Analysis on influence of long vertical grounding electrodes

Analysis on Influence of Long Vertical Grounding Electrodes
on Grounding System for Substation
Rong ZENG, Jinliang HE, Zanji Wang, Yanqing GAO
Dept. of Electrical Engineering, Tsinghua University
Beijing 100084, China

Abstract: Three dimensional grounding system is introduced to
decrease the grounding resistance, step and touch voltages of
grounding system in areas with high soil resistivity or with limited
areas for grounding system. The relationship between the number of
vertical grounding rods and the grounding resistance is discussed. The
new means to add grounding rods to the grounding system with
explosion grounding technique, have efficiently decreased the
grounding resistance in the actual grounding engineering. Reasons
why vertical grounding rods can efficiently decrease the maximum
touch and step voltages of the earth surface above the grounding
system are analyzed. Calculated results shows the vertical grounding
rods can also effectively decrease the influence of seasonal factor on
safety of grounding system. This paper provides the rule to choose the
vertical grounding rods in multi-layer soil based on the relationship
analysis between the number and the length of the vertical grounding
rods.
Key words: Grounding system, vertical grounding electrode, step
voltage, touch voltage, seasonal factor

I. INTRODUCITION
With the rapid increase of electrical load in recent years in
China, in order to promise the safety of the power system, it is
urgent to decrease grounding resistance of the grounding
system, especially when power generating stations or
substations are built in the soil with high resistivity. The

limitations of the land requisition or the landform make
researchers turn their sight from the horizontal grid to the
vertical rod. But so far most of the discussions on the vertical
rods are only samples of application or conclusion of project
experiences[ 13. Several researchers analyzed the role and the
design rule of rods, but they focused on the uniform soil. The
detailed discussion of three-dimensional grounding system
design in the different soil structures almost cannot be
found[2,3]. This paper will discuss how to design threedimension grounding system scientifically and economically.

Weimin SUN
Shandong Electric Power Bureau
Jinan 250001, shandong, China

Qi SU
Dept. of Electr. and Computer Sys. Eng.
Monash University
Clayton, Victoria 3168, Australia

11. NUMERICAL ALGORITHM RESEARCH OF

GROUNDING SYSTEM
Since 1972, scholars have introduced various numerical
algorithm into the calculation of grounding parameters. In 90’s
liner filter method and complex image method were used.
Numerical algorithm solves many problems emerged with the
calculation in experiential formula. Comprehensively
considering the actual grounding system structure and the noneven dispersion of the fault current in the different parts of the
grounding system, numerical algorithm helps to get exact result
of any complex grounding system and makes it possible to

compare the economic efficiency of the projects scheme on the
basis of technical feasibility.
Dawalibi has improved the theoretical model and optimized the
numerical algorithm over 20 years. His multi-layer soil model
numerical algorithm based on the base image method has come
into mature. CDEGS (grounding system parameters calculating
software developed by him and his collaborators) has been
widely used in the world. This software can not only get
comparatively accurate parameters of various grounding
system and also get grounding system parameters in the layered
soil. This paper makes simulative calculation by the means of
CDEGS.
111. DESIGNING RULE ANALYSIS OF VERTICAL
GROUNDING RODS

The discussion is based on a llOkV substation as shown in
Fig. 1 . The horizontal grounding grid is 150x150m2in area. The
even grounding conductor span of the grounding grid is 15m
and horizontal conductor radius is 0.01 Im (r,=0.01lm). The
uniform soil resistivity is 200R.m.

A. Number of Vertical Grounding Rods
Vertical rods are added to the existed horizontal grounding grid.
The length of the rods is 50m. The relationship between the
number N of the rods and the grounding resistance R is
illustrated in Fig.2. Here the rod radiuses are r2=3.5m and
r2=0.025m used in calculation, Radius of 3.5m is the result
considering the effect of explosion technique. From Fig.2, we
observed that while other conditions are fixed, grounding

0-7803-6338-8/00/$10.00(~)2000IEEE

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resistance decreases with the increase of the number of rods.
However, the decrease of R reaches saturation when N reaches
a certain number because the shielding effects increase with the
decrease of the interval among rods. Besides rods can restrain
the dispersed current on the grid, i. e. the total grounding
resistance is not the simple parallel connection of grounding
resistances of the grounding grid and vertical grounding rods.
There is a shielding coefficient of horizontal grounding grid to
the vertical grounding rods. The shielding coefficient increases
with the number of the grounding rods.

