2770260427702604.pdf

International Journal of Electrical Electronics and Telecommunication Engineering, ISSN: 2051-3240, Vol.44, Issue.2 1143

RECENT SCIENCE PUBLICATIONS ARCHIVES|July 2013|$25.00 | 27702604 |

*This article is authorized for use only by Recent Science Journal Authors, Subscribers and Partnering Institutions*

Optimal Grounding Grid Design to Suit Safety

Conditions

ABSTRACT

Optimization of the grounding grids design is an important

issue to safeguard those people who working in the

surrounding of grounded installations and satisfy the

minimum cost of the design. The optimization process is

carried out using a new application of charge simulation

method (CSM) to calculate the grounding resistance, earth

surface potential and therefore, the touch, step voltages

and the grid design cost. The calculated step and touch

voltages as well as the cost of grid design depend on the

grid dimensions. An evolutionary strategy technique is

used to get the optimization process. Numerical example is

introduced to explain the performance of this method and

to give valuable information about the grid parameters that

satisfy optimization. Experimental Works will be made to

compare between the calculated and measured value of the

optimized parameters. The experimental results explain

that the step and touch voltage of the optimal grid

configuration is less than that at the initial grid

configuration and this is prove of the validation of the

optimization process.

Keywords- grounding grid, charge simulation method, and earth surface potential.

1. INTRODUCTION

Grounding systems constitute one of the most important

parts of building constructions. The grounding systems

resistance has an essential influence on the protection of

grounded system. As it is stated in the ANSI/IEEE [1] 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 ensuring that the person in the

vicinity of grounded facilities is not exposed to the danger

of electric shock.

The most challenging problems stated has been to obtain

the potential distribution in large scale use of electricity as

(large electrical installations) when a fault current is

discharging into the soil via grounding system [2]. The

study of potential distribution leads to the knowing of step

and touch voltage which considered the important

parameters in grounding system design.

The grounding grid impulse characteristics depend on

grounding grid parameters and soil characteristics as well

as on the impulse current shape, magnitude and discharge

point. Some papers interest to study the transient

performance of grounding systems subjected to impulse

current such as lightning and switching [3-5] and a

computerized grounding analysis in uniform and two-layer

soil types became widespread, mainly because of the

enhanced accuracy, speed and flexibility afforded by the

use of computers. Several publications [6-11] have

discussed the analytical methods to calculate earth surface

potential (ESP) and grounding resistance for grounding

grid or rods when uniform and two-layer soils are

involved. Many efforts have been made to measure the

grounding resistance as well as the earth surface potential

using scale model [12-20].

To attain the objectives of grounding systems, 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 earths surface must be kept under certain tolerances (step, touch,

and mesh voltages) [1].

A well known technique that helps to get good accuracies

in field calculation is used. The computation of the Rg and

ESP is based on this technique which is the charge

simulation method [10, 11, 21]. The attractiveness of the

method, when compared with the other analytical methods

such as Finite Element and Finite Difference Methods

emanates from its simplicity in representing the

equipotential surface of the electrodes, its application to

unbounded arrangements whose boundaries extend to

infinity and its direct determination to the electric field

[22]. The major drawbak of the Charge simulation method

is that the number, position and the type of replaced

simulation charges and also the position of selected points

of writing the equation affect on the accuracy of the

method to solve the numerical problems [23]. The other

drawback is the difficulty of the application of the method

when the number of soil layer increased.

The optimization process of the grounding grid design is

accomplished by the evolutionary strategy technique. The

basic design quantities of the grounding grids are the touch

and step voltages as well as the design cost. These

previous quantities depend on the grid dimensions. The

dependence of the design quantities of the geometric

parameters is given by field computation based on

Sherif Ghoneim1,2 IEEE Member

1Faculty of Industrial Education-Suez University Egypt, 2Faculty of Engineering-Taif University KSA,

Email:[email protected]




equivalent charges (CSM). The soil is assumed to be

homogeneous.

2. CHARGE SIMULATION METHOD

The distribution of the earth surface potential (ESP) helps

us to determine the step and touch voltages, which are

very important for human safety. Charge simulation

method is used to calculate the ESP as in illustrated in

Figure 1.

The grid is divided into equal segments by the point

charges distribution along the axis of grid conductors.

