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SUBSTATION GROUNDING
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
Inna Baleva
SPRING 2012
ii
© 2012
Inna Baleva
ALL RIGHTS RESERVED
iii
SUBSTATION GROUNDING
A Project
by
Inna Baleva Approved by: __________________________________, Committee Chair Turan Gonen __________________________________, Committee Chair Salah Yousif ____________________________ Date
iv
Student: Inna Baleva
I certify that this student has 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 ___________________ Turan Gonen Date Department of Electrical and Electronic Engineering
v
Abstract
of
SUBSTATION GROUNDING
by
Inna Baleva
Statement of Problem
Designing a proper substation grounding system is quite complicating. Many parameters
affect its design. In order for a grounding design to be safe, it needs to provide a way to
carry the electric currents into the ground under both normal and faulted conditions. Also,
it must provide assurance that a person in the vicinity would not be endangered.
The grounding portion of substation design will be explored. In order to properly plan
and design the grounding grid, calculations of the following will be done: maximum fault
current, grid resistance, grid current, safe touch and step voltages, ground potential rise,
as well as expected touch and step voltage levels. Background information and guidelines
to design a substation grounding grid will be provided. A set of equations will be
presented to calculate whether the design is safe, and finally, an example will be provided
that can be used as a template.
vi
Sources of Data
IEEE Std. 80-2000
Conclusions Reached
A safe substation ground grid was designed.
_______________________, Committee Chair Turan Gonen
_______________________ Date
vii
TABLE OF CONTENTS Page
List of Tables .............................................................................................................. ix
List of Figures ............................................................................................................... x
Chapter
1. INTRODUCTION ..........……………………………………………………….. 1
2. LITERATURE SURVEY ....................................................................................... 3
2.1 Substation Grounding Overview................................................................. 3
2.2 Permissible Current Through a Human Body During the Fault ................. 4
2.3 Common Shock Situations ..........................................................................4
2.4 Design of a Substation Grounding System ..................................................5
2.5 Grid Connections ........................................................................................6
2.6 Material Selection .......................................................................................8
2.7 Soil Characteristics .....................................................................................9
2.8 Protective Surface Material .......................................................................10
2.9 Soil Resistivity Measurements ..................................................................12
2.9.1 Wenner’s Four-Pin Method .......................................................12
2.9.2 Schlumberger-Palmer Four-Pin Arrangement ...........................14
2.10 Ground Resistance ..................................................................................14
2.11 Design Procedures of a Grounding System ............................................15
2.12 Design Modifications ..............................................................................17
2.13 Construction of a Grounding System ......................................................18
2.13.1 Ground Grid Construction-Trench Method .............................18
2.13.2 Ground Grid Construction-Conductor Plowing Method .........19
2.13.3 Installation of Pigtails and Ground Rods .................................19
2.14 Computer Aided Design .........................................................................21
2.15 Special Danger Points .............................................................................21
2.15.1 Substation Fence Grounding ....................................................21
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2.15.2 Operating Handles ...................................................................22
2.15.3 Surge Arrestor Grounding ........................................................23
2.15.4 Control Cable Sheath Grounding .............................................23
3. THE MATHEMATICAL MODEL ...................................................................... 24
3.1 Introduction ...............................................................................................24
3.2 Tolerable Body Current Limits ..................................................................24
3.3 Circuit Equivalents for Common Shock Situations ..................................27
3.3.1 Resistance of the Human Body ..................................................27
3.3.2 Touch and Step Voltage ..............................................................27
3.4 Addition of Surface Layer ........................................................................31
3.5 Tolerable Step and Touch Voltage ...........................................................32
3.6 Conductor Sizing ......................................................................................34
3.7 Asymmetrical Currents .............................................................................37
3.8 Soil Resistivity Measurements ..................................................................37
3.9 Ground Resistance ....................................................................................39
3.10 Maximum Grid Current ..........................................................................40
3.11 Fault Currents ..........................................................................................41
3.12 Ground Potential Rise (GPR) ..................................................................42
3.13 Computing Maximum Step and Mesh Voltages .....................................43
3.13.1 Mesh Voltage (Em) ...................................................................43
3.13.2 Step Voltage (Es) ......................................................................46
4. APPLICATION OF MATHEMATICAL MODEL ................................................48
4.1 Introduction ...............................................................................................48
4.2 Initial Design .............................................................................................49
4.3 Design Using Copper-Clad Steel ..............................................................59
5. CONCLUSION .......................................................................................................61
Appendix ................................................................................................................... 62
References ................................................................................................................... 64
ix
LIST OF TABLES
Tables Page
1. Basic Range of Soil Resistivity....................... .……………………………….10
2. Typical Surface Material Resistivities ................ ……………………………. 11
3. Material Constants ..................... ………….…………………………………. 35
4. Material Constants .................................................. …………………………. 36
5. Typical Values of Df ............................................... …………………………. 38
6. Soil Resistivity Data Summary ............................... …………………………. 49
7. Conductor Properties .............................................. …………………………. 63
x
LIST OF FIGURES Figures Page
1. Basic Shock Situations ..................................... .………………………………. 7
2. Wenner’s Four-Pin Method ................................ ……………………………. 13
3. Schlumberger-Palmer Four-Pin Arrangement ................................................. 14
4. Design Procedure Block Diagram ................................................................... 20
5. Body Current vs. Time ..................................................................................... 26
6. Exposure to Touch Voltage ............................................................................. 28
7. Touch Voltage Circuit ...................................................................................... 28
8. Exposure to Step Voltage ................................................................................. 29
9. Step Voltage Circuit ......................................................................................... 29
10. Cs versus hs ......................................................................................................................................................... 32
11. Rectangular Grid with 22 Ground Rods .......................................................... 54
1
CHAPTER 1
INTRODUCTION
Safety and reliability are the two major concerns in the operation and design of an
electrical power system. These concerns also pertain to the design of substations. To
ensure that substations are safe and reliable, the substation must have a properly designed
grounding system.
The two main design goals to be achieved by any substation ground system under both
normal and fault conditions are:
1. To provide means to dissipate electric currents into the earth without exceeding
any operating and equipment limits
2. To assure that a person in the vicinity of grounded facilities is not exposed to the
danger of critical electric shock [4].
.
This project provides necessary background information for substation ground design. It
provides a set of guidelines that can be used, also it provides some design modification
suggestions that might help to alter the preliminary design if the mesh and step voltages
were greater than the tolerable voltages.
Also grounding system design was done for a transmission station using the IEEE Std.
80-2000 procedure as an example. Actual values from a transmission station were used
2
in the calculations, such as the measured soil resistivity, fault current, etc. Because
copper theft is a major problem, calculations using copper-clad steel were done as well.
3
CHAPTER 2
LITERATURE SURVEY
2.1 Substation Grounding Overview
Grounding is an important aspect of every substation. The function of a grounding system
is: to ensure the safety of personnel and the public, to minimize hazard from transferred
potential, to protect equipment, to provide a discharge path for lightning strikes, and to
provide a low-resistance path to ground. A good grounding system has a low resistance to
remote earth to minimize the ground potential rise (GPR) [2,4].
In order for a grounding design to be safe, it needs to provide a way to carry the electric
currents into the ground under both normal and faulted conditions. Also, it must provide
assurance that a person in the vicinity would not be endangered. Because there is no
simple relation between the resistance of the grounding system and the maximum shock
current a person can experience, a complete analysis must be done to consider many
different aspects such as the location of the ground electrodes, soil characteristics, etc [6].
People assume that any grounded object can be safely touched, but that is not always the
case. A low substation ground resistance doesn’t not guarantee safety [2-3]. There are no
simple relation between the ground system resistance and the maximum shock current
that a person might be exposed to [4].
4
2.2 Permissible Current Through a Human Body During the Fault
Humans are quite sensitive to AC currents ranging from 50-60 Hz. The effects of the AC
current going through a human body depend on the magnitude, duration, and also
frequency [6]. The threshold of perception for the human body is about 1mA. Currents
between 1-6 mA, often called let-go currents, usually do not impair a person from
controlling his muscles and releasing the energized object they were holding. Higher
currents ranging from 9-25 mA can cause pain and affect the muscle control so that the
energized object is hard if not impossible to release [1]. Still higher currents between 25-
75 mA can affect breathing and may cause fatality. If current is even higher, it could
result in ventricular fibrillation of the heart, which if not treated quickly, can result in
death [6]. When currents reach 100 mA and higher, above the ventricular fibrillation
level, it can cause burns, heart paralysis, and inhibition of breathing [1-3].
