1
Optimization Design of Substation Grounding Grid
Nuno Jorge Lopes Filipe
Instituto Superior Técnico, Universidade Técnica de Lisboa
Abstract – The author developed a program that, starting from a standard grounding grid project, apply an optimization method
that has the potential to reduce the conductive material used, while keeping the security at the substation. The method combines two
techniques: variable spacing technique developed by Sverak, which is well established and has proven results, and placement of
grounding rods, a technique that has been little explored in the literature but will be studied in detail in this work and its effectiveness
will be proven.
Index Terms— Conductor material saving, Ground rods, Optimization of substation grounding grid, Sverak’s method.
I. INTRODUCTION
he optimization of the design of substation grounding
grids is an issue that has assumed an increasing
importance, since it seeks to reduce the amount of conductive
material buried at the same time it must ensure an effective
and safe flow of the ground fault current through the soil .
Over the years there has been a growing concern with the
issue of optimization of grounding grids. There were many
publications in this theme. In [2-4] the authors introduced the
concept of optimal design of a grounding grid. Sverak used the
results obtained on those papers to develop his technique [6],
the variable space technique. Years later appeared the Chinese
method [12], which is based on a set of empirical equations,
obtained by numerical calculations and scaled down model
tests. It is not iterative, and has the potential to produce very
good results, but it can only be applied to grids with a high
number of conductors. There were many others techniques but
not has relevant has the above. The optimization technique
that stood out was Sverak’s method because it can be applied
to every grounding grid, it is simple and produces good
results.
The optimization of a grounding system can have two
distinct objectives: the grid is not safe so the aim will be to
ensure that it meets the tolerable values for step and touch
voltages, or the grid is already safe so the goal is to reduce the
amount of conductive material buried in order to reduce the
costs involved without compromising the security. This last
question has taken on a really importance these days because
of the difficult economic situation in which the country finds
itself.
The author developed a program (OPTIMA) [13] that has
the potential to analyze and optimize grounding grids. The
program was written in Matlab. One of its potentialities is to
analyze grounding grids in terms of the surface potential
distribution and the step and touch voltages. That allows
inferences about their safety or not. The method used to
analyze the profiles of potential distribution considers the
situation of non-uniform current density throughout the grid.
The methods presented in most of the literature make the
approximation that the fault current is distributed evenly
across the grid. But this situation does not represent the exact
reality, since the distribution of fault current through the grid
conductors varies dependently on the proximity of parallel
conductors of line crossings and the angle between
conductors. In addition, the method of analysis allows the user
to consider uniform or stratified (two layers) soil and also the
placement of grounding rods in several different
configurations, but it considers only its placement in the first
layer of the soil.
The optimization method developed, which is the principal
added value of this work, uses two different techniques. On
the one hand, uses a technique developed by Sverak variable
spacing, with some slight modifications, on the other uses the
placement of grounding rods, which is another important
optimization technique. The variable spacing technique
modifies the spacing between parallel conductors, shifting the
conductive material from the center to the periphery, which
has the highest current densities. The placement of grounding
rods allows a more effective flow of current in depth. These
two techniques are combined in an optimization method that
aims to find the grounding grid that uses the minimum amount
of conductive material necessary to respect the step and touch
voltages limits.
II. OPTIMIZATION METHODOLOGIES
1) Variable space technique
The variable spacing technique used in the program was
originally proposed by Sverak [6]. In an attempt to resolve the
well know fact that the touch voltages are higher in the corners
of the grid that those in the center, the proposed technique has
the basic idea of placing conductive material where it is
needed, thus moving conductive material to the periphery of
the grid. The center will have less conductive material, which
does not cause problems. This technique is an iterative process
that starts with an equally spaced grid that does not meet the
safety criteria, and introduces changes in the spacing between
successive conductors, until the grid can meet the safety
criteria. As a part of the optimization method developed in this
work this technique will be used with some modifications. The
objective of the method is to maximize the optimization
process so it will be used the maximum number of iterations in
Sverak’s method, 5 iterations. In a grid with a high density of
conductors this is the number that allows the optimization
process to take place, without violating the touch voltage limit
in the center of the grid. In each iteration i, the method
performs steps 1 through 6. The expression in step (1) derives
T
2
from the IEEE empirical formula to determine the correction
factor for grid geometry Ki. This corrective coefficient
simulates the effect of non-uniform current density along the
grid conductors, increasing from the grid center toward the
perimeter. This expression has been object of change trough
the years and its more recent version is presented in [1].The
step’s (2) expression determines the factor (A) for the
respective iteration that will be used in (3) to remove points of
a curve (Kci's). These points will be used to determine
distances (KDik's) in step 4. In step 5 the distance Di is
calculated, which will be used in the next step (6) to adapt the
distances KDik to the studied grid.
