Calculation of grounding resistance and earth

INTERNATIONAL JOURNAL OF ELECTRICAL0976 – 6545(Print), ISSN
International Journal of Electrical Engineering and Technology (IJEET), ISSN ENGINEERING
0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME
& TECHNOLOGY (IJEET)
ISSN 0976 – 6545(Print)
ISSN 0976 – 6553(Online)
Volume 3, Issue 3, October - December (2012), pp. 156-163
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CALCULATION OF GROUNDING RESISTANCE AND EARTH
SURFACE POTENTIAL FOR TWO LAYER MODEL SOIL

Hatim Ghazi Zaini
Taif University, Faculty of Engineering, Electrical department
h.zaini@tu.edu.sa

ABSTRACT

For two layer model soil, the calculation of apparent resistivity is considered very important
issue since the absent of a specified method to find it. Some empirical resistivity formula is
used in this paper to present the apparent resistivity of the two layer model soil. A current
simulation method technique which is a practical technique for calculating the grounding
resistance (Rg) as well as the Earth Surface Potential (ESP) of the grounding grids in two-
layer model soil which based upon the apparent resistivity of the two layer soil and
simulating current sources is used. it is analogous to the Charge Simulation Method. The
validation of the method is described by a comparison with the results in literatures.

Index terms--Grounding grids, two-layer soil, current simulation method, Computer methods
for grounding analysis, System protection.

I. NOMENCLATURE
Paij= Potential coefficient matrix related to apparent resistivity
P1ij, P2ij Potential coefficient matrix related to resistivity of layer 1 and 2 respectively
Ij =current source at point j
Vi= voltage at evaluation point i
ρa =apparent soil reistivity
ρ1 =soil reistivity of layer 1
ρ2 =soil reistivity of layer 2
d =distance between current source point and evaluation point in original grid
d' =distance between current source point and evaluation point in image grid
J =current density (A/m2)
F =field coefficient
zzi & zzj = the dimension of the contour point and current source in z direction respectively
Rg=grounding resistance
d0 = the depth to the boundary of the zones,

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International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN

K = the reflection factor (K=( ρ2- ρ1)/ ( ρ1+ ρ2))
z = the top layer depth
GPR=Ground potential rise (V)
Vtouch= touch voltage

II. INTRODUCTION
The knowledge of the grounding systems impulse characteristics has a great significance for
a proper evaluation of substation equipment stresses from lightning over-voltages and
lightning protection evaluation. As it is stated in the ANSI/IEEE a safe grounding design has
two objectives: the first one is the ability to carry the electric currents into earth under normal
and fault conditions without exceeding operating and equipment limits or adversely affecting
continuity of service. The second is how this grounding system ensures that the person in the
vicinity of grounded facilities is not exposed to the danger of electric shock.
To attain these targets, the equivalent electrical resistance (Rg) of the system must be low
enough to assure that fault currents dissipate mainly through the grounding grid into the
earth, while maximum potential difference between close points into the earth’s surface must
be kept under certain tolerances (step, touch, and mesh voltages). Analysis of substation
grounding systems, including buried grids and driven rods has been the subject of many
recent papers [1- 4].
Several publications [5-19] have discussed the analytical methods used when uniform and
two-layer soils are involved.
This paper uses a practical method to calculate the grounding resistance as well as the
earth surface potential for grounding grids which buried in uniform and two-layer soil. This
method is Current Simulation Method (CSM). The Current Simulation Method is analogous
to Charge Simulation Method.
The validation of a proposed method is explained by comparison between the results from
the proposed method and the other that formulated in [1].

III. CURRENT SIMULATION METHOD IN TWO-LAYER SOIL
The representation of a ground electrode based on equivalent two-layer soil is generally
sufficient for designing a safe grounding system. However, a more accurate representation of
the actual soil conditions can be obtained by using two-layer soil model [13].
As in the Current Simulation Method, the actual electric filed is simulated with a field
formed by a number of discrete current sources which are placed outside the region where the
field solution is desired. Values of the discrete current sources are determined by satisfying
the boundary conditions at a selected number of contour points. Once the values and
positions of simulation current sources are known, the potential and field distribution
anywhere in the region can be computed easily [20].
The field computation for the two-layer soil system is somewhat complicated due to the
fact that the dipoles are realigned in different soils under the influence of the applied voltage.
Such realignment of dipoles produces a net surface current on the dielectric interface. Thus in
addition to the electrodes, each dielectric interface needs to be simulated by fictitious current
sources. Here, it is important to note that the interface boundary does not correspond to an
equipotential surface. Moreover, it must be possible to calculate the electric field on both
sides of the interface boundary.
In the simple example shown in Fig. 1, there are N1 numbers of current sources and
contour points to simulate the electrode, of which NA are on the side of soil A and (N1- NA)
are on the side of soil B. These N1 current sources are valid for field calculation in both soils.
At the different soil interface there are N2 contour points (N1 +1,….., N 1+N2), with N2

