Modelling of substation grounding gridsA. El-Morshedy, Ph.D., A.G Zeitoun, Ph.D., and M.M. Ghourab

Indexing terms: Modelling, Transmission and distribution plant, System protection

Abstract: The aim of this study is to perform scale model tests on various grounding grids with and withoutground rods to determine their effective resistance to ground and the surface potential distribution duringground faults. The results obtained from the scale models will provide guidelines for accurate and safe design ofmodern complex grounding systems of AC substations.

1 Introduction

In modern extra-high-voltage and ultrahigh-voltage ACsubstations, grounding has become one of the dominantproblems of system design. It is essential to have an accu-rate design procedure for the grounding system. Ground-ing is of major importance to increase the reliability of thesupply service as it helps to provide stability of voltageconditions, preventing excessive voltage peaks during dis-turbances, and also a means of providing a measure ofprotection against lightning.

It is required that the voltage rise during a fault be keptto low levels. This dictates that ground resistances in high-voltage substations must be very low. The most commonmethod of obtaining low values of ground resistance athigh-voltage substations is to use interconnected groundgrids. A typical grid system for a substation comprises 4/0bare standard copper cable buried at a depth of from 30 to60 cm parallel to the surface of the earth and spaced in agrid pattern of about 3 to 10 m. At each junction of 4/0cable, the cables are securely bonded together [1]. Such agrid not only effectively grounds the equipment, but hasthe added advantage of controlling the voltage gradients atthe surface of the earth to safe values for human contact.Ground rods may be connected to the grid to have lowvalues of ground resistance when the upper layer of soil inwhich the grid is buried is of much higher resistivity thanthat of the soil beneath.

The best configuration of the grounding grid requiresstudying the effect of the parameters usually encounteredin practice. Such parameters are the length of the ground-ing grid, the number of meshes in the grid, the diameter ofthe grounding conductor, the depth of burial of the gridand the effect of using ground rods. It is impractical toinvestigate the effect of these parameters on full-size gridsbecause of the lack of controlled conditions and variationsin soil resistivity at the site. Scale models offer a practicaland inexpensive alternative solution. Scale model tests aregenerally employed to determine grounding resistance andsurface potential distributions during ground faults in thecase of complex grounding arrangements where accurateanalytical calculations are seldom possible [2-4].

The approximate formula for the percentage meshpotential given in Reference 3 indicates that if all dimen-sions of the grid are reduced by the same factor, the per-centage mesh potential remains unchanged. The shape ofcurrent and equipotential surfaces are unaltered. There-fore, it is possible to simulate the actual grounding gridswith the help of scale models and the potential profilesmeasured on a model may be used to determine the corre-sponding potentials on a full-scale grid.

Paper 4670C (P8, P9), first received 6th January and in revised form 8th April 1986

Dr. El-Morshedy and Dr. Zeitoun are with the Department of Electrical Engineer-ing, Faculty of Engineering, Cairo University, Cairo, Egypt. Mr. Ghourab is withthe Department of Electrical Engineering, Suez Canal University, Egypt

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 5, JULY 1986

2 Electrolytic tank

The dimensions of the electrolytic tank used for the experi-ments are 1.70 m x 1.00 m x 1.10 m. The inner surface ofthe tank is covered by a conducting sheath. Tap water hasbeen used as the electrolyte which serves as an adequatelyconducting medium and represents homogenous earth. Itselectric resistivity, as determined by the 4-electrodemethod, is 27 Qm.

The model grid was supported below the surface of theelectrolyte under tension so as to provide a horizontalconfiguration with the minimum distortion and sag. Nylonfish lines were attached to the grid, at different locations,to maintain the regular shape of the grid. To take mea-surements, a probe consisting of a copper wire inserted ina plastic tube, for mechanical support, was used. Only thetip of the wire was touching the surface of the water. Theprobe was supported on a 'T'-shaped wooden frame whichrested on the edges of the tank and could be moved acrossthe surface of the electrolyte at a constant depth in astraight line in any direction over any part of the grid.Scales mounted along the tank edges permitted accuratepositioning of the grid and probe.

3 Experimental layout

The experimental layout is shown in Fig. 1. An alternatingcurrent is used to avoid polarisation. The applied voltage

AC V C\\

t ank -

return melectrode

1 \JS

\£)probe

..water level

r ^ . l

Fig. 1 Experimental layout

to the model is obtained from a 220 AC source through avariac. The magnitude of this voltage is kept constantduring the different tests.

By measuring the voltage applied to the model and thecurrent flowing through the electrolyte between the modelgrid and the return electrode, the effective grid resistancecan be obtained. The potential of the test probe withrespect to the return electrode is monitored by a voltmeterof a very high internal resistance.

