IEEE Transactions on Power Apparatus and Systems, Vol. PAS-103, No. 9, September 1984

CURRENT FOR DESIGN OF GROUNDING SYSTEMS

B. ThaparPunjab Engineering College

Chandigarh.

Abstract - A simple method to estimate thecurrent for calculating the size of the ground-ingconductor and for evaluating the step,touchand transferred potentials, is presented. Thefactors effective in making these currents diff-erent from the total fault current have beenindicated. Various types of substations, diff-erent fault locations and a wide rangeof param-eters of aerial ground wire encountered inpractice are considered.Data presented emphasizesthe saving in grounding design costs that canbe realised by using maximum realistic groundcurrents rather than maximum calculated totalfault currents for evaluation of step & touchpotehtials.

INTRODUCTION

For the design of grounding systems inhigh voltage stations it is necessary to eval-uate the realistic value of the fault currentto be used in determining (a) the size of thegrounding conductor and (b) the step,touch andtransferred potentialsl. For determining thesize of the grounding conductor it is necessaryto know the maximum current, Ic,that wouldflow in any section of the grounding systemand for evaluating the potentials the maximumcurrent, IG' that would be discharged by thegrounding system to the ground is required.

Only-single line to ground fault is con-sidered as this gives the highest zero sequen-ce current in most cases. The -total fault cur-rent returns to the system through a number ofpaths.Only the current flowing through7thegrou-nding system at the station to the ground con-stitutes the current I . Accurate analyticalmethods to determine tie fault current distribu-tion between soil and ground conductor areavailable2,394. These methods require the useof the computer and the values of the networkparameters which may not be easy to measurewith certainty. For the design of groundingsystems, high degree of accuracy is not nec-essary because of the uncertainty of basic dataof the soil resistivity. This paper presents adirectly applicable simple method, to estimateI and I-. Because of their extensive use onlytge overfiead transmission lines are consideredin this paper.

FAULT LOCATION

The fault location which produces the max-imum I and IG may be either on the higher vol-tage side or lower voltage side of thestation transformer. It may be either inside

84 WM 147-5 A paper recommended and approvedby the IEEE Substations Committee of the IEEEPower Engineering Society for presentation at theIEEE/PES 1984 Winter Meeting, Dallas, Texas,January 29 - February 3, 1984. Manuscripts sub-mitted August 26, 1982; made available for print-ing November 28, 1983.

Sunil K. MadanPunjab State Electricity Board

Chandigarh (India).

or outside the station on a transmission line.Inside the station,the current supplied to thefault by the local transformer circulates i-nthe station itself and does not form part ofIG, whereas the current supplied to the faultthrough the transmission lines has to returnto the system through the grounding system andground or through the aerial ground wires ontransmission lines. When a fault is outside thestation the current supplied to the faultthrough the transmission line from the otherstations has negligible contribution to IG.Thecomponent of fault current supplied by thelocal transformer returns to the system via(i)overhead ground wires which have metallicconnection to the neutral through the stationstructure and(ii)the tower footing and ground-ing system of the station. The current flowingvia path (ii) constitutes IG. If the fault isnear a station, major part of the current suppli-ed by station will return via path(i) andif the fault is far away from the stationthe magnitude of the fault current supplied bythe station will be less because of the lineimpedance. Therefore, in most cases maximum IGwill be obtained for faults insidethe station.

The substations in an electric power sys-tem for purposes of determining IC and IG maybe classified into following categories.

1 Step up station at generating station,transformer connected in delta-wye.

2 Intermediate station(Power source on both sides).i) Wye-wye connected transformer.

ii) Auto transformer.iii) Delta-delta connected transformer.iv) delta-wye connected transformer.

3 Terminal station (Power source only on H.Vside). This can be considered as a specialcase of the Intermediate Station when thecontribution of the fault current fed fromthe lower voltage lines is zero.

Wye-wye connected transformers and auto-transformers may have a tertiary winding.The analysis presented in this paper can beapplied to stations having transformer withor without the tertiary winding.

