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Grounding Resistance Calculation Using FEM and Reduced Scale
Model
Thinh Pham Hong, Quan Do Van and Thang Vo Viet Department of
Power Systems-Hanoi University of Technology (HUT)
1- Dai Co Viet Street, Hanoi, Vietnam
Abstract- The grounding grid of a substation is one of the most
important parts in an electrical system from the point of view of
the safety of the people and equipment. Depending on the nature of
the phenomena involved in the system is fault or lightning current,
the behavior of grounding system is considered under steady state
or transient point of view. For safety purpose of grounding grid,
the ground resistance is more likely calculated by analytical or
numerical method by using potential distribution calculation along
soil structure. In comparison with the analytical method, Finite
Element Method (FEM) method in calculation of grounding resistance
is more flexible in analyzing asymmetrical geometry of the grid, as
well as in case of anisotropy of soil resistivity. However, with
the increase in size and complexity of substation grid, the FEM
method could not be applied due to the increase of divided
elements. This paper presents a reduced scale model for grounding
resistance calculation using FEM method. The results giving the
effect of electrode configuration on potential profile and
grounding resistance are also presented.
I. INTRODUCTION
The grounding system of a substation is one of the most
important parts in a power system. The purpose of the grounding
system is to provide a low impedance electrical contact between the
neutral of an electrical system and earth [1]. Depending on the
nature of the phenomena involved in the system is fault or
lightning current, the behavior of grounding system is considered
under steady state or transient point of view. For the purpose of
safety, the performance of a grounding system is evaluated by some
parameters such as ground resistance, touch voltage, step voltage,
mesh voltage [2]. The calculation method of grounding system using
analytical approaches [2, 3] in which the soil is considered as
uniform medium and the electrodes are considered as symmetric. When
the uniform soil approximation is no longer valid and the
electrodes contain irregularities, such methods may result in
unsafe or overdesigned grounding system [4]. Recently, Finite
Element Method (FEM) has been used as an excellent numerical method
to calculate the grounding system [5-7]. The main disadvantage of
this method is the limited capability of the computer in case of
too large dimension of grounding grid, specifically with the large
ratio between grid dimension and grounding electrode size. In
experimental works, the grounding system is always measured and
validated by reducing in size by the same scale factor of the
physical dimension of the grid [8-11]. But few investigations have
focused on the reduced scale model in simulation. This work
presents the FEM simulation of grounding grid using reduced scale
model in ANSYS program. The
calculation was first performed in simple configuration of
grounding electrode. Reduced scale model in simulation was used for
grounding grid of 16 square mesh, with and without ground rods. The
results could be effectively used for grounding grid design.
II. MODEL AND SIMULATION
The simulation of the grounding grid allows us to calculate the
grounding resistance and the potential profile above the ground
grid regardless of their shape and the geometry of the ground
electrode. Like any Finite Element Method (FEM) based calculation,
ANSYS program calculates the grounding resistance by using one of
the two methods [1]: A. Current Flow Analysis For an arbitrary
geometry, the resistance between two electrodes can be calculated
from the voltage V and the dissipated power P in the ground:
(1) In which the dissipated power P is determined by:
(2) Where: J: current density V: electrical conductivity E:
electric field B. Electrostatic Analysis Another method used to
calculate the grounding resistance in FEM is to know the stored
energy by the electric field in the ground:
(3) Where the stored energy by the electric field is given
by:
(4) The following simplifying hypotheses will be also taken into
account when calculating the grounding system:
- The soil is isotropic and uniform in each layer - The
non-linearity does not occur in the soil - The grid behavior at
power frequency is considered
in stationary regime. - In reduced scale model, all physical
dimensions of a
grounding grid are reduced by the same factor including the
conductor diameter and the buried depth. Thus, the current injected
in grounding system is unaltered and remained 1kA in any model.
- The grounding grid is buried in a semi-infinite earth, and in
order to not distort the field inside the
278978-1-4244-4559-2/09/$25.00 2009 IEEE
2009 Annual Report Conference on Electrical Insulation and
Dielectric Phenomena
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calculated medium [11] we considered a surrounding earth of the
grid having a diameter equal to at least three times the width of
the grid.
III. SIMULATION RESULTS
A. Ground resistance in uniform soils.
Ground resistance was first calculated in uniform soil of 400:.m
in resistivity. Fig. 1 shows the potential distribution in the soil
of a horizontal rod of 2m in length. Due to symmetry of the
electrode configuration, one-fourth of the vertical rod was
necessary to simulate in 3D model. The simulation results enabled
us to observe the step voltage, which was calculated the voltage
difference between 1m apart, along and perpendicular to the rod
(Fig. 2). The step voltage along the electrode shows a small
deviation from that is perpendicular to the electrode, and a
dangerous point in step voltage exists at 1m far from the electrode
end along the electrode. This behavior suggests that the maximum
step voltage for a horizontal rod should be calculated at a certain
point from the electrode ends. The effect of electrode length was
also examined and shown in fig. 6
Fig. 1. Potential distribution in the soil for 1 horizontal rod
of 0.020.02m in
size
Fig 2. Step voltage distribution on the soil surface, along and
perpendicular to
the horizontal rod
Fig 3. Grounding resistance of horizontal rod versus the
length
In order to increase the performance of the grounding system, 3
vertical rods have been added to the horizontal configuration to
form a mixed configuration. The voltage profile on the soil surface
was shown in fig. 3. It was obvious that maximum step voltage has
the same behavior than the previous case, but the maximum value has
been reduced in half (from |2400V to |1000V). The ground resistance
has been substantially decreased when using mixed configuration. It
was observed that 50: was the limited value in horizontal
configuration. However, the combination of vertical and horizontal
rods could reduce the grounding resistance to 8: (fig. 9). The
saturation at 4m of distance between two vertical rods was
correlated with the analytical results [1] in which the combination
may obtain the best efficiency if the distance between two vertical
rods should not exceed twice of their length.
