methodology and technology for power system grounding (he/methodology and technology for power...

6

Grounding System for Substations

Designing a grounding system for power plants and substations is a very complicated task, and both

outdoor and indoor equipment and structures should be considered. Computer aided design is a more

feasible option due to the complication of a substation grounding system. Some simplified design meth-

ods are introduced in this chapter. The key is to design a suitable grounding system according to the

fault current obtained from the method given in Chapter 5. IEEE Standard 80-2000 [1] introduced

detailed design procedures for a substation grounding system, part of the related content is presented

in this chapter.

6.1 Purpose of Substation Grounding

Generally, the grounding system of a substation mainly consists of horizontal conductors, which are

buried at the depth of 0.6–1.0m. Sometimes vertical ground rods are connected to the horizontal con-

ductors, as illustrated in Figure 6.1. For grounding as lightning protection, vertical rods are buried in the

locations where lightning protection rods, ground wires and surge arresters are placed, and these rods

are connected with the horizontal grounding grid.

6.1.1 Function of Substation Grounding

A power plant or substation with a reasonable grounding system is the key to the safe operation of a

power system. The grounding system of the substation is the unification of lightning protection ground-

ing, protective grounding and working grounding. The purpose of lightning protection grounding is to

lead the lightning current to the earth, to suppress a lightning overvoltage which might cause damage

to substation equipment or even put personnel in danger. For instance, the grounding system for a light-

ning protection rod, overhead ground wire and surge arrester only works when a lightning current

passes through it. The lightning current might exceed several hundred kilo-amperes, but it lasts only a

few dozens of microseconds.

The working grounding is designed for different operation modes of the power system. It assures the

reliable operation of electrical equipment and the secondary system in both normal and fault states of

the power system. It includes, for example, the solid grounding of the neutral points of the power sys-

tem, DC system grounding and the logic grounding of computers.

Protective grounding assures the safety of personnel when insulation is damaged. All the shells of

electrical devices are grounded. When their insulation is damaged, a current passes through the shell and

the grounding devices into the earth. The current through the grounding devices might vary significantly.

The grounding of an electrical device assures a low impedance path between the phase lines and the

shell of the device, which enables the protection circuit to cut the fault circuit in a short time.

Methodology and Technology for Power System Grounding, First Edition. Jinliang He, Rong Zeng and Bo Zhang.� 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd.

In order to guarantee the safety of personel, power apparatus and secondary devices in the substation,

the grounding resistance of the substation should be decreased to a low value. However, despite the poten-

tial dangers, limiting the touch voltage, step voltage and transfer voltage to safe levels is still an effective

way to guarantee the safety of personnel and devices. It is inevitable to calculate the full profile of poten-

tial distribution on the ground surface in order to examine the danger brought by a potential gradient on

the ground. However, the conventional way to predict the potential gradient on the ground is only suitable

for a simple configuration of electrodes. It is impossible to calculate the voltage potential at an arbitrary

position on the ground using those conventional formulas, especially when the grounding grid is compli-

cated. The development of computers makes it possible to use numerical methods to accurately predict the

potential distribution. Since the 1970s, through the implementation of numerical simulations on digital

computers, the potential distribution on the ground surface has been predicted in an efficient way.

6.1.2 Design Objective of a Substation Grounding System

The design objective of a substation grounding system is to keep operating personnel out of danger

from touch and step voltages and to keep all electric devices from damage.

The objectives can be achieved through fulfilling the following requirements in the design:

1. When a ground fault happens, a low impedance return path should be provided for the fault current,

and the impedance of the path should be low enough to make sure that the fault can be removed or a

fault alarm can be triggered quickly.

2. In both stable and transient operation states, the voltage on structures and sensitive electric applian-

ces in the substation should be suppressed to a safe level.

3. The electromagnetic interference on the secondary systems of a substation, such as measuring,

signaling and control systems, should be maintained at its minimum level.

4. The impacts on personnel, devices and structures caused by lightning should be suppressed to a

minimum level.

The design of a grounding system should include the grounding of all electric equipment and struc-

tures in the substation and safe grounding. The following aspects should be considered [1]:

1. Grounding grid: dissipate the maximum possible fault current safely and suppress step and touch

voltages.

2. Grounding of buildings: prevent a dangerous touch voltage caused by a fault and electrostatic

induction.

3. Grounding of auxiliary devices: prevent a dangerous touch voltage caused by a fault.

Figure 6.1 Configuration of a typical grounding system.

224 Methodology and Technology for Power System Grounding

4. Grounding of buried structures: prevent the transferred potential.

5. Grounding of control and instrument systems: limit the contact voltage to a safe level, ensure the

normal operation of devices and prevent the danger presented by high voltage led out and low volt-

age led in.

6.1.3 Requirement on the Grounding System of a Substation

During a short-circuit fault, part of the ground potential rise (GPR), which is the potential on the

grounding system when a ground fault happens, is applied to the insulation of the secondary system, so

the insulation of the secondary system in a substation, including secondary cables and devices, has to

endure a high AC power frequency voltage during the short-circuit fault.

The AC withstand characteristics of the secondary cables and devices have been experimentally inves-

tigated and discussed [2]. The AC power frequency breakdown voltages of the microcomputer protection

device and small-sized electromagnetic and solid state relays all are as low as about 2 kV. The minimum

3-s withstand voltages of secondary cables and devices are 6.5 and 2.0 kV, respectively, which means the

minimum 3-s insulation withstand voltage of the secondary system is 2 kV. In order to guarantee the

safety of the secondary system, during a short-circuit fault, the potential difference generated between

the core conductor and the shield sheath of the cable should be controlled to be smaller than the insula-

tion withstand voltage of the secondary system. In the past, the secondary cable required grounding the

shield sheath at one terminal to reduce low frequency EMI, so the GPR was assumed to apply to the

whole insulation of the secondary system. Thus, the maximum allowable limit of the GPR was con-

cluded as 2 kV in China Grounding Standard DL/T-621-1997 [3]. If the ratio between the potential dif-

ference on the insulation of the secondary system and the GPR is m, then the maximum ground potential

rise is the ratio of the AC insulation withstand voltage of the secondary system and m. For the safety of

the secondary system, the minimum 3-s insulation withstand voltage of the secondary system is used as

the AC insulation withstand voltage of the secondary system, which is 2 kV in China. Then the maxi-

mum ground potential rise can be calculated by 2000V/m, and the ratio m can be analyzed according to

the actual layout of the grounding system and the secondary cables in the respective actual soil model.

In China National Standard GB50065-2011 “Code for Earthing Design of AC Electrical Installations”,

the safe parameters of the grounding system include the step voltage, touch voltage and the GPR, and the

recommended maximum GPR is 5 kV. But for those substations in a high resistivity region, whose GPRs

are with difficulty reduced to 5 kV, the standard suggests the actual maximum value m of the ratio

between the potential difference on the insulation of the secondary system and the ground potential rise

should be used to determine the maximum GPR. The high potential of communication cables with metal

conductors and low voltage power wires should be isolated by isolation transformers against high GPR

transferred outside the substation, and the neutral protection surge arrester of 10 kV distribution side

should also be safe. Now optical communication cables are widely applied instead of metal wires, so the

high potential transfer of the communication system does not require more attention.

6.1.4 Specificity of Power Plant Grounding

The design of a grounding system for a power plant is very complicated. This is because the involved

outdoor area is huge and the grounding system of the surrounding structures should also be considered.

If there are underground power generation facilities or a system with several voltage levels, these

should receive attention. Moreover, as the requirement for signals in the control system increases, the

design of a grounding system becomes more difficult. The grounding system for a power plant differs

from that for a substation mainly in two aspects.

First, the power plant occupies a larger area and has huge underground structures and foundations.

These features have a remarkable influence on the grounding resistance. Second, many power plants

neighbor water resources, which can be utilized to lower the grounding resistance. For the grounding

system design, the operating personnel usually work indoor instead of outdoors. Inside the buildings, if

Grounding System for Substations 225

we can ensure that the insulation between the floor and the ground potential is high enough, or the floor

is a metal plate, or the spacing of a grounding mat inside the floor plate is sufficiently small, the safety

of personnel can be guaranteed. In this aspect, a power plant is similar to a gas insulation substation.

There are several different design methods for the concrete floor. A separated grounding mat inside the

concrete floor is suggusted; the spacing of the grounding mat inside the floor plate should be small and

the mat should be connected to the steel of the building in a multi-point way. The steel inside the con-

crete floor can be used as grounding points for equipment. However, IEEE Standard 665-1995 [4] sug-

gests that it is not necessary to use the requirement of step and touch voltages to determine the spacing

of the grounding mat inside the concrete floor.

6.1.5 Requirements for Grounding System Design

Grounding systems for substations or power plants should meet the following requirements:

1. The metal shells of all equipment and their exposed conductive objects without current passing

through, which might carry a charge caused by electrostatic induction, should be grounded.

2. The configuration of a grounding system should guarantee the return path of a fault current, so that

protection devices can react to a ground fault or over-current fault quickly and either remove the

fault circuit or provide warning to substation personnel.

3. When a ground fault happens, both step and the touch voltages should be suppressed to an accept-

able level.

4. All conductors including grounding wires should be protected against damage by the thermal stress,

thermo-mechanical stress, and electro-mechanical stress generated by a fault current.

5. The continuity of grounding conductors should be guaranteed. No switch is to be inserted into the

grounding conductors. The shells of electrical equipment cannot be used as part of the grounding

conductor.

6. Grounding conductors should have enough mechanical strength to withstand possible mechanical

stresses. The exposed part of the grounding conductors should be checked easily.

7. Corrosion of surrounding constructions and equipment caused by the grounding system should be

controlled to a low level.

6.1.6 Design and Construction Procedures for a Grounding System

The design procedure for a grounding system is described in IEEE Standard 80 [1]. The design and

construction procedures for a grounding system include the following steps:

1. Survey the substation site, determine the soil resistivity profile and the soil model.

2. Determine the geometry of the substation.

3. Determine the maximum grid current that flows between the grounding grid and surrounding earth.

A future increase in capacity should be considered. Note the difference between the maximum

current flowing into the earth and the maximum fault current.

4. Determine the size of the grounding conductor. The size of the grounding conductor is related to

the fault current. Generally, the cross-section of the grounding conductor should be different from

that of the feed of the grounding grid. The feed wire for the main equipment should be bigger than

the size of the grounding conductor.

5. Determine the shock duration. The more quickly a fault is disconnected, the less is the danger

faced by personnel. The worst condition should be considered. A more conservative design can

adopt the clearing time of a back-up protection system. It is normally assumed that the fault dura-

tion tj is equal to the shock duration, unless the fault duration is the sum of successive shocks, such

as from reclosures. The selection of tj should reflect both fast disconnecting for substations and

slow disconnecting for distribution and industrial substations. The choices of tj, which is listed in


Table 10.1, should result in the most pessimistic combination of fault current decrement factor and

allowable body current. Typical value for tj, ranges from 0.25 to 1.0 s. For a substation, the fault

clearing duration is about 0.15–0.5 s. But if a high-speed breaker is adopted, then in most cases,

the fault will be cleared in less than 0.15 s.

6. Determine the tolerable step and touch voltages.

7. Make a preliminary design of the grounding system.

8. Calculate the grounding resistance.

9. Calculate the maximum ground potential rise.

10. Calculate the touch, step and mesh voltages.

11. Analyze any dangerous locations subject to transferred potential. Design fences and structures

which might carry transferred potential. Design special places where coal, gas and oil can be stored.

12. Check and modify the preliminary design.

13. Construct the grounding system.

14. Measure the grounding system.

15. Verify the calculation results with the measurements. Verify the calculation results of steps 6 and

10 using the measured results. Check whether the grounding resistance meets the requirement, and

whether the mesh, touch and step voltages exceed the tolerable limit.

16. Improve the grounding system. According to the test results, if necessary, improve the grounding

system, shielding and fence structures.

6.2 Safety of Grounding Systems for Substations and Power Plants

6.2.1 Design Criteria of Grounding Systems

Substation design should ensure that the safety of devices and personnel inside the substation would not

be undermined by a fault current and should avoid damage caused by a potential gradient and transfer

voltage.

6.2.1.1 Basics of Grounding Safety

When a ground fault happens, the current injected into the earth produces a potential gradient inside

and outside the substation. If the design of the grounding system has not taken certain steps concerning

this problem, the potential gradient might be very big and might put the personnel inside and outside

the substation in danger in some scenarios.

In practice, even a precise computer simulation can hardly give a profile of potential distribution which

matches with the actual profile. This is because the actual grounding systems are very complicated and it

is impossible to get a full understanding of the soil structure in which the grounding system is located. It

is worth pointing out that only low grounding resistance cannot guarantee the safety of the personnel and

devices in a substation. A low grounding resistance substation might even have potential dangers, while a

high grounding resistance substation might be safe if certain deliberate design methods are adopted.

In addition to local potential gradient, some other factors might also bring a safety problem, such as

tolerable duration to electric shock, human body resistance, body condition and the probability of electric

shock. The allowable current and the allowable voltage of personnel have been discussed in Chapter 1.

6.2.1.2 Possible Causes of Accidents

It is important to know the possible causes of accidents in the design of substations. The following

causes of accidents are very typical and might occur in combination:

1. The relation of a high fault current with the geometry of the grounding system and soil resistivity.

2. A severe potential gradient at one point or several points in a substation caused by current injected

into the earth.


3. Because of the coincidence of time, location and position, a person steps on two points with a high

potential difference.