Fig. 1 gives the components of line to groundfault current in various paths for fault onhigher voltage or lower voltage side of thetransformer in various categories of substations.Notations used for the currents shown in thefigure are:

IFH,IFL,IFW,IFD

IHH,IHL

ILL'ILH

= Total fault current for faulton higher voltage side,lowervoltage side, wye side anddelta side of the transformerrespectively.

= Current fed from otherstationson higher voltage lines whenthe fault is on higher voltageside and lower voltage side ofthe transformer respectively.

= Current fed from other stationson lower voltage lines whenthe fault is on lower voltageside and higher voltage sideof the transformer respectively.

0018-9510/84/0900-2633$01.00 © 1984 IEEE

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1j rG= OD-IDi-t

Fig. 1.(a) Step up station-fault on highervoltage side.

(b) Step up station-fault on lowervoltage side.

(c),(e),(g) Intermediate station -fault on higher voltage side.

(d),(f),(h) Intermediate station-fault on lower voltage side.

(i) Intermediate station-fault onwye side.

(j) Intermediate station-fault ondelta side.

= Current fed from other stationswwon wye connected side of thetransformer when the fault ison- wye connected side.

IDD = Current fed from other stationson delta connected side of thetransformer when the fault ison delta connected side.

It = Current supplied by localtransformer.

IHi wi = Current diverted on groundwires of higher voltage linesand wye connected lines respect-ively due to,induction.

,? IDi = Current diverted on groundwires of lower voltage linesand delta connected lines res-pectively due to induction.

a= Current diverted from station

a through conduction by theground wires of all thetransmission lines terminatingon the station and, havingtheir ground wires connected togrounding system of the station.

A perusal of Fig. t.will indicate that themaximum value of I in all cases is the totalCfault current on higher voltage side or lowervoltage-side.The higher value of the two is tobe considered. However if care is exercisedand it is ensured that the total fault currentwill have atleast two paths to follow,Ic maybesafely taken as half of the total fault currentor even less depending on the actual configura-tion of the system. Maximum value of IG interms of various components of the 9ault curre-nt in each case is given in table I

It is observed that in all cases maximumvalue of IG is given by sum of the currents(in amps) supplied by other stations to theground on all transmission lines minus thecurrent diverted by the ground wires due toinduction and conduction.

DIVERSION OF CURRENT DUE TO INDUCTION

Fault current flowing in the line conductor,IL, induces current, I.,in the overhead groundwires, of the same line.

TABLE ICURRENT FOR DESIGN OF GROUNDING SYSTEMS

S.No. Type of station

1 Step up station IHH-I Hi-Ia2 intermediate station IF +I -I -I -IIHH LH Hi Li awye-wye

or auto-transformer ILL+IHL - Li - Hi -Ia3 Intermediate station I -I Hi a

delta-delta HH - -iaLLLI Hi Ia

4 Intermediate stationdelta-wye

5 Terminal station

IWW- IWi IaI I -I -ILDO Di aSame as for interme -diate station-contribu-tion of fault currentfrom low voltage linesis zero.

Note: 1. Where more than one current is men-tioned select the one that has thehigher value.

2. All currents are to be taken in ampsand not in p.u. values.

Ii = m IL (1)

where m = Z /Zgm gZ = Mutual impedance between phase

m9 conductor and the ground wires-ohms/

kmZ = Self Impedance of ground wire withg ground return-ohm/km.

Z and Z given by6:gm 9

Z = 0.000 988 fgm D

+j 0.002 8938 f log eD ohms/kmseparation

Zg = rc+O.000 988 fgc o.002 8938 f log1O GRD

+ jO.002 8938 f log1 e10GMR(GW)

(2)

ohms/km (3)

(0i tB'IWW-Iwi-la

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Where De = Equivalent depth of earth return= 658.4 -/f m

rc = Resistance of ground wire-ohms/km

p = Resistivity of earth - ohm-m

f = Frequency - Hz

The ratio m was calculated for the follow-ing ground wires and for all the configurationof conductors shown in Fig.2.