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current sources (N1+1,…..,N 1+N2) in soil A valid for soil B and N2 current sources (N1+N2
+1,…..,N1 +2N2) in soil B valid for soil A. Altogether there are (N1+N2) number of contour
points and (N1 + 2N2) number of current sources.
As in Fig. 1, h is the grid depth and z is the depth of top layer soil. In order to determine
the fictitious current sources, a system of equations is formulated by imposing the following
boundary conditions.
• At each contour point on the electrode surface the potential must be equal to the
known electrode potential. This condition is also known as Dirichlet’s condition on the
electrode surface.
• At each contour point on the dielectric interface, the potential and the normal
component of flux density must be same when computed from either side of the
boundary.
Thus the application of the first boundary condition to contour points 1 to N1 yields the
following equations.

N1 N1 + 2 N 2
∑ Pa i, j I j + ∑ P i , j I j = V .....i = 1, N A
1
j =1 j = N! + N 2 +1
N1 N1 + N 2
(1)
∑ Pa i, j I j + ∑ P2 i , j I j = V .....i = N A + 1, N1
j =1 j = N! +1

where,
ρa 1 1  ρ 1 1 
Pa i , j =  + ' , P i , j = 1  + ' 
1
4π d d  4π  d d 
ρ 1 1 
P2 i , j = 2  + '
4π d d 

Again the application of the second boundary condition for potential and normal current
density to contour points = N1+1 to N1+N2 on the dielectric interface results into the
following equations. From potential continuity condition:

N1 + N 2 N1 + 2 N 2
∑ P2 i , j I j − ∑ P i , j I j = 0....i = N1 + 1, N1 + N 2
1 (2)
j = N1 +1 j = N! + N 2 +1

From continuity condition of normal current density Jn:
J n1 (i ) − J n 2 (i ) = 0 for i = N1 + 1, N1 + N 2 (3)

Eqn. (3) can be expanded as follows:
 1 1  N1 1 N1 + N 2
 −
ρ ∑F I − ∑ F2 ⊥ i, j I j +
 1 ρ 2  j =1 a ⊥ i , j j ρ 2
 j = N ! +1
N1 + 2 N 2
(4)
1
∑ F1⊥ i , j I j = 0..........i = N1 + 1, N1 + N 2
ρ1 j = N ! + N 2 +1

where,

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Fa ⊥ i , j = −
∂Pa ij
=
ρa (
 zz i − zz j
+
) (
zzi − zz 'j 
 )
∂z  d3
4π d '3 
 

F1⊥ i , j =−
∂P ij
1 ρ
= 1
(
 zz i − zz j
+
) (
zzi − zz 'j 
 )
∂z 4π  d3 d '3 
 

F2 ⊥ i , j = −
∂P2 ij
=
ρ2 (
 zzi − zz j
+
) (
zz i − zz 'j )

∂z 4π  d3 d '3 
 

Fig.1. Fictitious current source with contour points for field calculation by current simulation
method in two-layer soil.

where, F┴,ij is the field coefficient in the normal direction to the soil boundary at the
respective contour point, ρa, ρ1 & ρ2 are the apparent resistivity nd resistivities of soil 1 and 2
respectively and zzi & zzj are the dimension of the contour point and current source in z
direction respectively. Equations 1 to 4 are solved to determine the unknown fictitious current
sources.
After solving 1 to 4 to determine the unknown fictitious current source points, the potential
on the earth surface can be calculated by using Eq. 1. Also, the ground resistance (Rg) can be
calculated using the following equation:
V
Rg = N1
(5)
∑I
j =1

where, V is the voltage applied on the grid which is assumed 1V.

The problem for the proposed method is how the apparent resistivity can be calculated. As
in [18], the apparent resistivity for two soil model calculates by the following formula;
ρ1
ρa = for ρ 2 < ρ1 (6)
   1 
1 +  ρ1  − 1 1 − e K (d 0 + 2 z )  
  
  ρ 2   
 
 
  
  
−1 
ρa = ρ2 × 1 +  ρ 2  − 1 1 − e K (d 0 + 2 z )   for ρ > ρ
  (7)
  ρ1     2 1
    
 
where, d0 is the depth to the boundary of the zones, K is the reflection factor (K=( ρ2- ρ1)/ (
ρ1+ ρ2)) and z is the top layer depth.

