IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, No.6 Nov./Dec. 1979

RESISTANCE MEASUJREMENTOF LARGE GROUNDING SYSTEMS

F. Dawalibi, MemberSafe Electrical Systems DM Ltd.Montreal, Canada

ABSTRACT

Difficult problems are encountered when the resis-tance of a large grounding system is measured by theuniversally used fall - of-potential method. It is thepurpose of this paper to analyse the basic factors in-volved and examine their effects on the accuracy of themeasurement. A typical grounding grid, buried in a two-layer soil, is analysed. The results obtained show thatthe exact location of the potential probe is influencedconsiderably by the size and arrangement of the returnelectrode and by the characteristics of the soil. Thepaper presents several curves and charts which are use-ful to evaluate these effects and avoid errors duringthe interpretation of the measurement results.

1.0 INTRODUCTION

The basic technique which is universally used[l,21for the measurement of a grounding system resistance isknown generally as the "fall-of-potential" method andis described later in this paper. However, this methodpresents many difficulties and sources of error whenused to measure the resistance of large grounding sys-tems as usually encountered in power system networks.These difficulties, which are not fully understood, oc-cur mainly because of the size and configuration of thegrounding system and soil heterogeneity.

The IEEE working group to revise Guide 81[21 wasaware of these problems and thus, decided to include aseparate section on large grounding systems. This sec-tion will be completed when additional informationand research work will become available.

Basically,ground resistance measurement consists ofmeasuring the resistance of a body of earth surroundingthe grounding system. Thus, only one end of the resis-tance is definitely available , i.e. at the groundingsystem itself. The other end is not practically availa-ble and is called "remote soil" , theoretically, at aninfinite distance from the grounding system.

The fall-of-potential method solves the problem ofthe remote soil end by using two auxiliary electrodescalled return electrode and potential probe. When thereturn electrode is placed at a finite distance fromthe grounding system and the potential probe is driven

A paper reccmmended and approved by theYEiR viower System Instrumentation and MleasurementsCommittee of the IEEE Power Engineering Society forpresentation at the IEEE PES Sumrr Meeting, Vancouver,British Columbia, Canada, July 15-20, 1g79.Manuscriptsubmitted January 31, 1979; made available for printingMay 4, 1979.

D. Mukhedkar, Senior MemberEcole PolytechniqueMontreal, Canada

at a specific location , then accurate measurement ofthe resistance is obtained. Unfortunately, the exactlocation of the potential electrode is well definedonly for some ideal cases such as hemispherical or verysmall electrodes buried in uniform or two-layer soils[3,4,51. In practice however, grounding systems consistof a complex arrangement of vertical ground rods andhorizontal conductors , usually buried in non-uniformsoils . In these cases , the potential probe positionmust be determined each time , using complex computercalculations[6,7,8,9,10]. The case of a large groundingsystem buried in uniform soil (assuming uniform currentdensity distribution in the conductors) has been analy-sed by Curdts[ll] and Tagg[41.These methods can not beused for short distances between the electrodes becausethe uniform current density hypothesis becomes unrea-listic as shown later in this paper. Furthermore, themethod developed by Tagg requires the Knowledge of thegrounding system "electrical centre". The existence andphysical meaning of this centre is uncertain andthe concept of "electrical center" needs to be proven.Reference [5] has also analysed briefly long horizontalwires buried in two-layer soils. However, uniform andlinear current density distribution were assumed. Theseassumptions are not realistic for short distancesbetween electrodes.

To the best of the authors knowledge, conventionalgrounding systems such as substation grids buried inlayered soils have not yet been analysed using accuratecurrent density distribution in the conductors of thegrounding system . It is the purpose of this paper toexamine the behaviour of the fall-of-potential methodwhen it is used to measure the resistance of groundinggrids buried in two layer soils for several arrangementsof the test electrodes.

2.0 THE FALL-OF-POTENTIAL METHOD

2.1 Description of the method

This method, shown in figure 2.1, involves passinga current I through the grounding system E and anotherelectrode called return electrode. The passage of thiscurrent produces at a distance X from E a voltage dropVx in the soil. Vx is measured by a potential probe P.The quotient Vx/I is an apparent resistance which undercertain conditions can give the true resistance RE ofthe grounding system. the simplest form of the fall ofpotential method is obtained when E, P and R are on thesame line. The most widely used arrangement is when Pis located between E and R. When Vx/I is plotted as afunction of the potential probe distance X, fall-of-po-tential curves , similar to those shown later in thispaper, are produced.