4. Because the contact resistance or other resistance connected in series is low, the current through a

human body cannot be suppressed to a safe level.

5. When a contact fault happens, or when a current flows through a human body, a long time delay

would be dangerous to that body under a certain current value.

It has been shown by studies that the danger of voltage cannot be eliminated under some conditions

unless all the power supplies are disconnected. But it is still possible and important to reduce the possi-

bility of an accident. In fact, the possibility of an accident can be minimized through deliberate and

proper design.

Chapter 1 discussed the grounding problem relating to personnel safety. The touch and step voltages

that the human body is subject to at fault condition are determined by the resistance of the human body,

the duration of the current flowing through the body, the resistivity of the surface soil, and the current

path. According to test results of human body resistance, the analysis of accidents and experiments

conducted on animals, the touch voltage and the step voltage should not exceed the values decided by

Equations 1.68–1.71, respectively.

6.2.2 Calculation of the Grounding Resistance of a Grounding System

In the design of the grounding system of a substation or power plant, the estimation of grounding resist-

ance is key in determining the geometry of the grounding system. In homogeneous soil, the minimum

value of the grounding resistance of a horizontal grounding grid can be calculated approximately by [5]:

R ¼ r

4

ffiffiffip

A

rð6:1Þ

where r is the soil resistivity (Vm) and A is the area of the grounding system (m2).

The area of the grounding system is a very important parameter in determining the grounding resist-

ance. Increasing the area of the grounding system has a more remarkable effect on reducing grounding

resistance than does increasing the amount of conductors in the grounding system. It mainly depends on

the configuration of the substation and is determined by the circumference of the peripheral fence and

buildings. If some buildings are included in the design blueprint, the peripheral conductors of the

grounding system should encircle those buildings. Although it is impossible to make the configuration

of a grounding system be an exact rectangle, a simple design program requires that the area is a rectan-

gle. The maximum rectangle should be determined when drafting the grounding system. Because the

maximum rectangle represents the four peripheral conductors, the grounding area can be estimated

from that rectangle [1].

Equation 6.1 is derived by assuming the grounding grid is a conductor plate. If we take into account

the actual structure of the grounding grid, the grounding resistance can be obtained by:

R ¼ 0:5rffiffiffiA

p ð6:2Þ

or [6,7]:

R � r

4

ffiffiffip

A

rþ r

LTð6:3Þ

where LT is the total length of the grounding conductors.

Equation 6.3 gives the maximum possible value of the grounding resistance of a substation. If extra

vertical conductors are added, simply adding their length into LT might give a conservative result. This is

because vertical conductors can reduce grounding resistance more effectively than horizontal conductors.


The following formula takes into account the influence of the burial depth of the grounding conduc-

tors [8]:

R ¼ r1

LTþ 1ffiffiffiffiffiffiffiffi

20Ap 1þ 1

1þ hffiffiffiffiffiffiffiffiffiffiffi20=A

p !" #

ð6:4Þ

where h is the burial depth of the grounding grid.

It should be noted that Equation 6.4 does not consider the influence of foundations, well type ground-

ing electrodes or large-sized structures. The Schwarz formula [9] can be used to consider such effects:

R ¼ R1R2 � R212

R1 þ R2 � 2R12

ð6:5Þ

where R1 is the grounding resistance of the grounding grid, R2 is the grounding resistance of all vertical

ground rods and R12 is the mutual resistance between grounding grid and ground rods:

R1 ¼ r

pLGln

2LG

h0

� �þ K1

LGffiffiffiA

p� �

� K2

� �ð6:6Þ

R2 ¼ r

2mpLRln

8LR

d2

� �� 1þ 2K1

LRffiffiffiA

p� � ffiffiffiffi

mp � 1� �2� �

ð6:7Þ

R12 ¼ r

pLGln

2LG

LR

� �þ K1

LGffiffiffiA

p� �

� K2 þ 1

� �ð6:8Þ

where r is the soil resistivity at burial depth h, LG is the total length of the grounding conductors, LR is

the average length of the ground rods, h0 ¼ ffiffiffiffiffiffiffiffid1h

p(when h¼ 0, h0 ¼ 0.5d1), A is the area of the grounding

grid (A¼ ab), a is the length of the long side of rectangle grounding grid, b is the length of the short side,

m is the number of vertical rods, K1 and K2 are coefficients related to the geometry of the grounding

system, d1 is the diameter of conductors of the grounding grid and d2 is the diameter of the vertical rods.

Similarly, the well type grounding electrode can be considered as a single ground rod with a ground-

ing resistance which is equal to the measured value. Moreover, as for a power plant, there are many

structures of different types and the grounding resistance of every structure should be calculated. When

the length of a vertical rod is greater than the equivalent radius of the grounding grid, r should be

adopted as the apparent soil resistivity. This should be treated as the equivalent resistivity looking from

the rod; and the reason is that the current is mainly dissipated into the earth from the bottom of the

vertical rod. In Figure 6.2 [9], where x is the ratio of the long side to the short side of the grounding

grid [4], curve A corresponds to h¼ 0, rA¼�0.05xþ 1.41. Curve B corresponds to h ¼ ffiffiffiA

p=10,

rB¼�0.05xþ 1.20. Curve C corresponds to h ¼ ffiffiffiA

p=6, rC¼�0.05xþ 1.13. In Figure 6.3 [9], curve

A corresponds to h¼ 0, rA¼ 0.15xþ 5.50. Curve B corresponds to h ¼ ffiffiffiA

p=10, rB¼ 0.10xþ 4.68.

Curve C corresponds to h ¼ ffiffiffiA

p=6, rC¼�0.05xþ 4.40 [4].

A horizontal grounding grid is recommended in China, its grounding resistance can be calculated

by [3]:

R ¼ 0:22rffiffiffiA

p ð1þ BÞ þ r

2pLln

4pA

hd� 4:52� 5B

� �ð6:9Þ

where B ¼ 1=ð1þ 4:6h=ffiffiffiA

p Þ, L is the total length of the horizontal conductors, d is the diameter of the

grounding conductors and h is the burial depth.

When a/b� 8 (a is the length of the long side of a rectangular grounding grid, b is the length of the

short side; for a square grid, a¼ b), the grounding resistance can be calculated by [3]:

R ¼ ð0:22� 0:007a=bÞ rffiffiffiA

p ð1þ BÞ þ r

2pLln

A

9hd� 5B

� �ð6:10Þ


6.2.3 Analysis of Grounding in Inhomogeneous Soil

6.2.3.1 Grounding Resistance of Horizontal Grounding Grid

When the thickness of the top soil layer is smaller than the size of the grounding grid and r1 � r2,

Laurent recommends the following two formulas to calculate the grounding resistance of a horizontal

grounding grid [10,11]:

R ¼ r24

ffiffiffip

A

rþ r1LG

ð6:11Þ

R ¼ 1:6r2LP

þ 0:6r1LG

ð6:12Þ

where LP is the peripheral length of the grounding grid and LG is the total length of the conductors in

the grid.

Figure 6.2 K1 in the Schwarz formula [9]. (Reproduced with permission from S.J. Schwarz, "Analytical

expressions for the resistance of grounding systems", AIEE Transactions, 73, 1011–1016, 1954.# 1954 IEEE.)

Figure 6.3 K2 in the Schwarz formula [9]. (Reproduced with permission from S.J. Schwarz, "Analytical

expressions for the resistance of grounding systems", AIEE Transactions, 73, 1011–1016, 1954.# 1954 IEEE.)


If the top soil layer is very thick, the following formula can be adopted to consider the influence of

burial depth [10]:

R ¼ 1:6r2LP

þ 0:6r1LG

þ r1H

Að6:13Þ

6.2.3.2 Grounding Resistance of a Grounding Grid with Vertical Ground Rods

Nahman et al. [12] proposed a formula to calculate the grounding resistance of a grounding grid in two-

layered soil through a modified Schwarz formula. Assume the resistivity of the top-layer soil is r1 with

thickness H and that of the bottom layer is r2. If all vertical ground rods are located in the top layer,

then the grounding resistance can be calculated by:

R2 ¼ r12mpLR

� �ln

8LR

d2

� �� 1þ 2K1Kp

LRffiffiffiA

p� � ffiffiffiffi

mp � 1� �2� �

ð6:14Þ

where Kp is the correction coefficient of soil inhomogeneity, which is related to the reflection

coefficient of soil K ¼ ðr2 � r1Þ=ðr2 þ r1Þ and the soil structural coefficient p. When r2 > r1,

p ¼ H=ffiffiffiA

p; when r2 < r1, p ¼ ðH � hÞ= ffiffiffi

Ap

.

The relationship between the correction coefficient Kp, reflection coefficient K and structural

coefficient p is illustrated in Figure 6.4 [12].

If vertical ground rods penetrate into the bottom layer, then the grounding resistance can be calcu-

lated by [5]:

R2 ¼ ra2mpLR

ln8La

d2

� 1

� �þ K1ð0ÞK 0

pr2

mpffiffiffiA

p ffiffiffiffim

p � 1� �2 ð6:15Þ

Figure 6.4 The relationship between the correction coefficient Kp, reflection coefficient K and structural

coefficient p [12]. (Reproduced with permission from J. Nahman, “Analytical expressions for the resistance of

rodbeds and of combined grounding systems in nonuniform soil,” IEEE Transactions on Power Delivery, 1, 3,

90–96, 1986.# 1986 IEEE.)


where:

La ¼ L2 þ L1r2=r1; ra ¼ r2LR=La ð6:16Þwhere L1 and L2 are the lengths of the rod parts in the upper and bottom layers, respectively (and L1þ L2¼LR), K1(0) is the value of correction coefficient K1 when h¼ 0 and the area is A, and K 0

p is the correction

coefficient corresponding to the grounding grid buried in the lower bottom layer, as illustrated in Figure 6.5.

When the horizontal grounding grid is buried in the top-layer soil, its grounding resistance can be

calculated by [12]:

R1 ¼ r1pLG

Kr ln2LG

h0þ N � 1

� �þ KpK1

LGffiffiffiA

p � 2ðxþ 1Þffiffiffix

p� ��

ð6:17Þ

where N is the geometry coefficient defined by Schwarz [9], as illustrated in Figure 6.6 and Kr is the

correction coefficient when the area is A and burial depth is h. When r2 > r1, p ¼ H=ffiffiffiA

p; when

r2 < r1, p ¼ ðH � hÞ= ffiffiffiA

p. The underlying assumption of the above formula is that all the vertical rods

are located inside the region of the horizontal grid.

Figure 6.7 shows the relationship between the correction coefficient Kr, the soil reflection coefficient

K and the structural coefficient p [12].

The mutual resistance between the horizontal grid and vertical rods is [12]:

R12 ¼ rapLG

ln2LG

Leþ N

� �þ r2pLG

K1ð0Þ LGffiffiffiA

p � 2ðxþ 1Þffiffiffix

p� �

ð6:18Þ

Le ¼ L1 þ L2r1=r2 ð6:19Þ

Figure 6.5 The relationship ofK 0p, p ¼ H=

ffiffiffiA

pandK, when the grounding grid is buried in the lower bottom layer [12].

(Reproduced with permission from J. Nahman, “Analytical expressions for the resistance of rodbeds and of combined

grounding systems in nonuniform soil,” IEEE Transactions on Power Delivery, 1, 3, 90–96, 1986.# 1986 IEEE.)


Figure 6.6 The relationship of geometry coefficient N and the ratio of width to length x of a grounding grid with

an area of A [12]. (Reproduced with permission from J. Nahman, “Analytical expressions for the resistance of

rodbeds and of combined grounding systems in nonuniform soil,” IEEE Transactions on Power Delivery, 1, 3,

90–96, 1986.# 1986 IEEE.)

Figure 6.7 The relationship between the correction coefficient Kr, the reflection coefficient of soil K and the

structural coefficient p [12]. (Reproduced with permission from J. Nahman, “Analytical expressions for the

resistance of rodbeds and of combined grounding systems in nonuniform soil,” IEEE Transactions on Power

Delivery, 1, 3, 90–96, 1986.# 1986 IEEE.)


Meanwhile, the following simplified formula can also be adopted to calculate the grounding

resistance of a compound grounding system which consists of horizontal grid and vertical rods [13]:

R ¼ 0:443r2ffiffiffiA

p r1r2

� �g

þ r1LG þmLe

ð6:20Þ

g ¼ 2HffiffiffiA

p þ nLeð6:21Þ

When H=ffiffiffiA

p � 0:3;ffiffiffiA

p=LG � 4; r1=r2 � 0:5, the above formula has a relatively high accuracy.

6.2.4 Simplified Formula for Calculating Step, Touch and Mesh Voltages

For an object with a reach of less than 1m, there is a high possibility that it connects to the grounding

grid directly or indirectly. Therefore, the touch voltage (which is the potential difference between the

peripherial conductor of the mesh, where the object is located, and the position with 1m of the periphe-

rial conductor) should use the potential difference between this grounded object and the mesh center.

This voltage is specified as the mesh voltage. The mesh voltage is typically bigger than the touch volt-

age, which is defined as the potential difference between the peripheral conductor of the mesh and the

position of 1m to the peripherial conductor.

