Resistance to ground of combined grid multiple rods electrodes

Nahman, Senior Member, IEEE Faculty of Electrical Engineering 11001 Belgrade, Yugoslavia Abstract - The resistance to ground of a wide set of square and rectangular grid electrodes c

IEEE Transactions on Power Delivery, Vol 11, No 3, July 1996 1337

RESISTANCE TO GROUND OF COMBINED

J.M Nahman, Senior Member, IEEE

Faculty of Electrical Engineering

11001 Belgrade, Yugoslavia

Abstract - The resistance to ground of a wide set of square

and rectangular grid electrodes combined with multiple rods,

buried in uniform and two-layer soils, has been analyzed

using available exact computer software Based upon the

results of this analysis, analytical expressions and graphs for

electrodes resistance to ground are provided, appropriate for

practical application

I INTRODUCTION The resistance to ground of substations ground

electrodes is one of the most important parameters

determining the potential rise of the grounded equipment

and other metalwork within substation with respect to the

remote earth as well as the potentials which might be

transferred outside the substation Several computer

models have been developed for the analysis of the ground

electrodes performances buried both in uniform and

nonuniform soils [1-4], making possible an exact

calculation of all ground electrodes parameters including

the resistance to ground Some approximate analwcal

expressions for grids [5-91 in uniform soil and in two-layer

soils [7,10-131 have been suggested Expressions for

rodbeds and combined grid-multiple rods electrodes in

uniform soil [5] and two-layer soils have been also

developed Ell-131 The expressions proposed by Schwarz

[ 5 ] , appropriately modified for soil nonuniformity, have

been demonstrated to provide very good estimates of the

resistance to ground of a wide set of electrodes shapes

which, unfortunately, is not the case with some other

available expressions, as discussed in [11,12] However,

the application of the modified Schwarz's approach

96 WM 003-4 PWRD A paper recommended and approved by the IEEE

Substations Committee of the IEEE Power Engineering Society for

presentation at the 1996 IEEEPES Winter Meeting, January.21-25, 1996,

Baltimore, MD Manuscript submitted July 24, 1995; made avaiable for

printing November 13, 1995

V.B Djordjevic Energoprojekt - Hidroinzenjering

1 1070 Belgrade, Yugoslavia implies the utilization of several graphs, including interpolations, which might be cumbersome in some cases Therefore, relatively simple analytical expressions for grids and combined grid-multiple rods electrodes with rods lengths being twice the upper soil depth have been proposed matching well with the exactly calculated data for a very wide set of electrodes and soil parameters [13] This paper studies square and rectangular grids combined with rods distributed along the grid perimeter only and both along the grid perimeter and within the grid A fixed rod length I = 3 m has been presumed A general analytical expression for the resistance to ground

of all electrodes shapes under consideration has been

derived for uniform soil case being in very good agreement with the exactly calculated data Correction factors for

two-layer soils are also provided as graphs and analytical expressions The expressions proposed can be used as a

good estimate of substation ground electrodes resistance to ground in practical design Furthermore, they explicitly indicate the effects of various parameters upon the

electrodes ground resistance which might serve as a good

orientation in the design phase

11 ANALYSIS OF THE RESISTANCE TO GROUND

A Ground electrodes

Square and rectangular grids have been analyzed with

2" , n = 0, 2, 4, 6, 8, meshes combined with vertical rods distributed evenly along the grid perimeter only (figs 1&2) and along the grid perimeter and along the diagonals

of the grid (figs 3624) Areas covered by the electrodes have been varied from 10 x 10 m2 up to 200 x 200 m2 , for square grids, and from 10 x 20 m2 up to 200 x 400 m2, for

rectangular grids

The grids are presumed to be buried at depth h = 0.5 m and rods are taken to be 3 m long Grids conductor and rods diameters qual 0.01 m and 0.064 my respectively The upper soil depths H = 1 m , 3 m, 5 m and 10 m have been considered (fig 5) The ratio of upper (PI) and lower

0885-8977/961$05.00 0 1996 IEEE

1338

(p2) soil layers

range (0.2, 5)