Fig 4. One-fourth of mixed configuration with 3 vertical rod of
2m and 1
horizontal rod of 4m
Fig 5. Step voltage distribution on the soil surface, along and
perpendicular to
the horizontal rod
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14
R,
Electrode length, m
0
2000
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8000
10000
12000
0 5 10 15 20 25 30
V
Distance from the electrode end, m
Along the horizontal rod
Perpendicular to the horizontal rod
0
5000 10000 15000 20000 25000 30000
0 5 10 15 20 25 30Distance from the electrode end, m
V Perpendicular to the rod Along the rod
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Fig 6. Ground resistance versus vertical rod spacing in mixed
configuration
B. Reduced scale model As the principle of the FEM is dividing
the studied volume into elements, a grounding system of a large
substation, especially in presence of vertical rods, may lead to
too many divided elements so that the computer could not solve it.
This could be one of reasons why previous works always used the FEM
to determine grounding resistance of very simple ground electrode
[7], of small grids with ground rods (the maximum of grid dimension
was 12m8m) [5], or of large grids (the maximum of grid dimension
was 100m80m) but without ground rods [6]. In this section, the
behavior of grounding grids of 16 meshes without and with 16 ground
rods installed in the boundary junction was simulated (fig. 7). A
variety of grids with outside dimensions 20m20m, 10m10m, and 4m4m
with and without ground rods, which correspond with scale factor of
1:1, 1:2 and 1: 5 respectively, were modeled in uniformed soil. The
other parameters including buried depth, soil resistivity and
electrode size were also reduced with the same scale factor (TABLE
I and II).
Y
X
X
Fig. 7. Grounding grid to be simulated
As shown in fig. 7 it is necessary to plot the surface potential
profiles along the center and diagonal lines of the grid (x and
y-axis). Typical profiles for a 16 mesh grid of three scale factors
without ground rods were plotted in fig. 8 and fig. 9.
Fig. 8. X-axis potential profile for 16 mesh grid without ground
rod
Fig. 9. Y-axis potential profile for 16 mesh grid without ground
rod
TABLE I
PARAMETERS AND SIMULATION RESULTS OF REDUCED SCALE MODEL IN GRID
WITHOUT GROUND RODS
In fig. 8 and 9, potential values versus the distance from the
grid center were normalized to original grid (20m20m) with the same
scale factor. That means 1 meter in x-axis and y-axis of 10m10m and
4m4m curves corresponds with 0.5m and 0.2m in the simulation
results respectively. Also, step voltage was calculated between 1m,
0.5m and 0.2m apart in each model. In comparison with the original
grid, the ground resistance in 1:2 and 1:5 models did have 4.97%
and 9.68% in difference while the step voltage had only 1.13% and
1.34%.
Scale
factor Grid
dimension
m
Grid
conductor
diameter
cm
Buried
depth
m
Soil
resistivity
.m
Ground
resistance
Max. step
voltage,
V
1 20x20 2 0.6 400 7.85 1251.9
1/2 10x10 1 0.3 200 8.24 1266
1/5 4x4 0.4 0.12 80 8.61 1268.7
0
1000
2000
3000
40005000
6000
7000
8000
9000
0 10 20 30 40 50
Y(m)
V
4mx4m 10mx10m
20mx20m
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 10 20 30 40 50X(m)
V
20mx20m
10mx10m
4mx4m
0
2
4
6
8
10
12
14
16
18
0 2 4 6 8Distance between two vertical rods, m
R, :
280
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Fig. 10. X-axis potential profile for 16 mesh grid with 16
ground rods
installed in surrounding junction
Fig. 11. Y-axis potential profile for 16 mesh grid with 16
ground rods
installed in surrounding junction
TABLE II PARAMETERS AND SIMULATION RESULTS OF REDUCED SCALE
MODEL IN GRID WITH
GROUND RODS
Scale
factor Grid
dimension
m
Grid
conductor
diameter
cm
Radius of
ground
rod
cm
Buried
depth
m
Soil
resistivity
.m
Ground
resistance
Max. step
voltage,
V
1 20x20 2 1 0.6 400 7.08 1175.1
1/2 10x10 1 0.5 0.3 200 7.63 1181.3
1/5 4x4 0.4 0.2 0.12 80 7.90 1179
In presence of ground rods, the difference between maximum step
voltage of reduced model and the original one was much more
improved, they were 0.53% and 0.33% in 1:2 and 1:5 models
respectively. However, the difference in ground resistance was
slightly higher in the previous case with 7.72% and 11.55%.
IV. CONCLUSION The 3D model of FEM was used for calculating
ground resistance and potential profile of different grounding
grids. The simulation offered a great flexibility in calculating a
complicated grounding system without any simplifying assumption.
The main disadvantage of FEM method when simulating physical
dimension of a grounding grid could be
overcome by using reduced scale model. Although verification on
field would be needed, reduced scale model in simulation could
provide an inexpensive solution, and it could be effectively used
for parametric studies for grounding grid design.
ACKNOWLEDGMENT
This article was funded in part by a grant from the Vietnam
Education Foundation (VEF). The opinions, findings, and conclusions
stated herein are those of the authors and do not necessarily
reflect those of VEF. Center for Development and Application of
Software for Industry (DASI) at HUT is gratefully acknowledged for
its help during this study
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and Transients,
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[8] A. Puttarach, N. Chakpitak, T.Kasirawat and C.
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0
1000
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5000
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7000
8000
9000
0 10 20 30 40 50Y( m)
V
20mx20m
10mx10m
4mx4m
0
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7000
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9000
0 10 20 30 40 50X(m)
V
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