When the size, burial depth and distance of the grounding grid are certain, Lawrence proposed the

following formulas to calculated the step, touch and mesh voltages [14]:

US1 ¼ ð0:10� 0:15Þri ð6:22ÞUT1 ¼ ð0:60� 0:80Þri ð6:23Þ

Um ¼ ri ð6:24Þwhere US1 is the step voltage at a distance of 1m, UT1 is the touch voltage at a distance of 1m, Um is the

potential difference between the grounding conductor and the center of the mesh of the grounding grid

and i is the current flowing into the earth through the conductor per meter.

The above formulas are evaluated approximately based on the average values of conductor diameter,

burial depth and the spacing between conductors. This approximation is always valid because these

parameters are in a logarithmic function. Their changes over a large range would not bring a big varia-

tion in the step, touch and mesh voltages. Considering the inhomogeneity of the current dissipating

from conductors, an inhomogenous coefficient should be adopted [4].

Koch et al. [15] analyzed test results of the inhomogeneity of currents flowing at different positions

in the grounding grid and revised Equation 6.24 to:

Um ¼ KmKirIG=LT ð6:25Þwhere IG is the maximum current flowing into soil in A; and the future increase or decrease network

should be taken into account. LT is the total length of the buried conductors (m). If the number of

parallel conductors is n, with spacing D, conductor diameter d and burial depth h, then Km is:

Km ¼ 1

2pln

D2

16hdþ 1

pln

3

4� 56� 78� � �

� �ð6:26Þ

The number of fractions in the brackets of the second term is less than the number of parallel conduc-

tors by 2. Ki is the correction coefficient of current inhomogeneity and the suggested value of Ki is

1.2� 1.3. As for soil with very inhomogeneous resistivity, Ki can be adopted as a bigger value.

Because the step voltage is less dangerous than the touch voltage and transfer voltage, its calculation

does not require very high accuracy. If the method of increasing resistivity of the ground surface, such


as paving or a layer of gravel, is adopted, and the layer does not extend beyond the wall, there is still a

potential danger caused by the step voltage, especially at the corner of the grounding grid.

In the design of a grounding system, many assumptions are adopted, such as: (i) the soil resistivity is

homogeneous, (ii) the grounding grid is formed by a perfect square and (iii) it is symmetrical. Even

under these assumptions, the current flowing out of the grid per unit length is still different, for instance

the current at the periphery is bigger than that at the center, while it reaches a peak at the corner.

The potential gradient changes correspondingly.

In fact, the actual grounding grid rarely meets these assumptions for homogeneous soil resistivity

and symmetrical geometry. However, the problem can also be solved with proper consideration of

irregular factors. Inhomogeneous coefficient Ki is commonly adopted to correct the calculation.

Like the potential gradient on the surface of ground, as long as the mesh spacing is kept at a proper

value and is distributed evenly, the potential gradient can be kept under a limit, even at the corner. If

most of the area is covered with wide mesh, while the area near the periphery is covered with narrow

mesh, a high mesh voltage can be avoided.

Another factor influencing the accuracy of calculation is soil homogeneity. If the top-layer soil has a

better conductivity than the bottom layer, the current flowing through the top layer is more than that

flowing through the bottom layer, and vice versa.

If the value of soil resistivity adopted in the calculation is close to the average value in the actual

system, then any local variation will be compensated automatically. The high grounding current flows

through areas of low resistivity. Under the same current density, a lower soil resistivity means a small

voltage drop. Meanwhile, if the soil resistivity varies suddenly at some position, the local potential

gradient will increase sharply.

Generally, an accurate value of correction coefficient Ki cannot be obtained. Therefore a relatively

large value should be adopted.

As for most cases, the whole grounding grid is assumed to be equipotential, which means that the

potential difference along the conductors can be neglected. Accuracy based on this assumption would

be enough high in practice. However, there still exists a potential difference between the different posi-

tions of the conductors in a large-size grounding grid. More current flows out at the higher potential

positions, and a small part of the current flows out at the lower potential position.

6.2.5 Formulas in IEEE Standard 80-2000 for Calculating Mesh and Step

Voltages

The formulas for calculating the mesh and step voltages introduced in the above section are very sim-

ple, which may bring certain error into the results. In IEEE Standard 80-2000, the formulas are modi-

fied according to the study by Mahonar [1].

6.2.5.1 Mesh Voltage

Mesh voltage is the maximum touch voltage inside a mesh. The mesh voltage in the preliminary design

is [1]:

Um ¼ rIGKmKi

LMð6:27Þ

where r is the soil resistivity, Km is the geometric correction coefficient of mesh voltage, Ki is the

correction coefficient of an irregular grid structure for considering the error introduced in the deduction

of Km (this coefficient only considers the peripheral meshes in which the worst step and touch voltages

happen) and IG is the maximum grid current that flows between the grounding grid and the surrounding

earth (including DC offset). Its value is smaller than the total current flowing to the surrounding earth

from the grounding grid.


The geometric correction coefficient Km is [1]:

Km ¼ 1

2pln

D2

16hdþ ðDþ 2hÞ2

8Dd� h

4d

!þ Kii

Kh

ln8

pð2n� 1Þ

" #ð6:28Þ

where D is the spacing between the parallel horizontal grounding conductors, d is the diameter of the

grid conductor, h is the burial depth of the grounding grid and Kii is the corrective weighting

coefficient adjusting the influence of inner conductors on the corner mesh. Note: the equivalent diam-

eter of flat steel d¼ b/2, where b is the width of flat steel. The equivalent diameter of equilateral

angle steel d¼ 0.84b, where b is the width of equilateral angle steel. The equivalent diameter of

non-equilateral angle steel d ¼ 0:71ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib1b2ðb21 þ b22Þ4

q, where b1 and b2 are the widths of two sides of

an equilateral angle steel.

The above formula is valid when the burial depth is between 0.25 and 2.50m. When vertical rods are

added at the corners or across the entire region of the grounding grid, Kii¼ 1.

When there is no vertical rod, or when there are only a few vertical rods but they are not added at the

periphery, then [1]:

Kii ¼ 1=ð2nÞ2=n ð6:29ÞKh ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ h=h0

pð6:30Þ

where n is the number of parallel conductors in the rectangle or equivalent rectangle grounding grid.

The following formula can take the irregularity of the grounding grid into account [11,12]:

n ¼ nanbncnd ð6:31ÞFor a square grounding grid, nb¼ 1. For square and rectangle grounding grids, nc¼ 1. For square,

rectangle and L-shaped grounding grids, nd¼ 1. In other cases [1]:

na ¼ 2Lc

Lp; nb ¼

ffiffiffiffiffiffiffiffiffiffiLp

4ffiffiffiA

ps

; nc ¼ LxLy

A

� � 0:7ALxLy

; nd ¼ DmffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiL2x þ L2y

q ð6:32Þ

where Lc is the total conductor length of grounding grid (m), Lps is the peripheral length of the ground-

ing grid (m), A is the area of the grid (m2), Lx is the maximum length of the grid in the x direction (m),

Ly is the maximum length of the grid in the y direction (m) and Dm is the maximum distance between

any two points on the grid (m).

For the purpose of a simple estimation of Km and Ki in the calculation of mesh voltage, we can use

n ¼ ffiffiffiffiffiffiffiffiffin1n2

p, where n1 and n2 are the number of conductors in the x and y directions, respectively. But it

should be noted that this formula will bring an error.

The correction coefficient of an irregular grid structure can be calculated by [1]:

Ki ¼ 0:644þ 0:148n ð6:33ÞFor grounding grids with no vertical rods, or for grids with only a few rods scattered throughout the

grid, but none located on the corners or along the perimeter of the grid, the effective burial length LM of

the grounding system is [1]:LM ¼ Lc þ LR ð6:34Þ

where LR is the total length of all vertical rods (m).

For grids with ground rods on all four corners, as well as along the perimeter and throughout the grid,

the effective burial length LM of the grounding system is [1]:

LM ¼ Lc þ"1:55þ 1:22

Lrffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

L2x þ L2y

q !#LR ð6:35Þ

where Lr is the length of each vertical rod (m), and all rods are assumed to be the same length.


6.2.5.2 Step Voltage

The step voltage is related to the geometric correction coefficient KS, the corrective coefficient Ki, the

soil resistivity r and the average current through per unit length grounding conductors [1]:

Vs ¼ rIGKSKi

Lsð6:36Þ

where IG is the maximum grid current.

For grids with or without ground rods, the effective burial conductor length Ls is [1]:

Ls ¼ 0:75Lc þ 0:85LR ð6:37ÞThe maximum step voltage is assumed to occur over a distance of 1m, beginning at the point above

the grid corner along the extension line of the diagonal line outside the corner. For the usual burial

depth of 0.25m< h< 2.5m, KS is [11]:

KS ¼ 1

p

1

2hþ 1

Dþ hþ 1� 0:5n�2

D

� �ð6:38Þ

The formulas for calculation of mesh and step voltages given above are based on the assumption of

homogeneous soil and even spacing of grounding conductors. A comparison between the results

obtained from those formulas and computer simulation results suggests that these formulas have a high

accuracy regardless of whether the grounding grid has or does not have vertical rods. The area of

grounding grids ranges from 6.25 to 10 000m2, the number of meshes ranges in one direction from 1 to

40, and the mesh size ranges from 2.5 to 22.5m2 [1].

6.2.6 Formulas to Calculate Touch and Step Voltages in Chinese Standards

The following formulas are adopted in the Chinese standard DL/T-621-1997 to calculate touch and step

voltages [3]. When a ground fault happens, the maximum touch voltage on the surface of grounding

grid is VTM, which is the mesh voltage:

VTM ¼ KtouchVG ð6:39Þwhere Ktouch is the touch voltage factor. VG is the potential rise in the grounding grid:

VG ¼ IGR ð6:40Þwhere IG is the maximum grid current that flows between grounding grid and the surrounding earth and

R is the grounding resistance of the grounding grid.

When the burial depth h is 0.6–0.8m, Ktouch is:

Ktouch ¼ KnKdKS ð6:41Þwhere the definitions of Kn, Kd and KS are given in Table 6.1.

Table 6.1 Kd, Kn and KS [3]. (Reproduced with permission from China Electric Power Industry DL/T621-1997,

"Grounding of AC electrical equipments," China Hydraulic and Electrical Engineering Press, Beijing, 1998)

Structure of grounding grid Rectangular mesh Square mesh Notes

Correction factor of conductor number, Kn 0.97/nþ 0.096 1.03/nþ 0.047 When n � 9 (one-directional

conductor number)

Correction factor of conductor number, Kn 0.545/nþ 0.137 0.55/nþ 0.105 When n � 10 (one-directional

conductor number)

Correction factor of conductor diameter, Kd 1.2-10d 1.2-10d Unit of d is m

Correction factor of grid area, KS 1:23-9:2=ffiffiffiA

p1:23-9:2=

ffiffiffiA

pWhen

ffiffiffiA

p � 16


When a ground fault occurs, the maximum step voltage is:

VSM ¼ KstepVG ð6:42Þwhere Kstep is the step voltage factor, which can be calculated using Equations 6.43 to 6.45.

Kstep ¼ 1:28L� L1

L� 2p

tan�1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA=p

ph� 0:4þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2þðh� 0:4Þ2

qvuut

264

8><>: � tan�1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA=p

phþ 0:4þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2þ ðhþ0:4Þ2

qvuut

375

þ L1

L

ln

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½h2 þ ðhþ 0:4Þ2�=½h2 þ ðh� 0:4Þ2�

qln½16 ffiffiffi

Ap

=ffiffiffiffiffiffipd

p �

9=; ð6:43Þ

When h¼ 0.6m, Equation 6.43 can be simplified into:


L� 0:477A0:25

þ L1

L� 0:61

lnð9:02 ffiffiffiA

p=dÞ

!ð6:44Þ

When h¼ 0.8m, Equation 6.43 can be simplified into:


L� 0:41A0:25

þ L1

L� 0:476

lnð9:02 ffiffiffiA

p=dÞ

!ð6:45Þ

where L is the total length of the grounding conductor, L1 is the perimeter of the grounding grid, d is the

diameter or equivalent diameter of the horizontal grounding conductors and A is the total area enclosed

by the grounding grid.

6.2.7 Transfer Potential

During a ground fault, a serious hazard may result from the transfer of high potential from the sub-

station grounding grid to outside locations. This may be transferred by those objects connected with

the grid, such as communication circuits, conduits, pipes, metallic fences, low-voltage neutral wires

and so on. In a region of high soil resistivity, it is very difficult to reduce the grounding resistance.

When a ground fault occurs, the GPR will be very high. For example, if the grounding resistance is

5V, the GPR will rise to 10 kV with a 2000A short-circuit current injected into the Grounding system.

The potential equalizing method can only solve the problem of high step and touch voltages. Certain

methods should be taken to solve the problem of high potential transferring outside the substation and

low potential introducing into the substation.

The main paths for high potential transferring outside the substation, and low potential introducing

into substation include: the low-voltage power supply system, communication circuits, rails, conduits

and pipes. Also, the structures inside the substation carry the GPR.

6.2.8 Methods for Improving the Safety of a Grounding System

Calculations based on the preliminary design indicate that dangerous potential differences can exist

within a substation, and the following possible remedies should be studied and applied where appropriate.

6.2.8.1 Decrease the Substation Grounding Resistance

Decreasing the grounding resistance of a substation will decrease the maximum GPR, and hence, the max-

imum transfer potential. The most effective way to decrease the grounding resistance is by increasing the

area occupied by the grid. Another method is to effectively decrease the resistivity of the soil region neigh-

boring the grounding grid, because the soil resistance of this region provides a large part of the grounding

resistance of the substation [1]. If a deep low-resistivity soil layer exists, the grounding resistance can be

effectively decreased by arranging long vertical ground rods or ground wells to penetrate into it.