GSS - 7/2.794, 7/3.15, 7/4.064, 19/2.642ACSR - (6Al+1St)/3.O0 (6A1+lSt)/3.66,(6Al+lSt)/

4.09,(12A1+7St)/2.924 ,(18Al+19St)/2.591.

Resistivity of earth was assumed to be 100 ohm - m.Variation of the earth resistivity from 50 to300 ohm-m will not cause an error of more than12% in the value of Iml.

1..I6.8,JF11.42., S

(a) (bI (cI (dl

a b* a

; 2~~3.28 3.39 42.

(e) (f) (g) (h) (i)

Fig. 2. Disposition of phase and ground conductorsfor various transmission lines-132 kV,220 kVand 400 kV (Dimensions in meters).

The results of calculations showed thatthe variation in configuration of conductorsand number of circuits, within practical limi-ts, had negligible effect on the ratio m. Theparameters that mainly affect m are material,size and number of the ground wires. Fig. 3gives variation of m with diameter of groundwire for GSS and ACSR conductors.

78

68

58

- 0.6

0.5

B 0.4

0.3

24- 0.21

8

0.Q

- TWO GROUND WIRESC'*GSs __ ---- ONE GROUND WIRE\ s ~~~~ ~~~~~ ~~ ~~~ ml ACSR

< ~~~~~~- ---L--__R

9 10 II12 I314 .56 En!0 g 9 10 11 12 I! 14O15D6 17 IDOUTSIDE DLAMETER, mr

DIVERSION OF CURRENT DUE TO CONDUCTIONOverhead ground wires and tower footing

resistance form a ladder network. If the numberof towers is 20 or more the length of the linecan be considered as infinite for the purposeof determining the admittance Y of the laddernetwork which is approximately given by4,7,8.

(4)Y = G+JB =I

Zspan Z x R2 + span t

Where Z = The self impedence of one span ofspan ground wire with ground return-

ohms/km.R = Average tower footing resistance

for the first 20 towers-ohms.

Z an can be determined with the help of(3). He resultant admittance Y' of all thelines connected to the station can be determinedby considering the ladder networks of all the

lines in parallel.Y'and the station groundingresistance, R , act in parallel. The currentdischarged te the ground from the stationis given by:

|GI lIdI |R + 'I= I' a (5)Where I' is the sum of currents supplied

by other stations to the ground over all trans-mission lines minus the current diverted bythe ground wires due to induction.

G,B and a have been computed for a largerange and number of practical values of the variousparameters.The charts shown in Figs.4 to 6 havebeen generated with the results obtained fromthe computer. Figs. 4 & 5 give the value of G& B respectively as functions of the diameter of theground wire, span length, tower footing resistanceand the number of ground wires used. To use thecharts one selects the diameter on the leftordinate & follows along a horizontalline whereit intersects the required curve of the span.One then proceeds vertically upto the intersectionwith the curve representing the tower footing

Fig. 3. m Versus outside diameter of ground wire.

o.7r

la

.1

Fig. 4. Value of G for overhead lines.

Fig. 5. Value of B for overhead lines.

CONCLUSIONS

Current diverted through induction in theACSR ground wires is about 3 times thecurrent diverted through induction in GSSground wires under similar situations forACSR & GSS wires having about the sametensile strength.

a In all cases the total fault current gov-erns the size of the conductor for thegrounding system.

3 The current to be adopted for calculatingthe potential gradient is equal to thesumof currents supplied by other stations tothe ground through transmission lines minusthe current diverted by the ground wiresdue to induction and conduction.

4 Maximum realistic currents IC and IG whenadopted for design calculations can resultin substantial saving in the cost of ground-ing system.

REFERENCES

1 "IEEE Guide for safety ingrounding", IEEE std. 80, 1976.

B

A0 .1 .* .3 .4 .5.

G X Rg

Fig. 6. Value of a for substations.