If the distance D is large enough (with respect tothe grounding system dimensions) the centre part of thefall-of-potential curves tends to the horizontal. Actu-

0018-9510/79/1100-2348$00.75 i 1979 IEEE

2348

2349

ally, the curve never becomes horizontal but it may ap-pear to do so owing to the lack of sensitivity of theinstruments used. It is usually accepted(without proof)that the flat section of the curve gives the true resi-stance RE. For large grounding systems, large distancesD may not be practical or even possible and as a resultthe horizontal section of the curve will not exist. Inthis case, accurate measurements will not be obtainedunless one has already a good idea of the exact probe Pposition.

des and soil characteristics.Let us define the following functions q, 4, and i

with respect to the coordinate system shown in figu-re 2.1 :

VR = T(D)E

VR = 4)(D-

VE = p(X)

(2.5)

(2.7)

According to equation (2.4) the measured resistan-ce R-V/I will be equal to the true resistance RE if:

VR -v -Vp = , that is:P E P

4(D-X) - q(D) - p(X) = 0----------(2.8)

Identical electrodes and large spacings

If electrodes E and R are identical 4=) and if Dis large enough such that VR = n (D) % 0 then condition(2.8) becomes.

4(D-X) - p(X) = 0 ; thus:

Xo = D/2

Fig. 2.1 Fall-of-potential method

2.2 Theory of the fall-of potential method

The potential of the remote soil is assumed to bezero. A current I enters the-grounding system E and re-turns through the return electrode R (see figure 2.2).The voltage difference between E and a point at the sur-face of the soil is measured using a potential probe P.

Let VG be the potential caused by electrode G(G = E or R) at point M (M = P or E). it is assumedthat electrode G carries a current of 1 ampere. Conse-quently VM is in V/A. The following equations can bewritten.

U = VE X(I)+VR x(-l) . (2.1)P P P

U = V x(I)+VR x(-I) ------(2.2)E E E

Up and UE are the potentials of electrodes PE respectively.

and

-I

j R 77

. .' ''' v .--+I/XE;

Hemispherical electrodes

If electrodes E and R are hemispheres and theirradius are small compared to X and D and if soil is uni-form , then the potential functions 4, 1, and 9 are in-versely proportional to the distance relative to thehemisphere centre. If the origin of the axis are at thecentre of hemisphere E then , equation 2.8 will be pro-portional to the following one:

1/(D-X) - l/D - 1/X = 0-----------(2.9)

The positive root of equation (2.9) is the exactpotential probe location XO:

XO = 0.618D

This is the usual 61.8% rule[ll]. If the potentialprobe P is at location P1 (E side, see figure 2.1) thenD-X should be replaced by D+X in equation (2.9).In thiscase the equation has complex roots only. This, alreadymentioned in [31, has not been noticed in guide IEEE 81[21 and in author's previous paper [51. If P is at lo-cation P2 (R side, see figure 2.1) then D -X should bereplaced by X-D in equation (2.9). The positive root of(2.9) is:

0

x

Fig. 2.2 Fall-of-potential theory

The voltage V measured by themethod is;

V = UE - Up ;Thus:

fall of potential

V = I(VE - VR _ YE Vp)---(2.3)E

VE is the potential rise of electrode E assuminga current of 1 ampere. This is by definition the resis-tance RE(or impedance of electrode E). Therefore, equa-tion (2.3) can be written as:

+ VR R ER = V/I = RE (VPVE-Vp)---(2.4)VR, Vp and Vp are functions of, the distance be-

tween the electrodes, the configuration of the electro-

XO = 1.618D

If this arrangement (R side) is assumed then, theresults of reference [51 are still applicable.