159


Equations 6 and 7 are valid for the boundary depth greater than or equal the grid depth. But
in [19], Eq. 7 is modified because at very large depth of upper soil layer, resistivity ρa given
by Eq. 7 tends to ρ2. This is physically incorrect if the electrode lies in the upper soil layer, as
assumed in [18]. Therefore, Eq. 7 is modified [19] as follows:
   −1 
ρ a = ρ1 × 1 +  ρ 2  − 1 1 − e K (d 0 + 2 z )   forρ > ρ
   (8)
  ρ1     2 1
    
 
For finite h and very large d0, resistivity ρa given by Eq. 8 tends to ρ1, which is in
compliance with physical reasoning.
When the boundary depth is lower than the grid depth, the apparent resistivity tends to ρ2.
Therefore, by using Eq. 6 and 8 for calculating the grounding resistance by Current
Simulation Method, the large different between the proposed method results and the results in
[1] is observed for K<-0.5 and this shown in Fig.2.
If Eq. 8 is modified as in 9 the results by the proposed method are good agreement with the
results in [1].
  ρ 2   
−1 
ρ a = ρ1 × 1 + 
  − 1 1 − e K (d 0 +15 z )   forρ 2 > ρ1
 (9)
  ρ1    

   
Figures 3 and 4 present the comparison of the results calculated by the proposed method
with the results reported in [1] for a square 30m*30m, 4 and 16 meshes grids buried at 0.5 m
depth in various two layer structures. It is noticed from Figs. 3 and 4 that the proposed
method gives a good agreement with the results in [1].

IV. GROUNDING RESISTANCE AND EARTH SURFACE POTENTIAL
It is clear that the Ground Potential Rise (GPR) as well as distribution of the Earth Surface
Potential (ESP) during flow the impulse current into the grounding system is important
parameters for the protection against electric shock. The distribution of the Earth Surface
Potential helps us to determine the step and touch voltages, which are very important for
human safe.
The maximum percentage value of Vtouch is given by:
GPR _ Vmin
Max Vtouch % = × 100 (10)
GPR
where, GPR is the ground potential rise, which equal the product of the equivalent resistance
of grid and the fault current and Vmin is the minimum surface potential in the grid boundary.
The maximum step voltage of a grid will be the highest value of step voltages of the
grounding grid. The maximum step voltage can be calculated by using the slope of the secant
line.
Figure 5 explains the Earth Surface Potential per Ground Potential Rise (ESP/GPR) when
the case is square grid, 36 meshes, grid dimension 60m*60m, vertical rod length that connect
to grid 6m, grid conductor radius 0.005m, grid depth 0.7m, the top layer to lower layer
resistivity 1000/100 ohm.m and the top layer depth 3m. Fig. 6 illustrates that the maximum
touch voltage occurs at the boundary of the grid near the corner mesh but the maximum step
voltage occurs outside the boundary of the grid near the edge of it.

160


K=0.9 K=0.9-[1]
0.5 K=0.5-[1]
0 K=0-[1]
-0.5 K=-0.5-[1]
-0.9 K=-0.9-[1]
10

Resistance (ohm)
1
0.1 1 10 100
0.1

0.01 Top layer depth (m)

Fig. 2. Relation between 4 meshes grid resistance and the top layer depth

K=0.9 K=0.9-[1]
K=0.5 K=0.5-[1]
K=0 K=0-[1]
K=-0.5 K=-0.5-[1]
K=-0.9 K=-0.9-[1]

10
Resistance (ohm)

1
0.1 1 10 100

0.1

0.01
Top layer depth (m)


K=0.9 K=0.9-[1]
K=0.5 K=0.5-[1]
K=0 K=0-[1]
K=-0.5 K=-0.5-[1]
K=-0.9 K=-0.9-[1]
10
Resistance (ohm)

1
0.1 1 10 100

0.1

0.01 Top layer depth (m)


161


1.2

1

0.8

ESP/GPR
0.6

0.4

0.2

0
80 60 40 20 0 -20 -40 -60 -80
Distance from the grid center (m)

Fig. 5. ESP/ GPR for 36 meshes square grid

1.2
ESP/GPR Step Voltage/GPR Touch Voltage/GPR
1

ESP, Step and Touch
0.8

Voltages/GPR
0.6

0.4

0.2

0
80 60 40 20 0 -20 -40 -60 -80
Distance from grid center (m)

Fig. 6. ESP, Step and Touch voltages / GPR for 36 meshes square grid

V. CONCLUSIONS
This paper aims to calculate the Earth Surface Potential due to discharging current into
grounding grid in two-layer soil by using a traditional but practical method which is the
Current Simulation Method. The validation of the method is satisfying by a comparison
between the results from the method and the results in [1]. It is seen that a good agreement
between the proposed method results and the results in [1].