Figure 2 shows the distribution of the point charges (dots)

for the grounding grid (1 mesh), the number of point

charges is distributed on the axis of the grid conductors

equally and also the evaluation points distributed on each

conductor as shown in Figure 2. The meshes of the grid

are always symmetrical.

The cross sectional area of conductor required depends on

many parameters like the short circuit current, the specific

heat of material and the ambient temperature. However,

for adequate mechanical strength the minimum area

recommended is 54.48mm squared for cupper, 24 mm

squared for steel and 3mm thickness for steel strips.

Fig. 1: Illustration of the charge simulation method to

calculate earth surface potential

Regarding the conductor material, it must have good

conductivity, be mechanically rugged and is resistant to

underground corrosion. A grid of cupper forms a galvanic

cell with other buried structures and pipes and is likely to

hasten the corrosion of the latter. Aluminum is not used

because of corrosion problem. The material most

commonly used presently is galvanized steel. The zinc

coating gets destroyed over a period of time. It is desirable

that a suitable allowance for corrosion be made when

determining the size of the conductor.

As in Figure 1, the fictitious charges are taken into account

in the simulation as point charges. The charges of the point

charges will be known by applying Eq. 1 [21];

n

j

jiji QP1

(1)

Where, Pij is the potential coefficient which can be

evaluated analytically for many types of charges by

solving Laplace or Poissons equations, i is the potential at contour points; Qj is the charge at the point charge.

The potential coefficients will be as in eq. 2;

ddP

ijij

ij'

11

4

1

(2)

Where, dij is the distance between contour point i and

charge point j and dij is the distance between the contour point i and image charge point j as shown in Figure 1.

The position of each point charges and each evaluation

(contour) point are determined in X, Y and Z coordinates

where the distance between the evaluation (contour) points

and the charge points are calculated as the following ;

Fig. 2: Distribution of point charges on the grid (1 mesh)

2'2'2''

222

ijijijij

ijijijij

ZZYYXXd

ZZYYXXd

where, Xj, Yj and Zj are the coordinates of the point

charge and Xi, Yi and Zi are the coordinates of the contour

point.

After solving eq. 1 by knowing the inverse matrix of Pij,

the magnitude of simulation charges is determined, as

soon as an adequate charge system has been developed,

the potential at any point xx outside the electrodes as

shown in Fig. 1 can be calculated again by using the

following equation;

n

j

jxxjxx QP1

(3)




where, xx is the voltage at the arbitrary point xx, Pxxj is the potential coefficient matrix for the point xx with all

point charges and Qj is the calculated point charges.

By the same way, the earth surface potential everywhere is

calculated. In the same time, the duality expression is used

to get the grid resistance from Eq. 4,

1

CR

V

Q

C

g

n

j

j

(4)

where, C is the capacitance of the grounding grid, V is the

voltage applies on the grid and defined as ground potential

rise (GPR), Qj is the charge of point charge that used for

the calculation, is the soil resistivity and is the soil permittivity.

The ESP is computed using Eq. 3, therefore, the touch and

step voltages will be known. Figure 3, shows the earth

surface potential profile along the diagonal axis for the

following case study: side length of the square grid is 60

m, soil resistivity is 1000 .m, grid conductor radius is 1cm and the grid depth is 0.7 m.

0

1000

2000

3000

4000

5000

6000

7000

8000

-80 -60 -40 -20 0 20 40 60 80

Distance from the grid center (m)

ES

P (

V)

Fig. 3: Earth surface potential per ground potential rise

along diagonal axis for the case of study

3. OPTIMIZATION PROCESS

Figure 4 describes the flow chart of the optimization

process for the grounding grids design. The quality factor

is based on the following parameters, the touch voltage,

safe limit value for touch voltage, step voltage, safe limit

value for step voltage, and the total cost of the design, the

proposed cost of the same case. The quality factor is

calculated according to Eq. 5. Equation 5 explains that the

quality factors depend on the grid parameters and soil

resistivity which are the grid side length and the length of

the vertical rods.