General case

If the soil is not uniform and/or electrodes E andR have complex configurations then, the functions 4,

and are not easy to calculate. In such cases, compu-

ter solutions are generally required [5,6,7,8,91.Computer program "MALT" was used to obtain the re-

sults shown in this paper [10,121. A four-mesh gridis analysed for several distances between the grid andthe return electrode and various types of soil. Thebasic theory on which "MALT" program is based have beenalready published in previous technical papers [5 to 9]However, for the sake of clarity and completeness , thefundamental potential equations are given in Appendix A.In references [5 to 91 the analytical expressions shownare not valid for non-horizontal conductors. The formu-

-

x

ID-1 0

x2x1

laes of Appendix A are valid for horizontal and non-ho-rizontal conductors. The ¢, n and * functions are thus,similar in form to the potential function E given inthis Appendix A.

3.0 DATA AND ASSUMPTIONS

3.1 Arrangement of the electrodes

The grounding system E which must be measured bythe fall of potential method is a 30x30m four-mesh gridburied at 0.5m below soil surface. The conductor ra-

dius is 0.Olm.The return electrode is(see figure 3.1):

a- A lm long vertical ground rod (0.Olm radius)b- Or an inclined conductor having one of it's

extremity (close to soil surface) at a constant distan-ce from the grid centre (20m) and it's other extremityat a distance which is different from one ease to theother. However , the depth of this extremity is keptconstant (lm). The conductor radius is also 0.Olm.

Case b is used to analyse the influence of largereturn electrodes on substation resistance measurementIt simulates for example a section of a transmissionline counterpoise disconnected from the substation gridand used as a return current electrode.

The return electrode is placed at distance D fromgrid E (lower extremity, of R; D=17 to 30(k).

The potential probe is placed at distance X fromthe centre of the grid. P is on the E-R line and can beinside or outside the ER segment (classical and alter-native fall-of-potential method respectively).

Soil surface

Il

Grounding system E

0.5 m Return Rb

/ 1.0 m (Inclinedcondtuctor)

--V-;;Da

I~~~~

I ----Return R

(Ground rod) a

Db

1.0 m

4.0 THE RESULTS

The computer results based on the above data are

summarized in the following figures. These are usefulto those involved with ground resistance measurements.

Basically the results shown in this paper can begrouped into two categories.

- Fall-of-potential curves- Current density distribution curves

The fall of potential curves show the data whichcould be expected from the measurements if the condi-tions assumed in this paper existed at the measurementsite . These curves are considered very useful becausethey show the large variations in the shape of the fallof potential curve. From these curves, the exact poten-tial probe location can be determined easily,once thetrue resistance RE is calculated.

The current density distribution curves are shownfor several reasons. First, the curves may be usedadvantageously for future reference.Second these curves

prove that uniform current density assumption is wrong

especially when the return electrode is close to thegrounding system. Since large distance between elec-trodes is very seldom easily obtainable, it is obviousthat accurate resistance measurement must take intoconsideration the non-uniform current density distribu-tion in the electrode conductors. Third, these curves

describe also the effects of a ground fault occuringclose to a substation,such as a phase to ground faultdeveloping between a transmission line conductor and a

tower in the vicinity of the substation.It is not possible to discuss in detail all the

results obtained. However the reader will certainlyarrive to additional interesting conclusions by carefulanalysis of the following figures.

4.1 Fall-of-potential results

Ground rod return electrode

Figures 4.1 , 4.2 and 4.3 show the fall-of-poten-tial curves calculated for several distances D, and inthe presence of uniform or two-layer soils. Figures 4.2and 4.3 correspond to a two-layer soil having respecti-vely high and low bottom layer resistivity.

Fig. 3.1 - Arrangement of the electrodes

3.2 Soil structure

The soil structure considered in this paper is ofthe uniform or two-layer type. The top layer resistivi-ty pi is kept constant (100 Q-m).The bottom soil resis-tivity P2 is variable. The variations of P2 are shownby the K reflexion factor. K=(p2-pl)/(p2+pl). If thesoil is uniform (P2=P1) then K=O. Other values of K as-sumed in this paper are ±0'.7, ±0.9 and ±0.9. The toplayer heigth H varies between 0.1 to 300m.

3.3 Similar arrangements

The results given in this paper can also be usedfor similar electrodes (with different dimensions) andother values of top-layer resistivity P1, provided ho-wever that some adjustments are made on the results, asexplained in Appendix A of reference [10].