Decreasing the grounding resistance of a substation does not mean an appreciable decrease in the

local potential gradient, because this depends on the arrangement of the grounding conductors.

6.2.8.2 Closer Grid Spacing

By employing a smaller spacing of grid conductors, the grounding grid becomes similar to a metal

plate. Thus the dangerous potentials within the substation can be eliminated, but at a cost. It is much

more difficult to decrease the dangerous potential differences outside the peripheral conductors, espe-

cially for a small substation in a high-resistivity region. However, by burying the grounding conductors

outside the fence, it is usually possible to ensure that the steeper gradient is immediately outside this

grid perimeter. Thus the most dangerous touch voltage can be controlled. Another effective and eco-

nomical way to control gradients is to increase the density of ground rods around the perimeter, while

the density in the center of the grid may be decreased. Another approach to controlling the peripherial

gradient and step voltage outside the substation fence is to bury two or more parallel conductors around

the perimeter at increasingly greater depths as the distance from the substation fence is increased.

Another approach to realizing a more uniform potential distribution on the ground surface above the

grounding grid is to arrange the grounding conductors with unequal spacings. This means the spacing

near the perimeter of the grid is small, but in the center of the grid the spacing is large. This approach

can effectively equalize the potential gradient and limit the number of conductors used in the ground-

ing system.

6.2.8.3 Increasing the Serial Resistance with the Human Body

Paving with a surface-layer material of high resistivity is another important method, because it

increases the resistance in series with a human body, and it decreases the current through the body,

consequently allowing for higher touch and step voltages.

A layer of high resistivity material, such as gravel and cobblestone, is often spread on the soil surface

above the grounding grid. The wet cobblestone adopted in the substation has a resistivity of 5000Vm.

If the thickness of the layer is 10–15 cm, the possibility of danger is decreased by one-tenth. Many

experiments have been carried out in Germany and results suggest that, when people stand on the wet

cobblestone layer and touch a water tap, the current is about one-20th of the current when people stand

on grass without a cobblestone layer.

It should be pointed out that the above conclusion is made under the assumption of a clean cobble-

stone layer. However, in reality, some stones are pushed into the earth and the gap is filled with dust and

soil, which decreases the insulation status of the high resistivity layer. The allowable step and touch

voltages after laying a high resistivity layer can be obtained using the formula given in Chapter 1.

If a high resistivity material layer has already been spread on the surface, but the safety requirement is

still not satisfied, the thickness of the layer should be increased. The upper limit of the thickness is 15 cm.

6.2.8.4 Diverting the Fault Current to Other Paths

By connecting overhead ground wires for transmission lines or by decreasing the tower footing resist-

ances in the vicinity of the substation, part of the fault current will be diverted from the grid. In connec-

tion with the latter, however, the effect on fault gradients near tower footings should be weighed.

Meanwhile, the fault current might flow through the ground wire of a transmission tower by selecting a

ground wire with a big cross-section and high conductivity. For a small substation located at high resis-

tivity area, this might be the only way to meet the safety requirement.

6.2.8.5 Limiting the Total Fault Current

If feasible, limiting the total fault current will decrease the GPR and all gradients in proportion. Other

factors, however, will usually make this impractical. Moreover, if accomplished at the expense of a

greater fault clearing time, the danger may be increased rather than diminished.


6.2.8.6 Setting the Groundings of Structures

A ban on approaching any area with a big potential difference would appear when a fault happens, so a

pedestrian should be set in this area to reduce the possibility of electrical contact. After the preliminary

design, if there is still a dangerous potential difference, methods should be taken to ease the situation.

The designers should take care of this problem in the design stage to make the construction easier.

6.2.8.7 Preventing the Use of Isolated Grounding

Generally, an isolated grounding within the region of a substation is a hazard and therefore it is rarely

adopted. Because the grounding wire and the protective wire are separated for electric equipment, it is

usually assumed that a short-circuit current would not flow through the protective wire and thus the

high potential of the protective wire would be avoided. However, this conclusion is problematic:

The resistance of the ground wire or protective wire is smaller than that of either one when they are

connected together. When the insulation is broken somewhere in the substation, there still is current flowing through the

protective wire. It is inevitable that grounding electrodes are connected to each other in the same area, because abso-

lute separation is impossible. Even if absolute separation is realized, there still might be a dangerous high potential at the connect-

ing point.

6.2.8.8 Safety Check of Existing Substation Grounding System

For an existing substation, in order to check whether the substation grounding is safe or not, the

following formula can be adopted. If the following requirement is met, the substation is considered

as safe [1]:KmKirI

ffiffit

p=LT � 0:17rs < 116 ð6:46Þ

6.3 Methods for Decreasing the Grounding Resistance of a Substation

Not only can decreasing the grounding resistance of a grounding system decrease the maximum ground

potential rise, but it also can decrease the maximum transfer potential. Several methods have been

applied to decrease the grounding resistance of a grounding system. Regular methods include enlarging

the grounding grid, connecting the main grounding grid to an additional external grounding grid,

increasing the burial depth of the grounding grid, utilizing natural grounding objects such as the steel

foundations of structures, adding long vertical grounding electrodes and exchanging the soils around

the grounding grid for low resistivity materials. These methods are suitable for different geological

situations but that does not mean they should be taken up independently.

In fact, in a specific soil environment, two or more methods should be taken up to decrease the

grounding resistance effectively. Adding deep vertical ground rods to the grounding grid is very effec-

tive, especially in urban substations with only a small area. This method can utilize the low resistivity

soil layer and eliminate seasonal influences. In order to decrease the grounding resistance, a special

method was proposed for decreasing the grounding resistance of grounding grids in a high resistivity

area, called the explosive grounding technique [16]. This method has been proven very effective in

China, and the only shortcoming of the explosive grounding technique is the high engineering cost.

6.3.1 Basic Methods for Decreasing Grounding Resistance

6.3.1.1 Expanding the Grounding Grid Area of a Substation

Substation grounding resistance can be calculated by Equation 6.3. From Equation 6.3 we can see that

the grounding resistance is inversely proportional to the square root of the area. The greater the area is,


the lower is the grounding resistance. Undoubtedly expanding the area of the substation grounding grid

is an effective method to decrease the grounding resistance.

The method of expanding the grid area in order to decrease the grounding resistance can only be used

in specific regions. For substations in mountain regions, it is not possible to expand the grid area. What

is more, for substations in urban districts, it is impossible to find suitable land to expand the grounding

grid area.

6.3.1.2 Connecting with an External Grounding

Connecting with an external grounding is a method which involves connecting the main grounding grid

of a substation with an auxiliary grounding grid which is laid in a low soil resistivity region outside the

substation in order to decrease the grounding resistance of the whole grounding system. It should be

noted that there is a significant potential difference between the substation grid and the auxiliary

grounding grid in a fault condition. When a high-frequency impulse, such as lightning, acts on the

system, the potential difference will be especially great. So it should be ensured that there are several

grounding conductors in parallel connecting the main grounding grid with the auxiliary grounding grid.

6.3.1.3 Increasing the Burial Depth of the Grounding Grid

From Equation 6.4, we can see that increasing the burial depth of a grounding grid will decrease the

grounding resistance if other parameters remain unchanged. But the effect of this method is not obvi-

ous, especially in a high soil resistivity region. Therefore an engineering project generally does not

adopt this method. The burial depth of a substation grounding grid is generally about 0.8m.

6.3.1.4 Using Natural Groundings

Natural groundings contain the steel reinforced concrete frames of buildings, hydropower intake trash

racks, gates, water pipes and so on. These natural groundings, because they themselves have a low

grounding resistance, should be connected with the main grounding grid in order to achieve the purpose

of decreasing the grounding resistance. Especially in a hydropower substation, using natural ground-

ings can decrease the grounding resistance effectively without increasing the investment.

6.3.1.5 Partially Changing the Soil

Soil resistivity directly affects grounding resistance. For some grounding devices that locate in a high

soil resistivity region, if it is difficult to use other methods to decrease the grounding resistance, the

method of partially changing the soil can be used. We can use a low resistivity soil or low resistivity

material to replace the original high resistivity soil around the grounding device.

6.3.2 Using Long Vertical Ground Rods to Decrease Grounding Resistance

In a high soil resistivity area, it is very difficult to meet the requirement on grounding resistance.

Especially in gas-insulated substations or small-sized substations, long vertical ground rods or ground

wells can be used to decrease the grounding resistance. Awell type grounding electrode is a long verti-

cal grounding electrode of a large size. The principle is to effectively make use of the low resistivity

layer underground and to maintain the stability of the grounding resistance.

The soil resistivity is usually non-uniform along both the vertical and horizontal distributions. For just

the vertical distribution, soil at different depths has different resistivities. Generally the soil within a few

meters of the ground surface has a relatively higher resistivity, but the resistivity is instable and changes

with season and climate. The deeper the soil is, the more stable is the resistivity. Especially in a high soil

resistivity region and where the common methods for decreasing the grounding resistance cannot be

used, the use of long vertical ground rods connected to the main grounding grid is an effective method to

decrease the grounding resistance. In a region where there is an underground aquifer, a ground rods is


likely to penetrate the water layer, and then the effect of decreasing grounding resistance will be better

[1]. A well type grounding electrode is not influenced by season or climatic conditions. Not only can it

decrease the grounding resistance, but it is also able to overcome the shortcomings of a small substation

area, which is an effective method in urban and mountainous areas. The diameter of a well type ground-

ing electrode is more than 7.5 cm, and its depth depends on the drilling equipment used. As the diameter

of a grounding electrode (ground rod together with backfilled low resistivity material) increases, it can

significantly decrease the total grounding resistance. If the well type grounding electrode contacts a water

layer underground, this will highly decrease the seasonal variation in grounding resistance and at the

same time will increase the current passing through this grounding electrode. A well type grounding

electrode must coordinate with low resistivity material to obtain low grounding resistance. Mud com-

posed of clay with high conductivity (such as bentonite) and water can be used as backfilling material.

Because a backfilling material can absorb moisture from the surrounding environment, the well type

grounding electrode does not need any maintenance and will not become dry. In addition, the deep-hole

explosion grounding technique can also be applied to form a huge range of low resistivity [17].

6.3.2.1 Usage Coefficient of Long Vertical Ground Rods

For a horizontal grounding grid with an area of 120 120m2, an unequal spacing grounding grid (as

introduced in Section 6.4) is applied. The soil resistivity is 1000Vm, the fault current flowing into soil

is 10 kA, the radius of grounding conductor is 10mm and the burial depth h of the grounding grid is

0.6m. Vertical ground rods are arranged along the peripheral grounding conductor of the grounding

grid. The arrangement of vertical ground rod has five different styles and the number of vertical ground

rods N in each is: (i) four (arranged as one in each corner), (ii) eight (one in each corner, one in each

side), (iii) 12 (one in each corner, two along each side), (iv) 16 (one in each corner, three along each

side), (v) 20 (one in each corner, four along each side). Each vertical ground rod is arranged with equal

spacing and the length L of a vertical ground rod can be 10, 30, 50, 70, 90, 110, 130 or 150m. The

equivalent radius r of the grounding grid is:

r ¼ffiffiffiffiffiffiffiffiffiA=p

pð6:47Þ

where A is the grounding grid area. The definition of the decreased ratio of grounding resistance after

using a vertical ground rod is [25]:

z ¼ 1� R=R0 ð6:48Þwhere R0 is the grounding resistance of grounding grid and R is the grounding resistance after adding

vertical ground rods.

The definition of the usage coefficient h of N vertical ground rods is:

h ¼ RC=R ð6:49Þwhere RC is grounding resistance of RP and R0 in parallel, and RP is the grounding resistance of N

vertical ground rods in parallel.

Figures 6.8 and 6.9 show the curves of the decreased ratio of grounding resistance and the usage

coefficient h of vertical ground rods with L/r and N after vertical ground rod addition. The following

conclusions can be obtained:

The decreased ratio j increases with the increase in the proportion L/r for vertical rod length L and

equivalent radius r of the grounding grid. As L/r increases, the usage coefficient decreases. When L/r> 1, the usage coefficient h tends to

saturation. When L is fixed, the usage coefficient correspondingly decreases with an increase in the number of

vertical electrodes (equivalent to decreasing the spacing between vertical ground rods). The reason

is that the shielding effect between vertical rods increases with an increase in the spacing between

vertical rods.


When L is fixed, the decreased ratio z of grounding resistance increases as the vertical ground rod

number N increases. When N increases to a critical value (from Figure 6.8 we can see the value of

N is 8), the decreased ratio increases slowly.

In the previous grounding design, the length of most vertical ground rods was from a few meters to

10m and they were arranged through the whole horizontal grounding grid. But their actual effect in

decreasing grounding resistance is not obvious; and the reason is that the vertical ground rods are too

short to decrease grounding resistance due to the shielding effect of the horizontal grounding grid. For a

long vertical ground rod, the following rules are useful in the design:

In order to decrease the shielding effect between a horizontal grounding grid and vertical ground rods

and to increase the usage coefficient of each vertical ground rod, it is more suitable to arrange the

Figure 6.8 The relationship between the decreased ratio of grounding resistance and L/r after a vertical

ground rod is added.