*

I*

4

same as the upper. Now a rod is arranged in the center of the
grid and another in the comer, to check which rod has better
resistance decreasing effects. The grounding resistance
decreasing rate is defined as:

here, R, is the grounding resistance after rods are added. Ro is
the grounding resistance of the horizontal grounding grid. The
equivalent radius of the horizontal grounding grid and is

defined as:

req= J

s/~

here, S is the area of the horizontal grounding grid.
The relationship between the grounding resistance decreasing
rate and the length of vertical grounding rods under different
rod locations are shown in Fig.3. Obviously, the resistance
decreasing effect of the rod arranged on the periphery of the
grid is better than that of the rod arranged in the center due to
the shielding effect between the horizontal conductor and the
vertical rods increases when the rod is arranged in the center of
thegrid.
’

Fig. 1 The arrangement of grounding grid

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10

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I

15

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I

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20

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25

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I

30

2.0

2.5

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35

Grounding Rod Number
Fig.2 The relationshipbetween the number N of the rods and the grounding
resistance R.

When the rod radius is 3Sm, their effects to decrease grounding
resistance reach 35%, which is better than that when the rod
radius is 0.025m.

B. Location of Vertical Grounding Rods
Usually rods are well distributed in the grid and the rod density
in the center of the grounding grid is often higher than that on
the periphery of the grounding grid. Contrast analysis illustrates
that such a design is improper. Horizontal grounding rid is the

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Fig.3 The relationship between the grounding resistance decreasingrate and the
length of vertical grounding rods under different rod locations.

Analyzing the results in Fig.3, the dispersed current by vertical
grounding rods on the periphery of the grids are more than
twice of the current dispersed by the rod of the same length in
the center of the grid. As a result rods should be arranged on the
periphery of the grid if rods are added to decrease the grounding
resistance. In this way the shielding effects between the grid
and rods can reach the minimum. With the number of the rods
increase, the advantage of this arrangement becomes apparent.
To increase the resistance decreasing effect and to decrease the

shielding coefficient of horizontal grounding grid to the vertical
grounding rods, the best way (if possible) is that rods are


arranged far away from the grid and connected with the grid
through the horizontal grounding conductors. This way can
benefit to fault current dispersing, efficiently decrease the
grounding resistance and can make the touch voltage
distribution rational.

The calculation conditions of two-layer soil are the same as that
of uniform soil. The soil resistivity of the upper layer, p , equals
200R.m, and the soil resistivity of the lower layer, f i equals
600Q-m., the upper soil layer depth is 20m. The analysis results
is shown in Fig.4 (b).

C . Length of Vertical Grounding RODS

We observed in Fig.4 that the two curves are almost in
superposition, i.e. grounding resistance decreasing rates of
horizontal grounding grids with different areas are almost the
same when the ratio of equivalent radius and the rod-length is
the same. Another analysis result from Fig.4 is that the two
curves coincide with each other when they are far from the
interface of the two layers; while they differ greatly when they
are near the interface. That is also the rule of current intensity
pass through the interface (discussed in Part 111).

Since parameters that influence the grounding resistance are too
much, all the discussion of this part is based on the horizontal

grounding grid with a fixed area. Analysis indicates that these
conclusions are still in effect when the area is changed.
Take a square horizontal grounding grid as an example, the
ratio of the grounding resistance decreasing rate to the vertical
grounding rod length, and another ratio of grounding resistance
decreasing rate to grounding grid radius are obtained. In the
analysis, the grounding resistivity is 200R-m. One used
horizontal grounding grid area is isox isom', while the other is
lOOx 1OOm'. The span between the horizontal conductors of the
grounding grid is 10m and the buried depth of the horizontal
grounding grid is 0.6m. The number of vertical grounding rods
are 4. The influence of the vertical grounding rod length on the
grounding resistance decreasing rate with different grid areas is
illustrated in Fig.4.

IV. ARRANGEMENT OF VERTICAL GROUNDING RODS
IN THE NONUNIFORM SOIL
The arrangement of long rods in the nonuniform soil from the
point of dispersed current distribution on the rods are discussed
here.
A. Current Distribution on A Single Rod

40

3.0

The calculation illustrates that in the similar soil conditions and
the same number of rods, the grounding resistance decreasing
rates do not change if the ratios of grounding-grid radius to
rod-length is fixed.

