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 ...
2009 Annual Report Conference on Electrical Insulation and Dielectric Phenomena
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 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.
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.
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:
INTRODUCTION
మ
ܴൌ In which the dissipated power P is determined by:
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
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ܲ ൌ ܧǤ ܸ݀ܬൌ ߪ ܧଶ ܸ݀
(1) (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: ఌ మ
(3) ܴൌ ఙଶௐ Where the stored energy by the electric field is given by: ଵ ܹ ൌ ܷܥଶ (4) ଶ 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
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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.
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SIMULATION RESULTS
R, ɏ
III.
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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
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0
2
4
6
8
10
Electrode length, m
12
14
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. 1. Potential distribution in the soil for 1 horizontal rod of 0.02×0.02m in size 30000 25000
V
20000
Perpendicular to the rod
15000
Along the rod Fig 4. One-fourth of mixed configuration with 3 vertical rod of 2m and 1 horizontal rod of 4m
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12000
0 0
5
10 15 20 25 Distance from the electrode end, m
10000
30
8000
Fig 2. Step voltage distribution on the soil surface, along and perpendicular to the horizontal rod
V
Perpendicular to the horizontal rod
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Along the horizontal rod
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5
10
15
20
25
30
Distance from the electrode end, m Fig 5. Step voltage distribution on the soil surface, along and perpendicular to the horizontal rod
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18
9000
16
8000
14
7000
12
6000
R, :10
V 5000
8
4000
6
3000
4
2000
2
1000
0
20mx20m 10mx10m 4mx4m
0 0
2
4 6 Distance between two vertical rods, m
8
0
20
30
40
50
X(m)
Fig 6. Ground resistance versus vertical rod spacing in mixed configuration
Fig. 8. X-axis potential profile for 16 mesh grid without ground rod
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 12m×8m) [5], or of large grids (the maximum of grid dimension was 100m×80m) 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 20m×20m, 10m×10m, and 4m×4m 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). X
10
9000 8000 7000
4mx4m
6000
10mx10m
V
5000
20mx20m
4000 3000 2000 1000 0 0
10
20
30
40
50
Y(m) 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
Y
Scale
Grid
Grid
Buried
factor
dimension
conductor
depth
m
diameter
m
Soil
Ground
resistivity resistance ȍ.m
Max. step voltage,
ȍ
V 1251.9
cm
X
1
20x20
2
0.6
400
7.85
1/2
10x10
1
0.3
200
8.24
1266
1/5
4x4
0.4
0.12
80
8.61
1268.7
In fig. 8 and 9, potential values versus the distance from the grid center were normalized to original grid (20m×20m) with the same scale factor. That means 1 meter in x-axis and y-axis of 10m×10m and 4m×4m 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%.
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.
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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.
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V
7000
20mx20m
6000
10mx10m
5000
4mx4m
ACKNOWLEDGMENT
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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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10
20
30
40
50
X(m) Fig. 10. X-axis potential profile for 16 mesh grid with 16 ground rods installed in surrounding junction
REFERENCES
9000 8000
[2] [3]
10mx10m
6000
V
[1]
20mx20m
7000
4mx4m
5000 4000
[4]
3000 2000
[5]
1000 0 0
10
20
30
40
50
[6]
Y( m) Fig. 11. Y-axis potential profile for 16 mesh grid with 16 ground rods installed in surrounding junction
[7]
TABLE II PARAMETERS AND SIMULATION RESULTS OF REDUCED SCALE MODEL IN GRID WITH GROUND RODS
[8] Scale
Grid
Grid
Radius of
Buried
factor
dimension
conductor
ground
depth
m
diameter
rod
cm
m
Soil
Ground
resistivity resistance ȍ.m
ȍ
Max. step voltage,
[9]
V
cm
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
[10] [11]
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
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