Figure 6.9 The relationship between the usage coefficient h of a vertical ground rod and L/r after a vertical ground

rod is added.


vertical ground rods along the peripheral conductors. If the conditions permit, we should arrange the

vertical ground rods as far outside the substation as possible, in order to make the spacing of vertical

ground rods at least equal to their length. The number and actual length of vertical ground rods can be determined according to the require-

ment on the grounding resistance and the geological structure of the substation site. The basic princi-

ple is that, when there is no low resistivity layer under the ground, the length of vertical ground rod is

generally not less than the equivalent radius of a horizontal grounding grid. And the number of verti-

cal ground rods should be generally more than four. However, we should pay attention to the fact

that: (i) the decreased ratio begins to become saturated when the number of vertical ground rods

increases to a critical value and (ii) the construction cost of vertical ground rods is relatively high. A full investigation of the substation region and the soil characteristics nearby should be made to

determine the soil structure. If there is a deep low resistivity layer, deep well grounding is suitable.

However, if the resistivity of the deep layer is higher than that of the surface layer, using deep well

grounding makes little sense.

6.3.2.2 Current Distribution along a Single Vertical Rod

The reflective coefficient of a two-layer soil is defined as K ¼ ðr2 � r1Þ=ðr2 þ r1Þ, where r2 and r1are soil resistivities. Figure 6.10 gives the distribution curves of the current intensity J dispersed into

earth along rod length x under different reflective coefficient. Here, the length L equals 20m; conductor

radius r2 equals 0.02m; top-layer soil resistivity r1 equals to 100Vm with the depth h of 7.5m [18].

From Figure 6.10, we observed that the current is well distributed along the rod except that current

intensity increases quickly at the bottom of the rod in the uniform soil. However, the high current

intensity area occupies a little percentage. As a result, the current distribution is considered as well-

distributed, this would not cause apparent error.

The dispersed current distributions differ with each other when the rods are in the two-layer soil. The

current intensity in the low resistivity soil layer is higher than that in the high resistivity soil layer. In

each layer the current distribution shows almost no change, but there is a sharp shift along the interface.

The difference in the current distributions in different layers rises when the reflective coefficient

increases. For example, when K equals 0.8, the current intensity is 300A/m in the top layer, but it is

only 25A/m in the bottom layer. Hence the proper choice of rod length not only decreases the ground-

ing resistance efficiently but also achieves a better economic effect.

Figure 6.10 Current distribution along rods in a two-layered soil [18]. (Reproduced with permission from Y. Gao,

R. Zeng, X. Liang, X. et al., “Safety analysis of grounding grid for substations with different structure,” Proceedings

of IEEE Powercon, Perth, Australia, pp. 1487–1492, 2000.#2000 IEEE.)


6.3.2.3 Arrangement of Rods in Two-layered Soil

Here we discuss how vertical ground rods affect the electrical behavior of a three-dimensional grounding

grid in a two-layer soil. The relationship between rod length and decreasing rate of grounding resistance

with different reflective coefficients is shown in Figure 6.11 [18]. The horizontal grounding grid area is

100 100m2, the horizontal conductor spacing is 10m and the top-layer soil resistivity is 200Vm. Four

vertical rods are arranged at the corners of the grid and the top-layer soil thickness h is 40m.

As illustrated in Figure 6.11, when the reflective coefficient K is lower than 0.5 (i.e., the soil resistiv-

ity of the bottom layer is high), adding vertical ground rods cannot efficiently decrease the grounding

resistance. Even if the rod length approaches the equivalent radius of the grounding grid, the decreasing

rate of grounding resistance is still lower than 10%. Therefore, the method of long rods does not fit the

situation that the soil resistivity of the bottom layer is very high. In contrast, when the soil resistivity of

the bottom layer is low, the addition of long rods can achieve good results.

From the current distribution curves in Figure 6.10, it is understandable that a turning point emerges

on the grounding resistance decreasing rate curve in Figure 6.11 when K< 0 and the rod length

approaches the top-layer depth. That is, the decreasing rate of grounding resistance increases remark-

ably when the rod length is longer than the top-layer depth; but when the rod length is 3.5 times the

depth of the top layer, the decreasing rate of grounding resistance approaches saturation. Thus the

effective rod length is determined by reflective coefficient K, and as a result, long rods cannot achieve a

good result when the resistivity of the bottom layer is apparently lower than that of the top layer.

6.3.2.4 Arrangement of Vertical Grounding Rods in Three-layered Soil

The soil structures of a three-layer soil according to soil resistivity can be divided into three types: high

resistivity layer (H), medium resistivity layer (M) and low resistivity layer (L). High resistivity is

assumed to be 1000Vm, low resistivity is 100Vm and medium is 500Vm. The top-layer depth is 10m

and the middle layer thickness is 50m. The horizontal grid and rods are all the same as those in the two-

layer soil. The influence of added vertical ground rods on the decreasing rate of grounding resistance is

shown in Figure 6.12 [18].

From Figure 6.12, just as in the two-layer soil, the vertical rods cannot decrease the grounding resist-

ance effectively when the top-layer resistivity is low. So in such a situation, long rods are not suitable.

Figure 6.11 Grounding resistance decreasing rate of vertical ground rods in a two-layered soil [18]. (Reproduced

with permission from Y. Gao, R. Zeng, X. Liang, X. et al., “Safety analysis of grounding grid for substations with

different structure,” Proceedings of IEEE Powercon, Perth, Australia, pp. 1487–1492, 2000.#2000 IEEE.)


In the situation of a strictly limited area with a high resistivity in the middle layer, the vertical rods

must reach the bottom layer with its low resistivity. Comparing the two curves of MHL and MLH in

Figure 6.12, we observed that, before the rods touch the bottom layer, the decreasing rate of grounding

resistance in the former is larger than that of the latter due to the role of the low resistivity middle layer.

When the soil structure is MLH, it is better that the rods do not reach the bottom layer. But in contrast,

when the soil structure is MHL, it is better that the rods should reach the bottom layer.

The protruding curve MLH in Figure 6.12 with a low resistivity middle layer illustrates the fact that

the grounding resistance almost stops decreasing when the vertical ground rod passes the middle layer.

Therefore the economic rod length is the sum of the depth of the upper and middle layers.

With a high resistivity top layer, rods can reach the best results. Just as in the two-layer soil, the rod

length is determined by the reflective coefficient K and layer structure. The effect of decreasing the

grounding resistance is below the interface with a smaller reflective coefficient, especially when the

resistivity of the bottom layer is lower than that of the middle layer.

6.3.2.5 Improving the Seasonal Safety of a Grounding Grid with Vertical Grounding Rods

Soil resistivity changes greatly during winter. For example, measured results at Muliduo in Qinghai,

China, show that the resistivity range from frozen to unfrozen soil is 500–15 000Vm. In the northwest

Figure 6.12 Influence of added vertical ground rods on the grounding resistance decreasing rate [18]. (Reproduced

with permission from Y. Gao, R. Zeng, X. Liang, X. et al., “Safety analysis of grounding grid for substations with

different structure,” Proceedings of IEEE Powercon, Perth, Australia, pp. 1487–1492, 2000.#2000 IEEE.)

Figure 6.13 A seasonally influenced soil layer with a surface granite layer [19]. (Reproduced with permission from

J.L. He, R. Zeng, Y.Q. Gao, Y.P. Tu, W.M. Sun, J. Zou, Z.C. Guan, “Seasonal influences on safety of substation

grounding system,” IEEE Transactions on Power Delivery, 18, 3, 788–795, 2003.# 2003 IEEE.)


of China, the depth of frozen soil can reach 1.6m, and the thickness can be 6.0m in the northeast of

China. The seasonal frozen soil layer will influence the safety of the grounding grid [19].

As shown in Figure 6.13 [19], when the surface soil layer forms a high resistivity layer in the freez-

ing season, the grounding resistance of a grounding grid increases with the thickness or resistivity of

the high resistivity layer. When the thickness of the high resistivity layer exceeds the burial depth of

the grounding grid, the grounding resistance would increase to 1.7–3.0 times that of the grounding

system in normal conditions. The touch voltage of the ground surface increases with the thickness or

resistivity of the freezing soil layer. When the thickness of the freezing soil layer exceeds the burial

depth of the grounding system, the touch voltage sharply increases. If the resistivity of the freezing

soil layer reaches 5000Vm, then the touch voltage will increase to reach 12 times the respective

value in normal conditions. The step voltage increases with the resistivity of the freezing soil layer.

Even if a granite layer is added, the limit of the touch voltage is still smaller than the actual touch

voltage [19].

Adding vertical ground rods can effectively decrease the touch voltage to improve the safety of a

grounding system. The relationship between rod length and touch voltage with different seasonal fac-

tors is shown in Figure 6.14 [19], in which the seasonal factor is represented by different high resistivity

soil layers. The touch voltage is a ratio between calculated values with the different seasonal factors

and calculated values which do not consider the seasonal factors. When the depth of the soil affected

by the season is smaller than the burial depth of the horizontal grounding grid and the rod length is

fixed, the surface touch voltage almost does not change with an increase in the resistivity of the upper

high resistivity soil layer. But with an increase in rod length, the surface touch voltage decrease reaches

saturation. When the depth of the seasonal soil layer affected by the season is higher than the depth of

the grounding grid, the surface touch voltage shows a linear increase with the increase in soil resistivity.

But the increase velocity decreases with the increase in rod length.

Rods buried on the periphery of the horizontal grounding grid not only decrease the touch voltage and

step voltage by improving the potential distribution, but also efficiently decrease the grounding resistance.

When vertical ground rods are added to the grounding system, the current dispersed by horizontal con-

ductors in the grounding grid decreases due to a large amount of fault current flowing into the soil through

vertical ground rods. As a result, the electrical field intensity of the soil surface above the grounding

system decreases greatly. As a result, the touch and step voltages on the surface decrease greatly.

Figure 6.14 The relationship between rod length and touch voltage in different seasonal factors [19]. (Reproduced

with permission from J.L. He, R. Zeng, Y.Q. Gao, Y.P. Tu, W.M. Sun, J. Zou, Z.C. Guan, “Seasonal influences on

safety of substation grounding system,” IEEE Transactions on Power Delivery, 18, 3, 788–795, 2003. # 2003 IEEE.)


6.3.3 Explosion Grounding Technique

6.3.3.1 Description of the Explosion Grounding Technique

If a huge deep distributed grounding system is created in the substation area, then the current injected

into the grounding system easily disperses to deeper soil layers. At the same time, the area available to

dissipate fault currents increases, resulting in a decrease in the ground resistance. Realistically, it is

difficult to construct a large grounding system within the area defined by most substations. A so-called

explosion grounding technique was proposed based on building a grounding system which extends to

great depths to realize this idea [16].

First, several vertical holes are drilled, then appropriate explosive agents are introduced into the

holes. The resulting explosions create various cracks in the soil. Finally, low resistivity materials

(LRM) are injected into the holes and cracks under high pressure. As a result, a large number of cracks

around the vertical conductors are filled with LRM and a large three-dimensional grounding network

consisting of the grounding conductors and cracks is formed, as illustrated in Figure 6.15a. The basic

idea for this method comes from the usual practice when building the foundations of transmission line

towers in rocky regions of triggering explosions in holes and filling them with concrete. It was noticed

that these kinds of tower foundations have very low grounding resistances. The LRM is usually an

inorganic material with a resistivity less than 5Vm. The explosion course is carefully planned, and the

region close to the surface remains intact, as shown in Figure 6.15b.

The basic principles upon which this new method is based are [16]:

1. Contacting Deep Soil Layers with Low Resistivity: It was observed that there are usually layers

which either have a low soil resistivity or are saturated with underground water in regions with high

resistivity. The new method can effectively use these low resistivity layers to decrease ground

resistances.

2. Reducing Contact Resistances: The low resistivity materials which fill the holes provide a very low

contact resistance between grounding conductors and soil.

3. Decreasing the Leakage Resistance: The measured ground impedance of a grounding system con-

sists of four parts: the impedance of bonding leads, the impedance of grounding conductors, the

contact resistance between grounding conductors and soil and the distributed resistance to remote

earth. The first and second parts are very small and can be neglected. The third part is normally

ignored during computation and is quite small when LRM are used to decrease contact resist-

ances, as is the case here. Consequently only the distributed (leakage) resistance is significant.

When this method is used, a large network of soil cracks filled with LRM is formed. This network

acts like a virtual extension of the grounding system into deeper soils, resulting in lower ground

resistances.

4. Links to Intrinsic Soil Cracks: It is known that intrinsic cracks exist in rocky areas. The cracks

caused by the explosion often connect with intrinsic cracks in the rock. These intrinsic cracks are

typically filled with moisture and usually extend to remote locations. The connected intrinsic cracks

and explosion cracks are filled with LRM by high pressure injection. When current is discharged

from the grounding system, it can flow to remote locations through the low resistivity soil cracks.

6.3.3.2 Effectiveness of the New Method in Decreasing Grounding Resistances

Because the deep distributed grounding system can connect with deeper low resistivity soil via intrin-

sic and explosion cracks filled with LRM, an explosion and geology factor K should be considered

when computing the resistance of the grounding system using the formula for a hemispherical elec-

trode of radius r as:

R ¼ r

2pKrð6:50Þ


The explosion and geology factor K is related to the degree of explosion and geology. For exam-

ple, K is dependent on the existence of deep layers of low resistivity, the existence of intrinsic

cracks and whether the cracks extend to remote locations with low resistivity soil. r is a modified

equivalent radius:

r ¼ hþ D ð6:51Þwhere h is the depth of the deepest hole and D is the equivalent reach of cracks, which is related to

the geological structure in the substation area. In lightly weathered rocky soil, D is in the range 5–

10m. In medium weathered rocky soil, D is in the range 10–15m and in heavily weathered rocky

soil, D is in the range 15–20m.