2.3 Common Shock Situations
There are three main electrical shock situations that can occur when a person is around a
substation. The first is a foot-to-foot shock which would involve the current going
through one foot and then out the other. This is typically caused by an increase in ground
potential rise which allows current to build up on the soil surface and then through
objects on the surface. The foot-to-foot shock is the least dangerous of the three because
the current does not go through vital organs such as the heart [4]. The second is hand-to-
feet which involves touching something that is electrified with the hand and having the
current pass into the ground through the feet. The final shock situation is a hand-to-hand
5
or metal-to-metal contact which would be touching something electrified with one hand
and having the current go through the other hand that is touching something else. These
shocks can usually be eliminated by connecting all the objects in the substation to the
grounding grid [4]. The use of a thin layer of surface material such as gravel around the
substation can greatly reduce the chance and strength of electric shocks. The gravel can
increase the resistance between the ground and a person thus making currents less likely
to pass through them. Figure 1 shows the different shock situations.
2.4 Design of a Substation Grounding System
The substation ground grid design is based on the substation layout plan. The following
points serve as guidelines to start a grounding grid design:
1. The substation should surround the perimeter and take up as much area as
possible to avoid high current concentrations. Using more area also reduces the
resistance of the grounding grid.
2. Typically conductors are laid in parallel lines. Where it is practical, the
conductors are laid along the structures or rows of equipment to provide short
ground connections.
3. Typical substation grid systems may include 4/0 bare copper conductor buried
0.3-0.5 m (12-18 in) below grade and spaced 3-7 m (10-20 ft) apart in a grid
pattern. The conductors should be securely bonded at cross-connections.
6
4. Ground rods may be installed at grid corners and junction points along the
perimeter. They may also be installed at major equipment, especially near surge
arresters.
5. The grid should extend over the entire substation and beyond the fence line [1-3].
6. The ratio of the sides of the grid meshes are usually 1:1 to 1:3 [1, 4].
To get started on the preliminary design, the following steps can be taken:
1. Draw the largest square, rectangular, triangular, T-shaped, or L-shaped grid that
will fit on the layout drawing [1].
2. Place grid conductors to produce square meshes, approximately 6.1-12.2 m (20-
40 ft)
3. Set the grid height equal to 0.4572 m (18 inches)
4. Set thickness of the surface material to 0.1016 m (4 inches)
5. Place ground rods around the perimeter [1].
2.5 Grid Connections
Typically different sized conductors are used in linking the substation to the grounding
grid. Any above-ground conductive material which could possibly become energized
such as a metal structures, machine frames, and transformer tanks or any metal parts that
could have a different potential from others should be tied together by the grounding grid
[4].
7
Figu
re 1
: Ba
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Situ
atio
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Ref.
IEEE
Std
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2000
Fig
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12. C
opyr
ight
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IEEE
. All
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erve
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8
All other equipment that could be the source of a fault current must also be connected to
the grid. Copper cable is often used for the connections, but in some cases the equipment
and buildings can be used as the conductor link [4]. Usually the grid connections are
securely welded together to prevent any failure during high fault currents.
2.6 Material Selection
Conductors can be of various materials including copper, copper-clad steel, aluminum, or
steel. Each type of conductor has advantages and disadvantages.
Copper is the most commonly used material for grounding. Copper has high conductivity.
Also, it is resistant to most underground corrosion because it is cathodic with respect o
most other metals [4]. It also has good temperature characteristics and thermal capacity.
The disadvantage of copper is that it is expensive and often stolen, leaving the equipment
ungrounded.
Copper-clad steel is usually used for ground rods, and sometimes for grounding grids.
Copper-clad steel has a fraction of the conductivity of copper, but it is adequate for use of
grounding. It combines the strength of steel with the conductivity of copper. Copper-clad
steel is less susceptible to theft than copper because it is a bimetallic product and has
virtually no recycle value.
9
Aluminum has good conductivity, but not as good as copper. Aluminum may corrode in
certain soils [4]. Aluminum costs less than copper, and theft is less of an issue. It’s fusing
temperature is about half of copper and its thermal capacity is about two thirds.
Steel can be used for ground grid conductors and rods, but corrosion is an issue. Steel has
good temperature characteristics and thermal capacity as well. Theft is not an issue for
steel.
2.7 Soil Characteristics
The earth’s soil can be considered to be a pure resistance and thus is the final location
that a fault current is dispersed. Soil resistance can contain a current up to a critical
amount which varies depending on the soil and at this point, electrical arcs can develop
on the surface of the soil that can electrify objects on the surface such as a person [4]. A
soil’s resistivity can be affected by the flow of current through it by being heated which
makes the soil dry out and become more resistive [4]. Wet soil has much less resistance
than that of dry soil so ideally the grounding grid and rods should be located in moist
earth. Typically soil resistance quickly increases when its moisture content is less than
15% of the soil weight and the resistance barely changes once the moisture content is at
least 22% [4]. Table 1 shows a basic collection of soil resistivity depending on the
moisture and type.
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Table 1: Basic Range of Soil Resistivity Ref. IEEE Std, 80, Table 8. Copyright ©2000. IEEE. All rights Reserved
Type of Earth Average Resistivity (Ω·m) Wet Organic Soil 10
Moist Soil 102 Dry Soil 103
Bedrock 104
Table 1 shows that wet or even moist soil have very small resistances so it is beneficial to
keep the grounding soil as damp as possible. A common practice to help accomplish this
is to use of a surface material layer such as gravel. Not only does a surface material
greatly reduce the amount of soil evaporation, but it typically has a high resistance which
reduces the magnitudes and chances of shock currents occurring [4]. Soil characteristics
and the type of surface layer to be used vary depending on the area in the world in which
the substation is located and what is required by the grounding system.
2.8 Protective Surface Material
In order to greatly reduce the shock current and increase the contact resistance between
the soil and the feet of people in a substation, a thin layer of a highly resistive protective
surface material just as crushed rock (gravel) is spread above the earth grade at a
substation. Generally a layer of the surface material is 3-6 inches and it extends 3-4 feet
outside the substation fence. If it is not extended beyond the substation fence, the touch
voltages become dangerously high [1].
11
The resistivity values for the surface material layers vary. The range depends on many
factors such as type of stone, size, condition of the stone, amount and type of moisture
content, atmospheric contamination, etc [1]. Table 2 shows typical resistivity values for
different types of surface materials. These values were measured by several different
parties in different regions of the United States. These values are not valid for every type
and size of stone in every region, thus tests need to be done for the resistivity in the
region’s substation [1].
Table 2: Typical Surface Material Resistivities. Ref. IEEE Std, 80, Table 7. Copyright ©2000. IEEE. All rights Reserved
Number Description of surface material (U.S. State where found)
Resistivity of sample Ω·m Dry Wet
1 Crusher run granite with fines (N.C.)
140 x 106 1300(ground water, 45 Ω·m)
2 1.5 in(0.04m) crusher run granite (Ga.) with fines
4000 1200(rain water, 100W)
3 0.75-1 in(0.02-0.025 m) granite (Calif.) with fines
- 6513(10 min after 45 Ω·m water drained)
4 #4 (1-2in) (0.025-0.05 m) washed granite (Ga.)
1.5 x 106 to 4.5 x 106 5000 (rain water, 100 Ω·m)
5 #3 (2-4 in) (0.05-0.1 m) washed granite (Ga.)
2.6 x 106 to 3 x 106 10 000 (rain water, 100 Ω·m)
6 Size unknown, washed limestone (Mich.)
7 x 106 2000-3000 (ground water, 45 Ω·m)
7 Washed granite, similar to 0.75 in (0.02m) gravel
2 x 106 10 000
8 Washed granite, similar to pea gravel
40 x 106 5000
9 #57 (0.75 om) (0.02 m) washed granite (N.C.)