,resistance, then continues from this intersec-tion horizontally to the right until the curverepresenting the number of ground wires isreached. From this point one follows verti-cally down and reads G or B. The resultantvalue of G'=and B ' of all the lines connected tothe station can be determined by directly addingthe values of G & B respectively for all theselines.

Fig. 6 gives the value of a as function ofG', B' a'd the station grounding resistance,R . To use this chart one selects the (G'xRoR tihe horizontal axis and (Bt x R t on tHevertical axis & locates the point given bythese co-ordinates. The value of a can then bedetermined from the values given on thecirculararc. Either scale A or scale B is to be usedon both horizontal and vertical axis.

substation

2 S.A Seebo, "Zero sequence current distrib-ution along transmission lines" , IEEETransactions PAS, Vol. PAS 88, 1969, pp910-919.

-3 F. Dawalibi, "Ground fault current distribu-tion between soil and neutral conductors"IEEE Transactions, PAS, Vol. PAS-99, 1980pp 452-459.

4 F. Dawalibi, D.Bensted, D.Mukhedkar, "SoilEffects on ground fault currents". IEEETransactions, PAS, Vol. PAS 100, 1981 pp.3442-3450.

5 S.K. Madan, "Current for design of Ground-ing grids in substations". M.Sc.ElectricalEngg. Thesis, Panjab University,1982.

6 C.F. Wangner, R.D. Evans,"Symmetrical compo-nents", McGraw-Hill Book Company, Inc,New York, 1933 (Book).

7 J.R. Alderton, P.C.Anderson,R.J.Cakebread,"Calculation and measurement of the imped-ance of an ehv substation", Proceedings IEE,Vol. 125, 1978 pp 1367-1375.

8 R. Verma, D. Mukhedkar, "Ground faultcurrent distribution in sub-station, towersand ground wire", IEEE Transactions, PAS,Vol. PAS-98, 1979, pp 724-730.

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i4wIL

.8

J.6

ccx

,g,0

.4

.2

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B.Thapar (S'61-M'63-SM'70 )was born in Ludhiana,India on

Sept. 1,193O.He received the

B.Sc.degree in ElectricalEngineering from BanarasHindu University, M.S. andPh.D. degrees in ElectricalEngineering from IllinoisInstitute of Technology,Chicago, in 1953,1960, and1963 respectively.

From 1953 to 1955 he was

with Punjab Public Works Department, ElectricityBranch,Chandigarh, India, working in PowerSystem operation section. In 1955 he joinedthe faculty of Punjab Engineering College,Chandi-garh, and is now a Professor of ElectricalEngineering. He has published a number ofTechnical papers and is co-author of a book on

power system transients.Dr. Thapar is a member of IEE, Fellow of

IE(India). He is working on a number of bodies

for the development of electrical education and

research in electric power systems.

Sunil K. Madan was born in

Delhi, India,on Jan.10,1950He received the B.E.degree inElectrical Engineering fromThapar Institute of Engineeringand Technology, Patiala, theProject Management diploma fromPunjabi University,Patiala, andM.Sc.Engineering degree inElectrical Engineering fromPunjab Engineering College ,Chandigarh in 1970, 1973 and

1982 respectively.From 1970 to 1972 he was with HindustanWire

Products Pvt.Ltd. Patiala as Assistant Devel-opment Engineer. In 1973 he joined the PunjabState Electricity Board, Patiala as AssistantEngineer and is now working as Assistant Exec-utive Engineer in the Hydel Designs Organisation,Chandigarh of Punjab State ElectrictyBoard andis responsible for the design of ElectricalSystems of Hydro Power Stations.

Mr. Madan is a member of Institution ofEngineers (India).

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DiscussionJ. Fortin (Hydro-Quebec, Montreal, Quebec, Canada): The subject ofcurrent distribution in ground design is of growing interest and I wouldlike to address my discussion to that specific point.