From many experimental results, the explosion and geology factor K has been classified into six

types according to geological situation. The results are given in Table 6.2 [16].

Figure 6.15 Cubic grounding system. (a) Three-dimensional view. (b) Side view.


6.3.4 Deep Ground Well

6.3.4.1 Principle of a Deep Ground Well for Decreasing the Grounding Resistance

The key to decreasing the grounding resistance of a substation is changing the soil resistivity around the

grounding system, because the grounding resistance of a substation is mainly determined by the resis-

tivity of the soil region around the grounding system. The resistivity of soil in nature is decided by the

water content and the property and density of the electrolyte solution, which has the characteristics of

ion conduction. Ordinarily, the resistivity of soil containing much water is small, and the resistivity of

dry soil is high. Experimental results from clay sample show that its resistivity changes very quickly

when the water content is less than 10%. When the water content of the clay sample is 2.5%, its tested

resistivity is 1400Vm, but when its water content increases to 10%, its tested resistivity decreases to

200Vm; and when its water content increases to 25%, its tested resistivity decreases to 15Vm.

As we know, if we dig a well in the earth, groundwater will move into the well. Utilizing deep wells

to decrease grounding resistance is a method which mainly uses deep wells to change the direction in

which groundwater moves in the soil surrounding ground rods and uses the gravity water, capillary

water and vaporous water in the groundwater to increase the humidity in the soil surrounding ground

rods, which decreases the soil resistivity near the grounding substation and consequently decreases the

grounding resistance of the ground rods [20].

The principle of a well can be explained by Figure 6.16 [20]. In the soil plane with depth h,

the pressure P1 on the sidewall of the well is atmospheric pressure and the pressure P2 on a

Figure 6.16 Diagram showing the principle of a water well [20]. (Reproduced with permission from J.L. He,

G. Yu, J.P. Yuan, R. Zeng, B. Zhang, J. Zou, Z.C. Guan, “Decreasing grounding resistance of substation by deep-

ground-well method,” IEEE Transactions on Power Delivery, 20, 2, 738–744, 2005.# 2005 IEEE.)

Table 6.2 Explosion and geology factor K in different geological conditions. (Reproduced with permission from

Q.B. Meng, J.L. He, J. Ma, F.P. Dawalibi, “A new method to decrease ground resistances of substation grounding

systems in high resistivity regions,” IEEE Transactions on Power Delivery, 14, 3, 911–917, 1999.# 1999 IEEE)

Geological condition Underground layer with low resistivity Explosion and geology factor K

Heavy weathering No 1.25–2.00

Heavy weathering Yes 1.67–3.33

Medium weathering No 1.00–1.25

Medium weathering Yes 1.25–2.00

Light weathering No 0.77–1.00

Light weathering Yes 1.00–1.43


groundwater molecule in the soil with depth h is the atmospheric pressure plus the soil pressure.

Thus, it is obvious:

P2 > P1 ð6:52ÞSo, the groundwater molecule would move towards the well due to the pressure difference, then

groundwater would accumulate in the well and a big soil region near the well would fill with water.

For this reason, the resistivity of a soil region full of groundwater is low. If we construct a metal tube

electrode as the sidewall of the water well, then the metal tube electrode has a low grounding

resistance. To maintain the pressure difference in order to lead water into the interior of the metal

tube, many small holes must be drilled into the tube.

During the process of the groundwater moving towards the well, a drag force would be encountered

in the soil. So, the final water level in the well is determined by the balance between the pressure differ-

ence and the drag force. This is a dynamic balance process related to the groundwater content.

6.3.4.2 Field Installation of a Deep Ground Well

As illustrated in Figure 6.17a, during the field installation of a deep ground well, first a vertical hole is

drilled in the soil. Ordinarily, a stainless steel tube or galvanized steel tube is adopted as the ground rod,

with a diameter of about 50mm, and small holes are arranged along the tube for groundwater to pass

through the tube. The steel tube is then inserted into the drilled hole. A deep ground well is connected by

several short steel tubes. Two short tubes are connected together by a straight fitting and the connecting

region is welded as shown in Figure 6.17b. The gap between the sidewall of the drilled hole and the steel

tube is filled with carbon powder with very low resistivity by pressure. The carbon powder filler has good

water absorbability, which can keep itself and the neighboring soil in a humidified state. Further, the

carbon powder has a good permeability and groundwater can easily move into the ground well through

it. In order to prevent the carbon powder from entering the steel tube, a special filtering film is used to

cover these permeable holes on the steel tube. Other materials, such as fine loess or bentonite, can be used

to fill the gap between the sidewall of the drilled hole and the steel tube. From the top of the steel tube to

the ground is 1m and a small aeration hole is left to keep the pressure in the well at atmospheric pressure.

Figure 6.17 Schematic diagram of a deep ground well (a) and the connection of two steel tubes for use in a deep

ground well (b) [20]. (Reproduced with permission from J.L. He, G. Yu, J.P. Yuan, R. Zeng, B. Zhang, J. Zou, Z.C.

Guan, “Decreasing grounding resistance of substation by deep-ground-well method,” IEEE Transactions on Power

Delivery, 20, 2, 738–744, 2005.# 2005 IEEE.)


6.3.4.3 Application of a Deep Ground Well

The deep ground well method was applied in the grounding system reconstruction engineering of the

110 kV Luohu substation in Heyuan City, Guandong Province, China. Being in southern China, there is

abundant groundwater [20].

The 110 kV Luohu substation locates in a hilly region. The old substation grounding grid was built in

September 1984 and the original area for this grounding grid was about 90 90m2 with a tested

grounding resistance of 1.79V. In 1989, the area of this grounding grid was enlarged to 90 120m2

and horizontal ground rods were added to connect the grounding devices of the transmission lines

together, as illustrated in Figure 6.18 [20]. The added area is about 3000m2 and the tested grounding

resistance is 1.35V.

The grounding system of the 110 kV Luohu substation was rebuilt at the end of 1999 by applying this

novel deep ground well method. Ten deep ground wells were added, and the lengths of these ten deep

ground wells are in the range 11–15m. According to the measured grounding resistance of every deep

ground well, the analyzed equivalent width is in the range of 0.26–2.04m and the average width is

1.44m. So the diameter of the equivalent region with low resistivity is 0.57–4.13m and the average

Figure 6.18 Schematic diagram of the grounding system with a deep ground well for the 110-kV Luohu substation

[20]. (Reproduced with permission from J.L. He, G. Yu, J.P. Yuan, R. Zeng, B. Zhang, J. Zou, Z.C. Guan,

“Decreasing grounding resistance of substation by deep-ground-well method,” IEEE Transactions on Power

Delivery, 20, 2, 738–744, 2005.# 2005 IEEE.)


diameter is 2.93m. The diameter of the ground well is 50mm, so the equivalent diameters are

11.4–40.8 times that of the ground well [20].

The principle of the deep ground well is to lead groundwater towards it, so the deep ground well

method can only be used in a region with groundwater. If there is no groundwater, it can only be

regarded as a popular vertical ground rod.

6.3.5 Slanting Grounding Electrode

The basic methods to decrease the grounding resistance of a substation are to expand the area of the

grounding grid and/or develop in a vertical direction, for example adding vertical ground rods to the

grounding grid. A slanting ground rod, which has the merits of both deep vertical grounding electro-

des and area enlargement without land expropriation, was proposed by He et al. [21], as shown in

Figure 6.19. Compared with vertical ground rods, the shielding effect among slanting ground rods is

very small. Thus, for the grounding grid, using a slanting ground rod to decrease the grounding

resistance is more effective than applying vertical ground rods with the same length. When the resis-

tivity of deep soil is higher than that of the surface soil layer, the effect of equalizing the potential

and reducing the grounding resistance by slanting ground rods will be better.

For a grounding grid with an area of 50 50m2, the conductor spacing is 10m, the soil resistivity is

100Vm and four 50 m slanting ground rods are arranged at the four corners of the grounding grid.

Changing the slanting angle of the ground rods, we can get the grounding resistance and the maximum

Table 6.3 The grounding resistance and maximum step voltage of the grounding grid with slanting ground rods

Slanting angle (�) Grounding resistance (V) Maximum step voltage (V)

Without ground rods 0.993 5.65

0 0.643 3.77

15 0.614 2.64

30 0.599 2.58

45 0.597 2.54

60 0.608 2.60

75 0.617 2.65

90 0.637 2.94

Figure 6.19 Grounding grid with slanting ground rods. (a) Top view. (b) Side view.


step voltage shown in Table 6.3. When the slanting angle is 0, it means the grounding eletrodes are

arranged vertically; but if slanting angle is 90�, it means the grounding eletrodes are arranged horizon-

tally. Obviously, adding slanting electrodes has a greater effect in reducing the grounding resistance and

step voltage compared with vertical rods and horizontal electrodes. When the slanting angle is in the

range from 30 to 60�, the effect is better.For a 220 kV substation with a grounding grid area of 171 142m2, the grounding resistance of the

horizontal grounding grid is 0.431V. When eight vertical ground rods (length 100m) and eight slanting

grounding electrodes (length 100m, slanting angle to the ground 20�) are added to the four corners and

the midpoints of the four sides of the grounding grid, the analyzed grounding resistance becomes

0.219V. When the engineering was finished, the tested grounding resistance was 0.22V.

6.4 Equipotential Optimal Arrangement of a Grounding Grid

From the analysis in the previous sections we know that a substation grounding system should meet the

requirements of two aspects. One is that the grounding resistance should be decreased to a certain value

to ensure that the touch voltage meets the requirement, the other one is that the ground potential should

be balanced as far as possible, in order to meet the requirement of step voltage. In a region of high soil

resistivity, it is difficult to decrease the grounding resistance. Therefore, it is very important to balance

the potential distribution on the ground. The equipotential optimal arrangement of a grounding grid is a

power technology for potential distribution on the ground.

Severak proposed the concept of using unequal spacing in a grounding grid to optimize the ground-

ing system [22]. In China, through many simulation experiments and calculations, the specific regular-

ity of an unequal-spacing arrangement was proposed by Huang et al. [23,24].

6.4.1 Principle of the Unequal-Spacing Arrangement

Generally, the grounding grid is arranged with equal spacing, that is to say, the distance between the

grounding conductors is basically equal. However, the principle of an unequal-spacing grounding grid

considers the shielding effect by the grounding grid to be a part of conductors in the middle of grid.

Therefore, the arrangement of grounding conductors should be sparse in the middle and dense around

the edges of the grid, in order to make full use of all grounding conductors. An equal-spacing ground-

ing grid and an unequal-spacing grounding grid are shown in Figure 6.20. The unequal-spacing

arrangement has specific characteristics, as follows.

6.4.1.1 Making Full Use of Grounding Conductors

For a horizontal grounding grid with an area of 200 200m2 (for a typical 220 kV substation), a burial

depth of 0.8m and a soil resistivity of 200Vm, the current distribution when the horizontal conductors

Figure 6.20 Grounding grid of (a) equal-spacing arrangement and (b) unequal-spacing arrangement.


are arranged in unequal spacing is shown in Figure 6.21, where only the results of one-quarter of the

grounding grid are given. Through the comparison of Figure 6.21 with Figure 4.3 we can see that the

leakage current density of each conductor has a large difference from one to another in an equal-

spacing arrangement grounding grid, and the leakage current density of the peripheral conductors is

about four times higher than that of the middle conductors. Sometimes this value will reach 10 times or

more. However, in an unequal-spacing grounding grid, the leakage current density of the middle con-

ductors increases and correspondingly that of the peripheral conductors decreases, the leakage current

density of each conductor is well distributed and the difference between the peripheral conductors and

the middle conductors is not that obvious. Therefore, an unequal-spacing arrangement can make full

use of each conductor. After using an unequal-spacing arrangement, the leakage current of all conduc-

tors is well distributed. This will effectively improve the ground potential distribution, decreasing touch

and step voltages.

For a grounding grid with an area of 120 80m2, calculation results show that, while the conductor

number is the same, the leakage current density of peripheral conductor 1 when using an unequal-spac-

ing arrangement is 15% lower than that when using an equal-spacing arrangement. Also, the mean

leakage current densities of the middle conductors 3, 4 and 5 when using an unequal-spacing arrange-

ment are respectively 9, 14 and 15% higher than when using an equal-spacing arrangement.

Figure 6.21 Leakage current distribution of each grounding conductor when using an unequal-spacing arrangement.


6.4.1.2 Equalizing Ground Potential Distribution

When using an equal-spacing arrangement, the ground potential distribution is unbalanced, which can

equalize the ground potential and decrease the touch voltage to improve the safety of a substation.

Analysis shows that the potential of the peripheral meshes when using an equal-spacing arrangement is

much lower than that of the middle meshes, just 13%. Also, the potential of the peripheral meshes is

much higher than that of the central mesh, at 179.3%. If we use the same amount of grounding conduc-

tors, when using an unequal-spacing arrangement, the difference between the maximum and the mini-

mum mesh potentials is only 1.37%. Therefore, using an unequal-spacing grounding grid can make the

ground potential well distributed and the potential of each mesh almost the same [23].

