dc offset decay exponentially each with different rate. But, it is assumed that the ac
73
component does not decay with time, instead remains constant with its initial value.
Thus, the asymmetrical fault current may be expressed as:
𝑖𝑓 (𝑡) = √2 ∗ 𝐸 ∗ 𝑌𝑎𝑐 [sin(𝜔𝑡 + 𝛼 − 𝜃) − 𝑒 −𝑡⁄𝑇𝑎 ∗ sin(𝛼 − 𝜃)]
(3.34)
The X/R ratio of the system fault location should be used for the X/R ratio, and it is
determined by the system subtransient fault impedance.
However in reality since fault occur at random with respect to the voltage wave,
and the shock contact may exist at the time of the fault is initiated, it is necessary to
assume that the maximum possible dc offset exist at the moment of accidental shock
contact.
Maximum dc offset occurs when: (𝛼 − 𝜃) = 𝜋/2 thus equation 3.34 becomes
𝑖𝑓 = √2𝐸 ∗ 𝑌𝑎𝑐 [𝑒 −𝑡⁄𝑇𝑎 − cos( 𝜔𝑡)]
(3.35)
It is necessary to establish an equivalent rms value of the current wave for the
maximum time of possible shock exposure since the data in the fibrillation threshold are
based on the energy content of a symmetrical sine wave of constant amplitude. This
value is determined in accordance with the effective asymmetrical fault current If as:
1
𝑡
2
𝐼𝐹 = √ ∫0 𝑓[𝑖𝑓 (𝑡)] 𝑑𝑡
𝑡
(3.36)
𝑓
Evaluating the integral of equation 3.36 in terms of 3.35, we get:
74
1
2
𝑡
𝐼𝐹 = 𝐼𝑓 ∗ √𝑡 ∫0 𝑓[𝑖𝑓 (𝑡)] 𝑑𝑡
(3.37)
𝑓
Therefore, the decrement factor Dfthe ratio of IF/If is:
𝑇
Df= IF/If = √1 + 𝑡𝑎 (1 − 𝑒
𝑓
−2𝑡𝑓
𝑇𝑎
)
(3.38)
Table 3.2 display decrement factor values for some specific X/R ratios and fault
durations. And equation 3.38 can be used to compute the decrement factor when the
ratio X/R and fault durations are known. A decrement factor of 1.0 can be used for fault
of 30 cycles or more in duration, since the effect of the dc offset current can be assumed
to be more than compensated by the decay of the subtransient component of the ac
current.
75
Chapter 4 – DESIGN OF SUBSTATION GROUNDING SYSTEM
4.1 Design Criteria
As stated before, there are two main design objectives to accomplice in the
substation ground system under any condition. The first is to provide means to dissipate
electric currents into the earth without exceeding any operation and equipment limits,
and the second is to prevent any person in the vicinity of the substation area to not be
exposed to the danger of critical electric shock. The design process described here is to
assuring the safety from dangerous step and touch voltages within, and immediately
outside, the substation fenced area. Because the mesh voltage is usually the worst
possible touch voltage inside the substation and the mesh voltage will be used as the
basis of the design procedure.
It is worth noting that the mesh voltage is more dangerous than the step voltage,
but the step voltage may be more dangerous outside the substation fence where there is
no assistance of the high resistivity of the surface layer which helps with safety. Thus,
the computed step voltages should be compared with the permissible step voltage after a
grid has been designed that satisfies the touch voltage criterion.
The mesh voltage will increase along meshes from the center to the corner of
the grid for equally spaced ground grids. The soil resistivity profile, number and
location of ground rods, spacing of parallel conductors, diameter and depth of the
conductors, the size of the grid all affect the rate of increase of the mesh voltage. The
76
corner mesh voltage is generally much higher than that in the center mesh, and this is
true unless the
grid is unsymmetrical, there are ground rods located on or near the perimeter, or there
are nonuniform conductor spacings. Yet, the mesh voltage may not be the worst-case
touch voltage if ground rods are located near the perimeter, or if the mesh spacing near
the perimeter is small. In these cases as stated in IEEE 80-2000, the touch voltage of the
grid may exceed the corner mesh voltage.
4.1.1 Critical Parameters
The maximum grid current 𝐼𝐺 , fault duration 𝑡𝑓 shock duration 𝑡𝑠 , soil resistivity
𝜌, and surface material resistivity 𝜌𝑠 have the most substantial impact on the grid
design. While parameters such as the conductor diameter and the thickness of the
surfacing material are less impactful, the area of the grounding system, the conductor
spacing, and the ground grid have significant impact on the mesh voltage.
4.2 Design Procedure
In the design of safe and reliable substation grounding system, the steps in the
block diagram in Figure 4.1 must be followed to the letter (IEEE- Standards Board,
2000).