VI. REFERENCES
[1] F. Dawalibi, D. Mukhedkar, “Parametric analysis of grounding grids”, IEEE Transactions
on Power Apparatus and Systems, Vol. Pas-98, No. 5, pp. 1659-1668, Sep/Oct: 1979.
[2] J. Nahman, and S. S Kuletich, “Irregularity correction factors for mesh and step voltages
of grounding grids”, IEEE Transactions on Power Apparatus and Systems, Vol. Pas-99,
No. 1, pp. 174-179, Jan/Feb: 1980.
[3] Substation Committee Working Group 78.1, Safe substation grounding, Part II, IEEE
Transactions on Power Apparatus and Systems, Pas-101, pp. 4006/4023, 1982.
[4] IEEE Guide for safety in AC substation grounding, IEEE Std.80-2000.
[5] Elsayed M. Elrefaie, Sherif Ghoneim, Mohamed Kamal, Ramy Ghaly, "Evolutionary
Strategy Technique to Optimize the Grounding Grids Design", The 2012 IEEE Power &
Energy Society General Meeting, July 22-26, 2012, San Diego, California, USA.
[6] Sherif Salama, Salah AbdelSattar and Kamel O. Shoush, "Comparing Charge and Current
Simulation Method with Boundary Element Method for Grounding System Calculations
in Case of Multi-Layer Soil, International Journal of Electrical & Computer Sciences
IJECS-IJENS Vol:12 No:04, August 2012, pp.17-24.
[7] Mosleh Maeid Al-Harthi, Sherif Salama Mohamed Ghoneim, "Measurements the Earth
Surface Potential for Different Grounding System Configurations Using Scale Model",

162


International Journal of Electrical Engineering and Technology (IJEET), Volume 3,
Issue 2 (July- September 2012) , pp.405-416.
[8] F. Navarrina, I. Colominas, “Why Do Computer Methods for Grounding Analysis
Produce Anomalous Results?,” IEEE Transaction on power delivery, vol. 18, No. 4, , pp
1192-1201, October 2003.
[9] I. Colominas, F. Navarrina, M. Casteleiro, "A Numerical Formulation for Grounding
Analysis in Stratified Soils", IEEE Transactions on Power Delivery, vol. 17, pp 587-595,
April 2002.
[10] F. Dawalibi, N. Barbeito, “ Measurements and computations of the performance of
grounding systems buried in multilayer soils”, IEEE Transactions on Power Delivery,
Vol. 6, No. 4, pp. 1483-1490, October 1991.
[11] F. Dawalibi, J. Ma, R. D. Southey, “ Behaviour of grounding systems in multilayer soils,
a parametric analysis”, IEEE Transactions on Power Delivery, Vol. 9, No. 1, pp. 334-
342, January 1994.
[12] M. M. A. Salama, M. M. Elsherbiny, Y. L. Chow, "Calculation and interpretation of a
grounding grid in two-layer earth with the synthetic-asymptote approach", Electric
power systems research, pp. 157-165, 1995.
[13] Cheng-Nan Chang, Chien-Hsing Lee, “ Compuation of ground resistances and
assessment of ground grid safety at 161/23.9 kV indoor/tzpe substation”, IEEE
Transactions on Power Delivery, Vol. 21, No. 3, pp. 1250/1260, July 2006.
[14] E. Bendito, A. Carmona, A. M. Encinas and M. J. Jimenez “The extremal charges
method in grounding grid design,” IEEE Transaction on power delivery, vol. 19, No. 1,
pp 118-123, January 2004.
[15] J. A. Güemes, F. E. Hernando “Method for calculating the ground resistance of
grounding grids using FEM,” IEEE Transaction on power delivery, vol. 19, No. 2, pp
595-600, April 2004.
[16] M. B. Kostic, G. H. Shirkoohi “Numerical analzsis of a class of foundation grounding
systems surrounded by two-layer soil,” IEEE Transaction on power delivery, vol. 8, No.
3, pp 1080-1087, July 1993.
[17] E. Mombello, O. Trad, J. Rivera, A. Andreoni, "Two-layer soil model for power station
grounding system calculation considering multilayer soil stratification", Electric power
systems research, pp. 67-78, 1996.
[18] J. A. Sullivan, “Alternativ earthing calculatons for grids and rods,” IEE Proceedings
Transmission and Distributions, Vol. 145, No. 3, pp. 271-280, May 1998.
[19] J. Nahman, I. Paunovic, “Resistance to earth of earthing grids buried in multi-layer soil,”
Electrical Engineering (2006), Spring Verlag 2005, pp. 281-287, January 2005.
[20] N. H. Malik, “A review of charge simulation method and its application,” IEEE
Transaction on Electrical Insulation, vol. 24, No. 1, February 1989, pp 3-20.

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