Substation Grounding

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A Project A Project

Presented to the faculty of the Department of Electrical and Electronic Engineering Presented to the faculty of the Department of Electrical and Electronic Engineering

California State University, Sacramento California State University, Sacramento

Submitted in partial satisfaction of Submitted in partial satisfaction of

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the requiiremerements fnts for tor the dhe degree egree of of

MA

MASTER OSTER OF SCIENCEF SCIENCE

in in

Electrical and Electronic Engineering Electrical and Electronic Engineering

b byy Inna Baleva Inna Baleva SPRING SPRING 2012 2012

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Inna Baleva Inna Baleva AL

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Inna Baleva Inna Baleva AL

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iii iii A Project A Project b byy Inna Baleva Inna Baleva A

Apppproved roved by:by:

________

_________________________________________________________, ___, CoCommmmitittteee e ChChaairir Tu

Turraan n GoGonneenn

________

_________________________________________________________, ___, CoCommmmitittteee e ChChaairir Sa

Sallaah Yh Youousif sif

________

___________________________________________ _____ Date

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iv

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

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v 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.

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vi IEEE Std. 80-2000

Conclusions Reached

A safe substation ground grid was designed.

_______________________, Committee Chair Turan Gonen

_______________________ Date

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vii 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

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viii

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 (E_m_{) ...43}

3.13.2 Step Voltage (E_s_{) ...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

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ix

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

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x

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. Csversushs ... 32

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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].

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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

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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.

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CHAPTER 2

L IT ERATURE 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].

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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

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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.

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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].

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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.

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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

Wet Organic Soil 10

Moist Soil 10

Dry Soil 10

Bedrock 10

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].

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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.

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, 45Ω·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 106to 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 106to 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 106to 30 x 106 10 000 to 6 x 106 11 Concrete 1 x 106to 1 x 109 a 21 to 100 a

Oven dried concrete. Values for air-cured concrete can be much lower due to moisture content.

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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].

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Figure 2: Wenner’s Four-Pin Method Ref. IEEE Std. 81-1983

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].

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2.9.2 Schlumberger-Palmer Four-Pin Arrangement

The Schlumberger-Palmer arrangement is another four-pin method. It is also called the Unequally- Spaced 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

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

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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.

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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.

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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.

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(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

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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].

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Figure 4 : Design Procedure Block Diagram.

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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

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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].

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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].

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CHAPTER 3 CHAPTER 3 TH

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3

3.2 .2 TToleolerrabable Bole Body Curdy Currreent Lnt L imitsimits A

A humhuman an body at 50body at 50HHz or z or 60Hz 60Hz can gcan gave ave duratiduration of on of the the currcurrenent lt leess thass than the n the valvalue ue thatthat ca

can can cause use veventrintricular fcular fiibribrillllaatition of the on of the heheaart. Vrt. Veentrintricular fcular fiibribrillllaatition is caon is causeused whd wheen thn thee body cur

body current replrent replaceaces the norms the normal al rhythmirhythmic contrc contractiaction of on of the hthe heaeart and mrt and may cause ay cause a la lackack of circulation and pulse [1-4,6].

of circulation and pulse [1-4,6].

Dalziel’s studies show that the no fibrillation current of magnitude,

Dalziel’s studies show that the no fibrillation current of magnitude, IIBB, at duration ranging, at duration ranging

ffrom 0rom 0.03-.03-3.0 s can 3.0 s can be be sisimmplply expressy expressed ed as:as:

B B s s k k II tt = = (3.1) (3.1) where where k k == SS_B_B

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a anndd

B B

II : r: rmms ms magagninitude tude of of the the currcurrenent through the t through the body (body (AA))

s s

tt : : duraduratition of on of the the current ecurrent exposure (s)xposure (s)

B B

S

S : : shock shock enenergyergy k

k : : constaconstant rent rellateated to ed to ellectriectric shock ec shock enenergyrgy

B

Basaseed on Dald on Dalzizieell’’s studs studiiees, 99.5% of s, 99.5% of pepeoplople cae can san saffeelly wiy withstathstand the nd the mmagagninitude tude of of thethe current without ventricular fibrillation. Dalziel also found that the shock energy constant current without ventricular fibrillation. Dalziel also found that the shock energy constant to vary wi

to vary with weth weiight ght [4][4]. F. For a por a peerson werson weiighing appghing approxiroximmatateelly 50 y 50 kg (kg (11110 l0 lb)b) kk =0.116,5500=0.116, thus the

thus the fformuormulla for a for allallowable body current beowable body current becomcomees:s:

5 500 0.116 0.116 B B s s II tt = = (3.2) (3.2) For a person weighing approximately 70 kg (155 lb)

For a person weighing approximately 70 kg (155 lb) kk =0.157, thus the formula for₅₅₀₀=0.157, thus the formula for al

alllowablowable e body currbody currenent bet becomecomes:s:

7 700 0.157 0.157 B B s s II tt = = (3.3) (3.3) Th

This is eeqquuaattioion n is is nnoot t vvaalulueed d fofor r vveerry y sshhoorrt t oor r vveerry y lolonng g dduurraattioionn..