77
FIELD DATA
STEP 1
A, ρ
CONDUCTOR SIZE
STEP 2
3Io, tc, d
TOUCH & STEP CRITERIA
Etouch
50 or 70’
Estep
STEP 3
50 or 70’
INITIAL DESIGN
STEP 4
D, n, LC, LT, h
GRID RESISTANCE
STEP 5
Rg , LC, LR
STEP 11
MODIFY DESIGN
GRID CURRENT
STEP 6
IG , tf
D, n, LC, LT
STEP 7
YES
IG Rg < Etouch
NO
MESH & STEP VOLTAGES
STEP 8
Em, Es, Ks,
Kj, Kii, Kh
STEP 9
NO
Em < Etouch
YES
STEP 10
NO
Es < Estep
YES
DETAIL DESIGN
STEP 12
Figure 4.1 Design procedure block diagram
4.3 Maximum Step and Mesh Voltages
The mesh voltage values are obtained as a product of the geometrical factor, Km;
a corrective factor, Ki, which accounts for some of the error introduced by the
78
assumptions made in deriving Km; the soil resistivity, ρ; and the average current per unit
of effective buried length of the grounding system conductor (IG/LM).
4.3.1 Mesh Voltages (Em)
𝐸𝑚 =
𝜌∙𝐾𝑚 ∙𝐾𝑖 ∙𝐼𝐺
(4.1)
𝐿𝑀
The geometrical factor Km is defined by the following formula below:
𝐾𝑚 =
1
2∙𝜋
∙ [𝑙𝑛
𝐷2
16∙ℎ∙𝑑
+
(𝐷+2∙ℎ)2
8∙𝐷∙𝑑
−
ℎ
4∙𝑑
]+
𝐾𝑖𝑖
𝐾ℎ
∙ 𝑙𝑛 [
8
𝜋(2∙𝑛−1)
] (4.2)
For grids with ground rods along the perimeter, or for grids with ground rods in the grid
corners, as well as both along the perimeter and throughout the grid area
𝐾𝑖𝑖 = 1
(4.3)
For grids with no ground rods or grids with only a few ground rods, none located in the
corners or on the perimeter.
𝐾𝑖𝑖 =
1
2
(4.4)
(2∙𝑛)𝑛
ℎ
𝐾ℎ = √1 + ℎ0 = 1𝑚 (grid reference depth) (4.5)
ℎ
0
The effective number of parallel conductors in a given grid, n, can be made
applicable to rectangular or irregularly shaped grids that represent the number of
79
parallel conductors of an equivalent rectangular grid by using the four grid shaped
components developed by Thapar, Cerez, Balakrishnan and Blank.
𝑛 = 𝑛𝑎 ∙ 𝑛𝑏 ∙ 𝑛𝑐 ∙ 𝑛𝑑 ( 4.6)
Where
𝑛𝑎 =
2∙𝐿𝐶
𝐿𝑝
(4.7)
nb = 1 for square grids
nc = 1 for square and rectangular grids
nd = 1 for square, rectangular and L-shaped grids
otherwise,
𝑛𝑎 = √
𝐿𝑝
(4.8)
4∙√𝐴
0.7∙𝐴
𝑛𝑐 =
𝐿𝑥 ∙𝐿𝑦 𝐿𝑥 ∙𝐿𝑦
[
]
𝐴
𝑛𝑑 =
𝐷𝑚
√𝐿2𝑥 +𝐿2𝑦
(4.9)
(4.10)
LC is the total length of the conductor in the horizontal grid in m
Lp is the peripheral length of the grid in m
80
A is the area of the grid in m2
Lx is the maximum length of the grid in the x direction in m
Ly is the maximum length of the grid in the y direction in m
Dm is the maximum distance between any two points on the grid in m
The irregularity factor, Ki, used in conjunction with the above defined n is
K i = 0.644 + 0.148 ∙ 𝑛 (4.11)
For grids with no ground rods, or grids with only a few ground rods scattered
throughout the grid, but none located in the corners or along the perimeter of the grid,
the effective buried length, LM, is
LM = LC + LR
(4.12)
Where
LR is the total length of all ground rods in m
For grids with ground rods in the corners, as well as along the perimeter and throughout
the grid, the effective buried length, LM, is
𝐿𝑟
𝐿𝑀 = 𝐿𝐶 + 1.55 + 1.22
[
√√𝐿2𝑥 +𝐿2𝑦
(
𝐿𝑅 (4.13)
)]
81
Where
LR is the length of each ground rod in m
4.3.2 Step Voltages (Es)
The step voltage values are obtained as a product of the geometrical factor, Ks;
the corrective factor, Ki; the soil resistivity, ρ; and the average current per unit of buried
length of grounding system conductor (IG/LS).
𝐸𝑠 =
𝜌∙𝐾𝑠 ∙𝐾𝑖 ∙𝐼𝐺
(4.14)
𝐿𝑠
For grids with or without ground rods, the effective buried conductor length, LS, is
𝐿𝑠 = 0.75 ∙ 𝐿𝐶 + 0.85 ∙ 𝐿𝑅
(4.16)
The maximum step voltage is assumed to occur over a distance of 1 m, beginning at and
extending outside of the perimeter conductor at the angle bisecting the most extreme
corner of the grid. For the usual burial depth of 0.25 m < h < 2.5 m, Ks is
1
𝐾𝑠 = [
1
𝜋 2∙ℎ
+
1
𝐷+ℎ
1
+ (1 − 0.5𝑛−2 )]
𝐷
(4.17)
82
Chapter 5 – APPLICATION OF SUBSTATION GROUNDING DESIGN
5.1 Introduction
This section demonstrates the step by step followed to design a safe and reliable
substation grounding system as described in section 4.2. It defines the necessary steps to
take in the event the initial design fails to meet the safe mesh and step voltage criteria.