0.5

The reflective coefficient of two-layer soil is defined as
k =(p,
A ,p, are soil resistivities. Fig.5 is 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; radius r, equals 0.02m; upper-soil
resistivity p, equals 100SZ.m; the depth h is 7.5m.

1.o
4

1.5

2.0

s

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(a) uniform soil

225
S:150m*150m
S:lOOm*l OOm

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5

10

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15

"

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20
'

x (m)
Fig3 Current distribution on the rods in the hvo-layer soil.

(b) two-layer soil

From Fig.5, we observed that the current is well distributed on
the rods except that current intensity increases quickly at the

Fig4 Influences of rod length on grounding resistance decreasing rate.

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bottom of the rods in the uniform soil. It also shows that current
intensity increases a little with the increase of depth. 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
rods are in the two-layer soil. The current intensity in the lowresistivity soil layer is higher than that in the high-resistivity
soil layer. In each layer current distribution almost has no
change but there is a sharp shift along the interface.
The difference of current distributions in different layers rises
when reflective coefficient increases. For example, when k
equals 0.8, the current intensity is 300"
in the upper layer,
but it is only 25A/m in the lower layer. Hence the proper choice
of rod length can not only decrease grounding resistance
efficiently but also achieve better economic effect.

B. Arrangement of Rods in Two-layer Soil
Here is the discussion how vertical grounding rods affect the
electrical behaviors of the three-dimensional grounding grid in
the two-layer soil. The relationship between the rod length and
the grounding resistance decreasing rate with different
reflective coefficient is shown in Fig.6. Here the horizontal
grounding grid area is lOOx loom*, the horizontal conductor

span is 10m; the upper layer soil resistivity is 200R.m. Four
steel rods are arranged on the comers of the grid, the upperlayer soil thickness h is 40m.

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Therefore, the method of long rods does not fit the situation that
the soil resistivity of bottom layer is very high. On the other
hand, when the soil resistivity of the bottom layer is low, adding
of long rod can achieve good results.
From current distribution curves in Fig.5, it is understandable
that a tuming point emerges on the grounding resistance
decreasing rate curve in Fig.6 when kapproaches the upper layer depth, i.e. the grounding resistance
decreasing rate increases remarkably when rod length is longer
than the upper layer depth; but when the rod length is 3.5 times
of the depth of the upper layer, the grounding resistance
decreasing rate approaches saturation. Thus the effective rod
length is determined by reflective Coefficient k, and as a result,
long rods can not achieve good result when the resistivity of the
bottom layer is apparently lower than that of the upper layer.

C. Arrangement of Vertical Grounding Rods in Three-layer Soil

In some situations, three-layer soil models are put forward to
avoid the remarkable error caused by simplification of soil
structure. Since the actual situations are too complex, the
analysis is based on the typical soil structure. But the result is
universal. The soil structures of 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 1000R.m, the low
resistivity is 100R-m and the medium is 500R.m. The upper
layer depth is 10m, the middle layer thickness is 50m. The
horizontal grid and rods are all the same as those in the twolayer soil. The influence of added vertical grounding rods on
the grounding resistance decreasing rate is shown in Fig.7.

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2

3

4

5

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1

2

3

4

L",
Fig.6 Relationshipbetween the grounding resistance decreasing role of rods in
the two-layer soil.

As illustrated in Fig.6, when reflective coefficient k is lower
than 0.5, i.e. the soil resistivity of the bottom layer is high, the
way of adding rods can not decrease the grounding resistance
efficiently.Even if rod length approaches the radius of grid, the
grounding resistance decreasing rate is still lower than 10%.

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Fig.7 The influence of added vertical grounding rods on the grounding
resistance decreasing rate.

From Fig.7, we observed that just as in the two-layer soil, the
vertical rods can not decrease the grounding resistance
effectively when the upper layer resistivity is low. So in such
situation, long rod is not suitable. In the situation of strictly
limited area and high resistivity layer in the middle layer, rods


should reach the bottom layer with low resistivity.
Comparing the two curves of “M,H,L” and “M,L,H in Fig.7,
we observed that before rods touch the bottom layer, the

grounding resistance decreasing rate of the former is larger than
that of the latter with the role of low resistivity middle layer.
When the soil structure is “M,L,H’, it is better that rods do not
reach the bottom layer. But in contrast, rods should reach the
bottom layer when the soil structure is “M,H,L”.
The protruding curve MLH in Fig.7 of low resistivity middle
layer illustrates that resistance almost stops decreasing when
vertical grounding rod passes the middle layer. Therefore the
economic rod length is the sum of the depth of the upper and
middle layers.
As the situation of high-resistivity upper layer, rods can reach
the best results. Just as in the two-layer soil, the rod length is
determined by reflective coefficient k and layer structure. The
effect to decrease the grounding resistance are below the
interface with. smaller reflective coefficient (see Fig.5 and its
analysis), especially when the resistivity of the lower layer is
lower than that of the middle layer.
V. SAFETY OF THE GROUNDING GRID IMPROVED BY
VERTICAL GROUNDING ROD