limit safet tlimit safet t

limit safet tlimit safet t

3

limit safe sslimit safe ss

limit safe sslimit safe ss

2

1

321F

VVfor )/V0.1(V-1

VVfor )/V0.9(V-1

VVfor )/V0.1(V-1

VVfor )/V0.9(V-1

cost pro. cost for cost) ro.0.1(cost/p-1

cost pro.costfor cost) ro.0.9(cost/p-1

,

Q

Q

Q

QQQQ

(5)

where, QF is the total quality factor, Vt, Vs are the

calculated touch and step voltages, Vt safe limit, Vs safe

limit are the safe limit of touch and step voltages for the

case study. The pro. Cost is the proposed cost. The cost,

step and touch voltages are function in the grid dimensions

and soil resistivity, also the proposed cost, safe limit of

step and touch voltages are function in grid dimensions

and soil resistivity,

The objective functions which define the relations between

the quality factors (Q1, Q2, Q3) and the design cost, touch

and step voltages respectively are illustrated in equation

(5) as well as Figure 5.

The optimization process is carried out as the following:

1. The first step is determining the cost, step and touch voltage of the grid at initial dimension.

2. Calculate the safe limit of step and touch voltage and suggest the proposed cost of design.

3. Calculate the quality factor (QF) of the grid at the initial dimension.

4. The ten generations of new grids will develop using random function and the new quality

factors of these grid generations are determined.

5. A comparison of these quality factors of the ten grid generations is made and takes the best grid

generation that has best quality factor.

6. A comparison between the quality factor of the best grid generation and the quality factor of the

initial grid is made.

7. When the quality factor of best grid generation is greater than that at initial grid, the best grid

generation will be taken as the new initial grid

and the search radius will increase to search about

another best grid generation. The search radius is

taken as 0.25 of the initial grid dimension and it

will increase as the designer want, i.e 10% for the

next generation, assume that the initial grid is

40m*40m, so, the search radius is 10m (25% of

the initial grid) and then this radius will increase

in this case with 1 m (10% of the search radius).

8. When the quality factor of the best generation is lower than that at initial grid, the initial grid will

be taken as the best and the search radius will

decrease with 10% of the search radius to search

about another best generation.




9. When the search radius decreases and reach specified limit, the optimization process will be

stopped.

10. It takes into account that the area of the new grid generation doesn't exceed 1.5 of the area of the

initial grid.

Start

Start values side length of grid and length of vertical

rods connected to it if available, radius of grid

conductors, Number of meshes, Depth of grid,

Soil resistivity, Permitivitty, and Starting search points

Calculate the initial quality

factor from the data given

Create new dimensions of grid

using random function to get N

next generations

Calculate the quality factor for each of the

N next generation

Is there a better

solution

Put quality factor and

corresponding grid

dimensions as the better

solution and then increase

the search pointsDecrease the search points

Is search points less than

limits

End

YesNo

Yes

No

Fig. 4: Flow chart of the program based on evolutionary

strategy to optimize the grounding grid design

Q1

Cost

1

Proposed cost

(a)

Q2

Touch voltage

1

Safe limit touch voltage

(b)

Q3

Step voltage

1

Safe limit step voltage

(c)

Fig. (5a, b, c): The relationships between the quality

factors and (cost, Vt, Vs)




4. NUMERICAL EXAMPLE

The next numerical example is produced to explain the

input and output data for the application and how this

application helps us to give the optimization design of

grounding grid that satisfies the safe condition for people

who are working or walking in the surroundings of the

grounded installations and also good economical results.

Starting values of the grid configuration:

Number of meshes (N) = 16, no of point charges=1000

points, side length of the grid in x direction (X) = 60 m,

side length of the grid in y direction (Y) = 60 m, grid

conductor radius = 10 mm, vertical rod length (Z) = 0 (no

vertical rod), depth of the grid (h) = 1 m, resistivity of the

soil ( 200 .m, the threshold value of safe touch and step voltages are computed as in reference [1] and taking

into account that the back up fault clearing time is 1 s with

the soil resistivity 1000 .m (uniform soil). The safe limit of the touch and step are Vtsl = 204 V and Vssl = 345 V,

the proposed cost is assumed 1000 Euro, for optimization

process, the search radius is 0.25 of the variation

parameters, the number of next generations is 10.

Table I shows the values of touch, step voltages and the

cost at the starting of the design and after using the

optimization algorithm.

Table I: Cost, Touch And Step Voltages For 16 Meshes

Grid

Vt

(V)

Vs (V)

Cost

(Euro)

Dimension for

16 meshes grid

Starting

design 248 152 388 60*60 m2

Optimized

design 200 144 450 76*82 m2

The cost of the optimized design is higher than that at

starting design but is still lower than the proposed cost.