Biegelmeier’s curve in Figure 5 shows the body current versus time. This curve has a Biegelmeier’s curve in Figure 5 shows the body current versus time. This curve has a 500m

500mA A lliimmiit ft for tior timmes es up to 0.2 s, then the up to 0.2 s, then the lliimmiit det decreasecreases to 50 ms to 50 mA A at 2 at 2 s ans and bed beyond.yond. Th

This is figfiguurre e aalslso o sshhoowws s a a ccoommppaarrisisoon n oof f tthhe e bbooddy y ccuurrrreennt t fofor r bbootth h a a 550 0 kkg g aannd d a a 770 0 kkgg person.

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IIn mn modeodern operarn operatiting prang practicticeces, rs, reecourse acourse affteter a ground fr a ground fauaullt it is coms commmon. Ion. In cin circumrcumstastancencess where

where there athere are reclre reclosures, a person mosures, a person miight eght experixperience ence the fithe first shock rst shock wiwithout permthout permaneanentnt iinjnjury. ury. BBut theut then an an an automutomatatiic reclc reclosure caosure can resun resullt it in ann anotheother shock r shock lleess thass than 0.33 sen 0.33 secondsconds of the first shock. This second shock that occurs after a short interval of time before the 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].

person can recover from the initial can cause a serious accident [1,4].

Figure 5 : Body Current vs. Time. Figure 5 : Body Current vs. Time. Ref.

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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

1000 B

R = 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.

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Figure 6 : Exposure to Touch Voltage.

Figure 7 : Touch Voltage Circuit.

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Figure 8: Exposure to Step Voltage.

Figure 9 : Step Voltage Circuit

Using Figure 6 or Figure 8, the Thevenin equivalent circuit for the current through the body, I , of a person is:_b

Th b Th B V I Z R = + (3.5) where:

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Th

V : Thevenin voltage between terminal H and F (V)

Th

Z : Thevenin impedance from point H and F (Ω) B

R : body Resistance (Ω)

The Thevenin equivalent impedance for the touch voltage accidental circuit is:

2 f Th R Z = (3.6) The Thevinin equivalent impedance for the step voltage accidental circuit is:

2 Th f Z = R (3.7) where: f

R : 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 resistanceR_f is:

4 f R b ρ = (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 Zthare:

For touch voltage accidental circuit

1.5 th

Z = ρ

(3.9) And for step voltage accidental circuit

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6 th

Z = ρ

(3.10) 3.4 Addition of Surface L ayer

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: 4 s f s R C b ρ   =     (3.11) The surface layer derating factor, Cs, can be calculated as:

0.09 1 1 2 0.09 s S s C h ρ ρ   −     = − + (3.12) where

ρ : resistivity of the earth (Ω·m)

ρs: resistivity of surface layer material (Ω·m)

hs: thickness of surface material (m)

Cscan 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 ρ ρ ρ − = + (3.13)

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Figure 10 : Csversus hs

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.

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( 2 )

step B f B

E = R + ⋅ ⋅R I

(3.14) For a body weighing 50 kg

50 0.116 (1000 6 ) step s s s E C t ρ = + ⋅ ⋅ _(3.15)

For a body weighing 70 kg

70 0.157 (1000 6 ) step s s s E C t ρ = + ⋅ ⋅ _(3.16)

For touch voltage, the limit is

2 f touch B B R E =  _R + _⋅I   (3.18)

50 0.116 (1000 1.5 ) touch s s s E C t ρ = + ⋅ ⋅ (3.19)

70 0.157 (1000 1.5 ) touch s s s E C t 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:

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For a body weighing 50 kg 50 116 mm touch s E t − = (3.21)

For a body weighing 70kg

70 157 mm touch s E t − = (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 4 0 0 10 ln m mm c r r a K T TCAP I A t α ρ K T −  ⋅   +  = _ _ _ _ +     (3.23)

If the conductor size is given in kcmil, the equation becomes:

3 0 0 5.07 10 ln m kcmil c r r a K T TCAP I A t α ρ K T −    +  = ⋅ _ _ _ _ +     (3.24) Where I : rms current (kA)

Amm2 : 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)

K 0 : equals 1/α0or (1/αr)- Tr (oC)

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Common values of αr, K 0 , Tm, ρr, and TCAP values can be found in Table 3.