An example illustrating the design of grounding systems at Hillsboro Central Substation
for Tri-Met Portland Westside light Rail Traction Power Substations is given with
matlab code for fast and accurate design.
Contrary to high voltage outdoor substations with all the equipment such as
buses, breakers, transmission towers, etc. exposed, all the equipment inside the
Hillsboro Central Substation such as 15 kv switchgear, 15 kv station service
transformer, ac panel boards, etc. are all enclosed and grounded and they are housed in
a grounded housed. Thus, it is safe to say that it is very conservative to follow the IEEE
80-2000 standard in the design of ac ground mats for traction power substation ac
equipment.
Please note that only formulas and results will be given here since the matlab
code has all the calculations and results. Table 5.1 below contains the initial data
required for the grounding system design (Kaustubh & Jamnani, 2012), (Thomas &
Pham, 1999).
83
Ground grid parameters
Value
Soil and system data
Grid shape
rectangular
Fault current split factor
Value
0.6
(Sf)
Depth of burial of grid (h)
0.52 m
Shock duration (ts)
0.5 sec
Length in X direction (Lx)
45 m
Fault duration (ts)
0.5 sec
Length in X direction (Ly)
50 m
Current projection factor
1.20
Spacing between
8m
Surface layer resistivity
1500 Ω. m
conductors (D)
No. of ground rods (Rd)
(Cr)
26
Surface layer thickness
0.2 m
(hs)
Length of ground rod (Lrd)
3m
Soil resistivity (Sr)
50 Ω. m
Ambient temperature (Ta)
40 0C
Fault current (If)
14218 A
Switchyard operator
50 kg
Proposed location soil
uniform
weight
type
Table 5.1 Input Data for the Grounding System Design
5.2 Initial Design of Hillsboro Central Substation
Step 1: Field data.
84
As stated in the table above, the biggest area for the substation grounding grid is a
rectangle of 45 m x 50 m. thus, the area of the ground grid is A = 2250 m2 with an
assumed soil resistivity of 1500Ω. m.
Step 2: Conductor size.
The system ground fault current is given in Table 5.1
If = 3I0 =14218 A
(5.1)
And X/R is assumed to be 10. X/R = 10.
Adding the current protection factor/ growth factor of 20%, the ground fault current is
If = 3I0 = 17061.6 A
Using Table 3.2 for the X/R ratio and our fault duration given in Table 5.1, we found
the decrement to be Df = 1.026.
Hence, the rms asymmetrical fault current is also
𝐼𝐹 = 𝐼𝑓 ∙ 𝐷𝑓 = 17505.2016 A
(5.2)
This current magnitude will be used to determine the minimum diameter of ground
conductors.
Assuming the use of copper-clad steel wire at ambient temperature (Ta) of 400 C with
melting temperature of 10840 C we get from Table 3.1, 𝐾𝑓 = 12.06
The required cross-sectional area in circular mils is
85
Akcmil = IF ∙ K f √t s = 149.2792 kcmil
(5.3)
Which would be in mm2,
Amm2 =
Akcmil ∙1000
1973.52
= 75.6534mm2(5.4)
The conductor diameter would be,
4∙Amm2
d=√
π
= 9.8145 mm or 0.0098145 m(5.5)
Base on this computation, a copper-clad steel wire as small as 3/0 can be used, but due
to the mechanical strength and ruggedness requirement, a larger 250 kcmil stranded
conductor with diameter will be used.
The new conductor diameter is d = 12.6987 mm or 0.012699 m
Step 3: Touch and step criteria.
For a 0.2 m or 7.874 inch layer of crushed rock surfacing, with resistivity of 1500 Ω. m
and for an earth with resistivity of 50 Ω. m, the reflection factor
K=
ρ−ρs
ρ+ρs
= -0.93548
(5.6)
Note since Matlab does not simple for 𝜌, in the code
𝐶𝑟 ≡ 𝜌 and 𝑆𝑟 ≡ 𝜌𝑠
(5.7)
86
For K = -0.93548 the resistivity of the crushed rock is to be derated by a reduction
factor
of approximately 0.82 after using Figure 5.1 or by calculation using equation 5.8 (IEEEStandards Board, 2000) ,
𝐶𝑠 = 1 −
𝜌
𝜌𝑠
0.09(1− )
2ℎ𝑠 +0.09
= 0.82245
(5.8)
As stated in the design criteria, the switchyard is operated by a person expected to
weight 50 or more.
87
Figure 5.1 Cs versus hs
For step voltage,
𝐸𝑠𝑡𝑒𝑝 = (1000 + 6𝐶𝑠 )
0.116
√𝑡𝑠
= 1378.3445 𝑉
(5.9)
And for the touch voltage,
𝐸𝑡𝑜𝑢𝑐ℎ = (1000 + 1.5𝐶𝑠 ∙ 𝜌𝑠 )
0.116
√𝑡𝑠
= 467.6227 𝑉
(5.10)
The step and touch voltages are respectively 1378.3445 V an 467.6227 V
88
Step 4: Initial design.