The very important issue for the optimization that the

touch and step voltage must be lower than the safe limit

value. From the table, the optimization algorithm helps to

decrease the touch voltage under the safe limit value and

keep the cost lower than the proposed cost.

Dawalibi in [24] explained that the effect of grid

conductor radius on earth surface potentials, is negligible

(at least, when the radius varies from 005m to 0.25m).

However the resistance decreases moderately when the

conductor radius is increased (a 25% resistance decrease

when radius is increased from 0.005m to 0.25m).

Therefore the radius of the conductor is constant at the

processing of the optimization.

The process of optimization will stop when the new grid

area exceeds 1.5 of the area of the initial condition.

5. EXPERIMENTAL WORK

The technique of using scale models in an electrolytic tank

to determine the surface potential distribution during

ground faults was introduced in many papers [12-20].

Dimensional analysis and Similarity Theory are closely

related and are used in experiments with models. In such

experiments, one replaces the investigation of a

phenomenon in nature by the investigation of an

analogous phenomenon in a model of smaller or larger

scale (usually under special laboratory conditions). If the

similarity conditions are fulfilled, it is necessary to know

the scale factors for all the corresponding quantities in

order to calculate all the characteristics in nature from data

on the dimensional characteristics in the model [20].

The purpose of the scale model experiment is to satisfy the

optimization process by using some scaled cases for initial

and optimal grid configurations to see if the step and touch

voltage is reduced or not. The elements of the

experimental setup are; Electrolytic tank that simulates the

homogenous earth with dimensions 75cm long, 75cm

wide, and 50cm height as in Figure 6, Powers supply (AC

or DC), some voltmeters and ammeter devices. The scale

factor between the reality and scale model is taken as

100:1. Distilled water with salted tap water is used as an

electrolyte, which serves as an adequately conducting

medium, representing the homogeneous earth and its

resistivity is 7.63 ohm.m. Change in the salinity causes a

change in the liquid resistivity. The initial case of the

grounding grid is 40 cm*40 cm grid and optimal case is 46

cm*46 cm. The following Table II depicts the variation of

the step and touch voltages between two cases. Figures 7

and 8 explain the ESP for the initial and optimal grid and

from these figures the step and touch voltage will be

computed as in table II.

Fig. 6: The Experimental setup

0

5

10

15

20

25

30

-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50

Distance from the center of grid (m)

ES

P(V

)

Fig. 7: The ESP of the initial grid configuration

(40cm*40cm)




0

5

10

15

20

25

-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50

Distance from the center of grid (cm)

ES

P (

V)

Fig. 8: The ESP of the optimal grid configuration

(46cm*46cm)

Table II: Touch and Step Voltages For 16 Meshes Grid

Vtmax (V)

Vsmax (V)

Depth

h (cm)

Dimension

for 16

meshes grid

Starting

design

5.6 1 0.5 40*40 cm

Optimized

design

4.3 0.5 0.5 46*46 cm

6. CONCLUSIONS

The paper aims to explain a practical technique which can

be used to calculate the earth surface potential (ESP) due

to discharging current into grounding grid. This technique

based on the charge simulation method (CSM). An

important advantage of CSM is the high accuracy of

potential field calculations which can be achieved without

large computational effort.

The use of an evolutionary computation (EC) technique

for the optimization of a grid design algorithm allows for

the attainment of optimal fitness (i.e. the best choice of

parameter values) through an automated process.

The experimental results explain that the step and touch

voltage of the optimal grid configuration is less than that

at the initial grid configuration and this is prove of the

validation of the optimization process.

REFERENCES

[1] IEEE Guide for safety in AC substation grounding,

IEEE Std.80-2000.

[2] I.Colominas, F.Navarrina, and M.Casteleiro,

Improvement of the computer methods for grounding analysis in layered soils by using high-

efficient convergence acceleration techniques Advances in Engineering Software 44 (2012), pp.

8091.

[3] F. Dawalibi, '' Electromagnetic Fields Generated by

Overhead and Buried Conductors''. Part I. Single

Conductor. Part II- Ground Network, IEEE

Transactions on Power Delivery, Vol. PWRD-1,

October 1986, pp. 105-119.