1. Calculate Kii for iteration i and for each spacing k, in the
vertical or horizontal direction:
1)(k1)0.172(n0.65K iki
where n is the total number of meshes in the given
direction .
2. Determine the A factor:
)10
i(0.9Ai
3. Find Kci for each spacing k in the given direction:
ici AK(1.3Kiik)
k
4. Find KDik for each spacing k in the given direction:
Kcik1
1DikK
5. Find the base distance:
n
1k
DikKD
Li
where L is the grid side length in the given direction.
6. Find the length of each spacing:
kk Diii KDL
Let’s consider the substation grounding grid
presented in figure 1, as the example to see how this method
works. The ground fault current is 2.5 kA, the soil’s first layer
has 10 m of length and resistivity of 200 Ω.m, the second
layer resistivity is 400 Ω.m, the depth of ground grid
conductors is 0.5 m, the area to be grounded is 120x70 m2 and
the spacing between parallel conductors is 10 m. The result of
the Sverak’s method (S.M.) is displayed in figure 2.
Grid
Resistance [Ω] Step Voltage [V]
Touch Voltage [V]
Before S.M. 1.6432 116.5 615.5
After S.M. 1.5852 | -3.5 % 117.9 | +1.2% 523.0 | -15%
From de results of table 1 it’s possible to see that Sverak’s
method causes a reduction of 15% on the touch voltage, which
is achieved only by the modification of the space between
parallel conductors.
2) Grounding Rods Collocation
The use of grounding rods is a common practice among the
grounding grid designers, in an attempt to reduce the surface
potential distributions.
The number of rods and their location will influence the
behavior of the grid. There are several studies on that
influence, as in references [7] and [8]. As stated in [7], the
grounding rods are good current drains, as the values of
current density are higher than average values of horizontal
conductors.
2.1) In this study it will be compared five different
configurations of grounding rods placement. The objective is
to determine the influence that different configurations have
on the following parameters: grid resistance, step and touch
voltages. It is used the grid presented on figure 2 and the
ground rods have 7 m in length. The results are shown in
figures 3, 4, 5, 6, 7 and table 2.
Rods on all intersections of the periphery – Configuration
1
(1)
(2)
(4)
(5)
(6)
(3)
Fig.5 – Configuration 3
Fig.3 – Configuration 1
Fig.1 - Grid before Sverak’s Method
Fig.2 - Grid after Sverak’s Method (5 iterations)
Table 1 – Results of the grids in figures 1 and 2.
3
Rods on all intersections – Configuration 2
Rod on all intersections plus midles of the periphery –
Configuration 3
Rods on all intersections of the periphery, plus 8 rods on
the grid’s corners – Configuration 4
Rods on the corners and the middles of the periphery –
Configuration 5
The reductions are calculated based on the values of
table 1 (after S.M.).
- The introduction of grounding rods causes a
noticeable reduction of the three parameters under study, grid
resistance, step and touch voltages, in all configurations.
- This reduction is more evident in the touch voltage,
in configuration 2 the voltage drop from 523 V to about 323V.
- Configuration 3 is the one that has the lower values
of resistance and step voltage.
- Configuration 2 it’s the one that has the lower touch
voltage value, followed by configuration 1.