Table 3-Material Constants

Description Material Conductivity (%) αrfactor at 20oC (1/oC ) K 0at 0oC (0oC ) Fusinga temperature Tm(oC ) ρr20oC (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

a_{From ASTM standards.}

b_{Copper-clad steel rods based on 0.254 mm (0.010 in) copper thickness.}

c_{Stainless-clad steel rod based on 0.508 mm (0.020 in) No. 304 stainless steel thickness over No. 1020 steel}

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The required area for a conductor given a current can be calculated as: 2 4 0 0 1 10 ln mm m c r r a A I K T TCAP t α ρ K T − =  ⋅   +     ₊      (3.25) or 0 0 197.4 ln kcmil m c r r a A I K T TCAP t α ρ K T =    +     ₊      (3.26)

Equation (3.26) can be simplified as:

kcmil f c

A = ⋅I K t (3.27)

where

K f : constant found in Table 4 which is based on the fusing and ambient

temperature of the material

Table 4-Material Constants

Material Conductivity

(%)

Tma(°C) K f

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

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The following equation can be used to convert the conductor size from kcmil to mm2: 2 1000 1973.52 kcmil mm A A = ⋅ (3.28)

The diameter of a conductor can be calculated as:

2 ( ) 2 mm c mm A d 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 f

I = I D⋅ (3.30)

The decremental factor, Df , can be calculated as:

2 1 1 f a t T a f f T D e t −     = + −     (3.31) where

tf : time duration of the fault (s)

a X T R ω = _(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.

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Table 5-Typical Values of 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 resistanceR is determined by dividing the voltage between the two inner probes by the current of the two outer probes. Using the mutual resistanceR, the soil resistivity can be calculated as follows:

2 2 2 2 4 2 1 4 aR a a a b a b π ρ = + − + + (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 aR

ρ = 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

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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:

4 g R A ρ π = _(3.35) Where

Rg : substation ground resistance (Ω)

ρ : soil resistivity (Ω-m)

A : area occupied by the ground grid (2₎

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:

4 g T R A L ρ π ρ = + (3.36) where

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The total burial length is the combination of the horizontal and vertical conductors in the grid as well as the ground rods. L Tcan be calculated as:

T C R

L = 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 1 1 20 1 20/ g T R L 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 g

I = 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

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g f f

I = 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 2 0 1 1 0 1 0 2 2 2 0 0 ( ) ( ) [( 3 _f ( )] ( ) ( 3 _f ) E R jX I R 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)

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0 1 2 0 1 2 0 3 _f ( ) E I R R R R j X X X = + + + + + + (3.42)

R1, R2, R0, X1, X2, andX0are 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:

2 0 1 ( 0 2) ( 2 0) E X I X X X X X ⋅ = ⋅ + + + (3.43)

The simplified single-line-to-ground zero-sequence fault current becomes:

0 1 2 0 E I X 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.” TheGPR is calculated as:

G g

GPR I R= ⋅ (3.45)

where

Rg : substation ground resistance (Ω)

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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 Emand 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 i m M I K K E L ρ ⋅ ⋅ ⋅ = _(3.46) where

ρ : resistivity of the earth (Ωˑm) LM : effective burial length (m)

K m : geometrical spacing factor

K i : irregularity factor

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2 1 ( 2 ) 8 ln ln 2 16 8 4 (2 1) ii m h K D D h h K h d D d d K n π π   + ⋅    = ⋅_ _ + − +_ ⋅ _ __ ⋅ _ _ ⋅ ⋅ ⋅ ⋅ ⋅ _ _ ⋅ − __ (3.47) where

D : spacing between parallel conductors (m) d : diameter of grid conductors (m)

h : depth of ground grid conductors (m)

K ii : corrective weighting factor adjusting for the effects of inner conductors on

the corner mesh

K h: corrective weighting factor adjusting for the effects of grid depth

The corrective weighted factor, K his:

0 1 h h K h = + _(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, K ii, is:

1 ii

K = (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, K ii, is:

2 1 (2 ) ii n K n = ⋅ (3.50)

where the geometric factor, n, is composed of factors na, nb, nc, andnd. The geometric

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a b c d n n n n n= ⋅ ⋅ ⋅ (3.51) where 2 _C a P L n L ⋅ = (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 p b L n A = ⋅ (3.56) 0.7 x y A L L x y c L L n A ⋅ ⋅ ⋅   =     (3.57) 2 2 m d x y D n L 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, K i, is used in conjunction with n. It is calculated as: 0.644 0.148

i

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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 R

L = 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 2 1.55 1.22 r M C R x y L L L L L 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].