Assuming an area of 2250 m2 with equally spaced conductors as shown in Figure 5.2
below with 5 m spacing, 9 vertical bares, 10 horizontal bares grid, and the grid is
buried
at a depth of 0.52 m. The total length of horizontal buried conductor is
Lst = l ∙ Lx + L ∙Ly = 905 m
(5.11)
45 m
Grid conductor
50 m
Ground rod
3m long
Figure 5.2 Square grid with 26 rods
89
Step 5: Determination of grid resistance.
Using Equation 5.12 for Lst = 905 m, and grid area A = 2250 m2, the total length of all
ground rods is
LR = Rd ∙ Lrd = 78 m
(5.12)
And the total length of buried conductor is
Lt = Lst + LR = 983 m
(5.13)
Thus, the grid resistance is
1
𝑅𝑔 = 𝜌 [𝐿 +
𝑡
1
√20∙𝐴
(1 +
1
1+ℎ√20⁄𝐴
)] = 0.51125 Ω
(5.14)
Step 6: Maximum grid current IG.
The maximum grid current IG is (IEEE- Standards Board, 2000),
IG = Df∙ Iff∙ Sf = 10503.121 A
(5.15)
Step 7: GPR.
Now it is necessary to compare the product of IG and Rg, or GPR, to the tolerable touch
voltage, Etouch
GPR = 𝑅𝑔 ∙ 𝐼𝐺 = 5369.7596 V
(5.16)
This GPR far exceed the safe touch voltage of 467.6227 V in step# 3, thus further
design evaluations are necessary.
90
Step 8: Mesh voltage.
Km is computed from equation 4.1 through equation 4.3
The effective number of parallel conductors in a given grid, n, can be made applicable
to rectangular or irregularly shaped grids that represent the number of parallel
conductors of an equivalent rectangular grid.
n = na∙nb∙nc ∙nd
(5.17)
Km is the geometrical factor
Ki is the corrective factor
For grid with ground rods, Kii = 1.
The perimeter of the grid area is
Lp = 2∙Lx + 2∙Ly = 190 m
(5.18)
na = 2∙Lst/Lp= 9.5263 (5.19)
𝐿𝑝
nb = √4∙√𝐴
nc = 1
nd = 1
n = na∙nb∙nc ∙nd = 9.5329
(5.20)
91
The effective buried length LM to be used in the case of grids with ground rods in the
corners, as well as along the perimeter and throughout the grid is
𝐿𝑟
𝐿𝑀 = 𝐿𝐶 + [1.55 + 1.22 (
√𝐿2𝑥 +𝐿2𝑦
)] 𝐿𝑅 = 1030.1 m
(5.21)
The irregularity factor is
Ki = 0.644 + 0.148∙n = 2.058
The grid reference depth in is
ho = 1m
The corrective weighting factor that emphasizes the effects of grid depth, simplified
method is
𝐾ℎ = √(1 + ℎ/ℎ𝑜) = 1.2329
The spacing factor for mesh voltage, simplified method
1
𝐷2
𝐾𝑚 = 2∙𝜋 ∙ [𝑙𝑛 16∙ℎ∙𝑑 +
(𝐷+2∙ℎ)2
8∙𝐷∙𝑑
ℎ
𝐾
8
− 4∙𝑑] + 𝐾𝑖𝑖 ∙ 𝑙𝑛 [𝜋(2∙𝑛−1)] = 0.6119
ℎ
Finally, the mesh Em is computed from equation (4.1) and equation (4.12)
𝐸𝑚 =
𝜌∙𝐾𝑚 ∙𝐾𝑖 ∙𝐼𝐺
𝐿𝑀
= 641.0452 V
(5.24)
(5.23)
92
For grids with or without ground rods, the effective buried conductor length, LS, is
𝐿𝑠 = 0.75 ∙ 𝐿𝐶 + 0.85 ∙ 𝐿𝑅 = 803.5500 m (5.25)
The spacing factor for step voltage, simplified method is
1
1
1
1
𝐾𝑠 = 𝜋 [2∙ℎ + 𝐷+ℎ + 𝐷 (1 − 0.5𝑛−2 )] = 0.4090
(5.26)
The step voltage values are obtained as a product of the geometrical factor, Ks; the
corrective factor, Ki; the soil resistivity, ρ; and the average current per unit of buried
length of grounding system conductor (IG/LS).
𝐸𝑠 =
𝜌∙𝐾𝑠 ∙𝐾𝑖 ∙𝐼𝐺
𝐿𝑠
= 549.2127 V
(5.27)
Step 9: Compare the mesh voltage to the touch.
The mesh of 641.0452 V exceeds the safe touch voltage of 467.6227 V which was
found in step 3, thus the grid design must be modified.
5.3 Modified Design of Hillsboro Central Substation
Following the design flow chart in section 4.2, we could not proceed to step 10
due to the failure to meet the criterion of step 9. There are two procedures to modifying
the grid design to meet the tolerable touch voltage requirements. The first method
consists of reducing the available ground fault current which is almost technically
impractical and economically bleeding. Thus, the second method which consists of
changing any or all of the following: grid conductor spacing, total conductor length,
grid depth, addition of ground rods, changing the conductor material, etc. In this project,
93
the preliminary design will be modified to include 38 ground rods instead 26, each 7 m
long from 3m, around the perimeter of the grid as show in Figure 5.3, and the depth of
burial of the grid from0.52 m to 0.7m. This second time, only the result of each step
will be provided since the step by step Matlab code and result will include the
computations. An example of grid layout is shown in Figure 5.4(Schaerer, 2011).
