IEEE Transactions on Power Apparatus and Systems, Vol. PAS-97, No. 5, Sept/Oct 1978

DESIGN OF A LOW RESISTANCE GROUNDING SYSTEMFOR A HYDRO-ELECTRIC PLANT

LOCATED ON HIGHLY RESISTIVE SOILS

R. Verma, Member, IEEERousseau, Sauve, Warren Inc.

A. Merand P. BarbeauSocieti d'Energie de la Baie James

Consultants / Montreal, CanadaMontreal, Canada g

Abstract-A design procedure to achieve a reasonably low ground- buried copper conductor. Even the fact that the powerhouse and surgeing resistance for a hydro-electric generation and transmission complex&chamber are in contact with water was of little help due to the highsituated on extremely resistive rock-bed terrains is presented. Advantage t resistivity and relatively small volumes of water involved.is taken of nearby available volumes of water and low resistivity soils tot The intake structure, however, is in direct contact with the largedecrease the otherwise high resistance to ground of the plant. The papei volume of water of the forebay. Its resistance to ground could, there-gives a description of the grid being used, together with possible methods ofore, be brought to a value closer to what we were aiming for.of calculation for the various parts of the grounding network, taking Consequently, the grounding grid was designed to take advantageinto account the existence of multi-layer grounding paths. Though, of this situation, by interconnecting, through heavy copper conductors,there have been several papers written on theoretical methods for vari-k.the powerhouse, surge chamber, switchyard and intake structure. Itous electrode configurations, there is very little literature available `would then appear as several electrodes to ground connected in parallel,dealing with such a specific application and related calculationi the overall resistance to ground being the equivalent resistance of this

M network.1. INTRODUCTION Advantage could also be taken of the nearby deposit of low re-

sistivity clay, where ground rods could be buried and connected to theIt is often difficult, at the design stage, to assess the efficiency of above grounding grid to further decrease the overall ground resistance,

a grounding network, especially when the high resistivity of the sur- should this become necessary after the resistance measurements.rounding terrain makes it difficult to achieve a low resistance path to I An isometric view (Fig. 1) illustrates these various grounding grids.remote earth. All metallic enclosures are connected to the relevant grid through con-

This paper gives a description of the initial design as well as the ductors of a size depending on the location of the associated equipment.main guidelines used in the calculation of the ground resistance of thelLG-2 hydro-electric power plant, the first of several plants to be built Calculated Valuesby the Societe d'Energie de la Baie James in the Northern part of theProvince of Quebec, in Canada.

The project includes essentially a 16 unit, underground, 5328 MW TABLE Ipowerhouse, a 735 kV switchyard installed above the powerhouse, an Ground Resistance of Various Gridsintake structure, 16 underground penstocks and an underground surgechamber. The site is located on the Canadian Shield, and consists Location Ground Resistance (Q)mainly of outcropping precambrian rock of very high resistivity (up to , Surge chamber 19235000 S2-m as measured), with scattered deposits of glacial and post- < Draft tube 204glacial overburden materials. Among these, an extensive clay zone Powerhouse 178(resistivity 40 to 70 Q2-m) is situated nearby. Water resistivity in the Intake 0.6area is also very high (up to 500 Q2-m as measured). Ground rods 4

It is realized that the results of calculations given in this paper will 9 Switchyard 43have to be verified by site tests after construction. However, since the > Overall value including ground rods 0.5project will not be completed until 1982, no comparison between Overall value without ground rods 0.6analytical and measured values can be given at this stage.

2. DESCRIPTION OF THE GROUNDING GRIDTable I gives a summary of the ground resistance for each area.

, The calculations are detailed in subsequent sections. The values 0.5 orThe two criteria for such a design are:iThetwocriterianforsu chsy afdersignare: 0.6 ohm give a maximum voltage rise of the mesh of about 8000 voltsi) to ensure safety of personnel;ii) to ensure reliable operation of the relaying systems. which was considered acceptable.To meet these requirements, it is necessary to attain a low value D

of the total resistance to ground of the overall plant (in the order of METHODS USED IN CALCULATING THE RESISTANCES0.5 2), as well as safe values of touch and step potentials (the calcula-A General Proceduretions that were performed to check these potentials are not include er din this paper). ih a .