- Comparing now configurations 1 and 4 (which is
similar to 1 but has 8 more rods in the corners) it appears that
the introduction of these eight additional conductors has
advantages in reducing the grid resistance and step voltage,
but causes an increase on the touch voltage.
- Configuration 5 has a better ratio between the
addition of conductive material and the gains in terms of touch
voltage.
The optimization method developed will include two
configurations, so it has to be chosen two of the above
represented. For this choice one has to take into account that
the program aims to reduce the material used in the
construction of the grid and that the most crucial parameter of
those three is the touch voltage because it is the one that
usually exceeds the security values. So taking into account the
conclusions listed above, are selected the configurations 1
(rods on the periphery) and 5 (rods at the corners and middles)
for the following reasons: configuration 5 achieves a good
touch voltage reduction with little added material;
configuration 1 has lower touch voltage comparing with 3 and
4, with less material. The configuration 2 is not used because
the gain that it has in terms of touch voltage reduction does
not justify for the additional material it uses.
2.2) Now it will be done a study about the effect that the
increasing of grounding rods length has on the following
parameters: grid resistance, step and touch voltages. The grid
used for the study is the one in figure 1, equally spaced. It is
used configuration 1 of grounding rods, rods on all
intersections of the periphery. The rods length considered are
from 1 meter to 9 meters. The results are shown in table 3,
which are represented graphically in figure 8 (the values were
normalized for an easy comparison).
Fig.6 – Configuration 4
Fig.7 – Configuration 5
Fig.4 – Configuration 2
Table 2 – Results for the different grounding rods configurations
Grid Resistance|
Reduction (%)
Step Voltage [V] | Reduction
(%)
Touch Voltage [V] | Reduction
(%)
Additional Material
(%)
Conf_1 1.5230 | 3.9% 83.7 | 29% 328.8 | 37.1 % 12.45%
Conf_2 1.5168 | 4.3% 79.7 | 32.4% 322.7 | 38.3% 28.02%
Conf_3 1.4910 | 5.94% 76.6 | 35.0% 409.2 | 21.8 % 22.15%
Conf_4 1.5116 | 4.64% 81.2 | 31.1% 401.3 | 23.3% 14.69%
Conf_5 1.5683 | 1.07% 110.9 | 5.9% 377.2 | 27.88% 2.9%
Fig.5 – Configuration 3
4
As would be expected the increase of the rods length
causes a reduction in the three parameters studied here.
Looking at figure 8 it becomes clear that the use of grounding
rods as little effect on the grid’s resistance. The most obvious
reductions are found on step and touch voltages, with a
slightly larger reduction on the first.
For the program developed it has to be chosen two
sizes of grounding rods. As the program has to consider the
limitation that the rods are entirely in the first layer, one
cannot choose two fixed sizes, so it is chosen the following
rod lengths:
- h/2 rounded to the next lower;
- h-1;
h being the thickness of the first layer.
III. PROPOSED OPTIMIZATION METHOD
1) Description and Flowchart
The method described in the flowchart (figure 9)
consists on the following: it’s given as input an equally spaced
grid without grounding rods, as well as the other problem data.
Then it is carried out an optimization by Sverak’s method to
take advantage of all benefits associated with this technique.
Step and touch voltages are calculated and are tested to see
whether the values are below or above the tolerable values.
There are two possible results, which will decide which path it
will be taken:
- Voltages below the tolerable values;
- Voltages above the tolerable values.
Results below the tolerable values:
The basic idea is to remove material, one conductor
each direction, then the grid is optimized (Sverak’s method),
and it’s step and touch voltages are calculated. If the results
are below the limits, repeat the procedure. This will end when
it is obtained a grid, optimized in terms of spacing, which does
not respect the limits. At this point, the information about the
number of conductors each direction is available. It is around
this number that it will be found the optimal configuration. So
it will be tested a group of grid configurations with and
without grounding rods with a number of conductors around
the obtained number. Then the configurations are compared in
order to see which one requires less material and respects the
tolerable voltage limits. That will be the optimal grid. Table 4
exemplifies the tested configurations.
Results above the tolerable values:
The basic idea is similar to the above explained, but
in this case it will be added material, one conductor each
direction to obtain a grid that respects the tolerable limits.