179OHMS§

7~~~~~~IEB

_~~~~~~~~~~~~~~~~~~~~~~~~~~ r,

V;5 ~SI

1 12 IFORM SOIL

3 B

2/

/ ~~~~~~~~~~~~~~~~~~TRUERESISTANCEI ~~~~~~~~~~~~~~~~~~~~1.779TAHMT

50 100 150 200 250

POTENTIAL PROBE LOCATION-METERS

Fig.4.1 Electrodes spacing effects-Uniform soil

2350

160

140

120

i100

w soo

6E0

40

20

Fig. 4.2 Electrodes spacing effects-Two-layer soil

3.6 [

3.2

2.$

2.4

2.0

1.6

1.2

0.0

0.4

I

10 - - iz 46 s5

POTENTIAL RBE LOCATION-METERS

Fig. 4.5 Top layer heigth effects (K=0.98)

16 E . R16

- fi -

D 500

141- I R ; H

i 12.

0I-

I 108

PEIAL POICE LOCATIONERS

Fig. 4.3 Electrodes spacing effects-Two-layer soil

17.59 OHMS- -,.

TW-UYER SOILKK0.98

10 20 30 40 50POTENTIAL PBE LOCATION-METERS

Fig. 4.6 Top-layer heigth effects (K=0.98)

These figures show that , an horizontal curve sec-

tion (practically speaking) exists only when distance Dis in the order of 10 times the grid dimension ("i300).The fall-of-potential curves have a similar shape whe-

ther K = 0.0, 0.7 or -0.7. However this is because the

top layer H is the same (H -2m). This does not hold anymore for other H values as shown by figures 4.4, 4.5and 4.6 (K= ±0.98 and D= 50m)).

1.6[

1 1.2

0.8

0.41

1.78-OHME

.45 OIM

t/ ' Hww/, .Lzt..J /-/

I/ .-. S

ME-T-H= mm0.

/ 0.240O1' Y

10 20 30 40

POTENTIAL PROBE LOCATION-METERS

The required potential probe position expressed interms of the distance D and top layer heigth H is givenby the curves of figures 4.7 and 4.8 respectively. The-se figures should be compared with the ones given in[51

80

so

o 60s

40

2

0-

= 0

50

TWO-LAYER SOIL (K-0.7 mz2m)UNIFORM SOIL (K-0.0)

O-LAYER SOIL (K:-0.7 m=2M)UNIFORM SOIL (K0.0)-INCLINED RETURN

UNIFORM SOIL-HEMISPHERICAL ELECTRODE

.......

,~~~~~~~~~~~~~ it

...

0 5o0 100 150

RETURN ELECTRODE LOCATION-METERS

200

Fig. 4.7 Exact potential probe position-VS-Distance

I

I.

2351

Fig. 4.4 Top layer-heigth effects (K---0.98)

2352

100

3.0

2.5

, 2.0

t-10 1.5

I 1.0

0.5

0.1 1.0 10.0 100.0

H TOP-LAYER HEIGTH-RETERS

Fig. 4.8 Exact potential probe position-Vs-heigth

D=20F .

E e.

-D

E IR

10 20 30 40 50 60POTENTIAL PROBE LOCATION-METERS

Fig.4.10 Ground rod return electrode-Uniform soil

The horizontal section of the curves shown in fi-gure 4.7 (large values of D) corresponds to the 61.8%classical rule [ll].This is logical because the hemis-pherical electrode approximation is now valid for largeD values. For small values of D ( in the order of griddimension), the exact potential electrode position mustbe increased when D decreases.This conclusion hold alsofor uniform and two-layer soil conditions. However thisposition is closer to the return electrode when K ispositive than for negative K values.

Figure 4.8 gives the exact potential probe posi-tion as a function of the top layer heigth H. The cur-ves of figure 4.8 exhibit maximum and minimum valuesfor positive and negative K values respectively. Thisis very similar to what was obtained in the case ofsmall electrodes [5]. However, the curves present somedistorsion when H is approximately equal to the depthof burial of the grounding grid ( 0.5m). This is alsosimilar to what is mentioned in [12]. The author's havenot yet a satisfactory physical explanation for thiscurious behaviour.