190 x 106 8000 (ground water, 45 Ω·m)
10 Asphalt 2 x 106 to 30 x 106 10 000 to 6 x 106 11 Concrete 1 x 106 to 1 x 109 a 21 to 100
a Oven dried concrete. Values for air-cured concrete can be much lower due to moisture content.
12
2.9 Soil Resistivity Measurements
Before the design of the grounding system begins, soil resistivity measurements need to
be taken at the substation[1]. Stations with uniform resistivity throughout the entire area
are rarely found. Thus, measurements should be made at multiple locations within the
site. Usually there are several layers, and each has a different resistivity. If there are large
variations, more readings should be taken at these locations [4]. Lateral changes may
occur as well, but in general the changes are gradual and negligible [4].
There are a number of measuring techniques. With two-point methods, rough
measurements of the resistivity of undisturbed earth can be made. Three-point method or
variation of depth method measured ground-resistance test several times. Each time the
burial depth of the test electrode is increased by a certain amount. But this method is not
recommended if large volume of soil needs to be investigated. Four-pin methods are the
most accurate method of measuring the average resistivity of large values [5].
2.9.1 Wenner’s Four-Pin Method
The Wenner’s four-pin method is the most common. This method is also called the
Equally- Spaced Four-Pin method. [5]. In this technique, four probes are driven into the
ground in a straight line to a depth b, at equal distances a apart. The voltage between the
two inner probes is measured and is divided by the current of the two outer probes. This
gives a value of the mutual resistance R. The Wenner’s four-pin method is shown in
Figure 2 below [5].
13
Figure 2: Wenner’s Four-Pin Method Ref. IEEE Std. 81-1983
Figure 3(a). Copyright © 1983. IEEE. All rights reserved.
The resistivity measurement records should include temperature data and information on
the soil moisture conditions at the time that the measurements were done. Also record all
data available on any buried conductors already known or suspected. Buried conductors
in contact with the soil can invalidate readings if they are close enough by altering the
test current flow pattern [4].
The Wenner four-pin method is popular for a number of reasons. This method obtains
soil resistivity data for deeper layers without having to drive the test pins to those layers.
Also, no heavy equipment is needed [1,3]. The results are not greatly affected by the
resistance of the test pins or the holes created by driving the test pins into the soil [1].
A shortcoming of the Wenner method is that the magnitude of the potential between the
two inner electrodes rapidly decreases when their spacing is increased to large values.
And often times commercial instruments cannot measure such low potential values [5].
14
2.9.2 Schlumberger-Palmer Four-Pin Arrangement
The Schlumberger-Palmer arrangement is another four-pin method. It is also called the
Unequally- Spaced Four-Pin method [5]. This method is similar to the Wenner’s Four-
Pin method. For this method, there is a larger spacing between the current electrodes. The
potential probes are brought closer to the corresponding current electrodes. Doing this
increases the measured potential value. Figure 3 shows the Schlumberger-Palmer
arrangement [5].
Figure 3: Schlumberger-Palmer Four-Pin Arrangement Ref. IEEE Std. 81-1983
Figure 3(b). Copyright © 1983. IEEE. All rights reserved.
2.10 Ground Resistance
The ground resistance for a substation needs to be very low to minimize the ground
potential rise and increase the safety of the substation [2,6]. The ground resistance is
usually 1 Ω or less for transmission and other large substations [1-4] . In distribution
substations, the usual acceptable range is 1-5Ω [4]. Resistance primarily depends on the
area to be occupied. Also resistance can be decreased for a given area by using ground
15
rods and adding more grid conductors. If it is impossible to reach a desired ground
resistance by adding more grid conductors and/or ground rods, the soil surrounding the
electrode can be modified.
Sodium chloride, magnesium, and copper sulfates, or calcium chloride can be used to
increase the conductivity of the soil immediately surround the electrodes. Another
method is to place a ground enhancement material around the rod. Other methods are
mentioned in IEEE Std. 80-2000 [4].
2.11 Design Procedures of a Grounding System
The design process of a substation grounding system requires many steps. The following
steps were established by the IEEE Standard 80-2000 for the design of the ground grid:
Step 1: The property map and general location plan of the substation should provide good estimates of the area to be grounded. A soil resistivity test will determine the soil resistivity profile and the soil model needed. Step 2: The conductor size is determined. The fault current 3I0 should be the maximum expected future fault current that will be conducted by any conductor in the grounding system, and the time, tc, should reflect the maximum possible clearing time (including backup). Step 3: The tolerable touch and step voltages are [to be] determined. The choice of time, ts, is based on the judgment of the design engineer. Step 4: The preliminary design should include a conductor loop surrounding the entire grounded area, plus adequate cross conductors to provide convenient access for equipment grounds, etc. The initial estimates of conductor spacing and ground rod locations should be based on the current, IG, and the area being grounded.
16
Step 5: Estimates of the preliminary resistance of the grounding system in uniform soil can be determined. For the final design, more accurate estimates of the resistance may be desired. Computer analysis based on modeling the components of the grounding system in detail can compute the resistance with a high degree of accuracy, assuming the soil model is chosen correctly. Step 6: The current, IG, is determined. To prevent overdesign of the grounding system, only that portion of the total fault current, 3I0, that flows through the grid to remote earth should be used in designing the grid. The current, IG, should, however, reflect the worst fault type and location, the decrement factor, and any future system expansion. Step 7: If the GPR of the preliminary design is below the tolerable touch voltage, no further analysis is necessary. Only additional conductor required to provide access to equipment grounds is necessary. Step 8: The calculation of the mesh and step voltages for the grid as designed can be done by the approximate analysis techniques for uniform soil, or by the more accurate computer analysis techniques. Step 9: If the computed mesh voltage is below the tolerable touch voltage, the design may be complete (see Step 10). If the computed mesh voltage is greater than the tolerable touch voltage, the preliminary design should be revised (see Step 11). Step 10: If both the computed touch and step voltages are below the tolerable voltages, the design needs only the refinements required to provide access to equipment grounds. If not, the preliminary design must be revised (see Step 11). Step 11: If either the step or touch tolerable limits are exceeded, revision of the grid design is required. These revisions may include smaller conductor spacing, additional ground rods, etc. More discussion on the revision of the grid design to satisfy the step and touch voltage limits is given in [Section 2.12] Step 12: After satisfying the step and touch voltage requirements, additional grid and ground rods may be required. The additional grid conductors may be required if the grid design does not include conductors near equipment to be grounded.
17
Additional ground rods may be required at the base of surge arresters, transformer neutrals, etc. The final design should also be reviewed to eliminate hazards due to transferred potential and hazards associated with special areas of concern [4, pp. 88-89].
The block diagram in Figure 4 illustrates the procedure to design the ground grid.
2.12 Design Modifications
If the calculated grid mesh and step voltages are greater than the tolerable touch and step
voltages, then the preliminary design needs to be modified. The following are possible
remedies:
(a) Decrease total grid resistance: If the total grid resistance is decreased, the maximum
GPR is decreased; hence the maximum transferred voltage is decreased. An effective
way to decrease the grid resistance is to increase the area occupied by the grid. Deep
driven rods or wells can be used also if area is limited.
(b) Decrease grid spacings: Decrease the mesh size by increasing the number of parallel
conductors in each direction. Dangerous potentials within the substation can be
eliminated. For the perimeter, a ground conductor can be buried outside the fence, or
increase the density of ground rods at the perimeter.
(c) Increase the thickness of the surface layer: a practical limit may be 6 inches.
(d) Limit total fault current: If feasible, limiting the total fault current will decrease the
GPR and gradients in proportion.
(e) Diverting greater part of the fault current to other paths
18
(f) Barring access to limited areas: if practical, can reduce the probability of hazards to
personnel [1,4].
2.13 Construction of a Grounding System
The method chosen for construction depends on the size of the grid, soil type, size of
conductor, burial depth, equipment available, cost of labor, and physical or safety
restrictions. There are two common ways to install the ground grid. These methods are
the trench method and the cable plowing method. Both methods use machines. If the job
site is too small or there is not enough space to move the machines around, then the
ground grid is installed by hand digging [4].