Figure 6.22 shows the potential distribution on the ground surface where the size of the substation

grounding grid is 50 50m2. For an equal-spacing arrangement, the spacing is 10m; for an unequal-

spacing arrangement, the spacings are 3, 7, 10, 7 and 3m from one side to the opposite side of the

grounding grid. The soil resistivity is 100Vm and Figure 6.23 shows the ground potential rise distribu-

tion along the diagonal line of the grounding grid. Obviously, the potential distribution on the ground

surface becomes much more uniform after the grid is arranged with unequal spacings.

Figures 6.24 and 6.25 show the respective step and touch voltage distribution under equal-spacing

and unequal-spacing arrangements. After the grounding grid is arranged with unequal spacing, the step

and touch voltage distributions inside the substation become more uniform, and the highest touch volt-

age is greatly reduced when the grid is in unequal spacing.

Figure 6.26 shows the touch voltage distribution curves respectively for equal-spacing and unequal-

spacing arrangements, while the area of the horizontal grounding grid is 150 150m2 and the soil

resistivity is 200Vm. The touch voltage of the equal-spacing grounding grid is high and unbalanced.

However, using an unequal-spacing arrangement can effectively decrease the touch voltage and balance

touch voltage distribution. The maximum touch voltage of grounding grid with an equal-spacing

arrangement is 1.930 kV, while it is 1.122 kV under an unequal-spacing arrangement, a decrease of

42%. Therefore, the unequal-spacing arrangement can greatly decrease touch voltage. Sometimes, the

reduction is 50–60%.

6.4.1.3 Saving Grounding Conductors

From the previous analysis we know that the touch voltage of a grounding grid with an unequal-spacing

arrangement is obviously lower than that of an equal-spacing arrangement when the same number of

grounding conductors are used. Therefore, for the same safe limit, an unequal-spacing arrangement can

decrease the number of grounding conductors. Analysis shows that an unequal-spacing arrangement

can save more than 30% in steel [24].

6.4.2 Regularity of the Unequal-Spacing Arrangement

Analysis states that, when the mesh potential fluctuates within a range, the arrangement of grounding

conductors has nothing to do with the grid area, but is only related to the number of conductors along

the directions of length and width. Figure 6.27 shows a rectangular grounding grid, in which the per-

centage Sik of the length Lik of the ith conductor along the direction of length or width is:

Sik ¼ Lik

L 100% ð6:53Þ

where L is the side length of the grounding grid; along the direction of length, L¼ L1, and along the

direction of width, L¼ L2.

When the number n1 and n2 of conductors along the directions of length and width are fixed, then the

total segments of a grounding grid along the directions of length and width are fixed. The conductor


segment number along the direction of length is k1¼ n1� 1, and the conductor segment number along

the direction of width is k2¼ n2� 1.

The relationships between Sik, the conductor segment number k and the conductor serial number

i counting from the edge are shown in Table 6.4 [24]. When the grounding grid is symmetrical, if

the number of conductor segment number k of a certain direction is odd, (kþ 1)/2 data are listed,

and if k is even, then k/2 data are listed. Other data can be obtained according to the symmetric

property of the grounding grid. The data when k� 6 are not considered, and the fitting formula to

calculate Sik is [24]:

Sik ¼ b1 expð�ib2Þ þ b3 ð6:54Þ

Figure 6.22 Potential distribution on the ground surface of a grounding grid with (a) equal-spacing and

(b) unequal-spacing arrangements.


where b1, b2 and b3 are constants related to the number k. When 7 � k � 14:

b1 ¼�1:8066 þ 2:6681 lg k � 1:0719 lg2 k

b2 ¼�0:7649 þ 2:6992 lg k � 1:6188 lg2 k

b3 ¼ 1:8520 � 2:8568 lg k þ 1:1948 lg2 k

8><>:

Figure 6.23 Potential distribution on the ground surface along the diagonal line of a grounding grid with equal-

spacing and unequal-spacing arrangements.

Figure 6.24 Step voltage distribution on the ground surface of a grounding grid with (a) equal-spacing and



when 14< k� 25:

b1 ¼�0:00064 � 2:50923=ðk þ 1Þb2 ¼�0:03083 þ 3:17003=ðk þ 1Þb3 ¼ 0:00967þ 2:21653=ðk þ 1Þ

8><>:

Figure 6.24 (Continued)

Figure 6.25 Touch voltage distribution on the ground surface of a grounding grid with (a) equal-spacing and



and when 25< k� 40:

b1 ¼�0:0006 � 2:50923=ðk þ 1Þb2 ¼�0:03083þ 3:17003=ðk þ 1Þb3 ¼ 0:00969 þ 2:2105=ðk þ 1Þ

8><>:

The empirical formulas to calculate grounding resistance, the maximum touch voltage and the maxi-

mum step voltage of a grounding grid with an unequal-spacing arrangement are obtained by fitting

Figure 6.25 (Continued)

Figure 6.26 Touch voltage distribution along the diagonal line of the grounding grid of a grounding grid with

equal-spacing and unequal-spacing conductor arrangements.


analysis results [24]. The grounding resistance is related to the burial depth h of the grounding grid (m),

the shape of the grounding grid, the number of meshes m, the number of grounding conductors n and

the diameter of conductors d (m):

R ¼ kRhkRLkRmkRnkRd 1:068 10�4 þ 0:445=ffiffiffiS

p r ð6:55Þ

Table 6.4 The relationship between Sik, conductor segment number k and conductor serial number i, counting

from the edge [24]. (Reproduced with permission from X.L. Chen, J.Y. Zhang, Y. Huang, Grounding lecture notes,

Chongqing University, Chongqing, China, 1990)

k Conductor serial number i, counting from the edge

1 2 3 4 5 6 7 8 9 10

3 27.50 45.00

4 17.50 32.50

5 12.50 23.50 28.33

6 8.75 17.50 23.75

7 71.4 13.57 18.57 21.43

8 5.50 10.83 15.67 18.00

9 4.50 8.94 12.83 15.33 16.73

10 3.75 7.50 11.08 13.08 14.58

11 3.18 6.36 9.54 11.36 12.73 13.46

12 2.75 5.42 8.17 10.00 11.33 12.33

13 2.38 4.69 6.77 8.92 10.23 11.15 11.69

14 2.00 3.86 6.00 7.86 9.28 10.24 10.76

15 1.56 3.62 5.35 6.82 8.07 9.12 10.01 10.77

16 1.46 3.27 4.82 6.14 7.28 8.24 9.07 9.77

17 1.38 2.97 4.35 5.54 6.57 7.47 8.24 8.90 9.47

18 1.14 2.58 3.86 4.95 5.91 6.67 8.15 8.15 8.71

19 1.05 2.32 3.47 4.53 5.47 6.26 7.53 7.53 8.11 8.36

20 0.95 2.15 3.20 4.15 5.00 5.75 7.00 7.00 7.50 7.90

Figure 6.27 Rectangular grounding grid with unequal-spacing arrangement.


where kRh, kRL, kRm, kRn and kRd are, respectively, the influential coefficients of the burial depth, the

shape, the number of meshes, the number of conductors and the diameter of the conductors:

kRh ¼ 1:061� 0:070ffiffiffih

5p

kRL ¼ 1:144� 0:13ffiffiffiffiffiffiffiffiffiffiffiffiL1=L2

pkRn ¼ 1:256� 0:367

ffiffiffiffiffiffiffiffiffiffiffiffin1=n2

p þ 0:126n1=n2

kRm ¼ �1:168� 0:079ffiffiffiffim5

p �kRN

kRd ¼ 0:931þ 0:0174=ffiffiffid3

p

8>>>>>>>><>>>>>>>>:

where r is the soil resistivity (Vm), L1 and L2 are respectively the length and width of the grounding

grid (m) and m is the number of grounding grid meshes, m¼ (n1� 1)(n2� 1).

The maximum touch voltage is related to the burial depth, grounding grid shape, number of conduc-

tors, diameter of the conductors and area S of grounding grid (m2):

UTM ¼ kTLkThkTdkTSkTnkTmVGM ð6:56Þwhere VGM¼ IGR (kV) is the maximum ground potential rise, IGM is the maximum grounding fault

current flowing into grounding grid (kA), R is the grounding resistance of the grounding grid, kTL, kTh,

kTd, kTS, kTn and kTm are respectively the influential coefficients of the shape, burial depth, diameter of

the grounding conductors, area of the grounding grid, number of grounding conductors and mesh num-

ber of the grounding grid:

kTL ¼ 1:215� 0:269ffiffiffiffiffiffiffiffiffiffiffiffiL2=L1

3p

kTh ¼ 1:612� 0:654ffiffiffih5

p

kTd ¼ 1:527� 1:494ffiffiffid5

p

kTn ¼ 64:301� 232:65ffiffiffin6

p þ 279:65ffiffiffin3

p � 110:32ffiffiffin

p

kTS ¼ �0:118þ 0:445ffiffiffiS12

p

kTm ¼ 9:727 10�3 þ 1:356=ffiffiffiffim

pn ¼ n2=n1

8>>>>>>>>>>><>>>>>>>>>>>:

The maximum step voltage is similar to the maximum touch voltage, relating to the burial depth,

shape, number of conductors, diameter of the conductors and area S of the grounding grid:

USM ¼ kSLkShkSdkSSkSnkSmU0 ð6:57Þwhere kSL, kSh, kSd, kSS, kSn and kSm are respectively the influential coefficients of the shape, burial

depth, diameter of the grounding conductors, area of the grounding grid, number of grounding conduc-

tors and mesh number of the grounding grid:

kSL ¼ 29:081� 1:862ffiffil

p þ 435:18l þ 425:68l1:5 þ 148:59l2

kSh ¼ 0:454 expð�2:294ffiffiffih3

p ÞkSd ¼ �2780þ 9623

ffiffiffid36

p � 11099ffiffiffid18

p þ 4265ffiffiffid12

p

kSn ¼ 1:0þ 1:416 106 expð�202:7nÞ � 0:306 exp½29:264ðn� 1Þ�kSS ¼ 0:911þ 19:104

ffiffiffiS

p

kSm ¼ kSnð34:474� 11:541ffiffiffiffim

p þ 1:43m� 0:076m1:5 þ 1:455 10�3m2

n ¼ n2=n1l ¼ L1=L2

8>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>:


6.4.3 Unequal-Spacing Arrangement with Exponential Distribution

6.4.3.1 Definition of Unequal-spacing Arrangement with Exponential Distribution

Arranging the conductor spacing in an exponential distribution, the spacing of the nth mesh counting

from the central mesh can be calculated by [26, 27]:

dn ¼ dmaxCn ð6:58Þ

where C is defined as the compression ratio, which is a constant �1. The larger the compression ratio is,

the more uniform is the arrangement. When the compression ratio is equal to 1, the grounding grid is

arranged with equal spacing. When we arrange N conductors along the horizontal conductor with length

L with an unequal-spacing arrangement, we can obtain the spacing dmax of the central mesh as [26]:

dmax ¼ Lð1� CÞ1þ C � 2CN=2

; whenN is even ð6:59Þ

dmax ¼ Lð1� CÞ2ð1� CðN�1Þ=2Þ ; whenN is odd ð6:60Þ

When the area of the grounding grid and soil structure are fixed, there is an optimal compression ratio to

make the ground potential and touch voltage distributions most uniform. Through tentative calculations,

the optimal compression ratio can be obtained.

6.4.3.2 Optimum Compression Ratio for a Grounding Grid in Two-layered Soil

For a grounding grid, there is an optimum compression ratio (OCR). The grounding grid designed with

an OCR has the best safety. The compression ratio is related to the side length of the grounding grid.

For a grounding grid with area 80 80m2, h¼ 5m, K¼�0.6 and the analyzed results state that the

relationship curve between the grounding resistance and the compression ratio has an obvious “U”

shape as shown in Figure 6.28. Also, it has an obvious minimum at compression ratio 0.79. Although

changing the compression ratio can change the grounding resistance, basically the grounding resistance

of the grounding grid is determined by the area of the grounding grid. The influence of the compression

ratio on the grounding resistance is very small. So, when we determine the OCR, we mainly consider

the minimum step and touch voltages.

Figure 6.28 Influence of compression ratio on the grounding resistance of a grounding grid.


The relationship between the touch voltage and the compression ratio C is shown in Figure 6.28.

When C¼ 0.79, the touch voltage UT reaches its minimum.

But, the curve US-C between the step voltage and the compression ratio does not have an obvious

regularity, as shown in Figure 6.29, but has the following trend: whether the compression ratio is small

or large, the step voltage increases as the compression ratio decreases or increases. But when the com-

pression ratio is in the middle, the value of the step voltage is very small, but is not a fixed regularity.

The maximum step voltage is on the periphery of the grounding grid, and it is mainly decided by

the conductors on the rim of the grounding grid. With a change in compression ratio, the current

through the peripheral conductor also varies, but this change does not have a fixed regularity. As

observed from Figure 6.30, the step voltage reaches its minimum when the compression ratio is

0.79, and this is the same with the touch voltage and grounding resistance.

Usually, the step voltage is small and its maximum permissible value is high, so the step voltage can

be easily satisfied. But the touch voltage is high and its maximum permissible value is low, so it is

difficult to satisfy the touch voltage. So, in the grounding grid design, only the maximum of the touch

Figure 6.30 Influence of compression ratio on the step voltage.

Figure 6.29 Influence of compression ratio on the touch voltage.


voltage need be considered. If the touch voltage is in the safe region, then the step voltage is also in the

safe region.