The ground resistance for each area described above was calculatedby one or several methods, depending upon the geometrical structure of

Description the grounding grid and on the nature of the surrounding media. Valuesl obtained by different methods for each area were, in general, reasonably

The powerhouse, surge chamber and switchyard being built in or close to one another and the most conservative value was usually takenon the rock, it was not possible to obtain a resistance to ground less as the design value.than an order of a multiple of ten ohms for any of these areas by using The main guidelines for the calculations are given in the following

paragraphs. More detailed references can be found in Appendix I. In allPaper F 77 731-3, recommended and approved by the IEEE Substations the calculations, the basic definition of the ground resistance of a body

Committee of the IEEE Power Engineering Society for presentation at the IEEE kPES Summer Meeting, Mexico City, Mex., July 17-22, 1977. Manuscript submitted was kept in mind, it being the resistance in the path of the currentFebruary 7, 1977; made available for printing May 16, 1977. flowing from the body to remote earth.

0018-9510/78/0900-1760$00.75 0 1978 IEEE

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3.1 Powerhouse 3.2 Surge Chamber

The following elements were considered to contribute to thegrounding of the powerhouse:

- Grounding conductors buried in concrete.- Rock bolts installed to support the arch roof of the powerhouse.- Steel linings in the lower portion of the penstock, the scroll case

and the draft tube of each unit and directly in contact with thewater.

a) Conductors buried in concrete:

Copper conductors in the form of a grid (abcd, Fig. 1) are buriedat the turbine floor. The ground resistance, calculated using equations(11), (12), and (13), appears in Table II. A design value of 178 Q2 wasadopted.

b) RockBolts in the Arch Roof:

Equation (19) was applied to calculate the ground resistance ofthis multi-electrode network. The calculated ground resistance for thepowerhouse was 89.7 Q2. This value was considered too high for thebolts to be of any use in the grounding, especially considering the factthat there is no electrical apparatus nearby.

n = number of bolts = 35192b = diameter of bolt = 3 cmk, = 1.0, factor for ratio of length (440 m) to width (34 m) of

the mesh.LI = length of bolt = 5.25 mp = 35000 Q2-m (rock)

c) Steel Linings in Contact with Water:

Because of the high rock resistivity, the lowest resistance path toremote earth is through the water in the penstock to the forebay.Equation (1) below gives the resistance of this column of water simplyregarding it as a cylindrical conductor, not taking into account the non-

uniform current density across the section:

R =(1)

Where, Q = length (m)z = radius (m)p = resistivity of water (Q1-m)

For, = 177 m, y = 3m and p = 400 Q2-m (an average value),R amounts to 2504 Q2 and for 16 penstocks in parallel, the equi-valent resistance is 156.5 fl (without mutual effect). This is ob-viously too high a resistive path to be effective for passage ofground fault currents. Taking into account the variable currentdensity would further increase this value.

Copper conductors in the form of a grid (efgh, Fig. 1) are buried inthe surge chamber. The ground resistance, calculated by the same

methods as in section 3.1 a) appears in Table II. A design value of192 Q2 was adopted.

3.3 Draft Tube

Copper conductors (ij), Fig. 1, are embedded in the concrete ofeach draft tube. Table II shows ground resistance obtained by equations(18) and (17). A design value of 204 Q2 was taken.