CSOl

resistivities has been varied within the

CS64

C§04

Fig 1, Sample combined square eledrodes

CS16

CS256

Fig 2 Sample combined rectangular electrodes

Fig 3 Sample combined square electrodes

throughout the grid

CRD16

Fig 4 Sample " b i n d rectangular electrodes

with rods spread throughout the grid

0.5 m

P

2

Fig 5 Presumed electrcde and soil stratification

B Resistance to ground for uniform soil The resistances to ground for a set of 140 electrodes samples buried in uniform soil have been calculated by completely modeling The electrodes samples have been generated from the patterns displayed in figs 1 to 4 by varying parameters A and H:

From the results obtained the following general expression for the resistance to ground has been deduced, agreeing well with the calculated data

where A is the area covered by the grid in r d , N i s the total number of the grid meshes and l i s the individual rod length in m This expression has been confirmed to be

valid for all electrodes shapes from figs 1 to 4

1339

the graphs in figs 6 - 12 plotting C, as a function of pip,

As factor C,values are very slightly affected by the rods distributed within the grid, for these electrodes the graphs for corresponding electrodes having only peripheral rods canbeused

Furthermore, as shown [13], (1) yields very good estimates

for grids alone also, when I= 0 has to be inserted

The calculations performed have shown that the rods

distributed within the electrodes grids very slightly af€ect

the resistance to ground values This is owing to the

screening effect among the grid conductors and rods

located within the grid which reduces the currents

emanating from these rods

Table 1 quotes exact ground resistance values and

corresponding errors of (1) for a representative set of

ground electrodes samples It is observable that (1) has

yielded very good estimates of ground resistances in all

cases

Table 1 Resisten- to ground of electrodes samples

for uniform soil with p = 100Qn

C Nonunifonnity correction factor

To extend the application of the uniform soil resistance

formula to the two soil layer case, a resistance

nonuniformity correction factor C, is introduced

R = c,R;,

In (2) R denotes the resistance to ground of a ground

electrode when buried in the two - layer soil and R, is the

resistance to ground of the same electrode buried in

uniform soil with resistivity being equal to the resistivity

of the upper layer of the two - layer soil

Factor C, has been calculated for 2200 cases generated

for electrodes shapes from figs 1 to 4 by varying

the results of this calculations have been used to construct

1340

3K

I 1

0,o

P2/P 1 Fig 8 Factor Cr vakm for CS electrodes for upper soil depth H = 1Om

I I I I 1 1 1 1 1

I I I I I I I I I I I I I I l l

P2/Pl

Fs 10 Factor Cr v a k for CR electrodes for upper soil depth H = 5m

7 -

I I I I I I l l I I I 1 1 1 1 1

Fig 9 Factor Cr v a k s for CR electrodes for upper s o l depth H = Im Fig 11 Factor Cr v a h for CR electrodes for upper soil depth H = l h

1341

statement As observable, factor C, values for CRD for all electrodes shapes in figs 1 to 4 Maximum error of electrodes in fig 12 are practically the same as these for (3) & (4) for the electrodes analyzed has been established

the corresponding CR electrodes, displayed in fig 9 to be 18% In the great majority of the cases being studied

the errors are less than lo%, in absolute terms

435 " ' " [

T

Consider electrode CS 64 covering area A = 100 x 100 m', buried in a two layer soil with resistivities pI = 50 Rm and

pz = 250 Rm Depth of the upper soil layer is H= 10 m

F o r p = p , = 50 a m , A = 100 x 100 m2, N = 64 and k3m, we obtain by applying (1)

R,, = 0.13- 50 ( 1 - lie) log,, ( 24,,00) = 0.228 n

100

By inserting X = 10 m and A = 100 x 100 m' in

expression (4) for pipI >1, we calculate

x =0.5710g10(~)+0.0610g1~(10~10)log,,(64~1~)

x = 0.657

P2/Pl and, then, according to (3) and (2)