2.13.1 Ground Grid Construction-Trench Method
Markers are placed on the perimeter to identify the spacing between the parallel
conductors. These markers serve as a guide for the trenching machine. The trench
machine is used to dig trenches along the side having a larger number of parallel
conductors to a specified depth, usually 0.5 m (1.5 ft). Conductors are then installed in
these trenches and the ground rods are driven and connected to the conductors. Pigtails
for the equipment grounds are also placed at this time. These trenches are then backfilled
with dirt up the cross connections.
Cross-conductor trenches are then dug, again using markers as guides. Conductors are
installed and any remaining ground rods are driven and connected to the conductors. Also
19
remaining pigtails are connected. Then cross-type connections are made between the
perpendicular conductor runs. Finally the trenches are filled with dirt [4].
2.13.2 Ground Grid Construction-Conductor Plowing Method
This method is economical and quick when conditions are favorable and the proper
equipment is available. This method plows the conductors in using a special narrow
plow. This plow can be attached to, or drawn by, a tractor or a four-wheel drive truck.
The conductor is laid on the ground either in front of the plow or a reel of conductor is
fed into the ground along the blade of the plow. For the cross conductors, they are
plowed in at a slightly less depth in order to avoid damaging the previously laid
conductors. The points of crossing and points where ground rods are to be installed are
then uncovered and connections are made [4].
2.13.3 Installation of Pigtails and Ground Rods
Pigtails are left for grounding connections to equipment or structures. Pigtails can be the
same cable size as the underground grid, or a different size. This depends on the number
of grounds per device as well as the magnitude of the ground fault current.
Ground rods are installed using a hydraulic hammer, air hammer, or other mechanical
devices. Two ground rods are joined by either using a exothermic method or a threaded
or threadless coupler [4].
20
Figure 4 : Design Procedure Block Diagram. Ref. IEEE Std. 80-2000 Figure 33. Copyright © 2000. IEEE. All rights reserved.
21
2.14 Computer Aided Design
Computers are frequently used in designing substation grounding systems. Some reasons
to use computer analysis are
1. The parameters exceed those of the simplified design equations.
2. A two-layer or multi-layer soil model is preferred due to significant variations
in soil resistivity.
3. Uneven grid conductor or ground rod spacing.
4. Flexibility in determining local danger points
5. Presence of buried metallic structures/conductors that are not connected to the
grounding system introduces complexity
6. Preliminary design can be optimized and analyzed [1,4].
2.15 Special Danger Points
There are several danger points within a substation such as the fence, equipment
operating handles, surge arrestors, etc. One has to make sure that they are properly
grounded to ensure safety.
2.15.1 Substation Fence Grounding
It is critical to ground the substation fence because the fence is generally accessible to the
public. The touch potential on both sides of the fence needs to be within the calculated
tolerable touch potential limit. The substation fence should be connected to the main
22
ground grid. An outer grid conductor should be installed a minimum of 0.91 m (3 feet)
outside the fence. Connections to the outer grid conductor should be made at all corners
posts and at line posts every 12.92-15.24 m (40-50 feet). The gatepost should be bonded
securely to the fence. It is also recommended that all gates swing inward [1,4].
2.15.2 Operating Handles
Equipment operating handles represent a significant concern if not adequately grounded
because it requires the presence of an operator near a grounded structure. If a fault
occurs, the operator may be subjected to an electrical shock. If the grounding system was
designed with IEEE Std. 80, then the touch and step voltages near the operating handle
should be within safe limits. But in most cases additional means are taken in order to
provide a greater safety factor for the operator. Some practices include connecting the
switch operating shaft to a ground mat. The ground mat is directly connected to the
ground grid and also the switch operating shaft. The operator stands of the mat when
operating the switch. Using these techniques provides a direct bypass to ground [4].
Utilities use different practices to ground the switch operating shaft. About half of the
utilities provide a direct jumper between the switch shaft and the ground mat. The other
half provided a jumper from the switch shaft to the adjacent grounded structural steel and
the steel is used as part of the conducting path. About 90% of utilities use a braid for
grounding the switch shaft [4].
23
2.15.3 Surge Arrestor Grounding
Surge arrestors need to be reliably grounded to ensure protection of the equipment they
are protecting. They should be connected as close as possible to the terminals of the
equipment it’s protecting and have as short and direct path to the grounding system as
possible and practical [4]. Also arrestor leads should be as free from sharp bends as
practical [1].
2.15.4 Control Cable Sheath Grounding
Metallic cable sheaths may attain dangerous voltage levels with respect to ground if not
effectively grounded. All grounding connections should be made to provide a permanent
low-resistance bond. Cable sheaths should be grounded at two or more locations [1,4].
24
CHAPTER 3
THE MATHEMATICAL MODEL
3.1 Introduction
In order to design a proper and safe substation grounding system, various safety
parameters must be found such as the touch and step voltage levels. Each grounding
system must be uniquely designed in order to have the mesh and step voltages below the
tolerable touch and step voltages of the personnel that might be working at the site when
a fault occurs. This chapter provides the process and equations to safely design a
substation grounding system.
3.2 Tolerable Body Current Limits
A human body at 50Hz or 60Hz can gave duration of the current less than the value that
can cause ventricular fibrillation of the heart. Ventricular fibrillation is caused when the
body current replaces the normal rhythmic contraction of the heart and may cause a lack
of circulation and pulse [1-4,6].
Dalziel’s studies show that the no fibrillation current of magnitude, IB, at duration ranging
from 0.03-3.0 s can be simply expressed as:
Bs
kIt
= (3.1)
where Bk S=
25
and
BI : rms magnitude of the current through the body (A)
st : duration of the current exposure (s)
BS : shock energy k : constant related to electric shock energy
Based on Dalziel’s studies, 99.5% of people can safely withstand the magnitude of the
current without ventricular fibrillation. Dalziel also found that the shock energy constant
to vary with weight [4]. For a person weighing approximately 50 kg (110 lb) 50k = 0.116,
thus the formula for allowable body current becomes:
500.116
Bs
It
= (3.2)
For a person weighing approximately 70 kg (155 lb) 50k = 0.157, thus the formula for
allowable body current becomes:
700.157
Bs
It
= (3.3)
This equation is not valued for very short or very long duration.
Biegelmeier’s curve in Figure 5 shows the body current versus time. This curve has a
500mA limit for times up to 0.2 s, then the limit decreases to 50 mA at 2 s and beyond.
This figure also shows a comparison of the body current for both a 50 kg and a 70 kg
person.
26
In modern operating practices, recourse after a ground fault is common. In circumstances
where there are reclosures, a person might experience the first shock without permanent
injury. But then an automatic reclosure can result in another shock less than 0.33 seconds
of the first shock. This second shock that occurs after a short interval of time before the
person can recover from the initial can cause a serious accident [1,4].
Figure 5 : Body Current vs. Time. Ref. IEEE Std. 80-2000 Figure 5. Copyright © 2000. IEEE. All rights reserved.
27
3.3 Circuit Equivalents for Common Shock Situations
3.3.1 Resistance of the Human Body
The human body can be approximated as a resistance for DC and 50 Hz or 60 Hz AC
currents. The current path is considered from one had to both feet or from one foot to the
other. The internal resistance of a human body is approximately 300 Ω. The body
resistance including skin ranges from 500-3000 Ω [4]. For simplicity, IEEE Std 80-2000
represents the resistance of a human body from hand-to-feet and also from hand-to-hand,
or from one foot to the other as
1000BR = Ω (3.4)
3.3.2 Touch and Step Voltage
The accidental circuit in Figure 6 is the result of hand-to-feet contact. The voltage found
in this circuit is referred to as touch voltage because it results from someone touching an
electrified object while the feet are in contact with the ground. In most cases the limiting
factor for a grounding design is the tolerable touch voltage [1]. Figure 7 serves as a visual
aid in displaying a typical hand-to-feet circuit through a person.
Another accidental circuit occurs as a result of foot-to-foot contact as seen in Figure 8.
The voltage found in this circuit can be referred to as the step voltage because it would
result from someone standing on soil which has current build up on its surface due to a
ground potential rise [4]. Figure 9 serves as a visual aid in displaying a typical foot-to-
foot circuit through a person.