287

4 Scale factor selection

There are several points in choosing the proper scale factorfor the model grids. One of these is the maximum size gridwhich could be accommodated in a given size tank.Another is the original specifications for this grid.

A scale factor of 100 :1 is a convenient choice for thesize of grid used. Typical grid conductors are made for 4/0copper, with a diameter of 1.35 cm. The conductor diam-eter of the model is 0.135 mm, but this size of wire is notavailable and it is difficult to construct a model with thissmall diameter. A few tests showed that it is not necessaryto scale the wire diameter by the same scale factor as theother grid dimensions. This will be discussed later inSection 6.4. As the wire diameter is always small comparedwith the mesh spacing, a change in wire diameter has noeffect on the potential profiles. Thus all model grids aremade of 1 mm conductor diameter, which is available, andit is also easy to build models with this diameter.

A few tests were carried out to determine the maximumsize of a model grid which can be used in the tank avoid-ing the distortion of the electric field due to the tank walls.It is concluded that the maximum size of the model gridused must be 25 cm x 25 cm to minimise boundary effectsdue to the tank walls.

5 Test procedures

The grid was first installed and adjusted to the properdepth. The grid was then energised and the voltages andcurrents were monitored and the grid resistance could beobtained. The probe carriage was aligned over the centreline of the grid. The potential values were recorded atintervals of 2 cm starting from the grid centre and endingat approximately 10 cm outside the grid. The positionsconsidered cover the area of one quarter of a grid, due tosymmetry.

6 Test results

For a scale factor of 100 :1, a variety of grids with outsidedimensions 10 m x 10 m, 20 m x 20 m, 25 m x 25 m and10 m x 20 m were modelled and tested in uniform soil.The effect of changing the parameters usually encounteredin practice was examined. These parameters includenumber of meshes, depth of burial of the grid, grid conduc-tor diameter and the effect of using ground rods with dif-ferent lengths.

The maximum number of meshes for a model grid was16 and the maximum length of the modelled ground rodswas 7 cm. The maximum depth of the model grid was4 cm, with the majority of the tests run at a depth of 1 cm.

For all grids tested, the applied voltage and currentwere recorded in addition to the surface potential profiles.The potential profiles were recorded along lines parallel tothe side of the grid, and along lines parallel to the diagonalof the grid. The profiles are designated by the distance ofthat profile from the centre line profile or from the diago-nal profile. The location of the profiles were chosen suchthat maximum and minimum potentials throughout thegrid could be determined.

The maximum mesh potential is found at the pointwithin the grid boundary where the surface potential islowest. The mesh potential is then the potential betweenthis point and the grid; it is in fact the touch potential,Etouch, which would be experienced by a person standing atthis point and touching some apparatus connected to thegrid. It is generally found in the corner mesh at a point in

the centre of the mesh. The maximum percentage value ofEtOuch is given by

V -A — V •F _ grid mxn <nn

htouch - y X 1 U U

grid

where Vmin is the minimum surface potential.The maximum step potential Estep occurs along the

diagonal just outside the grid where the slope of therecorded surface potential against distance is maximum.

Both mesh and step potentials are normalised to thegrid potential so that the results may be compared to thefull scale case. The grid resistance is also inversely pro-portional to the scale factor of the model. If a scale factorof 100 is used, the resistance measured on the model willbe 100 times that which would exist in the full scale situ-ation for the same ground resistivity.

Typical profiles for a 16-mesh grid of 10 cm x 10 cm,1 mm conductor diameter, at a depth of 1 cm are shown inFigs. 2 and 3 for the normal and diagonal profiles. Thesurface potential is given as a percentage of applied gridvoltage and the horizontal axis is in cm measured from the

ABCDEF

tage

vol

gri

o

oc

&aUo

8580

75

70

6560

55

50

45

40

35

3025

i

i

1

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50 50

Fig. 2

5 2.5 0 2.5 Edistance from grid centre line,cm

Normal profiles of surface potential for a 16-mesh 10 cm x 10 cmgrid, 1 mm conductor diameter, 1 cm depth

//

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distance from centre line.cm5/2 50

Fig. 3 Diagonal profiles of surface potential for a 16-mesh10 cm x 10 cm grid, 1 mm conductor diameter, 1 cm depth

288 IEE PROCEEDINGS, Vol. 133, Pt. C, No. 5, JULY 1986

centre of the grid. From these figures, the maximum andminimum potentials throughout the grid could be deter-mined.