Fig 12 Factor Cr values for CRD electrodes for upper soa depul H = hn

The factor C, values can be fairly well assessed using

the empirical expression

with

X =

0.657

C = [ z) = 2.879

R = 2.879 * 0.228 = 0.656

Exact value of R for the case under consideration is R =

0.628 R which means that the relative error of the

approximate approach equals 4,6%

P

for -2 < 1

05910g1, (I;)+ -

0 5 7 1 0 g l o ( ~ ) +

IV CONCLUSIONS +0.01610g,, (4.2H)Oog,,( N f i ) ) * PI

(4) Graphs and approximate analpcal expressions are suggested for the calculation of the resistance to ground of square and rectangular grid electrodes combined with multiple rods, buried in uniform and two-layer soils The

expressions derived and the graphs provided can be used

in practical substations ground electrodes design

for -> P2 1

PI

+o.o6log,,(1oH)~og,,(~

1342

[l] F.Dawalibi, D.Mudhedkar, "Multi step analysis of

interconnected grounding electrodes", IEEE Trans., PAS 95,

N0.1, Jan 1976, pp.113-119

[2] J.Nahman, "Digital calculation of earthing systems in

nonuniform soil", Archiv f Elektrotehn., Bd 62, No.1, 1980,

pp 19-24

[3] J.Nahman, D.Salamon, "Earthing system modelling by

element aggregation", Proc IEE, Pt C, Vol 133, No.1,

Jan~ary 1986, pp.54-58

[4] E.B.Joy, N.Paik, T.E.Brewer, R.E.Wilson, R.P.Webb,

A.Meliopoulos, "Graphical data for ground grid "lysis",

IEEE Trans., PAS-102, No.9, Sept 1983, pp.3038-3048

[5] S.J.Schwan, " Resistance of grounding systems", Trans

Amer Inst Elec Engrs., Vo1.73,1954, pp.1010 1016

[6] P.G.Laurent, "Les bases generales de la technique des mises

la terre dans les installations electriques", Bull Soc Fr

Electr., Vol 1, 1951, pp.368402

[7] P.G.Laurent, "Guide sur la calcul, Fexecution et la mesure

des prises de terre", Rev Gen Electr., Vol 81, 1972,

pp.455467

[SI J.Nahman, S.Skuletic, "Resistances to ground and mesh

voltages of ground grids" Proc.IEE, Pt C, Vo1.126, No.1,

1979, pp.57-61

[9] Y.L.Chow, M.M.A.Salama,"A simplified method for

the substation grid resistance", IEEE Trans.,

calculating

PWRD-9, N0.2, April 1994, pp.736-742

[lo] M.M.A.Salama, M.M.EI Sherbiny, Y.L.Chow, "A formula

for resistance of substation grounding grid in two layer soil",

IEEE PES 1995 Winter M paper 95 WM 001 8 PWRD

[I I] J.Nahman, D.Salamon," Analytical expressions for the

resistance of grounding grids in nonuniform soil", IEEE

Trans PAS-103, No.4, April 1984 pp.880-885

[ 121 J.Nahman, D.Salamon, "Analytical expressions for the

resistance of rodbeds and of combined grounding systems in

nonuniform soil", IEEE Trans PWRD-1, No.3, July 1986

pp 90-96

[13] J.Nahman, VDjordjevic, "Resistance to earth of grid and

combined earth electrodes in uniform and two-layer soils"

submitted for publication to IEE Proc Part C., Dec 1994

Jovan M Nahrnen was born in Belgrade, Yugoslavia He received his Dipl Eng grade in Electric Power Engineering from the Electrical Engineering Faculty, University of Belgrade, in

1960, and TechD from the same University in 1969 In 1960 he joined the Faculty of Electrical Engineering, Belgrade, where he

is employed as a Professor at the Power System w e n t

Dunng the past several years Dr Nahman was active as a

consultant to the industry where he led some research in

pundug systems and neutral grounding and power system planning and reliability

Vladimir B Djordjevic was born in Belgrade, Yugoslavia

He received his Dipl Eng grade in Electric Power Engineering

from the Electrical Enginaxing Faculty, University of Belgrade,

in 1989, and M.Sc from the same University in 1992 In 1989 he

joined the Energoprojekt - Hidroinzenjering Co Ltd., Belgrade, where he is employed as design engineer for hydro power plants, irrigation systems and water treatment plants During the past

few years he was active as an associate to the Faculty of

Electrical Engineering, Belgrade, where he participated in some research in grounding systems