28
Figure 6 : Exposure to Touch Voltage. Ref. IEEE Std. 80-2000 Figure 6. Copyright © 2000. IEEE. All rights reserved.
Figure 7 : Touch Voltage Circuit. Ref. IEEE Std. 80-2000 Figure 8. Copyright © 2000. IEEE. All rights reserved.
29
Figure 8: Exposure to Step Voltage.
Ref. IEEE Std. 80-2000 Figure 9. Copyright © 2000. IEEE. All rights reserved.
Figure 9 : Step Voltage Circuit
Ref. IEEE Std. 80-2000 Figure 10. Copyright © 2000. IEEE. All rights reserved.
Using Figure 6 or Figure 8, the Thevenin equivalent circuit for the current through the
body, bI , of a person is:
Thb
Th B
VIZ R
=+ (3.5)
where:
30
ThV : Thevenin voltage between terminal H and F (V)
ThZ : Thevenin impedance from point H and F (Ω)
BR : body Resistance (Ω)
The Thevenin equivalent impedance for the touch voltage accidental circuit is:
2f
Th
RZ =
(3.6) The Thevinin equivalent impedance for the step voltage accidental circuit is:
2Th fZ R= (3.7)
where: fR : ground resistance of one foot
In circuit analysis, a human foot is represented as a conducting metallic disc and
resistance of the shoes and socks are neglected.
The equation to calculate the ground resistance fR is:
4fRbρ
= (3.8)
where: ρ : earth’s resistivity (Ω·m) b : radius of a foot taken as a metallic disk (typically 0.08m)
Using a circular plate of approximately 0.08m, the equations for Zth are:
For touch voltage accidental circuit
1.5thZ ρ= (3.9)
And for step voltage accidental circuit
31
6thZ ρ= (3.10)
3.4 Addition of Surface Layer When possible, substations place a layer of highly resistive material such as crushed rock.
The addition of a surface layer changes the ground resistance, Rf . The new ground
resistance becomes:
4s
f sR Cbρ =
(3.11)
The surface layer derating factor, Cs, can be calculated as:
0.09 11
2 0.09s
Ss
Ch
ρρ
−
= −+ (3.12)
where ρ : resistivity of the earth (Ω·m) ρs : resistivity of surface layer material (Ω·m) hs : thickness of surface material (m)
Cs can also be approximated by first calculating the reflection factor between the different
materials, K, and then using Table 10.
The reflection factor is calculated as:
s
s
K ρ ρρ ρ−
=+ (3.13)
32
Figure 10 : Cs versus hs Ref. IEEE Std. 80-2000 Figure 11. Copyright © 2000. IEEE. All rights reserved.
3.5 Tolerable Step and Touch Voltage
When designing a substation grounding system, the maximum tolerable voltages must be
calculated in order to create a proper ground grid. These voltages depend on the soil
resistivity, soil layer and the duration of the shock current. The maximum driving voltage
of any accidental circuit shouldn’t exceed the step voltage and touch voltage limits.
For step voltage the limit is:
33
( 2 )step B f BE R R I= + ⋅ ⋅ (3.14)
For a body weighing 50 kg
500.116(1000 6 )step s s
s
E Ct
ρ= + ⋅ ⋅ (3.15)
For a body weighing 70 kg
700.157(1000 6 )step s s
s
E Ct
ρ= + ⋅ ⋅ (3.16)
For touch voltage, the limit is
2f
touch B B
RE R I
= + ⋅
(3.18)
For a body weighing 50 kg
500.116(1000 1.5 )touch s s
s
E Ct
ρ= + ⋅ ⋅ (3.19)
For a body weighing 70 kg
700.157(1000 1.5 )touch s s
s
E Ct
ρ= + ⋅ ⋅ (3.20)
If no protective surface layer is used in the substation, Cs = 1 and ρs=ρ .
If there is metal-to-metal contact, both hand-to-hand and hand-to-feet contact, ρs=0 since
the ground is not included in this situation. In this case, the touch voltage limit equations
are:
34
For a body weighing 50 kg
50116
mm touchs
Et− = (3.21)
For a body weighing 70kg
70157
mm touchs
Et− = (3.22)
3.6 Conductor Sizing
The symmetrical current can be calculated based on the material and the size of the conductor used as:
2
40
0
10 ln mmm
c r r a
K TTCAPI At K Tα ρ
− +⋅= +
(3.23)
If the conductor size is given in kcmil, the equation becomes:
3 0
0
5.07 10 ln mkcmil
c r r a
K TTCAPI At K Tα ρ
− += ⋅ +
(3.24)
Where I : rms current (kA) Amm
2 : conductor cross section (mm2) Akcmil : conductor cross section (kcmil) Tm : maximum allowable temperature (oC) Ta : ambient temperature (oC) αr : thermal coefficient of resistivity at reference temperature Tr (1/ oC) ρr : resistivity of the ground conductor at reference temperature Tr (µΩ-cm) tc : duration of current (s) K0 : equals 1/ α0 or (1/ αr)- Tr (oC) TCAP : thermal capacity per unit volume (J/𝑐𝑚2 ∙ )
35
Common values of αr, K0, Tm, ρr, and TCAP values can be found in Table 3.
Table 3-Material Constants Ref. IEEE Std 80-2000 Table 1. Copyright © 2000. IEEE. All rights reserved
Description Material
Conductivity
(%)
αr factor at
20oC
(1/ oC )
K0 at
0oC
(0oC )
Fusinga
temperature
Tm (oC )
ρr 20oC
(µΩ-cm)
TCAP thermal capacity [J/(cm3·oC)]
Copper,
annealed soft-
drawn
100.0 0.00393 234 1083 1.72 3.42
Copper,
commercial
hard-drawn
97.0 0.00381 242 1084 1.78 3.42
Copper-clad
steel wire
40.0 0.00378 245 1084 4.40 3.85
Copper-clad steel wire
30.0 0.00378 245 1084 5.86 3.85
Copper-clad steel rodb 20.0 0.00378 245 1084 8.62 3.85
Aluminum, EC grade 64.0 0.00403 228 657 2.86 2.56
Aluminum, 5005 alloy
53.5
0.00353 263 652 3.22 2.60
Aluminum, 6201 alloy
52.5 0.00347 2268 654 3.28 2.60
Aluminum-clad steel wire
20.3 0.00360 258 657 8.48 3.58
Steel-1020 10.8 0.00160 605 1510 15.90 3.28 Stainless-clad steel rodc
9.8 0.00160 605 1400 17.50 4.44
Zinc-coated steel rod
8.6 0.00320 293 419 20.10 3.93
Stainless steel, 304
2.4 0.00130 749 1400 72.00 4.03 aFrom ASTM standards. bCopper-clad steel rods based on 0.254 mm (0.010 in) copper thickness. cStainless-clad steel rod based on 0.508 mm (0.020 in) No. 304 stainless steel thickness over No. 1020 steel core.
36
The required area for a conductor given a current can be calculated as:
24
0
0
1
10 lnmm
m
c r r a
A IK TTCAP
t K Tα ρ
−=
+⋅ +
(3.25)
or
0
0
197.4
lnkcmil
m
c r r a
A IK TTCAP
t K Tα ρ
= + +
(3.26)
Equation (3.26) can be simplified as:
kcmil f cA I K t= ⋅ (3.27)
where
Kf : constant found in Table 4 which is based on the fusing and ambient temperature of the material
Table 4-Material Constants
Ref. IEEE Std 80-2000 Table 2. Copyright © 2000. IEEE. All rights reserved Material Conductivity
(%) Tm
a (°C) 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 53.4 652 12.41 Aluminum 6201 Alloy 62.5 654 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 14.72 Zing-coated steel rod 8.6 419 28.96 Stainless steel 304 2.4 1400 30.05
37
The following equation can be used to convert the conductor size from kcmil to mm2 :
2
10001973.52kcmil
mm
AA ⋅= (3.28)
The diameter of a conductor can be calculated as:
2
( ) 2 mmc mm
Ad
π=
(3.29)
3.7 Asymmetrical Currents
If the effect of the dc offset is needed to be included in the fault current, the values of the
symmetrical current is found by:
F f fI I D= ⋅ (3.30)
The decremental factor, Df, can be calculated as:
2
1 1f
a
tTa
ff
TD et
− = + −
(3.31)
where tf : time duration of the fault (s)
a
XTRω
= (3.32)
The typical decremental factors can also be found from Table 3.