6.1 Effect of ground rodsGround rods are of particular value when the upper layerof soil in which the grid is buried is of much higher resis-tivity than that of the soil beneath. There are two philos-ophies in grid design. The first one recommends theextensive use of ground rods in grids, practically one ateach cross connection [5]. The second trend in grid designignores the ground rods or, if necessary, a few ground rodsare installed.

To examine the effect of adding ground rods to thegrounding grid, a 16 mesh grid 10 cm x 10 cm with 25ground rods of length 3 cm located at each conductorjunction, 1 mm conductor diameter at a burial depth of1 cm was tested. Fig. 4 gives the normal profiles of surface

= 75

I ?0S> 65

3 60| * 55

1 508. A5

3 35

11

1

ABCDEF

50 5 50distance from grid centre line,cm

Fig. 4 Normal profiles of surface potential for a 16-mesh 10 cm x 10 cmgrid, with 25 ground rods of 3 cm length and 1.5 mm diameter, 1 mm con-ductor diameter, 1 cm depth

potential as a percentage of applied grid voltage. FromFigs. 2 and 4, it is concluded that the addition of drivenrods will decrease the grid resistance by about 50%,whereas the maximum value of touch potential decreasesby 12%.

enO

1o>

o

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9085

80

7570

65

60

55

50

4540

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Fig. 5 Diagonal profiles of surface potential for a 16-mesh20 cm x 20 cm grid, with ground rods of different lengths, 1 mm conductordiameter, 1 cm depth

6.2 Effect of length of ground rods and number ofmeshes

To determine the effect of length of ground rods andnumber of meshes on grid resistance and maximum valuesof touch and step potentials, a series of tests were per-formed on a 20 cm x 20 cm grid, at a depth of 1 cm, witheither 4 or 16 meshes. The lengths of the tested groundrods varied from 0 cm to 7 cm. The ground rods werelocated at each conductor junction.

Fig. 5 shows the main diagonal potential profiles for amodel grid with different lengths of ground rods, whereasFig. 6 shows the diagonal profiles for square grids withdifferent number of meshes. Figs 7 and 8 illustrate the

8075

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f.50.5 45S 40&35

I 30I 25

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Fig. 6 Diagonal profiles of surface potential for a 20 cm x 20 cm grid,with different number of meshes, 1 mm conductor diameter, 1 cm depth

65

60

55

50

45

40

35

0 1 2 3 4 5 6 7length of ground rods,cm

Fig. 7 Grid resistance against length of ground20 cm x 20 cm grid, 1 mm conductor diameter, 1 cm depth

4 mesh16 mesh

rods for a

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40

35

30

25

20

15

10

0 1 2 3 4 5 6 7length of ground rods,cm

Fig. 8 Maximum touch potential against length of ground rods for a20 cm x 20 cm grid, 1 mm conductor diameter, 1 cm depth

4 mesh16 mesh

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 5, JULY 1986 289

variation of grid resistance, maximum Etouch as a functionof the number of meshes and the length of ground rods.The values of Etouch are taken along the main diagonal ofthe grid in the corner mesh.

It is concluded that the resistance of the grid decreaseswith the increase of the length of ground rods. Themaximum value of Etouch decreases with the increase of thenumber of meshes and with the increase of the length ofground rods.

6.3 Effect of grid depthTests to determine the effect of grid depth on grid per-formance, in uniform soil were conducted. The grids testedwere 25 cm x 25 cm, with different numbers of meshes.The grids were tested at depths of 0.5, 1.0, 2.0 and 4.0 cm.

Figs. 9 and 10 show the variations of the grid resistance,

50

45

40

35

30

« 25

200 1 2 3 4

depth of grid ,cm

Fig. 9 Grid resistance against grid depth for a 25 cm x 25 cm grid, withdifferent number of meshes, 1 mm conductor diameter

4 mesh16 mesh

5

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depth of grid,cm

Fig. 10 Maximum touch potential against grid depth for a25 cm x 25 cm grid, with different number of meshes, 1 mm conductor diam-eter

4 mesh16 mesh

maximum touch potentials against grid depth and numberof meshes. These curves indicate that these quantities areinversely related to the depth of the grid and the numberof meshes.

6.4 Effect of conductor diameterTo determine the effect of increasing the grounding gridconductor diameter on the grid resistance and the percent-age touch and step potentials, a 20 cm x 20 cm, 4-meshsquare grid with different conductor diameters was tested.The potential profiles for grids with 0.5, 1.0 and 2.0 mmconductor diameters are plotted in Fig. 11. Table 1 givesthe values of grid resistance and maximum values of touchand step potentials for the tested grids.