Soil resistivity changes greatly in winter. For example, the
measure results of Muliduo in Qinghai, China show that the
resistivity range of frozen and unfrozen soil is 500 to
15000n* m. In the north-east of China, the depth of frozen soil
can reach 1.6m. The relationship between rod length and the
touch voltage in different seasonal factors is shown in Fig.8, the
seasonal factor is presented by different high resistivity soil
layers. The touch voltage is a ratio between the calculated
values with the calculated ones without considering the
seasonal factor. 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 the increase of the
resistivity of the upper high resistivity soil layer; while with the
increase of rod length, the surface touch voltage decrease
becomes 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 have a linear increase with the
increase of the soil resistivity. But the increase velocity
decreases with the increase of the rod length.
Rods buried on the periphery of the horizontal grounding grid
can not only decrease the grounding resistance efficiently, but
also can decrease the touch voltage and step voltage by
improving the potential distribution. Table 1 records the
influence of rod buried around the grounding grid on the touch
and step voltages. Here the horizontal grounding grid is buried
in the uniform soil without the seasonal soil layer.

From Table 1, we can conclude that the vertical rods play a
great role in decreasing the touch voltage. When the number of
rods is 12, the maximum touch voltage decreases to 40%. When
the number reaches 32, touch voltage decreases to 63.49%. The
reasons are: first, the vertical grounding rods decrease GPR
(grounding potential rise) which directly influences the touch
and step voltages; second, when vertical grounding rods are
added to the grounding system, the dispersed current by
horizontal conductors of grounding grid decreases due to a
large amount of fault current flowing into the soil through
vertical grounding rods, and as a result, the electrical field
intensity of earth surface above the grounding system decreases

greatly. For example, when the number of rods is 12, the
dispersed current on the horizontal grid is 25%, while the
current on the rods is 75%. When it is in the nonuniform soil,
especially the resistivity of the upper layer is apparently larger
than that of the lower layer, the percentage of the current on the
rods are larger, It can reach 90%.As a result, the touch and step
voltages on the surface decrease greatly.
Table1 the influence of number of the rods on the maximum touch and step
voltages

20.63
26.98
30.16
33.33
39.05
45.71
50.79
63.49

2
4

6
8
12
16
20
32

1

j

10 3,4: iith vertical rod1

7.69
32.3 1
38.46
41.54
46.15
53.85
58.46
69.23

/

1

groundinggrid
burial depth

J
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0.4

0.8

1.2

1.6

Depth (m)
Fig8 The relationshipbetween rod length and the touch voltage in different
seasonal factors

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VI.CONCLUSI0N
1.

The proper number of the vertical grounding rods can be
obtained from analyzing the number and the grounding
resistance decreasing rate. The resistivity-decreasing
effects differ greatly with different radius when the rod
length is fixed. To reach best results, rods should be
arranged on periphery of the grid instead of in the center.

2.

The discussion of rod length in various nonuniform soil
shows it is wrong that long rods can always reach better
results. The choice of rod length, location and the number
are determined by the soil structure.

3. The influence of seasonal factor on the grounding and
touch voltages is discussed. The vertical grounding rods
can effectively decrease the influence of seasonal factor on
safety of grounding system

VII. REFERENCES
[ 11 H.G. Sarmiento,R.J. Fortin, D. Mukhekar, “Substationground impedance:
comparative field measurements with high and low current injection
methods,” IEEE Transactions on Power Apparatus and System, V01.103,
no.7, July 1984, pp. 1677-1683.

[2] H.G. Sarmiento, R. Velazquez, “Survey of low ground electrode
impedance measurements,”IEEE Transactions on Power Apparatus and
System, V01.102, no.9, Sept. 1983, pp. 2842-2849.
[3] DUT621-1997. Grounding for AC electrical installations.Beijing: China
Electrical Power Industry Ministry, China, 1997.
[4] F.P. Dawalibi, D. Mukhedkar, “Resistance measurement of large
grounding systems,” IEEE Transactions on Power Apparatus and System,
Vo1.98, n0.6, June 1979, pp. 2348-2354.
[ 5 ] S.T. Sobral, S.J. Horta, D . k Mukhedkar, “A proposal for ground

measurement techniques in substations fed exclusively by power cables,”
Transactions on Power Delivery, Vo1.3, no. 4, Sept. 1983, pp. 2842-2849.