3.8 Soil Resistivity Measurements
The methods for soil resistivity measurements are discussed in 2.9. Since the Wenner’s
four-pin method is the most common, only calculations for this method will be discussed.
38
Table 5-Typical Values of Df Ref. IEEE Std 80-2000 Table 10. Copyright © 2000. IEEE. All rights reserved Fault Duration, tf Decrement factor, Df
Seconds Cycles at 60 Hz
X/R =10 X/R =20 X/R =30 X/R =40
0.00833 0.5 1.576 1.648 1.675 1.688 0.05 3 1.232 1.378 1.462 1.515 0.10 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 1.2026 1.052 1.077 1.101 0.75 45 1.018 1.035 1.052 1.068 1.00 60 1.013 1.026 1.039 1.052
As mentioned in 2.9 the mutual resistance R is determined by dividing the voltage
between the two inner probes by the current of the two outer probes. Using the mutual
resistance R, the soil resistivity can be calculated as follows:
2 2 2 2
421
4
aRa a
a b a b
πρ =+ −
+ +
(3.33)
where ρ : soil resistivity (Ω·m) R : measured resistance (Ω) a : distance between adjacent electrodes (m) b : depth of the electrodes (m)
If b<<a the above equation (3.33) can be simplified to
2 aRρ π= (3.34)
For small probe spacing, the current tends to flow near the surface; but for large spacing,
more of the current penetrates deeper soils. Thus it is a reasonable to assume that the
39
resistivity measure for a probe of spacing a represents the apparent soil resistivity of
depth a [1].
3.9 Ground Resistance
One of the first steps in determining the size and layout of the grounding system is the
estimation of the total resistance to remote earth. Resistance primarily depends on the
area of the grounding system. In early stages of the design, the area to be occupied is
usually known [4,6]. As an approximation, the minimum value of the substation
grounding resistance in uniform soil can be estimated as:
4gRA
ρ π= (3.35)
Where
Rg : substation ground resistance (Ω) ρ : soil resistivity (Ω-m) A : area occupied by the ground grid (𝑚2)
Laurent and Niemann proposed a method of calculating the substation ground resistance
by adding a second term. This equation gives an upper limit of the substation ground
resistance. This proposed equation is:
4g
T
RA L
ρ π ρ= + (3.36)
where LT : total burial length of conductors (m)
40
The total burial length is the combination of the horizontal and vertical conductors in the
grid as well as the ground rods. LT can be calculated as:
T C RL L L= + (3.37) where
LC : total length of grid conductor (m) LR : total length of ground rods (m)
A better approximation was determined to include the grid depth
1 1 11
20 1 20 /gT
RL A h A
ρ
= + + + (3.38)
where h : depth of the grid (m)
This equations shows that a larger the area and the greater the total length of the
grounding conductor used would resulting a lower ground grid resistance.
3.10 Maximum Grid Current
A portion of the fault current will flow through the grounding grid to the earth. This is
called the grid current and must be calculated. The maximum grid current, IG, can be
calculated as:
G f gI D I= ⋅ (3.39)
where IG : maximum grid current (A)
Df : decrement factor for the duration of the fault (From Table 5) Ig : rms symmetrical grid current (A) The symmetrical grid current, Ig, is the portion of the symmetrical ground fault current
that flows between the grid and surrounding earth. It is expressed as:
41
g f fI S I= ⋅ (3.40)
where Ig : rms symmetrical grid current (A)
If : rms symmetrical grid fault current (A) Sf : fault current division factor
3.11 Fault Currents
Many different faults can occur in a system. It is difficult to determine the fault type and
location that would result in the greatest current flow between the ground grid and the
surrounding earth. When determining the applicable faults types, the probability of
occurrence needs to be considered. It is recommended to consider single-line-to-ground
and double-line-to-ground faults [2,3,6].
In the case of a double –line-to-ground fault, the zero-sequence fault current is:
2 20
1 1 0 1 0 2 2 2 0 0
( )( ) [( 3 ( )] ( ) ( 3 )f f
E R jXIR jX R R R j X X R jX R R jX
⋅ +=
+ ⋅ + + + + + + ⋅ + +(3.41)
where I0 : symmetrical rms value of zero sequence fault current (A) E : phase-to-neutral voltage (V) Rf : estimated resistance of the fault, normally assumed 0 (Ω) R2 : negative sequence equivalent system resistance (Ω) R1 : positive sequence equivalent system resistance (Ω) R0 : zero sequence equivalent system resistance (Ω) X2 : negative sequence equivalent system reactance (Ω) X1 : positive sequence equivalent system reactance (Ω) X0 : zero sequence equivalent system reactance (Ω)
In the case of a single –line-to-ground fault, the zero-sequence fault current is:
42
01 2 0 1 2 03 ( )f
EIR R R R j X X X
=+ + + + + +
(3.42)
R1, R2, R0, X1, X2, and X0 are computed looking into the system from the point of fault.
In most cases, the resistances are ignored. Thus the zero-sequence fault current equations
are simplified.
The simplified double-line-to-ground zero-sequence fault current becomes:
20
1 0 2 2 0( ) ( )E XI
X X X X X⋅
=⋅ + + +
(3.43)
The simplified single-line-to-ground zero-sequence fault current becomes:
01 2 0
EIX X X
=+ +
(3.44)
3.12 Ground Potential Rise (GPR)
Ground potential rise (GPR) is defined as: “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.” The GPR is calculated as:
G gGPR I R= ⋅ (3.45)
where Rg : substation ground resistance (Ω) IG : maximum grid current (A)
43
3.13 Computing Maximum Step and Mesh Voltages
Computer programs have been developed to determine the grid resistance the mesh and
step voltages. But if for some reason a designer wants to calculate the values of Em and Es
without the assistance of a computer algorithm, or it is not economically feasible to use a
computer program, IEEEE Std. 80-2000 compiled a set of equations that can be used to
calculate maximum step and mesh voltage without the use of a computer [1,4].
3.13.1 Mesh Voltage (Em)
Mesh voltage is a form of touch voltage. Mesh voltages represent the highest possible
touch voltages that may be encountered within a substation’s grounding system. Mesh
voltage is the basis for designing a safe grounding system, both inside the substation and
immediately outside. In order for the grounding system to be safe, the mesh voltage has
to be less than the tolerable touch voltage. Otherwise the substation ground grid design
needs modification [1,4].