290

It is concluded that the grid conductor diameter has asmall effect on the grid resistance and on the percentage

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oo.

face

75

70

65

60

55

50

4540

50 10 0 10distance from grid centre line,cm

50

Fig. 11 Diagonal profiles of surface potential for 4-mesh 20 cm x 20 cmgrid, with different conductor diameters, 1 cm depth

Table 1: Effect of conductor diameter on the grid per-formance

Grid conductor Grid resistance % Etouch % Estep

diameter, mm Q

0.51.02.0

62.7862.259.3

33.532.031.5

11.09.59.0

touch and step potentials. Thus the effect of conductordiameter can be neglected.

6.5 Comparison between the effect of groundrods and the additional horizontal conductors

The effects of ground rods against the additional horizon-tal conductors on the grid resistance, maximum values oftouch and step potentials were investigated. Scale modelgrids of 20 cm x 20 cm with 4 and 16 meshes. For the4 mesh model grid, ground rods of 7 cm length were addedat each conductor junction.

A comparison of these test results is presented inTable 2. It is concluded that, for approximately the same

Table 2: Effect of ground rods against additional horizontalconductors for a 20 cm x 20 cm grid

16-mesh 4-mesh

length of ground rods, cmTotal conductor length, cm

gr,d

Maximum Etouc

0200

51.832

71834225

length of conductor, ground rods are more effective interms of reducing the grid resistance and maximum valueof touch potentials than adding horizontal conductors.

6.6 Rectangular gridsA series of tests were performed for 10 cm x 20 cm rec-tangular model grids with rectangular meshes. Fig. 12gives the normal profiles for a 16 mesh grid with 1 mmconductor diameter, at a depth of 1 cm.

Table 3 gives the values of resistance and maximumtouch potentials for 10 cm x 20 cm model grids with dif-ferent numbers of meshes. It is seen that the grid resistanceand maximum touch potential decrease with the increasein the number of meshes.

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 5, JULY 1986

Table 3: Dependence of grid performance on number ofmeshes for rectangular grids, 10 cm x 20 cm

Numberof meshes

Gridresistance, Q

Maximum touchpotential, % ofgrid voltage

48

16

706866.7

3230.528.7

BD F

ga*

I

80

75

70

65

60

55

50

45

40

35

30

I1

i

50 5 2.5 0 2.5 5 50distance from grid centre line,cm

Fig. 12 Normal profiles of surface potential for 16-mesh 10 cm x 20 cmrectangular grid, 1 mm conductor diameter, 1 cm depth

7 Comparison between model testsand theoretical equations

A comparison between experimental and theoreticalresults of the grid resistance and mesh potential wascarried out to obtain the nearly accurate theoreticalmethod which can be used.

Some analytical methods using simplified equations areused [6-8] to obtain the resistances of 25 m x 25 msquare grids with different numbers of meshes, at a depthof 1 m. The resistivity considered was that of water. Scalemodel tests on these grids were performed, and the resist-ance values are obtained for different numbers of meshes.By dividing these values by the scale factor, the full scaleresistance values are obtained.

Table 4 presents a comparison of the grid resistances

Table 4: Comparison between theoretical and experimentalvalues of resistance

Number ofmeshes

14

1664

Schwarz

0.540.5360.5270.513

Grid

Laurent

0.7470.6580.5850.538

resistance,

recentLaurent

0.5940.5400.4980.467

Q

Koch

0.5940.5940.5940.594

J. Nahman

0.6480.5670.5130.474

Scalemodel

0.5180.4930.4430.424

obtained from model tests and simplified equations.Fig. 13 shows the results obtained from model tests andtheoretical equations for 25 m x 25 m grids, buried at adepth of 1 m. It is noticed that the values of resistanceobtained using recent Laurent equation is the closest oneto the values obtained from model tests, the percentagedeviation is about 9%higher than the experimental values.

The mesh potential can be obtained mathematically asa percentage of the grid potential rise by the Thapor equa-tion [3]. A comparison between these theoretical values

and those obtained from model tests for 25 m x 25 mgrids, buried at a depth of 1 m, with different numbers of

0.8

1 2 3 4 5 6 7number of meshes along one side

Fig. 13 Grid resistance against number of meshes for a 25 m x 25 mgrid with experimental and theoretical methods

(i) Schwarz(ii) Laurent

(iii) Recent Laurent(iv) Koch(v) J. Nahman

(vi) Scale model

55r

50

0io>a75

•o

C7I

"o

45

40

35

30

1 "| 20oQ.

r. 15E 10

1 2 3 4 5 6 7 8 9number of meshes along one side

Fig. 14 Corner mesh potential against number of meshes for a25 m x 25 m grid, with experimental and theoretical methods# Thapor eqn.O scale model

meshes is given in Fig. 14. It is noticed that the scalemodel values are higher by about 8%.