3.4 Intake Structure

The following elements were considered to contribute to thegrounding of the intake structure:

- Grounding conductors embedded in the concrete.- Steel trash-racks in permanent contact with the forebay water.- A number of conductors laid on the floor of the forebay and

connected to the intake grounding mesh.

a) Grounding Conductors Embedded in Concrete:

(Mesh klmn, Fig. 1). Equation (15) (considering the mesh equiva-lent to a vertical plate) or equation (13) were used to calculate theground resistance.

mesh lengthheightdepthdiameter of wire

- 402.7 m= 30.75 m= 1/2 (height)= 2 cm

The resistance is 1.3 Q2 and 2.17 QZ using the first and secondmethods respectively and assuming p (concrete) is 400 Q2-m. This cal-culation is valid only for an infinite concrete medium. The effects ofunderlying rock and forebay water were taken into account by the fol-lowing relation4 (see Appendix III):

Resistance of mesh to ground = resistance of mesh to concrete(considering concrete as an infinite volume) - resistance of an elec-trode formed by the intake structure into infinite concrete + re-

sistance of concrete bound by water and rock. (2)The first term is already calculated above.Equation (16) was used to determine the second term, regarding

the intake as an equivalent horizontal cylinder shown in Fig. 2.The cylinder cross-section is taken equal to the intake cross-section,and its length is the same as that of the intake. For an average width of6 m and a depth of 36 m, the diameter of this cylinder would be 16.6 m.For: L = 400 m

d = 16.6mh = 18 mp = 400 Q2-m (concrete),

we get: R= 0.94Qi

TABLE II

Ground Resistance of Various Grids

MESH AREA BURIED COPPER RESISTANCE (ohms)Length (m) Width (m) Length (m) Diam. (cm) Depth (cm) Laurent' Schwarzz Dwight

Turbine floor 460 23 1285 1.61 45.7 178 112 261(grid abcd)

Surge chamber 455 20.6 1047 1.61 45.7 192 117 275(grid efgh)

Gallery at draft tube 457 (single 457 1.61 45.7 - 203 204(conductor ij) conductor)

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Putting in matrix form,

C[] = CR] [fI ]nr (3)

n = number of electrodesVl = V2 = .... Vn = V, being potential rise of each electrodeRii = electrode resistance to groundRij = mutual resistance between electrodes i and jII, 12,.... In are currents in the respective electrodes

Since V1 = V2 = .... Vn = V, the values of I,, 12 .... In can be obtainedin terms of V through inversion of [R]. Since the copper conductorconnecting the electrodes is connected to the system grid at both endsand at the center, the symmetrical distribution of current allows theorder of the matrix to be reduced to n/2. The values of [R] can be ob-tained as follows:

Riii can be calculated by equation (15) or (14), considering it ineither case as a vertical plate in water.

Ri can be calculated with a reasonable approximation, using equa-tion (4) below1'2:

2i;x(4)

xij = distance between electrodes i and j (should be greater than thelinear dimension of each electrode)

p = resistivity of waterFrom these, knowing matrix [RI, [RI-' can be found. The totalground resistance Rt would then be:

R = Vt En

i-lThe trash-racks are equally spaced at 22.5 meters. For a trash-rack13.3 m x 13.6 m, Rii = 8.23 Q2 by the first method and 8.33 Q2 by thesecond method. The value of Rt = 1.32 Q2.A d

Fig. 2. Equivalent Cylinder (longitudinal view)

The third term of (2) requires the apparent resistivity pa due tothe dual medium (water and rock). This was calculated using equation(24). The circle equivalent to the intake structure (400 m long, 6 mwide) has a radius of 27.6 m, with its center at mid depth of water. Thisyielded a value pa = 1.39 p (water).

Substituting pa for p in equation (16), the resistance of the con-crete in contact with water and rock was calculated to be 1.42 Q2.

Equation (2) then becomes:R=2.17-0.94+1.42=2.65Q2.

b) Trash-Racks:

Each trash-rack can be regarded as a vertical electrode in water,and since all of them are inter-connected through the buried copperconductor, as shown in Fig. 1, they act as parallel electrodes. For calcu-lation of ground resistance, the apparent resistivity due to the combinedeffect of water and rock has to be considered, as well as the mutual ef-fect of parallel currents flowing to water via these electrodes.