The mesh voltage can be calculated as:
G m im
M
I K KEL
ρ ⋅ ⋅ ⋅= (3.46)
where ρ : resistivity of the earth (Ωˑm) LM : effective burial length (m) Km : geometrical spacing factor Ki : irregularity factor
The geometrical spacing factor, Km, for mesh voltage is:
44
21 ( 2 ) 8ln ln2 16 8 4 (2 1)
iim
h
KD D h hKh d D d d K nπ π
+ ⋅= ⋅ + − + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ −
(3.47)
where
D : spacing between parallel conductors (m) d : diameter of grid conductors (m) h : depth of ground grid conductors (m) Kii : corrective weighting factor adjusting for the effects of inner conductors on the corner mesh Kh : corrective weighting factor adjusting for the effects of grid depth
The corrective weighted factor, Kh is:
0
1hhKh
= + (3.48)
where h0 : grid reference depth (h0 =1)
For ground grids with ground rods along the perimeter and throughout the grid, as well as
in the corners, the corrective weighting factor, Kii, is:
1iiK = (3.49)
For grids with no ground rods, or few ground rods scattered throughout the gird, but none
located along the perimeter or in the corners, the corrective weighting factor, Kii, is:
21
(2 )ii
n
Kn
=⋅
(3.50)
where the geometric factor, n, is composed of factors na, nb, nc, and nd. The geometric
factor, n, is:
45
a b c dn n n n n= ⋅ ⋅ ⋅ (3.51)
where
2 Ca
P
LnL⋅
= (3.52)
nb = 1 for square grids (3.53)
nc = 1 for square and rectangular grids (3.54)
nd = 1 for square, rectangular, and L-shaped grids (3.55)
Otherwise:
4
pb
Ln
A=
⋅ (3.56)
0.7
x y
AL L
x yc
L Ln
A
⋅⋅⋅
=
(3.57)
2 2m
d
x y
DnL L
=+
(3.58)
where
LC : total length of conductor in the horizontal grid (m) Lp : peripheral length of grid (m) D : spacing between parallel conductors (m) d : diameter of grid conductors (m) h : depth of ground grid conductors (m) A : area of grid (m2) Lx : maximum length of grid in the x-direction (m) Ly : maximum length of grid in the y-direction (m) Dm : maximum distance between any two points on the grid (m)
The irregularity factor, Ki, is used in conjunction with n. It is calculated as:
0.644 0.148iK n= + ⋅ (3.59)
46
For grids with no ground rods, or few ground rods scattered throughout the gird, but none
located along the perimeter or in the corners, the effective buried length, LM, is:
M C RL L L= + (3.60)
where
LR : total length of all ground rods (m)
For ground grids with ground rods along the perimeter and throughout the grid, as well as
in the corners, the effective buried length, LM, is:
2 21.55 1.22 r
M C R
x y
LL L LL L
= + + +
(3.61)
where
Lr : total length of each ground rods (m)
3.13.2 Step Voltage (Es)
If a grid system is designed for safe mesh voltages, the step voltages will be within
tolerable limits. Step voltages are usually smaller than touch voltages because both feet
are in series rather than parallel. Also, the body can tolerate higher currents through a
foot-to-foot path because it doesn’t pass through vital organs such as the heart. For the
ground system to be safe, the step voltage has to be less than the tolerable step voltage
[1,4,6].
The mesh voltage can be calculated as:
47
S i GS
S
K K IEL
ρ ⋅ ⋅ ⋅= (3.62)
The effective buried conductor length LS is:
0.75 0.85S C RL L L= ⋅ + ⋅ (3.63)
The step factor KS for the step voltage is given by
21 1 1 1 (1 0.5 )2
nSK
h D h Dπ− = + + − ⋅ +
(3.64)
Where
D : spacing between parallel conductors (m) h : depth of ground grid conductors (m) n : geometric factor composed of factors na, nb, nc, and nd
48
CHAPTER 4
APPLICATION OF MATHEMATICAL MODEL
4.1 Introduction
The purpose of this chapter is to show the application of the grounding design. In order to
design a safe grounding grid, the 12 step procedure discussed in 3.13 will be used. The
following assumptions and design criteria will be used:
1. Soil was uniform between test point and test locations were out of the influence of any existing underground utilities
2. Two –Layer soil model was utilized, average soil resistivity of 64.84 Ωˑm was determined
3. Total clearing time of a line to ground fault is 0.5 seconds. 4. Grid will be buried 18” (0.4572 m) 5. Crushed rock layer inside the substation is 4” (0.1016 m) 6. Ground rods will be 10’ (3.05m) 7. Resistivity of the crushed rock layer is 3000 Ωˑm 8. Switchyard operator is 50kg or heavier 9. 230kV line-to-ground fault currents is utilized 10. X/R ratio is 10 11. Current division factor Sf =0.6 12. Ground fault current is known, If = 12725 85∠− A 13. Safety/Growth factor is 20%
Mesh and step voltages will be calculated and will be compared to the tolerable touch and
step voltages. If necessary, the preliminary design will be altered until all the
requirements for a safe ground grid are met.
49
4.2 Initial Design
Step 1: Field Data
The property purchased for this substation is oddly shaped. But as stated in the
preliminary design suggestions, the biggest rectangle was drawn to determine the area.
For the initial design a rectangle of 144m x 120m will be assumed. The area occupied is
217280 mA = (4.1)
Once the property was purchased, field measurements were taken in order to determine
the soil resistivity. The soil resistivity values were obtained utilizing the Wenner Four pin
method. Soil resistivity testing was done at six locations. Table 6 shows the summary of
the soil resistivity data collected.
Table 6
Soil Resistivity Data Summary Depth Average
Resistivity Minimum Resistivity
Maximum Resistivity
Layer Layer Avg Resistivity
Layer Min Resistivity
Layer Max Resistivity
5 3597 1245 11682 0-5 3597 1341 11682 10 2509 1149 4405 5-10 3699 1067 11618 15 2833 2011 6033 10-
15 9441 1384 23125
20 6251 1149 16470 15-20
4920 503 5362
50 33993 8618 59369 20-50
20432 20432 20432
75 48835 17236 80435 50-75
147145 17236 277053
100 56496 36387 76605 75-100
41312 15595 67029
All 13638 1149 80435
Based on the soil resistivity measurements, the average soil resistivity of 64.84 Ω·m was
determined.
50
Step 2: Conductor size
The ground fault current was given as
03 12725 85 AfI I= = ∠−
(4.2)
With a X/R ratio = 10
Since a safety/growth factor of 20% is part of the design criteria, the ground fault current
of 15270 will be considered for calculations. Thus
03 15270 85 AfI I= = ∠−
(4.3)
Using Table 5 for a fault duration for 0.5 seconds and the X/R ratio of 10, the decrement
factor Df = 1.026.
The effective rms value of approximate asymmetrical current is calculated as follows:
(15270)(1.026)15667 A
F f fI I D= ⋅
==
(4.4)
Assuming the use of copper wire and an ambient temperature of 40°C. Table 4 is used to
obtain the conductor cross-sectional area. For a hard-drawn copper wire with a melting
temperature of 1084°C and 0.5 s, Kf = 7.06 and the cross-sectional area in circular mils is:
15.667 7.06 0.578.2125
kcmil f cA I K t
kcmil
= ⋅
= ⋅=
(4.5)
Converting kcmil to mm2:
2
2
10001973.52
78.2125 10001973.52
39.631
kcmilmm
AA
mm
⋅=
⋅=
=
(4.6)
51
Because Amm2 = πd2/4, the conductor diameter is:
24
4 30.5788
6.24mm or 0.00624m
mmA
dπ
π
⋅=
⋅=
=
(4.7)
The conductor diameter is approximately 6.24mm or 0.00624m if it’s a solid conductor.
Based on this calculation, according to Table 7, a copper wire as small as #1 AWG can
be used. Due to mechanical strength and ruggedness, a larger 4/0 AWG stranded
conductor will be used.
Looking up a 4/0 AWG stranded conductor in Table 7, it is determined that the area is
107.2mm2. Thus, the diameter of a 4/0 AWG conductor is:
24
4 107.2
11.68mm or 0.01168m
mmA
dπ
π
⋅=
⋅=
=
(4.8)
Step 3: Touch and Step Criteria
For a crushed rock surfacing layer of 0.1016 m (4 inches) with resistivity of 3000 Ωˑm ,
and with the soil resistivity of 64.84 Ωˑm, the reflection factor K is computed as
52
64.84 300064.84 30000.96
s
s
K ρ ρρ ρ−
=+
−=
+= −
(4.9)
Using Figure 10, for the value of K= - 0.96, the resistivity of the crushed rock is to be
derated by a reduction factor of approximately Cs = 0.69. The reduction factor can also be
calculated as follows:
0.09 11
2 0.0964.840.09 130001
2(0.1016) 0.090.699677
ss
s
Ch
ρρ
−
= −+
− = −
+=
(4.10)
As stated in the design criteria, the switchyard operator is 50 kg or heavier. Thus,
calculations of touch and step voltages will be only done for a 50 kg person.
For a 50 kg person, the step and touch voltages are calculated as follows:
500.116(1000 6 )
0.116(1000 6 0.6997 3000)0.5
2230.18
step s ss
E Ct
V
ρ= + ⋅ ⋅
= + ⋅ ⋅
=
(4.11)
53
500.116(1000 1.5 )
0.116(1000 1.5 0.6997 3000)0.5
680.581
touch s ss
E Ct
V
ρ= + ⋅ ⋅
= + ⋅ ⋅
=
(4.12)
Step 4: Initial Design
Assuming a layout of 144m x 120m with equally spaced conductors as shown in Figure
11 with spacing D = 24m. The grid burial depth h=0.4572m. The grid wire pattern is 6 x
7 and the grid conductor combined length is
(7 120 ) (6 144 ) 1704CL m m m= × + × = (4.13)
Assume that 22 ground rods, 3.05m (10ft) long are used as shown in Figure 11 below.