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S i G S S K K I E L ρ ⋅ ⋅ ⋅ = (3.62)

The effective buried conductor length LSis:

0.75 0.85

S C R

L = ⋅ + ⋅L L (3.63)

The step factor K Sfor the step voltage is given by

2 1 1 1 1 (1 0.5 ) 2 n S K h D h D π −   = _ + + − _ ⋅ +   (3.64) Where

D : spacing between parallel conductors (m) h : depth of ground grid conductors (m)

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CHAPTER 4

APPL ICAT ION OF MAT HEMATI CAL M ODEL

4.1 I ntroduction

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

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4.2 I nitial 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

2 17280 m

A

=

_(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.

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Step 2: Conductor size

The ground fault current was given as

0 3 12725 85 A f I = = 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

0

3 15270 85 A

f

I = = 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 f I = I D⋅ = = (4.4)

Assuming the use of copper wire and an ambient temperature of 40°C. Table 4is 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, K f =7.06 and the cross-sectional area in circular mils is:

15.667 7.06 0.5 78.2125 kcmil f c A I K t kcmil = ⋅ = ⋅ = (4.5) Converting kcmil to mm2: 2 2 1000 1973.52 78.2125 1000 1973.52 39.631 kcmil mm A A mm ⋅ = ⋅ = = (4.6)

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Because Amm2= πd2/4, the conductor diameter is: 2 4 4 30.5788 6.24mm or 0.00624m mm A d π 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:

2 4 4 107.2 11.68mm or 0.01168m mm A d π 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

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64.84 3000 64.84 3000 0.96 s s K ρ ρ ρ 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 1 1 2 0.09 64.84 0.09 1 3000 1 2(0.1016) 0.09 0.699677 s s s C h ρ ρ   −     = − +  ₋      = − + = (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:

50 0.116 (1000 6 ) 0.116 (1000 6 0.6997 3000) 0.5 2230.18 step s s s E C t V ρ = + ⋅ ⋅ = + ⋅ ⋅ = (4.11)

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50 0.116 (1000 1.5 ) 0.116 (1000 1.5 0.6997 3000) 0.5 680.581 touch s s s E C t V ρ = + ⋅ ⋅ = + ⋅ ⋅ = (4.12)

Step 4: I nitial 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 ) 1704 C

L = × 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) 67.1 R

L = = m _(4.14)

The total length of buried conductor, L Tis:

1704 67.1 1771.1 T C R L L L m = + = + = (4.15)

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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 L T=1771.1 m

and having the grid areaA =17280 m, the resistance is

1 1 1 1 20 1 20/ 1 1 1 64.84 1 1771.1 20 17280 1 0.4572 20/17280 0.2555 g T R L A h A ρ    = _ + _ + __ +        = _ + _ + __ ⋅  +    = Ω (4.16)

Step 6: Maximum grid current IG

In order to calculateIGwe must combined Equations 3.39 and 3.40.

g f f

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and 0 3 (1.026) (15270) (0.6) 9400.21 A G f g f f I D I D I S = ⋅ = ⋅ ⋅ ⋅ = ⋅ ⋅ = (4.18) Step 7: GPR

GPR is calculated in order to compare to the tolerable touch voltage.

9400.21 0.2555 2401.85 V G g GPR 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: M esh Voltage and Step Voltages To calculate mesh voltage:

The components for the geometric factor, n, is calculated as follows:

2 2 1704 2 144 2 120 6.4545 C a P L n L ⋅ = ⋅ = ⋅ + ⋅ = (4.20)

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4 528 4 17280 1.002 P b L n A = = ⋅ ⋅ = (4.21) 1 c n = _(4.22) 1 d n = _(4.23)

The geometric factor, n, is calculated as follows:

6.4545 1.002 1 1 6.46745 a b c d n n n n n= ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ = (4.24)

With the obtained value of n, the irregularity factor K i is calculated as:

0.644 0.148 0.644 0.148 6.46745 1.601 i K = + ⋅n = + ⋅ = (4.25)

Because the design has ground rods in the corners and around the perimeter, the corrective weighting factor, K ii and the effective burial length, LM, are:

1 ii K = _(4.26) 2 2 2 2 1.55 1.22 3.05 1704 1.55 1.22 67.1 (7 120) (6 144) 1808.21 r M C R x y L L L L L L m       = + +   ₊            = + +    _ ⋅ + ⋅ _   = (4.27)

The corrective weighted factor , K h, for a ground grid conductor being buried a depth of