Calculation considering water only:

All electrodes are at the same potential, given by equation (3)below:

Vl = I.R + I2RI 2 + *- -@ + InRInV2 = I2R21 + I2R22 + *m-m + InRn 2n

V IIR + 2R + + I Rn n1 nL n nn

Calculation considering the effect of rock:

To take this into account, an additional term Ra must be added,which can be calculated from equation (23b).For, h = 22.5 m (for minimum water level)

Q = 13.5mPI (water) = 400 Q2-mP2 (rock) = 35000 Q2-mRa = 9.52 Q

This modifies the earlier value of Rii to 17.75 Q2. On account of this,the diagonal elements of the [RI matrix get modified, changing thetotal resistance to 1.93 Q2.

The matrix [RI (reduced to size n/2) is shown in Appendix II,with and without the effect of rock; the current distribution in eachtrash-rack is also shown in Appendix II.

c) Conductors in the Forebay:

The problem involves a 2-layer medium (water, Pi, on rock, P2)-Since the electrode layout is horizontal, equation (24) was used to de-termine the apparent resistivity pa. To optimize the resistance withrespect to the length, number of conductors, area covered by theseconductors and depth of immersion, computer was used to evaluateboth the apparent resistivity and the grid resistance to ground.

To calculate the ground resistance of a single conductor (500kcmil), equation (18) was used, replacing p by pa. The mutual re-sistance between conductors and the overall resistance were determinedutilizing the same procedure used for the trash-racks.

Values obtained are shown in Table III. A design value of 1.71 fQusing 4 conductors (each 1000 m long) was adopted.

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TABLE IIIGround Resistance of Conductors in the Forebay

Length (m)

a forh = 1P1 dR (1 cable) (Q)

120 300 450 600 800 1000 1250 1500 2000 2500 3000 3500 4000

3.22 4.45 5.2 5.28 6.54 7.15 7.85 8.5 9.5 10.5 11.36 12.12 12.84

16.65 10.96 9.12 8.02 7.05 6.37 5.77 5.32 4.67 4.23 3.9 3.64 3.43

R (2 cables) (SI) 8.32 5.53 4.62 4.08 3.6 3.26 2.96 2.73 2.41 2.19 2.03 1.89 1.79

R (3 cables) (Q) 5.75 3.86 3.25 2.88 2.56 2.33 2.13 1.98 1.76 1.62 1.51 1.42 1.35

R (4 cables) (Q) 4.16 2.83 2.39 2.12 1.87 1.71 1.56 1.45 1.28 1.20 1.09 1.03 .98

PI = 400 Q-m, P2 = 35000 Q-m, width of forebay = 400 m, conductors are equally spaced.

3.5 Switchyard

The grounding grid of the switchyard covers an area of 503 m X305 m and involves 11000 m of copper conductors buried 0.5 m belowgrade. Applying Laurent' equation (1) and taking p as 35000Q2-m,the ground resistance is 43 Q2.

3.6 Ground Rods in Nearby Clay

As stated above, the site offers the possibility of installing groundrods in clay of relatively low resistivity. As will be shown in the follow-ing analysis (Table IV), to ensure a reasonably low path to ground, thisdeposit should be of sufficient extent and depth.

Fig. 3 shows a grid made of 36 rods arranged in a hollow square.Though different number of rods may be tried, this arrangement affordsan optimum value6.

Design of the Rod-bed:

Since the resistivity of rock (P2 ) iS much higher than that of clay(p, ), the rod separation p has to be less than h. For optimum design,one could use the ratio h/p as two6. Also, since the rods must be burieddeep enough to minimize the influence of the high resistivity frozensurface layer in winter, the ratio6 between frozen layer thickness androd separation was taken as 0.2. Minimum resistance is achieved byusing a long rod, buried below the frozen layer. However, the rod shouldbe kept well above the underlying rock.

.b Surface

h 21aY (p.)