45 m
G rid c o n d u c to r
50 m
Figure 5.3 Square grid with 38 rod
G ro u n d ro d
(7 m lo n g )
94
Figure 5.4 Example of grid layout
Step 5: Determination of the grid resistance.
The grid resistance is 0.49951 ohms
Step 6: Maximum grid current IG calculation.
The maximum grid current is 10503.121 A
Step 7: GPR.
The GPR is 5246.4199 V and far exceed the safe touch voltage of 467.6227 V, thus
95
further design evaluations are necessary.
Step 8: Mesh and Step voltage.
The mesh voltage is 457.3593 V and the step 320.9346 V.
Step 9: Compare the mesh voltage to the touch
The mesh 457.3593 V is below the safe touch voltage 467.6227 V, thus we can proceed
to step 10 contrary to the initial design which required some modifications.
Step 10: Compare the Step Voltage to the Tolerable Step volt.
The step 320.9346 V is well below the tolerable step voltage 1378.3445 V, now we can
proceed to step 12.
Step 11: Modify design.
Not necessary for this example.
Step 12: Detailed design.
A safe design has been obtained. At this point, all equipment pigtails, additional ground
rods for surge arresters, etc., should be added to complete the grid design details.
96
Chapter 6 – CONCLUSION
The design of the grounding system of a substation is one of the first important
steps in the design of an AC substation because it is the foundation everything else must
be built upon. The grounding system provides a convenient low resistance connection to
the substation structure, thus, limiting the ground potential rise to a value below the
tolerable touch voltage or to a value low enough to result in a value of mesh voltage
below the tolerable touch voltage for the safety of the personnel and equipment. As
state before, the grounding system provides a means to safely discharge lightning
strokes to earth, reduces step and touch potentials to safe levels and confines dangerous
soil currents to inaccessible areas. It also allows the detection of ground fault currents
by protective relaying systems, provides low impedance paths through the earth for load
currents, and provides a common ground reference which assists in the coordination of
insulation throughout the system (El-Dessouky, El-Aziz, & Khamis, 1998), (Phan,
1990), (Thomas & Pham, 1999).
This project provides a detail report on the design and implementation of substation
grounding systems mostly based on the knowledge acquired from IEEE standard 802000. All the major steps in the design and implementation of substation grounding are
described and a block diagram in Figure 4.1 provides the sequences of the steps to
design the ground grid. An example of the ground grid design is provided with the
design of Hillsboro Central ac substation for the Tri-Met Portland Westside Light Rail.
The preliminary design failed to meet the required safety criteria and indicated that
dangerous potential differences and mesh voltage can exist within the substation. The
97
design was modified to decrease the total grid resistance by adding more ground longer
rods, reducing the spacing between the ground conductors, and moving the ground grid
a little deeper beneath the soil. The result of these changes to the grounding design is a
safe and reliable substation grounding system for the personnel and equipment.
98
Appendix
% Mamadou Keita & Arnel Molina Master Project Matlab's Code
clc
% Initial data
Lx=input('Please enter the length in X direction ');
Ly=input('Please enter the length in Y direction ');
ts = input('What is the fault duration in second ');
X_R = input('What is the X/R ratio ');
Cr = input('Enter the crushed rock resistivity ro_s ');
hs = input('Enter the surface layer thickness hs ');
Sr = input('Enter the soil resistivity ');
Wt = input('Please enter the minimum weight of the switchyard
operators ');
% Step# 1
% Grid area
disp('****** Step# 1 Grid area ******')
disp('')
A = Lx * Ly; % Substation grid area
disp(['Substation area is ',num2str(A),' m^2 '])
disp('')
% Step# 2
% Conductor sizing
disp('****** Step# 2 Conductor sizing ******')
disp('')
If = input('Please enter the symmetrical ground fault current ');
disp('We know If = 3*Io') % where Io is the ground fault current.
% Taken Future growth and safety or current projection factor, we add
20%
% of the fault current.
Iff = If * 1.2; % The symmetrical ground fault current with future
growth
% taken into account.
disp(['The new symmetrical ground fault If = ',num2str(Iff) ,' A'])
disp(['Using table# 10 for fault duration of ',num2str(ts),'s, and
X/R value of ',num2str(X_R)]);
Df = input('Please enter the value of the decrement factor (Df): ');
IF = Df * Iff ;
current.