According to the above discussion, the touch voltage is selected as the target function to deter-

mine the OCR. The compression ratio where the touch voltage reaches its minimum is the OCR. At

the same time, the grounding resistance of the grounding grid and the step voltage also reach their

minimum.

The OCR is influenced by the reflective coefficient of a double-layer soil, the thickness of the top-

layer soil and the grounding grid area, which decreases with the increase in reflective coefficient. When

the soil resistivity of the bottom-layer soil is smaller than that of the top-layer soil, the arranged hori-

zontal conductors are more uniform than when the soil resistivity of the bottom-layer soil is higher than

that of the top-layer soil. From many calculation results, the relationship between the OCR, the thick-

ness h of the top-layer soil and the reflective coefficient K is illustrated in Figure 6.31, and

the relationship between the OCR and the reflective coefficient of a double-layer soil is illustrated in

Figure 6.32.

The OCR increases with the grounding grid area. That is to say, the larger the area of the grounding

grid is, the more uniform will be the arrangement of the grounding conductors. If the reflective

coefficient K¼�0.3, the relationship between the side length of the grounding grid and the OCR is as

Figure 6.31 Relationship between the OCR and the thickness of the top-layer soil. (a) 100 100m2 grounding

grid. (b) 200 200m2 grounding grid.


shown in Figure 6.33 [27]. It is observed that the OCR increases as the side length increases, and the

longer the side is, the more uniform is the conductor distribution on this side of the grounding grid.

The empirical expressions to calculate the OCR of a double-layer soil are obtained by the least

square fit from many analysis results. The relationship between OCR, h and K is fitted from the calcu-

lated results, according to the side length of the grounding grid, and the OCR can be calculated by [27]:

OCR ¼ a0 þ a1 expð0:0001hÞ þ a2 expðbhÞ ð6:61Þwhere:

b ¼ �0:3503� 9:6311 expð�0:03666LÞa0 ¼ a01 þ a02K þ a03K

2

a1 ¼ a11 þ a12K þ a13K2

a2 ¼ a21 þ a22K

8><>:

Figure 6.33 Relationship between the OCR and the grounding grid area with K¼�0.3 under different thicknesses

of top-layer soil [27]. (Reproduced with permission from W.M. Sun, "The research of optimal design of substation

grounding system in non-uniform soil," PhD Dissertation of Tsinghua University, Beijing China, 2001.)

Figure 6.32 Relationship between the OCR and the reflective coefficient when the side length of the grounding

grid is 100m.


When the side length of the grounding grid is different, the respective coefficients in Equation 6.61

are as shown in Table 6.5 [27].

Seasonally frozen soil leads to a change in the soil model, which affects the safety of the grounding

system. The design of a grounding system considering seasonally frozen soil should be based on a full

investigation of the actual maximum depth of frozen soil and actual layered soil models. The final

design scheme of the grounding system should be determined synthetically from two phases. First the

grounding system is designed in a normal soil model and its safety is checked in a frozen soil model;

second it is designed in a frozen soil model and its safety is checked in a normal soil model [28].

6.4.4 Influence of Vertical Grounding Electrodes on OCR

In order to analyze the influence of vertical electrodes on the OCR, a grounding grid with an area of

80 80m2 was studied. There are nine conductors on every side; and four vertical ground rods are

arranged on the four corners of the grounding grid. The resistivity of the top-layer soil is 200Vm, and

its thickness H is 5m. Ordinarily, vertical ground rods are arranged on the sides of the grounding grids

in order to provide a shielding effect between the horizontal grounding grid and the vertical electrodes,

making full use of all the vertical electrodes.

As shown in Figure 6.34, the OCR increases when vertical electrodes are added to the grounding grid.

The reason is that a large portion of current flows into the earth from the vertical electrodes, and this

Table 6.5 Coefficients of fitting formula [27]. (Reproduced with permission from W.M. Sun, “The

research of optimal design of substation grounding system in non-uniform soil,” PhD Dissertation of

Tsinghua University, Beijing China, 2001)

Coefficients L� 100m 100m< L� 175m 175m< L� 250m L> 250m

a01 0.44 0.38 �0.51 0.32

a02 �77.43 �50.65 �33.18 �15.44

a03 15.63 13.88 18.49 13.42

a11 0.033 0.19 1.15 0.38

a12 76.9 50.21 32.82 15.16

a13 �15.56 �13.83 �18.44 �13.38

a21 �0.067 �0.037 �0.029 �0.022

a22 0.50 0.41 0.34 0.26

Figure 6.34 Relationship between the OCR and the reflective coefficient.


portion of current flowing to earth from the horizontal conductors decreases. Shielding effects among the

horizontal conductors reduce, and the current flowing into the earth from every horizontal conductor

becomes even, so the conductor arrangement in the optimum arrangement becomes more uniform.

6.5 Numerical Design of a Grounding System

Using numerical analysis to design a grounding system can overcome the blindness of traditional sim-

ple design [25]. Numerical design follows these steps: it measures the apparent soil resistivity and

obtains a layered soil model, it calculates the grounding resistance, estimates the fault current division

factor and calculates the step and touch voltages. It applies different methods to achieve the goal of the

project, comparing all possible methods to propose a final solution for the grounding system. Two

actual grounding system designs are presented in this section.

6.5.1 Grounding System Design of a 220-kV Substation

By analyzing the measured apparent soil resistivity as it changes with probe spacing as obtained by the

Wenner configuration, the substation site can be described as four layers, as shown in Figure 6.35.

The area of the substation site is about 130 120m2, and if we arrange a horizontal grounding grid

here, assuming that the burial depth is 0.8m, with the horizontal conductors spaced at 10m, using

27 conductors, the calculated grounding resistance is 0.95V. It is estimated that the grounding resist-

ance should be decreased to about 0.5V, so that the step and touch voltages can satisfy the requirement

placed on them.

If we simply increase the area of the grounding grid to satisfy the requirement on step and touch

voltages, the calculation shows that, when the area of grounding grid is expanded to 300 360m2, the

grounding resistance is reduced to 0.48V. But this area is nearly seven times larger than that of the

original grounding grid, which is not practicable.

If we do not increase the substation area, we can arrange 12 vertical ground rods uniformly around

the peripheral conductors of the horizontal grounding grid. The relationship between the length of ver-

tical ground rod L and grounding resistance is shown in Figure 6.36. We can conclude it is very difficult

to decrease the grounding resistance to less than 0.5V if we only use vertical ground rods. The main

reason is that the resistivity of the deep soil layer is too high. When the length of the vertical ground rod

reaches 450m, the grounding resistance will be decreased to about 0.5V.

If we use the explosion grounding technology introduced in Section 6.3.3 to construct vertical

ground rods, the equivalent radius of a vertical ground rod after the explosion is assumed to be 4.5m.

The relationship between grounding resistance and length of vertical ground rod constructed by the

Figure 6.35 Layered soil structure parameters.


explosion method is shown in Figure 6.36. Using explosion grounding technology can decrease the

length of the ground rod from 450 to 300m, but this is still unacceptable.

According to the actual conditions, we can consider using an auxiliary horizontal grounding grid and

explosion grounding technology to synthetically decrease the grounding resistance. The finally recom-

mended design scheme is shown in Figure 6.37. The area of the main grounding grid is 140 140m2

and the number of horizontal grounding conductors is 27. An auxiliary grounding grid with an area of

120 120m2 is built, which is connected with the main grounding grid through two 100m ground

electrodes. Thus, a total of 21 vertical ground rods with a length of 50m are arranged around the

grounding grid on the peripheral conductors of the grounding grid, and these vertical rods are con-

structed by the explosion grounding technique. After building the grounding system according to the

design scheme, the measured grounding resistance is 0.43V, which is very close to the designed value

0.42V.

The maximum grounding grid current is 16 kA and the ground potential rise of the grounding grid

shown in Figure 6.38 without those vertical rods can reach 9200V. The distribution of the potential on

the ground surface is seriously non-uniform and the step voltage around the substation can reach

Figure 6.37 Recommended grounding system design scheme.

Figure 6.36 Influence of a vertical ground rod on the grounding resistance of a horizontal grounding grid.


1400V. After the vertical ground rods are added, the step voltage outside the substation is less than

400V. Outside the substation, as the ground surface potential falls quickly, so the touch voltage corre-

spondingly rises greatly. In the region just a step away from the substation, it is generally impossible

that people have the chance to touch the metal conductors connected with the grounding grid. So the

touch voltage is not dangerous to people.

According to IEEE Standard 80-2000, the maximum allowable touch voltage UT50 and step voltage

US50 of a person with a weight of 50 kg are calculated as 700 and 2365V, respectively.

The main reason why vertical ground rods can decrease the grounding resistance and improve the

distributions of ground surface potential and touch voltage is that they can effective shunt the fault

current. For the total 16 kA fault current, the current diffused from the vertical ground rods is 9 kA and

that diffused from the horizontal grounding grid is only 7 kA.

6.5.2 Grounding System Design of a 1000-kV UHV Substation

The design of the grounding system for the Jindongnan 1000 kV ultra high voltage AC substation

in China is introduced in [29]. First, the fault current division factor is determined to calculate the

maximum grid current for the design of the grounding system. One 1000-kV transmission line and

five 500 kV transmission lines are connected with the Jidongnan 1000 kV ultra high voltage substation.

The fault current division factors are different in the 500 kV system side and the 1000-kV system side,

and this changes with the grounding resistances, as shown in Figure 6.38 due to the unknown grounding

resistance. The grounding resistance is not higher than 0.1V. In this condition, the fault current

division factor in the 500 kV system side is 0.643, and the respective maximum grid current is 0.6431.2 63¼ 48.6 kA, where 1.2 is the attenuation coefficient. The respective fault current division factor

in the 1000 kV system side is 0.812, and the respective maximum grid current is 0.812 1.2 50¼48.7 kA. So, the maximum grid current is determined as 48.7 kA for the grounding system design.

According to the measured soil resistivity data for the Wenner configuration, a multi-layer soil model

is obtained: the resistivity and the thickness of the upper soil layer are 45.7Vm and 2.35m, those of

the middle layer are 20.0Vm and 87.6m and the resistivity of the bottom soil layer is 122Vm. The

Jindongnan 1000 kV substation is located in a seasonally frozen soil region, and the thickness of

the frozen soil is 0.66m during the winter.

Figure 6.38 Relationship between the fault current division factor and the grounding resistance.


The area of the grounding system is shown in Figure 6.39. The grounding resistance is calculated as

0.078V, and the respective GPR is 3.9 kV. In order to overcome the influence of the seasonally frozen

or dry soil layer, we have to increase the burial depth of the grounding grid. The influence of the burial

depth of the horizontal grounding grid on the characteristics of the grounding system is shown in

Table 6.6. The maximum touch voltage first decreases and then increases with increasing burial depth

of the grounding grid. The optimal depth of the grounding grid is decided as 1.0m.

The optimal arrangement of the horizontal grounding grid with unequal spacing can effectively

decrease the step and touch voltages. If the grounding grid is designed with equal spacing, the respec-

tive grounding resistance is 0.078V and the maximum touch and step voltages are 928 and 97V.

Table 6.6 The influence of burial depth of the horizontal grounding grid on the characteristics of the grounding

system

Burial depth (m) Grounding resistance (V) GPR (V) Maximum touch voltage (V) Maximum step voltage (V)

0.8 0.078 3926 949 104

1.0 0.078 3924 928 96.9

1.5 0.077 3894 932 94.2

2.0 0.077 3884 941 96.9

Figure 6.39 Grounding system design scheme of the 1000 kV Jindongnan substation.


Ordinarily, the optimal compression ratio as introduced in Section 6.4.3 is used to represent the opti-

mal design of a horizontal grid. The optimal compression ratio is determined as 0.65 for the grounding

grid of the 1000 kV Jindongnan substation. When the grounding grid is arranged under this optimal

compression ratio, the grounding resistance is 0.076V and the maximum touch and step voltages are

700 and 92V. The touch voltage under the optimal design decreases about 24.6% compared with the

result in the normal design.

Also, a high resistivity layer of 5 cm is paved on the surface of the substation ground to further

improve the safety of the grounding system. The surface soil becomes dry in the summer season. We

assume a soil layer with thickness of 1.5m is dried during the summer and the respective soil resistivity

increases to 500Vm. The results in different cases are shown in Table 6.7. Although increasing the burial

depth of the grounding grid can improve the safety of the grounding grid, it is difficult to realize in

engineering. So, a burial depth of 1.0m was selected for the horizontal grounding grid and 5 m vertical

rods were added at the cross-points of grounding conductors to improve safety during the dry season.

From the analysis above, the grounding system design diagram is shown in Figure 6.39. The periph-

eral conductors of the horizontal grounding grid are optimally designed under an optimal compression

ratio of 0.68, and the middle conductors of the grounding grid are arranged equally spaced at 20m. The

burial depth is 1.0m and 120 vertical rods with a length of 5m are added at all the cross-points of

the horizontal conductors in the grounding grid to improve the safety of the grounding system during

different seasons.

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Table 6.7 The influence of a dry soil layer on the characteristics of the grounding system

Scheme Grounding

resistance (V)

GPR (V) Maximum touch

voltage (V)

Maximum step

voltage (V)

In normal season with burial depth of 1.0m 0.077 3874 698 100

In dry season with burial depth of 1.0m 0.113 5404 2220 212

In dry season with burial depth of 2.0m 0.076 3830 701 73.6

In dry season with burial depth of 1.0m, adding

5-m vertical rods at the cross-points of the

grounding conductors

0.083 3814 743 83.6


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