Cross-section

_Ipf4 4/0 Copper sonductor

Plan View

1--' *- *0 * *Plan View

electrode having the shape of the volume of clay into infinite clay+ resistance of clay in rock. (5)The resistance R of a single rod in clay is calculated by equation(21):R=4.3Q (usingh=20m, z=2m,p lOnm, LI = lOm)The resistance of 36 rods forming a hollow square may be calcu-lated by equation (22). Equation (6) below gives the equivalenthemisphere radius re to be used in this equation:

2Rrre

Hence re = 1.47 m,

(6)

redistance between rods

From equation (22), the total ground resistance R22 for 36 rodsis 0.26Q.

Interconnection:

The resistance RI, of the buried copper conductor grid connect-ing the rods is calculated by using equations (11 ) or (12).

For, z = 2mL = 360m2a = 1.32 cm, (diameter of conductor)Rll = 0.31 fS from equation (I 1)RI, = 0.29 Q2 from equation (12)

Mutual Resistance:

The mutual resistance R12 between the copper mesh and theelectrodes is calculated by equation (20).

For, L = 360 mLI lOnmA =9OmX90mz =2mp =40S-m

we get: R,2 = R21 = 0.18 Q2

Fig. 3. Rods (36) in a hollow square.

Ground Resistance:

As for the intake structure, the effect of the underlying rockcan be taken into account by using the following relation4 (see Ap-pendix I1I):

Resistance of the grid to remote earth = resistance of grid to clay(considering clay as having an infinite volume) - resistance of an

Ground Resistance of Clay:

The clay overburden is regarded as a half ellipsoid. To calculate itsresistance, equation (7) is used.

Resistance of clay = 2ffC (7)

C = capacitance of the clay combined with its image over the sur-face of the earth, the combined electrode being considered asin air

p = resistivity of the underlying rock in fQ-mCase 1: a - b>c

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Table IV shows values of capacitance and resistance based on p (rock)as 35000 Q2-m.

- '/aZ - c2

arc sin /ai - cZa

All dimensions are in metres and refer to Fig. 4 below.

Case 2

a 0 b

Capacitance - Va2 _ cyF (0o, k)

wrhere, k2 a - < 1a _-c

(8)TABLE IV

Ground Resistance of Clay

(9)

sin Oo ' <a2

OoF (Oo, k) do

° y1 - k2sin20For 40 very close to v/2, this integral can be approximated to:

=- [122+13) 4 35 .2<1-+l(j) k +(2tW) k +( 4-~)k ,k2

a (m) b (m) c (m) Capacitance (m) R Q

121 121 25 86.67 64.3

2500 800 30 1134.0 4.9

3340 1060 30 1522.4 3.7

The R values given in Table IV correspond to the third term in rela-tion (5). The second term is obtained by dividing by p rock (35000)and multiplying by p clay (40).

This clearly shows that the dimensions of the clay medium playan important role in determining the value of the ground resistance forthe grid.

The dimensions of the clay deposit at the site permit us to use aground resistance of 3.7 Q2.

Total Ground Resistance of the Grid:

The total grid resistance to ground as obtained from expression (5)is:

Ground Rods in Clay

Clay Ellipsoid

Fig. 4. Ground Rods and Grid in Clay

R11R22 - R12R

R11 + R22 - R12 - R

3.7 x 40______ + 3.735000 (10)

With R,1 = 0.31 a, R22 = 0.26 Q2 and R12 = R21 = 0.18 Q2, total gridresistance = 3.9 Q2. The first term is the resistance2 of grid and rod-bedin infinite clay.

CONCLUSIONS

Some useful elements, mainly the intake structure and water, anda nearby deposit of low resistivity material of sufficient dimensions havebeen shown to be effective in reducing the overall ground resistance ofthe LG-2 site. It has also been shown that some elements, for instancethe penstock lining in contact with the water are not always as effectivegrounding paths as they are often believed to be.

