optimization design of substation grounding grid design of substation grounding grid ... he...

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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.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).




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%


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);


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



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.


Reduction (%)

I.P. 3.8823 693.2 441.1 2940

O.P. 3.9115 633.1 229.7 2280 | - 22.4



7

REFERENCES

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Grounding in a two Layer Earth Structure- Part I analytical study”, IEEE

Transactions on Power Apparatus and Systems, Vol. PAS-94, No. 2, pp. 252-261, Março/Abril 1975.

[3] Dawalibi, F.; Mukhedkar D.; “Optimum Design of Substation

Grounding in a two Layer Earth Structure- Part II”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-94, No. 2, pp. 262-266,

Março/Abril 1975.

[4] Dawalibi, F.; Mukhedkar D.; “Optimum Design of Substation Grounding in a two Layer Earth Structure- Part III”, IEEE Transactions

on Power Apparatus and Systems, Vol. PAS-94, No. 2, pp. 266-272,

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Grounding Electrodes”, IEEE Transactions on Power Apparatus and

Systems, Vol. PAS-95, No. 1, Janeiro/Fevereiro 1976. [6] Sverak, J.G.; “Optimized Grounding Grid Design Using Variable

Spacing Technique”, IEEE Transactions on Power Apparatus and

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Grids”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-

98, No. 6, Nov./Dez. 1979. [8] Sverak, J.G.; “Simplified Analysis of Electrical Gradients Above a

Grounding Grid, Part I: How Good is the Present IEEE Method?”, IEEE

Transactions on Power Apparatus and Systems, Vol. PAS-103, No. 103, pp. 7-25, Janeiro 1984.

[9] “INSTALAÇÕES AT E MT. SUBESTAÇÕES DE DISTRIBUIÇÃO”,

EDP distribuição, Fevereiro 2007. [10] Heppe, R. J., “Computation of potential at surface above an energized

grid or other electrode, allowing for non-uniform current distribution”,

IEEE Transaction on Power Apparatus and systems, Vol. Pas-98, No. 6,

Nov./Dec. 1979, pp. 1978-1989.

[11] F. Dawalibi, D. Mukhedkar, “Behaviour of Grounding Systems in

Multilayer soils: A Parametric Analysis”, IEEE Transactions on Power Delivery, Vol. 9, No. 1, January. 1994, pp. 334-342.

[12] Huang, L.; Chen, X.; Yan, H.; “Study of Unequally Spaced Grounding

Grids”, IEEE Transactions on Power Delivery, Vol. 10, No. 2, pp. 716-722, Abril 1995.

[13] Filipe, N., “Optimização de terras em subestações”, (in portuguese)

Master Thesis on Electrical and Computers Engineering, October 2011.

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