Inclined return electrode

The results obtained for this case are shown infigure 4.9. This figure should be compared with figure4.10 which corresponds to the ground rod return elec-trode case but drawn at the same scale in order to simplify the comparison. Note the shape of the curves forD distances of 75, 100 and 300m.

3.0

2.5

= 2.0c

V)

1.50-

1.0

0.5

, D.- 401D= 30M,I rUNIFORM SOILI

l_K=0.0 _

TRUERESISTANCE1.78 OHMS

A II ..A 1 _ _

10 20 30 40 50 60POTENTIAL PROBE lOCATION-METERS

Fig. 4.9 Inclined return electrode-Uniform soil

The required potential electrode location is shownin figure 4.7. It is quite obvious that the size of thereturn electrode has a considerable effect on the exactpotential probe location. Thus, when a large electrode,such as a counterpoise section of a transmission lineor a pipeline system , is used as a return electrode,the exact potential probe location is considerably clo-ser to the grounding system. When the size of the re-turn electrode is increased , the distance of the probeto the grounding system must be reduced.

The alternative fall-of-potential method

In section 2.2 , it was shown that when soil isuniform and the electrodes hemispherical, one can mea-sure the ground resistance by placing the potentialprobe at 1.618D ( return electrode side ). Figure 4.11gives the required potential probe location VS distanceD for this alternative method. These curves should becompared to those shown in figure 4.7 (classical me-thod). The alternative method could be used advanta-geously in combination with the classical one.

z, 160

0

< 140m

a

a, 120

100

.. UNIFORM SOIL-HEMISTHERICAL ELECTRODE

TWO-LAYER SOIL (K=-0.7 4'2m)UNIFORM SOIL (K'0.0)TWO-LAYER SOIL (K-0.7 H'2M)

GRID 4 E.v pEDGE E R H

10 20 30 40 50

RETURN ELECTRODE LOCATION-METERS

Fig.4.11 Alternative fall-of-potential method

4.2 Current density distribution

Figures 4.12, 4.13 and 4.14 show the current den-sity distribution along the grid conductor which is theclosest to the return electrode. The current density isgiven for several distances D and for uniform and two-layer soils. The figures show that the current densityat the conductor centre may be several times higher

A I .t I -.-

.

2353

than the current density at the conductor extremity (up CONCLUSIONSto 30 times for K = 0.7 and Dz17 ). This fact confirmsthat uniform-or linear current density assumptions are This paper has shown and discussed the influencenot adequate and lead to wrong results. of the placement and arrangement of the test electrodes

Even when D is large , the current density is not on the measurement of large grounding systems buried inuniform. However the variations are much less than in uniform or two - layer soils. The following importantthe case of small distances D. conclusions were obtained:

/ \ . 0=2O -Small distances between a grounding system and a

1.6\ - 3 Nreturn electrode, lead to an exact potential probe dis-1.6 ......... --D 4tance which is larger than the accepted 61.8% value..14 / \ _ _D=4501. /\ D-79M-The exact potential probe location is always lar-

1.2 D=1O ger when the deep soil has a higher resistivity than.D=300 the top soil one.

1.0 / (ALSO. E ONLY)-For a constant electrode spacing , there is a

2 0.8 _. -'- - -- -- **4 top layer heigth which will cause a maximum or a mini-mum on the value of the exact potential probe distance.

0o.6 ==>The maximum value is obtained for positive K values.

0.4L *R -It is possible to measure the true ground resis-

UNIF SOIL amDtance by placing the potential probe at the return

0.2 | KsO.O w____K_nO_ electrode side. This is not possible when the probe is-TF R placed at the grounding system side.

O 6 12 18 24 30 -The size and location of the return electrfode ha-POSITION N 6ID CNUKTOR - ETERS ve considerable effects on the exact potential probe

Fig.4.12 Current density distribution (K=0.O) location.

The calculations which assume uniform currentTO 3.T/AO , density distribution in the conductors of the grounding

TO VA * ------D= 20r system, will give inaccurate results if the distance

1.6 _-8 / 8 ' \ D= 25M between the electrodes is not large enough.