%The effective rms value of approximate asymmetrical
99
disp(['The effective rms value of asymmetrical current IF is
',num2str(IF),' A'])
% Assuming the use of copper-clad steel wire with ambient temperature
(Ta)
% of 40 degree celcius with melting temperature of 1084 degree
celcius we
% get from table# 2,
disp('Assuming the use Copper-clad steel wire at ambient temperature
(Ta)')
disp('of 40 degree celcius with melting temperature of 1084 degree
celcius')
disp('we get from table# 3.1 the constant Kf')
disp('')
Kf = input('Enter the value of Kf ');
Akcmil = IF * Kf * sqrt(ts)./1000 ; % For copper-clad steel, the
required
% cross-sectinal area in circula
mils
% is
disp(['The cross-sectional area is in circular mils is
',num2str(Akcmil),' kcmil'])
% When converted in mm^2 we get
Amm2 = (Akcmil * 1000)./1973.2;
disp(['The cross-sectional area in mm^2 is ',num2str(Amm2),])
% Because Amm2 = pi*d^2 / 4, the conductor diameter is:
d = sqrt(Amm2*4/pi);
disp(['The conductor diameter is ',num2str(d),' mm or
',num2str(d/1000),' m'])
% Base on this computation, a Copper-clad steel wire as small as 3/0
can be used,
% but due to the mechanical strength and ruggedness requirement a
larger
% 250 kcmil stranded conductor with diameter.
Akcmil1 = input('Input the cross-sectional area of the chosen
conductor ');
dd = sqrt(Akcmil1*4/pi); % The chosen conductor diameter after
dd1 = dd / 1000;
% converting the conductor diameter in
milli-metter
disp(['The set conductor diameter is ',num2str(dd),' mm or
',num2str(dd1),' m'])
% Step# 3
% Step and touch criteria
100
disp('****** Step# 3 Step and touch criteria ******')
disp('')
hs1 = hs*39.37; % Converting the surface layer thickness hs in inch.
K = (Sr - Cr)/(Sr + Cr); % The reflection factor
disp(['for a ',num2str(hs),' m or ',num2str(hs1),' inch layer of
crushed rock surfacing,'])
disp(['with resistivity of ',num2str(Cr),' ohm*m and for an earth with
resistivity of ',num2str(Sr),])
disp([' ohm*m, the reflection factor K = ',num2str(K),])
% The reduction factor Cs
Cs =1- 0.09*(1 - Sr/Cr)/(2*hs + 0.09);
disp(['For K = ',num2str(K),' the resistivity of the crushed rock is
to be derated by a reduction factor of '])
disp([' approximately Cs = ',num2str(Cs),' after calculation of using
fig# 11 on page# 22 of IEEE std 80-2000'])
disp('As stated in the design criteria, the switchyard is operated by
a person spected to')
disp(['weight ',num2str(Wt),' or more'])
if (Wt > 50)
% step voltage 70 kg
Estp = (1000 + 6*Cs*Cr)*0.157/sqrt(ts);
% touch voltage 70 kg
Toch = (1000 + 1.5*Cs*Cr)*0.157/sqrt(ts);
else
% step voltage 50 kg
Estp = (1000 + 6*Cs*Cr)*0.116/sqrt(ts);
% touch voltage 50 kg
Toch = (1000 + 1.5*Cs*Cr)*0.116/sqrt(ts);
end
disp(['The step and touch voltages are respectively ',num2str(Estp),'
V and ',num2str(Toch),' V']);
101
% Step# 4
Initial design
%
disp('****** Step# 4 Initial design ******')
disp('')
D
h
l
L
=
=
=
=
input('Please
input('Please
input('Please
input('Please
enter
enter
enter
enter
the
the
the
the
grid spacing in m ');
depth of the grid beneath earth ');
number of vertical bares ');
number of horizontal bares ');
%while (Em < Toch && Es < Estp)
disp(['Assuming an area of ',num2str(A),' with equally spaced
conductors as shown in'])
disp(['the figure below with ',num2str(D),' m spacing, grid buried at
a depth of ',num2str(h),' m'])
Lst = l * Lx + L * Ly; % Total length of buried conductor in the
% horizontal grid in m
disp(['Total length of the conductor in the horizontal grid is
',num2str(Lst),' m'])
% Step# 5
Determination of the grid resistance
%
disp('****** Step# 5
Determination of the grid resistance******')
disp('')
Rd = input('Please enter the total number of rods to be place in the
grid ');
Lrd = input('Please enter the length of the rods to be place in the
grid ');
% The total grid
LR = Rd * Lrd; %
Lt = Lst + LR; %
disp(['The Total
perimeter calculation
Total length of all ground rods in m
Total length of buried conductor
length of buried conductor is ',num2str(Lt),' m'])
% Grid resistance calculation
Rg = Sr * (1/Lt + 1/sqrt(20*A)*(1 + 1/(1 + h*sqrt(20/A))));
disp(['The grid resistance is ',num2str(Rg),' ohms'])
102
% Step# 6
Maximum grid current IG calculation
%
disp('****** Step# 6 Maximum grid current IG calculation ******')
disp('')
% Combining equation (63) and equation (64) from the IEEE std 80-2000
we
% get
Sf = input('Please enter the split factor of the fault current ');
IG = Df * Iff * Sf ;
% The maximum grid current
disp(['The maximum grid current is ',num2str(IG),' A'])
%
to
%
% Step# 7
Now it is necessary to compare the product of IG and Rg, or GPR
the tolerable touch voltage, Toch calculated in step 3
disp('****** Step# 7 ******')
disp('')
GPR = IG * Rg;
% Ground potential rise.
if (GPR < Toch)
disp(['The GPR',num2str(GPR),' V is well below the safe touch
voltage',num2str(Toch),' V'])
disp('Now we can proceed to step# 12')
else
disp(['The GPR ',num2str(GPR),' V far exceed the safe touch voltage of
',num2str(Toch),' V'])
disp('Further design evaluations are necessary')
end
%
% Step# 8
Mesh and step voltage
disp('****** Step# 8 Mesh and step voltage ******')
disp('')
% Km is computed from equation (81) through equation(83) from IEEE std
% 80-2000
103
% The effective number of parallel conductors in a given grid, n, can
be
% made applicable to rectangular or irregularly shaped grids that
represent
% the number of parallel conductors of an equivalent rectangular grid.