Then a group of grid configurations will be tested with a
number of conductors around the obtained. The resulting grid
from this process is the one that uses less material and respects
the tolerable voltage values. Table 4 will present the tested
configurations.
The configurations tested on 6 and 6' are the same
type. From 4 and 5 results a grid that does not meet the safety
criteria, let’s consider this the axb grid. From 4 'and 5' results a
grid that meets the safety criteria, grid cxd. Considering now a
grid (Nc_x)x(Nc_y), it is obtained: Nc_x = a+1 or Nc_x = c;
Nc_y = b+1 or Nc_y = d;
Grid Resistance
[Ω]
Step Voltage [V] Touch Voltage
[V]
Rods 1 m 1.6292 111.0 583.8
Rods 2 m 1.6177 105.3 554.5
Rods 3 m 1.6071 99.9 528.1
Rods 4 m 1.5970 94.9 504.4
Rods 5 m 1.5872 90.3 483.2
Rods 6 m 1.5776 86.2 464.0
Rods 7 m 1.5683 82.4 446.7
Rods 8 m 1.5591 79.1 431.1
Rods 9 m 1.5502 76.0 417.0
Table 3 – Results considering rods with different lengths
Fig.8 – Graphical representation of table 3 results
Fig. 9 – Optimization Method Flowchart
5
Conf. Conductors in x
direction Conductors in y
direction Rods conf.
Rods length
1 Nc_x Nc_y 0 0
2 Nc_x-1 Nc_y-1 1 h/2
3 Nc_x-1 Nc_y-1 1 h-1
4 Nc_x-1 Nc_y-1 2 h/2
5 Nc_x-1 Nc_y-1 2 h-1
6 Nc_x-1 Nc_y 0 0
7 Nc_x-1 Nc_y 1 h/2
8 Nc_x-1 Nc_y 1 h-1
9 Nc_x-1 Nc_y 2 h/2
10 Nc_x-1 Nc_y 2 h-1
11 Nc_x-2 Nc_y-2 1 h/2
12 Nc_x-2 Nc_y-2 1 h-1
13 Nc_x-2 Nc_y-2 2 h/2
14 Nc_x-2 Nc_y-2 2 h-1
15 Nc_x-2 Nc_y-1 1 h/2
16 Nc_x-2 Nc_y-1 1 h-1
17 Nc_x-2 Nc_y-1 2 h/2
18 Nc_x-2 Nc_y-1 2 h-1
2) Application Examples
The substation grounding grid taken as the base case
(figure 10) is an equally spaced grid, with 21 conductors in
each direction and has no rods. In this example the ground
fault current is 1.8 kA and duration time 0.6 s, the soil’s first
layer has 10m of thickness and resistivity of 400 Ω.m, the
depth of ground gird conductors is 0.5m, the area to be
grounded is 70x70 m2 and the spacing between parallel
conductors is 3.5 m. The gravel layer put on the soil’s surface
has 2500 of resistivity and 0.1 m of thickness.
With this information the developed program
calculated the following values:
Tolerable step voltage: 2461.2 V
Tolerable touch voltage: 767.3 V
Total conductor length: 2940 m
The optimization method will be applied to this grid
considering three different situations:
1. Second layer resistivity = 200 Ω.m;
2. Second layer resistivity = 400 Ω.m (homogeneous
soil);
3. Second layer resistivity = 800 Ω.m.
The results obtained by the method were:
1. Second layer resistivity = 200 Ω.m;
R [Ω] UTMax [V] USMax [V] L [m] |
Reduction (%)
I.P. 1.6786 484.8 305.9 2940
O.P. 1.8160 742.0 249.2 1100 | - 62.6
I.P. - Initial project;
O.P. – Optimized project;
R - Grid resistance;
UTMax - Maximum touch voltage value;
USMax - Maximum step voltage value;
L -Total conductor length;
2. Second layer resistivity = 400 Ω.m (homogeneous soil);
R [Ω] UTMax [V] USMax [V] L [m] |
Reduction (%)
I.P. 2.5124 575.6 364.7 2940
O.P. 2.6029 584.0 218.3 1580 | - 46.3
Table 4 – Tested configurations on the optimization method
Fig. 11 – Optimized grid obtained for case 1
Fig. 10 – Base case grid
Table 5 – Results for the optimized grid obtained in case 1
Table 6 – Results for the optimized grid obtained in case 2
Fig. 12 – Optimized grid obtained for case 2
6
3. Second layer resistivity = 800 Ω.m
In all three cases the grounding rods have 5m longs.