[4] M.I.Lorentzou, N. H.Hatzairgyriou, B. C. Papadias,

''Time Domain Analysis of Grounding Electrodes

Impulse Response'', IEEE Transactions on Power

Delivery, Vol. 18. No. 2. April. 2000, pp. 517-524.

[5] Alain Rousseau and Pierre Gruet "Measurement of

a lightning earthing system", SIPDA 2005.

[6] J.M.Nahman, V.B.Djordjevic, Nonuniformity correction factors for maximum mesh and step

voltages of ground grids and combined ground

electrodes, IEEE Trans. Power Delivery, Vol. 10, No. 3, Jul. 1995, pp. 1263-1269.

[7] Cheng-Nan Chang, Chien-Hsing Lee, Computation of ground resistances and assessment of ground

grid safety at 161/23.9 kV indoor/type substation, IEEE Transactions on Power Delivery, Vol. 21, No.

3, July 2006, pp. 1250/1260.

[8] J.A.Gemes, F. E.Hernando Method for calculating the ground resistance of grounding grids using

FEM, IEEE Transaction on power delivery, Vol. 19, No. 2, April 2004, pp 595-600.

[9] F.Navarrina, I.Colominas, Why Do Computer Methods for Grounding Analysis Produce

Anomalous Results?, IEEE Transaction on power delivery, Vol. 18, No. 4, October 2003, pp 1192-

1201.

[10] 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, January 2004, pp

118-123.

[11] S.Serri Dessouki, S. Ghoneim, S. Awad," Ground

Resistance, Step and Touch Voltages For A Driven

Vertical Rod Into Two Layer Model Soil",

International Conference Power System

Technology, POWERCON2010, Hangzhou, China,

October 2010.

[12] S.Serri Dessouki, S. Ghoneim, S. Awad," Earth

Surface Potential For Scaled Vertical Rod Into Two

Layer Soil Model", 17th ISH2011, Hanover-

Germany, August 2011.

[13] B.Thapar, S. L. Goyal, Scale model studies of grounding grids in non-uniform soils, IEEE Transactions on Power Delivery, Vol. PWRD-2,

No. 4, 1987, pp. 1060-1066.

[14] C.S.Choi, H. K. Kim, H. J. Gil, W. K. Han, and K.

Y. Lee, The potential gradient of ground surface according to shapes of mesh grid grounding

electrode using reduced scale model, IEEJ Trans.




On Power and Energy, Vol. 125, No. 12, pp. 1170,

2005.

[15] B.Thapar, K.K.Puri, Mesh Potential in high voltage station grounding grids, IEEE Transaction on Power Apparatus and Systems, Vol. Pas-86, 1967,

pp. 249-254.

[16] A.Elmorshedy, A. G. Zeitoun, and M. M. Ghourab,

Modelling of substation grounding grids, IEE Proceedings, Vol. 133, Pr. C, No. 5, July 1986.

[17] I.F.Gonos, Experimental study of transient behavior of grounding grids using scale model, Measurement science and Technology. 17 (2006),

pp. 2022-2026.

[18] R.Caldecott, D.G.Kasten, Scale Model Studies of Station Grounding Grids, IEEE Trans. Power Apparatus and Systems, Vol. PAS-102, No. 3,

1983, pp. 558-566.

[19] S.Ghoneim, H.Hirsch, A.Elmorshedy, R.Amer,

"Measurement of Earth Surface Potential Using

Scale Model", UPEC2007, Brighton University,

England, September 2007.

[20] L.I. Sedov, Similarity and Dimensional Methods in

Mechanics, Science Press, Beijin (1982) (in

Chinese).

[21] 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.

[22] M.Abdelsalam High voltage Engineering- Theory and Practice, 2nd edn, 2000.

[23] J.Faiz and M.Ojaghi,"Instructive Review of

Computation of Electric Fields using Different

Numerical Techniques", Int. J. Engng Ed. Vol. 18,

No. 3, 2002, pp. 344356, printed in Great Britain.

[24] F.P.Dawalibi, D.Mukhedkar ''Parametric analysis of

grounding grids'' IEEE Transactions on Power

Apparatus and Systems, Vol. PAS-98, No. 5,

Sep/Oct 1979, pp. 1659-1667.

2770260427702604.pdf

Documents

Transcript of 2770260427702604.pdf