% n = na*nb*nc*nd
% Km is the geometrical factor
% Ki is the corrective factor
Kii = 1;
Lp
na
nb
nc
nd
=
=
=
=
=
2*Lx + 2*Ly; % Perimeter of the grid area
2*Lst/Lp;
% Geometric factor
sqrt(Lp/(4*sqrt(A)));
% Geometric factor
1;
% Geometric factor
1;
n = na*nb*nc*nd ;
% The effective buried length LM to be used in the case of grids with
% ground rods in the corners, as well as along the perimeter and
throughout
% the grid.
LM = Lst + LR * (1.55 + 1.22*(Lrd/sqrt(Lx^2 + Ly^2)));
Ki = 0.644 + 0.148*n;
% The irregularity factor Ki
ho = 1; % The grid reference depth in meter
Kh = sqrt(1 + h/ho);
emphasizes the
% The corrective weighting factor that
% effects of grid depth, simplified method
Km = (1/(2*pi))*(log((D^2./(16*h*dd1))+((D+2+h)^2)./(8*D*h)(h./(4*dd1)))+ (Kii/Kh)*log(8./(pi*(2*n-1))));
% Finally, the mesh Em is computed from equation (80) and equation
(90)
% IEEE sdt 80-2000
Lm = Lt + LR;
% Effective length of Lt + LR for mesh voltage, if no
% ground rods is used or only few inside the grid.
if (Rd < 5)
equation
% If the number of rods is less than 5 then use
%Em = (Sr*IG*KM*Ki)/Lm;
Em = (Sr*IG*Km*Ki)/Lm; % Mesh voltage.
104
else
% If the number of rods is more than 5 use equation
% Em = (Sr*IG*KM*Ki)/LM;
Em = (Sr*IG*Km*Ki)/LM; % Mesh voltage.
end
Ls = 0.75*Lt + LR*0.85; % Ls is the effective buried conductor length
for
% grid with or without ground rods.
Ks = (1/pi)*( 1/(2*h) + 1/(D + h) + 1/7 * (1-0.5^(n-2))); % Spacing
factor
% for step voltage, simplified
method
Es = (Sr*Ks*Ki*IG)/Ls; % Step voltage.
disp(['The mesh and step voltage are respectively ',num2str(Em),' V
and ',num2str(Es),' V'])
% Step# 9
Compare the mesh voltage to the touch
%
disp('****** Step# 9 Compare the mesh voltage to the touch ******')
disp('')
if (Em < Toch)
disp(['The mesh ',num2str(Em),' V is well below the safe touch
voltage ',num2str(Toch),' V'])
disp('Now we can proceed to step# 10 ')
else
disp(['The mesh ',num2str(Em),' V far exceed the safe touch voltage
of ',num2str(Toch),' V'])
disp('The grid design must be modified')
end
% Step# 10
%
Compare the step voltage to the tolerable step voltage
disp('*** Step# 10 Compare the step volt. to the toterable step volt.
***')
disp('')
if (Es < Estp)&&(Em < Toch)
105
disp(['The step ',num2str(Es),' V is well below the tolerable step
voltage ',num2str(Estp),' V'])
disp('Now we can proceed to step# 12 ')
else
disp(['The step ',num2str(Es),' V far exceed the tolerable voltage
of ',num2str(Estp),' V'])
disp('The grid design must be modified')
end
%end
disp('A safe design has been obtained. At this point, all equipment
pigtails, additional ground ')
disp('')
disp('rods for surge arresters, etc., should be added to complete the
grid design details.')
106
The result of the simulation using the initial data.