- The results obtained show that the optimization method
developed made possible material savings in all three
cases. That reduction is more evident in case 1, were it
was possible to use less 62.6 % of conductive material.
- All grids obtained respect the tolerable voltage values.
- It is possible to see that in all three cases the grid
resistance increased, which was caused by the reduction
of the used material. As a consequence the ground
potential rise increased (G.R.P. = Grid resistance * Total
current)
- By using the optimization techniques the surface potential
distribution become more uniform. The last is the reason
why the step voltage decreased, in all cases.
- The touch voltage is the result of the subtraction between
the ground potential rise and the point at the surface
where the potential is the lowest. In the optimization
process the conductive material is removed and, as a
consequence, the potential distribution values at the
surface become higher. So the touch voltage depends on
those two parameters. That’s the reason why in the first
two cases it increased, because the G.P.R. increase was
higher than the potential increase, and in the last case (3)
it was the opposite situation, so the touch voltage
decreased.
- It is possible to see from figs. 11, 12 and 13 that the
density of the grid is proportional to the second layer
resistivity, when the resistivity is 200 Ω.m the grid is 7x7
and when the resistivity is 800 Ω.m the grid is 16x16.
When the resistivity increases it is more difficult to drain
the current, which causes the need for more conductive
material.
- The final result of the optimization method depends on
the grid data. It is possible to see that case 1 uses more
grounding rods than the other two. That final result can be
a grid with or without rods, and is the grid that for the
particular situation uses less material and still respects the
tolerable values.
IV. CONCLUSIONS
In this paper the computer program OPTIMA is
presented [13]. The algorithm implemented has the potential
to optimize a grounding grid by combining two techniques,
Sverak’s method (variable space technique) and the placement
of grounding rods. This optimization is supported by an
analysis method that allows the calculation of step and touch
voltages, grid resistance and the potential distribution at the
surface.
This paper discusses two different optimizations
techniques that are combined in the optimization method:
Sverak’s method, variable space technique, modifies
the space between parallel conductors. With this
simple trick it is possible to achieve a high reduction
of the touch voltage, which is the optimization main
objective since this parameter is the one that often
violates the limits.
Introduction of grounding rods. In this matter, the
paper shows two studies. In the first, it is proved that
it is on the grid’s periphery that the rods are more
necessary and produces the best results. In the second
it is proved that the increases on the rods length
causes an evident reduction on the step and touch
voltages, while the grid resistance remains practically
the same. Those two studies are evidence of the
optimization potential of this technique, because it
can cause great reductions on both step and touch
voltages.
The optimization method developed combines the
potential of those techniques and makes a search for the
optimal grid that uses less conductive material and still
respects the tolerable values for the voltages. From the study
example it can be seen that:
The method made possible great savings in terms of
conductive material. The reduction on case 1 was
approximately 63%. This savings represents a great
reduction on project’s budget.
The resistivity of the soil has a large influence on the
optimization’s result. A smaller resistivity originates
a grid with fewer conductors than a soil with a higher
resistivity.
The two optimization techniques combined produce
much better results than using just one of them.
This method is simple to use, produces notable
results and represents a great added value to the
optimization of grounding grids in substations.
R [Ω] UTMax [V] USMax [V] L [m] |
Reduction (%)
I.P. 3.8823 693.2 441.1 2940
O.P. 3.9115 633.1 229.7 2280 | - 22.4
Fig. 13 – Optimized grid obtained for case 3
Table 7 – Results for the optimized grid obtained in case 3
7
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