22(3.05) 67.1RL m= = (4.14)
The total length of buried conductor, LT is:
1704 67.11771.1
T C RL L L
m
= += +=
(4.15)
54
Figure 11- Rectangular Grid with 22 Ground Rods
Step 5: Determination of grid resistance.
Using the total length of buried conductor calculated in the previous step LT = 1771.1 m
and having the grid area A = 17280 m, the resistance is
1 1 1120 1 20 /
1 1 164.84 11771.1 20 17280 1 0.4572 20 /17280
0.2555
gT
RL A h A
ρ
= + + +
= + + ⋅ + = Ω
(4.16)
Step 6: Maximum grid current IG
In order to calculate IG we must combined Equations 3.39 and 3.40.
g f fI I S= ⋅ (4.17)
55
and
03
(1.026) (15270) (0.6)9400.21 A
G f g
f f
I D ID I S
= ⋅
= ⋅ ⋅ ⋅
= ⋅ ⋅=
(4.18)
Step 7: GPR
GPR is calculated in order to compare to the tolerable touch voltage.
9400.21 0.25552401.85 V
G gGPR I R= ⋅
= ⋅=
(4.19)
This far exceeds 680.581 V that was determined in Step 3 as the safe touch voltage.
Thus, further design evaluation is necessary.
Step 8: Mesh Voltage and Step Voltages
To calculate mesh voltage:
The components for the geometric factor, n, is calculated as follows:
2
2 17042 144 2 1206.4545
Ca
P
LnL⋅
=
⋅=
⋅ + ⋅=
(4.20)
Since we have a rectangular grid
56
4
5284 17280
1.002
Pb
LnA
= =⋅
⋅=
(4.21)
1cn = (4.22)
1dn = (4.23)
The geometric factor, n, is calculated as follows:
6.4545 1.002 1 16.46745
a b c dn n n n n= ⋅ ⋅ ⋅= ⋅ ⋅ ⋅=
(4.24)
With the obtained value of n, the irregularity factor Ki is calculated as:
0.644 0.1480.644 0.148 6.467451.601
iK n= + ⋅= + ⋅=
(4.25)
Because the design has ground rods in the corners and around the perimeter, the
corrective weighting factor, Kii and the effective burial length, LM, are:
1iiK =
(4.26)
2 2
2 2
1.55 1.22
3.051704 1.55 1.22 67.1(7 120) (6 144)
1808.21
rM C R
x y
LL L LL L
m
= + + + = + +
⋅ + ⋅ =
(4.27)
The corrective weighted factor , Kh , for a ground grid conductor being buried a depth of 0.4572m is:
57
0
1
0.457211
1.20715
hhKh
= +
= +
= (4.28)
Plugging everything in, the geometrical spacing factor, Km, for mesh voltage is
2
2
1 ( 2 ) 8ln ln2 16 8 4 (2 1)
1 24 (24 2 0.4572) 0.4570ln2 16 0.4572 0.011672 8 24 0.011672 4 0.011672
iim
h
KD D h hKh d D d d K nπ π
π
+ ⋅= ⋅ + − + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ −
+ ⋅= ⋅ + − ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
1 1 8 + ln2 1.225 (2 6.46745 1)
1.20256π π
⋅ ⋅ ⋅ ⋅ −
=
(4.29)
Finally the mesh voltage, Em , is computed as follows:
64.84 9400.21 1.20256 1.6011808.21
648.98 V
G m im
M
I K KEL
ρ ⋅ ⋅ ⋅=
⋅ ⋅ ⋅=
=
(4.30)
To calculate step voltage:
The effective buried conductor length LS for this design is:
0.75 0.850.75 1704 0.85 67.11335.04
S C RL L L
m
= ⋅ + ⋅= ⋅ + ⋅=
(4.31)
Using burial height of h = 0.4572m, spacing between conductors D = 24m, and n =
6.46745, the step factor KS for the step voltage is computed as follows:
58
2
6.46745 2
1 1 1 1 (1 0.5 )2
1 1 1 1 (1 0.5 )2 0.4572 24 0.4570 24
0.373786
nSK
h D h Dπ
π
−
−
= + + − ⋅ + = + + − ⋅ +
=
(4.32)
The step voltage, Es, is computed as follows:
64.84 0.373786 1.20715 9400.211335.04
206.00 V
S i GS
S
K K IEL
ρ ⋅ ⋅ ⋅=
⋅ ⋅ ⋅=
=
(4.33)
Step 9: Em vs. Etouch
Once the mesh and step voltages are calculated, the results are compared in order to see if the touch voltage is below the mesh voltage. As calculated in equations (4.12) and (4.29) the touch voltage and mesh voltage are:
50 680.581 VtouchE =
648.98 VmE =
Comparing the results, the mesh voltage is smaller than the tolerable touch voltage.
Step 10: Es vs. Estep
Similarly the step voltage is compared to the tolerable step voltages. As calculated in equations (4.11) and (4.32) the tolerable step voltage and step voltage are:
50 2230.18 VstepE =
206.00 VSE =
Comparing the results, the step voltage is much lower than the tolerable step voltage.
59
Step 11: Modify design. Modification to design is not necessary because the mesh and
step voltages are both below the tolerable touch and step voltages.
Step 12: Detailed design. A safe design is obtained. At this point equipment pigtails,
additional ground rods for surge arrestors, etc should be added to complete the design.
4.3 Design Using Copper-Clad Steel
If copper theft is a problem, copper-clad steel can be used. If a 40% copper-clad steel
conductor is to be used at ambient temperature of 40 oC, the required cross-sectional area
in circular mils is:
0
0
197.4
ln
197.415.6673.85 245 1084ln
0.5 0.00378 440 245 40115.836 kcmil
kcmil
m
c r r a
A IK TTCAP
t K Tα ρ
= + +
=+
⋅ ⋅ + =
(4.34)
Converting kcmil to mm2:
2
2
10001973.52
115.836 10001973.52
58.695
kcmilmm
AA
mm
⋅=
⋅=
=
(4.35)
Because Amm2 = πd2/4, the conductor diameter is:
60
24
4 58.695
8.64mm or 0.00864m
mmA
dπ
π
⋅=
⋅=
=
(4.36)
The conductor diameter is approximately 8.64mm or 0.00864m if it’s a solid conductor.
Based on this calculation, according to Table 7, a copper-clad wire as small as 2/0 AWG
can be used. Due to mechanical strength and ruggedness, a larger 4/0 AWG stranded
conductor will be used. Thus the calculations would remain the same as done for a 4/0
AWG copper above.
61
CHAPTER 5
CONCLUSION
Substation grounding is a crucial part of substation design. The design has to be both safe
and reliable. There are many steps to design a safe and effective grid. Hand calculations
may be a tedious and difficult. Doing calculations and modifications to the design can be
a long process. Computer programs have been developed to make the substation
grounding design easier, and more accurate.
This project provides an overview of substation n grounding and the most essential
elements of a substation grounding grid design based on the IEEE Std. 80-2000. This
project provides equations that are involved with a grid design. Finally an equation is
provided using real world data. This example was designed to meet the design criteria for
a safe ground grid.
62
APPENDIX
63
Table 7-Conductor Properties Ref. NFPA-70, NEC-2008, Table 8. Copyright ©2008. NEC. All rights Reserved
64
REFERENCES
[1] Design Guide for Rural Substations”, Rural Utilities Service. United States Department of Agriculture. June 2001.
[2] Gonen, Turan. “Electric Power Distribution System Engineering.” CRC Press. 2008.
[3] Gonen, Turan. “Electric Power Transmission System Engineering: Analysis and Design.” CRC Press. 2009.
[4] "IEEE 80-2000 IEEE Guide for Safety in AC Substation Grounding."
[5] "IEEE 81-1983 IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Ground System.”
[6] Markovic, D. Miroslav. “Grounding Grid Design In Electric Power Systems.” TESLA Institute, 1994.
[7] NFPA 70-2008. National Electrical Code. 2008.