Different methods have been compiled and applied in this paper tocalculate the resistance of the above and other elements of the under-ground power plant and proved valuable as a way to select the most ef-ficient grounding paths at the design stage. These methods are generaland can be applied to other types of plants as well.

To get realistic results, careful measurements should be made todetermine the resistivities. The resistivity of concrete for instance, willvary with the amount of water it contains; resistivity of the concrete ofa dam in contact with water is not the same as that for a powerhousebuilt on rock. Therefore, it is essential that the design be checked bycareful measurements after completion of the installations. Still thevalues obtained can be very useful to the designer, since in such a work,overdesign could be costly and underdesign may prove dangerous.

ACKNOWLEDGEMENIrS

The authors express their appreciation to the Management ofRousseau, Sauve, Warren Inc. and Societe d'Energie de la Baie Jamesfor their cooperation. Mr. Verma, who is a registered Doctoral studentwishes to thank Concordia University for the facilities offered.

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APPENDIX I

ANALYTICAL EXPRESSIONS FOR RESISTANCE OFGROUNDING SYSTEMS

p = resistivity of homogeneous medium, Q2-mpa = apparent resistivity due to two layers of different resistivity, Q2-mR = resistance to remote earth of a grid, Q2

A. RESISTANCE OF GROUNDING GRIDS

I Resistance of a ground grid occupying the same area as anequivalent circular plate from Laurent'

R 2 p + P4r L (11)

L = total length of the buried conductor, mr = radius in metres of a circular plate occupying the same area

as the grid, m2. Resistance of an intermeshed grounding network from Schwarz2:

L_ 2L ]-k2 (12)1TL g al

L = total length of all conductors in metresa V/72Y for conductors buried at a depth of z in metres, ora = a for conductors on earth surface2a = diameter of conductor, mA = area covered by conductors, m2k, and k2 are co-efficients depending upon the dimensions of thearea (refer to paper2 ).

B. GROUND RESISTANCE OF A LOOP OF WIRE, A CIRCULARPLATE OR A RECTILINEAR ELECTRODE

I Ground resistance of a ring of wire from Dwight3:

R= 2 [loge 8D +loge 4D (13)

D = diameter of the ring, md = diameter of the wire, mS/2 depth of the ring, m

2. Ground resistance of a vertical circular plate from Dwight3:7 a2 99 a4** (4

R = P + 4p |+ 24 + 39 4 +--v-3 (14)8a 4rrS 24 ~ 320 S j

a =radius of the plate, mS/2 = depth, m

3. Ground resistance of a vertical or horizontal circular plate fromAIEE5 Guide 80:

R =P [1 - r ] (15)8y 2. 5h + y

= radius of the plate, mh = depth of the centre of the plate, m

4. Ground resistance of a rectilinear electrode from AIEEs Guide 80:

R = 0.366 P og + log 3L (16)L 2d 8h'(6

L = length of electrode, mh = depth below surface, md = diameter of the electrode, m

C. GROUND RESISTANCE OF A BURIED HORIZONTAL WIRE

1. Ground resistance of a buried horizontal wire from Dwight3:

R = log- +10g64L - 2 + S S S4RrL [o a S 2L 16L2 512L41

2L =length, m (17)S/2 = depth, ma =radius, m

2. Ground resistance of a straight horizontal wire from Schwarz2:

R=L- [loge3, - 1] (18)

For, a<L and 2Z<LL = conductor length, mZ = depth (m) to which conductor is buried2a = conductor diameter, ma' =V a-za = a if conductor is on surface

D. RESISTANCE OF A ROD-BED

I Combined resistance of several closely spaced rods from Schwarz2:

R = P [lg b4L12K_LI (n _ 1)2] (19)2ITnL I b VA

LI = length of each rod, m2b = diameter of each rod, mn = number of rods in area AK, = a co-efficient, function of the ratio between length and

width of the area (refer to paper2)

2. Mutual ground resistance R12 between rod-bed and grid to whichit is attached from Schwarz2.

R12 = L [loge- + K, -- K2 + 1 (20)

