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
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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.