Please enter the length in X direction 45
Please enter the length in Y direction 50
What is the fault duration in second .5
What is the X/R ratio 10
Enter the crushed rock resistivity ro_s 1500
Enter the surface layer thickness hs .52
Enter the soil resistivity 50
Please enter the minimum weight of the switchyard operators 50
****** Step# 1 Grid area ******
Substation area is 2250 m^2
****** Step# 2 Conductor sizing ******
Please enter the symmetrical ground fault current 14215
We know If = 3*Io
The new symmetrical ground fault If = 17058 A
Using table# 10 for fault duration of 0.5s, and X/R value of 10
Please enter the value of the decrement factor (Df): 1.026
107
The effective rms value of asymmetrical current IF is 17501.508 A
Assuming the use Copper-clad steel wire at ambient temperature (Ta)
of 40 degree celcius with melting temperature of 1084 degree celcius
we get from table# 3.1 the constant Kf
Enter the value of Kf 12.06
The cross-sectional area is in circular mils is 149.2477 kcmil
The cross-sectional area in mm^2 is 75.6374
The conductor diameter is 9.8135 mm or 0.0098135 m
Input the cross-sectional area of the chosen conductor 126.65
The set conductor diameter is 12.6987 mm or 0.012699 m
****** Step# 3 Step and touch criteria ******
for a 0.52 m or 20.4724 inch layer of crushed rock surfacing,
with resistivity of 1500 ohm*m and for an earth with resistivity of 50
ohm*m, the reflection factor K = -0.93548
For K = -0.93548 the resistivity of the crushed rock is to be derated by a reduction factor of
approximately Cs = 0.92301 after calculation of using fig# 11 on page# 22 of IEEE std 80-2000
As stated in the design criteria, the switchyard is operated by a person spected to
108
weight 50 or more
The step and touch voltages are respectively 1526.815 V and 504.7403 V
****** Step# 4 Initial design ******
Please enter the grid spacing in m 8
Please enter the depth of the grid beneath earth .5
Please enter the number of vertical bares 7
Please enter the number of horizontal bares 8
Assuming an area of 2250 with equally spaced conductors as shown in
the figure below with 8 m spacing, grid buried at a depth of 0.5 m
Total length of the conductor in the horizontal grid is 715 m
****** Step# 5 Determination of the grid resistance******
Please enter the total number of rods to be place in the grid 26
Please enter the length of the rods to be place in the grid 3
The Total length of buried conductor is 793 m
The grid resistance is 0.52385 ohms
****** Step# 6 Maximum grid current IG calculation ******
Please enter the split factor of the fault current .6
109
The maximum grid current is 10500.9048 A
****** Step# 7 ******
The GPR 5500.8498 V far exceed the safe touch voltage of 504.7403 V
Further design evaluations are necessary
****** Step# 8 Mesh and step voltage ******
The mesh and step voltage are respectively 881.6521 V and 559.0816 V
****** Step# 9 Compare the mesh voltage to the touch ******
The mesh 881.6521 V far exceed the safe touch voltage of 504.7403 V
The grid design must be modified
>>
The result of the simulation using the modified data.
Please enter the length in X direction 45
Please enter the length in Y direction 50
What is the fault duration in second .5
What is the X/R ratio 10
Enter the crushed rock resistivity ro_s 1500
Enter the surface layer thickness hs .2
110
Enter the soil resistivity 50
Please enter the minimum weight of the switchyard operators 50
****** Step# 1 Grid area ******
Substation area is 2250 m^2
****** Step# 2 Conductor sizing ******
Please enter the symmetrical ground fault current 14215
We know If = 3*Io
The new symmetrical ground fault If = 17058 A
Using table# 10 for fault duration of 0.5s, and X/R value of 10
Please enter the value of the decrement factor (Df): 1.026
The effective rms value of asymmetrical current IF is 17501.508 A
Assuming the use Copper-clad steel wire at ambient temperature (Ta)
of 40 degree celcius with melting temperature of 1084 degree celcius
we get from table# 3.1 the constant Kf
Enter the value of Kf 12.06
The cross-sectional area is in circular mils is 149.2477 kcmil
The cross-sectional area in mm^2 is 75.6374
111
The conductor diameter is 9.8135 mm or 0.0098135 m
Input the cross-sectional area of the chosen conductor 126.65
The set conductor diameter is 12.6987 mm or 0.012699 m
****** Step# 3 Step and touch criteria ******
for a 0.2 m or 7.874 inch layer of crushed rock surfacing,
with resistivity of 1500 ohm*m and for an earth with resistivity of 50
ohm*m, the reflection factor K = -0.93548
For K = -0.93548 the resistivity of the crushed rock is to be derated by a reduction factor of
approximately Cs = 0.82245 after calculation of using fig# 11 on page# 22 of IEEE std 80-2000
As stated in the design criteria, the switchyard is operated by a person spected to
weight 50 or more
The step and touch voltages are respectively 1378.3445 V and 467.6227 V
****** Step# 4 Initial design ******
Please enter the grid spacing in m 5
Please enter the depth of the grid beneath earth .7
Please enter the number of vertical bares 9
Please enter the number of horizontal bares 10
112
Assuming an area of 2250 with equally spaced conductors as shown in
the figure below with 5 m spacing, grid buried at a depth of 0.7 m
Total length of the conductor in the horizontal grid is 905 m
****** Step# 5 Determination of the grid resistance******
Please enter the total number of rods to be place in the grid 38
Please enter the length of the rods to be place in the grid 7
The Total length of buried conductor is 1171 m
The grid resistance is 0.49951 ohms
****** Step# 6 Maximum grid current IG calculation ******
Please enter the split factor of the fault current .6
The maximum grid current is 10500.9048 A
****** Step# 7 ******
The GPR 5245.3129 V far exceed the safe touch voltage of 467.6227 V
Further design evaluations are necessary
****** Step# 8 Mesh and step voltage ******
The mesh and step voltage are respectively 457.2628 V and 320.8668 V
****** Step# 9 Compare the mesh voltage to the touch ******
113
The mesh 457.2628 V is below the safe touch voltage 467.6227 V
We can proceed to step# 10
*** Step# 10 Compare the step volt. to the toterable step volt. ***
The step 320.8668 V is well below the tolerable step voltage 1378.3445 V
Now we can proceed to step# 12
A safe design has been obtained. At this point, all equipment pigtails, additional ground
rods for surge arresters, etc., should be added to complete the grid design details.
>>
114
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116