L1 = length of rod, mL = length of buried conductor of the grid, mA = area covered by conductors, square metres

K, K2 = co-efficients (refer to paper2)

3. Ground resistance of a vertical rod from Schwarz2:

R = 41gLI _ 1l+logl+.Z/Ll +27RL1P geL b

1 e 1 + 2Z/Ll

loge 4Z/Li + 4 (Z/LI)2 ] (21)

b<Lj Li 1 + 4Z/Lj + 4 (Z/Ll)2LI = length of rod, m2b = diameter of rod, mZ = depth of earth fill over top of rod, m

4. Ground resistance of a number of equally spaced rods forming ahollow square from Tagg6:

R = N Ka (Resistance of one rod) (22)N

equivalent hemisphere radius representingresistance of a single roddistance between rods

N =number ofrodsK = a factor depending upon the number of rods and their

spacing (refer to book6).

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5. Ground resistance R' of a rod driven in an upper layer (Pi),taking into account the effect of a second layer (P2) below fromTagg6:

R' -R+Ra (23a)R = resistance of rod considering layer pi above as infiniteRa = additional resistance due to effect of layer (P2 ) below

n nh/~12irR. n=1 - 2 loge (nh/ - 1) (23b)

K P2 -PlP2 +Pi

Q = length of rod, mh height of layer pI, m

E. APPARENT RESISTIVITY OF STATION GROUND IN NON-UNIFORM SOILS FROM ENDREYNI7

Ratio N between apparent resistivity (pa) and top layer resistivity(Ps) for electrodes having dominant dimension as horizontal:

(24)c m rKm+ + 2Km + K1m-

N = pa =1+ mO m L. Cm Cm-]N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Pi loge 16a + Ko+

do CO+

P2 - PiP2 + P1

Km , Cm = /TTTTm)Km Vi-M)+m'2 o

'cx + m2 a

K,m+= cx

2a + (m + 0)2p Cm+ = v/ + M +c 2

Km-= ,Cm- =

lo a + (m _ 0)2 +(m_)

Z = depth of wireh depth of layer Pi

Equivalent radius of thea electrode in metresh h(in metres)

P2 = resistivity of the bottom layerdo = diameter of the conductor, m

TABLE VCURRENT DISTRIBUTION IN TRASH-RACKS

Current II I2 I3 I4 Is I6 I7 i8=I16 =I15 =114 =113 =112 =11 =110 =I9

Consi-dering

water 7.02 4.85 4.59 4.39 4.29 4.21 4.18 4.16 x-02Vinfi-nite

Consi-deringeffect -2of 3.95 3.39 3.23 3.14 3.08 3.04 3.03 3.02 x10 vr.ockbelowwater

APPENDIX III

CONCEPT FOR FORMULATION OF EQUATIONS (2) AND (5)

Assume an electrode M buried in medium A, bound by surface S(see Fig. 5). The body A is in turn buried in medium B considered asbound by remote earth R. The ground resistance to a current flowingfrom electrode M is constituted of the resistance of A and B in series1,i.e.,

R = RA + RB

Fig. 5. Electrode Buried In Top Medium A

APPENDIX II

MATRIX [RI FOR THE TRASH-RACKS

FR]

8.41 3 1.60 1.16 .95 .84 .77 .75

3.00 8.44 3.03 1.65 1.21 1.01 .91 .86

1.60 3.03 8.48 3.08 1.71 1.28 1.10 1.02

1.16 1.65 3.08 8.54 3.15 1.80 1.39 1.26

.95 1.21 1.71 3.15 8.63 3.26 1.96 1.63

.84 1.01 1.28 1.80 3.26 8.79 3.50 2.33

.77 .91 1.10 1.39 1.96 3.50 9.16 4.20

.75 .86 1.02 1.26 1.63 2.33 4.20 11.03

For 2-layer medium of water on rock, the diagonalelements getting modified to 17.93, 17.96, 18, 18.06,18.15, 18.31, 18.68, 20.55.