VIII. BIOGRAPHIES
Dr. Rong ZENG was born in Shaami, P. R. China in 1971. He received his B.
Sc. Degree, M. Eng., and Ph.D. Degree from the Department of Electrical
Engineering, Tsinghua University, respectively in July 1995, July 1997, July
1999. And now, he is a lecturer in the same department, Tsinghua University.
His research interests include high voltage technology, grounding technology,
power electronicsand computer application.
Dr. Jinliang HE was bom in Changsha, P. R China, in 1966. He received the
Ph.D. degree from Tsinghua University in Electrical Engineering, in March
1994. In July 1996, he became an associate professor in the same department.
From 1994to Jan 1997,he was the head of high voltage laboratory inTsinghua

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University. During April 1997 to April 1998, he was a visiting scientist in
Korea Electro-technologyResearch Institute. He is a SM of CES. Now he is
vice chief of High Voltage Research Institute in Tsinghua University. His
research interests include overvoltages and EMC in power systems and
electronic systems, groundingtechnology,power apparatus, dielectricmaterial,
and power distribution automation. He is the author of three books and 80
technical papers. His E-mail address is

Dr.Wang Zanji was bom in Fuqing Fujian, China, in 1946.Hereceived his B.
S. Degree, M. S. Degree, and Ph. D. Degree from Dept. of Electrical
Engineering Tsinghua University, all in electrical engineering, respecitvely in
1970, 1985, and 1990. He became a lecturer in the Department of Electrical
Engineering, Tsinghua University, in 1983. And in 1990, He became an
associateprofessor. In 1993, he was promoted as a professor. Since may 1995,
he have been being the Dean of the Department of Electrical Engineering,
Tsinghua University. And at present, he is a SM of CES, member of CES
Standing Council, Chairman of Editorial Working Committee of CES, Vice
Chairman of Education Working Committee of CES; SM of CSEE, member of
Theoretical Electrotechnics committee of CSEE, member of Transmission
Commitbe of CSEE; and chairman of Organizing Committee, IPEMC’2000,
Aug. 2000, Beijing. His research fields include circuit theory and application,
numerical computation of electromagnetic field, electromagnetic transient,
fault location and protective relay, static electrification in EHV power
transformer, soft computing and multi-objective optimization, communication
in power system, and chaos. He is the author ofmore than 40 technique papers.

Mr. Yanqing GAO received his B. Sc. From the Department of Electrical

Engineering, Tsinghua University in July, 1999. And now he is a Ph.D.
candidatein the Department ofElectrical Engineering Tsinghua University, his
research fields include overvoltagein power system, groundingtechnology.
Mr. Weimin SUN obtained his B. Sc. Degree from the Department of
Electrical Engineering, Shondong Industry University in July, 1984, M. Eng.
Degree from EPRI, China, in 1989. And now he is a senior engineer in
Shandong Electrical Power Bureau, his research fields include high voltage
technology and power distribution.

Dr. Qi SU received his MEng in 81 (WUHEE, China) and PhD in 90 (UNSW,
Australia). He was a tests and operations engineer from 71-78, an Honorary
Research Associate with the University of Western Australia in 1985 and a
Lecturer in the University of New South Wales in Sydney from 90-91. Since
1992, he has been with Monash University in Melboume and is now a Senior
Lecturer and the Head of High Voltage and Insulation Condition Monitoring
Group in the Department of Electrical and Computer Systems Engineering. He
also took short term positions as a Senior Fellow in Singapore National
University in 1998 and a Guest Professor at the Technical University of
Denmark in 1999. Dr.Su’smain research interests include insulation condition
monitoring reliability-centredmaintenance, fuzzy diagnosis of electricalplant,
high voltage tests, transformer and generator high frequency models, system
disturbance location, pattern recognition using artificial intelligence and webbased engineering education. He holds two Australian patents and has
published over 100 journal and conference papers. He is a Charlered
ProfessionalEngineer, a member of CIGRE AustralianPanel 11 (Generators) &
21 (Power cables) and a Senior Member of IEEE since 1991.