8 Conclusions

During these investigations experimental methods are usedto calculate resistance, mesh and step potentials for severalgrounding grids, with and without ground rods, at differ-ent depths, number of meshes, and different grid conductordiameters.

(i) The resistance of the grid decreases with increasingthe number of meshes. The decrease is quite rapid at thebeginning but slow when the number of meshes exceeds16; a better way of reducing the resistance is to increasethe area enclosed by the grid. Also the values of mesh andstep potentials are inversely related to the number ofmeshes.

IEE PROCEEDINGS, Vol. 133, Pt. C, No. 5, JULY 1986 291

(ii) The grid resistance, mesh and step potentials areslightly reduced with the increase of conductor diameter,but the variation is small for sizes of conductor that wouldbe used.

(iii) Addition of driven rods to the grid decreases theresistance, but if the grid area is increased, the addition ofrods do not help to decrease the grid resistance. Also meshand step potentials are decreased with increasing thelength of ground rods.

(iv) The grid resistance, mesh and step potentials aredecreased with increasing the burial depth of grid.

(v) Additional conductors in the form of ground rodsare more effective in improving grid performance com-pared with additional horizontal conductors.

9 Acknowledgment

The authors appreciate the facilities made available in theHigh Voltage Laboratory, University of Cairo, and the

assistance they received with the experiments from thetechnical staff.

10 References

1 'IEEE Guide for safety in alternating-current substation grounding'IEEE no. 80, 1961

2 ARMSTRONG, H.R., and SIMPKIN, L.J.: 'Grounding electrodepotential gradients from model tests', Trans. Amer. Inst. Electr. Eng.,1960, PAS-79, pp. 618-623

3 THAPAR, B., and PURI, K.K.:'Mesh potentials in high-voltagegrounding grids', IEEE Trans., 1967, PAS-86, pp. 249-254

4 CALDECOTT, R., and KASTEN, D.G.: 'Scale model studies ofstation grounding grids', IEEE Trans., 1983, PAS-102, pp. 558-566

5 JENCEN, C: 'Grounding principles and practice, II—Establishinggrounds', Electr. Eng., 1945,64, pp. 68-74

6 SCHWARS, S.J.: 'Analytical expressions for the resistance of ground-ing systems', Trans. Amer. Inst. Electr. Eng., 1954, PAS-73, pp. 1011-1016

7 LAURENT, P.G.: 'General fundamentals of electrical grounding tech-niques', translated from Bull. Soc. Fr. Electr., 1957,1, pp. 368-402

8 NAHMAN, J., and SKULETICH, S.: 'Resistances to ground and meshvoltages of ground grids', Proc. IEE, 1979,126, (1), pp. 57-61

Book ReviewShort-circuit currents in three-phase systemsRichard RoeperSiemens Aktiengesellschaft, John Wiley & Sons, 1975,167pp., £17.95ISBN 0-471-90707-3

In the design of electrical machines and power systems anessential element is the calculation of the maximum cur-rents likely to occur due to short-circuit faults. This bookprovides a logical and systematic approach to short-circuitanalysis for the practising engineer based on the VerbandDeutscher Electrotechniker (VDE) regulations.

It commences with a section describing the transientshort-circuit currents which occur during the period fromfault initiation until the steady-state fault condition isreached. A single-phase, constant voltage system is con-sidered initially with the short circuit remote from the gen-erator. The loaded and unloaded cases are describedbefore the analysis is extended to the three-phase situationwith short circuits close to the generator. Fault currents ininterconnected systems and the short-circuit characteristicsof various motor loads are then described.

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rents for a range of zero-to-positive sequence impedanceratios and phase-angle differences.

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The short-circuit impedances of various fault systemsmet with in practice are also listed and these form a usefulreference source.

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The author concludes with a brief section on digitalcomputer calculation of short-circuit currents. It wouldhave added greatly to the usefulness of the text had thissection been expanded to include a selection of modernanalytical methods. However, the extensive use of workedexamples coupled with the tables of characteristic values ofthe parameters of a range of synchronous generators,transformers and other equipment make this book anextremely useful source of data.

The VDE regulations are based on electrical practice inGermany and may be at variance with other countries'systems, particularly with respect to neutral earthing.However, if these differences are borne in mind and somevariations in notation are accepted, this book should be ofgreat value to all power systems engineers.

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4738C

292 IEE PROCEEDINGS, Vol. 133, Pt. C, No. 5, JULY 1986