If the body (medium B) bound by surfaces S and R was of thesame material as A, there would be a single medium path. If the surfaceS is close enough to an equipotential of this new medium, the value ofRA remains the same, and the total ground resistance becomes:

R'= RA + RAWhere, RA = resistance through body A (bound by surface S),

same as above

A resistance through body A' (bound by surfacesS and R)

R' is obviously the ground resistance of the electrode M in an in-finite medium A and can be easily calculated. RA is the resistance of anelectrode having the shape S in an infinite medium A. This can be cal-culated if the shape S of the electrode being considered is simple.

Hence, RA R'-RA

RB is the resistance of an electrode having the shape S in an infinitemedium B. The formula is the same as for R', replacing PA by PB-

Hence, R= RA + RB

or, R=R' -RA:tRB.

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REFERENCES

[ I] P. G. Laurent, "Les bases ginerales de la technique des mises a laterre dans les installations electriques", Bulletin de la SocidteFrancaise des Electriciens, 7ieme serie, tome 1, no. 7, July 1951,pp. 368-402.

[2] S. J. Schwarz, "Analytical Expressions for the Resistance ofGrounding Systems", AIEE Transactions, Vol. 73, part III-B,1954, pp. 101 1-1016.

[3] H. B. Dwight, "Calculations of Resistances to Ground", AIEETransactions, Vol. 55, Dec. 1936, pp. 1319-1328.

,[41 E. J. Fagan and R. H. Lee, "The Use of Concrete-Enclosed Rein-forcing Rods as Grounding Electrodes", I.E.E.E. Transactions onIndustry and General Applications, Vol. IGA-6, No. 4, July/August 1970, pp. 337-348.

[51 "Guide for Safety in A.C. Substations Grounding", IEEE Standard#80, 1961.

[61 G. F. Tagg, Earth Resistances, George Newnes Limited, London,Great Britain, 1964.

[7] J. Endreyni, "Evaluation of Resistivity Tests for Design of StationGrounds in Nonuniform Soil", AIEE Transactions, Dec. 1963,pp. 966-970.

gkRajindma Verms was born in Punjab, India onJune 15, 1940. He received the B.Sc. Engg.degree in Electrical Engineering from PunjabEngineering College, Chandigarh, India in 1962and won a Gold Medal with Honors, and the M.Engg. degree from the Nova Scotia TechnicalCollege, Halifax, Nova Scotia, Canada in 1971.

He worked as Lecturer and then AssistantProfessor from 1962 to 1964 in the ElectricalEngg. Department of the Punjab EngineeringCollege, Chandigarh, and since 1964 worked as

Assistant, Senior and Project Engineer on Indian Railways. Presently,

he is with R.S.W. Inc., Consultants, Montreal, since 1974, and is aRegistered Doctoral Student at Concordia University, Montreal. He is aRegistered member of the Order of Engineers of Quebec.

Alain Merand was born in France in 1939. Hegraduated in electrical engineering from the"Ecole Nationale Superieure d'Electrotechniquede Grenoble" in 1964.

He has been since involved with variousdesign responsibilities, mainly concening 735kV switchyards and transmission lines, andhydroelectric power plants. He is presentlyworking with Rousseau, Sauve, Warren Inc., inMontreal, as project engineer in connection withthe electrical design of the LG-2 and LG-4 power

plants in the James Bay area.Mr. Merand is a member of the Order of Engineers of Quebec.

Plerre Barbeau was born in Montreal, Quebec,Canada on April 5, 1943. He received the B.Sc.degree in electrical engineering from EcolePolytechnique de Montreal, Quebec, Canada in1965.

He joined the engineering department ofHydro-Quebec in 1969. In 1973 he was transfer-red to the James Bay Energy Corporation as aspecialist in Power Apparatus.

Mr. Barbeau is a member of the Order ofEngineers of Quebec.