1.4 j Nii _..D= 308ACKNOWLEDGEMENTS

/ \ ", >The authors express their appreciation to the Na-1 l.0 {\ + t ._"-t'<tional Research Council of Canada for providing the ne-

4B - =. _ .,r .-.-- .-, cessary financial support of the work. The authors also0.8 - acknowledge the cooperation and facilities offered by

0= =- ~z.6-... 0 -> Ecole Polytechnique and Safe Electrical Systems DM Ltd.

D = 1001a APPENDIX A0.4 >/ ~ 8 ( ONLY)

/ tJ,- 0" a IL that In a previous paper [ 7 ],the authors have shown0.2 _' --1_ | K=0.7 1 * that the potential P at a point M (u,v,w) in the soil

- -.m - Rl- tmay be written as follows

0 6 12 18 24 0 p1i m

P)SITIO 01 GRID CO)DWJTOR-METERS P(u,v,w)4T K [F(u,v,w,upk)+F(u,v,w ,up)]Fig.4.13 Current density distribution (K-0.7)

t Where:TO: Whrm is the number of conductors in the electrode.

1.6 A/Ne D=17M u is the length of the conductor K.pk. D=2ON i is the current density in conductor k.

1.4 -\ - D=25N k

/ \ *- D=3M It was also shown [8] that the function F is defi-a1.2 - --_____ D=5 ned as:

/\ ~~~~~D=0115

kZ~I1 ~ (ALSO. NLY) F(u,v,w,uk)-EXKnEinhlPk ivE(w+2nh)sUn2________-' However the above expression is valid for horizon-0.4

* 3- tal conductors only. The general expression, valid for0.2 LAER soi horizontal and non-horizontal conductors is:

0.2 I Ks 4.7 1

t i~~~~i~~zziz.:H2~E~tN =fl n lU -B -l B1I --I62 IS --F I2-2 F(u,v,w,u k)= LK Einh p +sinh __ ]POSITION Ol 6RID CONDUCTOR-METERS CC-BlC-B

Fig.4.14 Current density distribution (K=-O.7) Where:

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B = u + 2nhsin5

C = B + V + (W + 2nhcos5)2u, v, w and S are defined by equation (2) and fi-

gure 1 of reference [8].

REFERENCES

1- P. D. Morgan, H. G. Taylor, " Measurement of the re-sistance of earth electrodes", World Power, 1934, 21pp. 76 and 131.

2- IEEE Guide No. 81, " Measuring ground resistance andpotential gradients in the earth" May 1962.

3- G. F. Tagg, " Measurement of the resistance of anearth electrode system covering a large area", Proc-IEE Vol. 116, No. 3, March 1969.

4- G. F. Tagg, " Measurement of earth electrode resis-tance with particular reference to earth-electrodesystems covering a large area", Proc. IEE, Vol. 111,No. 12, December 1964, pp. 2118-2130.

5- F. Dawalibi, D. Mukhedkar, " Ground electrode resis-tance measurement in non-uniform soils ", IEEE Tran-sactions, Vol. PAS-93, No. 1, Jan. 1974, pp. 109-116

6- T. N. Giao, M.P. Sarma, "Effects of two-layer earthon the electric field near HVDC electrodes ", IEEETransactions, PAS-91, No.6, November 1972, pp. 2346to 2355.

7- F. Dawalibi, D. Mukhedkar , " Optimum design of sub-station grounding in two-layer earth structure", Pa-rt I, II and III, IEEE Transactions, Vol. PAS 94,No.2, March/April 1975.

8- F. Dawalibi, D. Mukhedkar, " Resistance calculationsof interconnected electrodes ". IEEE TransactionsVol. PAS-96, Jan./Feb. 1978.

9- F. Dawalibi, D. Mukhedkar, "Transferred earth poten-tials in power systems", IEEE Transactions, Vol. PAS-97, No. 11, Jan./Feb. 1978.

10-F. Dawalibi, D. Mukhedkar, " Parametric analysis ofgrounding grids", IEEE Transactions paper F79243-7,N.Y. 1979.

ll-E. B. Curdts , " Some of the fundamental aspects ofgrounding resistance measurements " , AIEE Transac-tions, Vol. 77, Part I, 1958, pp. 760.

12-F. Dawalibi, D. Mukhedkar, "Influence of ground rodson grounding grids", IEEE Transactions paper F79245-2, N. Y. , 1979.