Equation 5 used in introducing the admittance of overhead groundwires (and by extension also that of the distribution neutrals), in con-juction with the reduction of cost mentioned in conclusion 4, may leadthe designer to reduce the use of burried copper conductor and rod toa minimum. This seems to indicate that if this admittance is high, thesoil resistivity of the site is not important to the designer.

In consequence the fault currents will rebound to the outside whereit is impossible to control the protection against step and touch potentials.

It does not seem sufficient, to me, to design a grid such that:a) The size of the grounding conductors is enough for the maximum

fault current.b) The crushed-stone layer insures a protection against step and touch

potentials.I think that the evolution of the grid design must whenever possible

minimise the rebounding of the fault currents away from the station andnot the opposite.

Based on this I cannot agree with the orientation suggested by yourconclusion 4. It is desirable that a discussion of the subject, among theintervenning parties, can clarify the concerned IEEE committees'positions.As for the choice of installation for protection of communication

cables. I think it would be realistic to consider the group of neutrals con-nected to the grid when the station is energized. Your paper could bevery helpful in the assessment of the station's G.P.R. as additional con-nections are made to the station's grounding grid.

Manuscript received February 15, 1984.

S. J. Arnot and E. P. Dick (Ontario Hydro, Toronto, ON, Canada):The authors have presented a convenient method for estimating the faultcurrent splits at stations fed by several overhead lines, assuming theselines are not inductively coupled. For completeness, we should point outthat this theory was published at least 17 years ago [1] including the ad-ditional effect of counterpoise. It is routinely applied to grounding designand inductive coordination using computer programs [2]. This referencealso includes the effect of several lines on the same right-of-way. However,the graphical method of this paper is handy alternative. A cursory checkof Figs. 3 to 6 showed that the estimated is within 10 percent of moredetailed calculations.

In our opinion, further work is needed1) for cable fed stations preliminary results with cable shielding

calculated from [3] show that the GPR at intermediate overheadline/cable junctions can be higher than at the faulted station dueto induction.

2) for assymmetric (dc offset) faults the dc component of the faultcurrent split through the station ground impedance is not propor-tional to the 60 Hz component [4].

Two small errors in the paper were noted: Z span following (4) shouldhave units of ohms and B in Figs. 5 and 6 should be negative in sign.

REFERENCES

[1] J. Endrenyi, Analysis of transmission tower potentials during groundfaults, IEEE Trans. Power App. Syst. PAS-86, no. 10, p. 1274, Oc-tober, 1967.

[2] M. S. Tibensky and L. J. Perfecky, Methods for RMS symmetricalstation ground potential rise calculations for protection of telecom-munications circuits entering power stations" IEEE Trans. PowerApp. Syst. PAS-100, no. 12, p. 4785, December 1981.

[3] L. M. Wedepohl et al, "Transient Analysis of Underground PowerTransmission Systems" IEEE Proc 120, no. 2, p. 253, February 1973.

[4] A. S. Morched, "Fault Current Calculation for Ground PotentialRise Studies", paper 82-EC-80, Canadian Electrical Association, Pro-ceedings Spring Meeting, Montreal, March 1982.

John F. White (Bonneville Power Administration EKSE, Vancouver,WA): and Eldon J. Rogers (Vancouver, WA): The authors have presentedan excellent guide for determining current distribution in the groundingcomplex. Besides those indicated by the authors, there are many addi-tional pathways that fault currents follow on return to their sources. Theycould include buried counterpoise, grid tie conductors, control cableshields and direct burial bare concentric neutrals (URD). These addi-tional paths could parallel with or intersect at an acute angle overheadfault current carrying phase conductors. Will the authors indicate howtheir method is adaptable to these additional fault current paths? At BPAour standard practice is not to connect overhead ground wires (OHGW)to our grounding grids. To reduce transmission losses, tower footing cor-rosion and prevent transfer of grid potential to remote locations con-tinuous OHGWs are sectionalized and only grounded at the center ofeach 30 mile section.

In general, the size of the grounding grid conductors are determinedby current carrying requirements, by their ruggedness and longevity whileburied in the earth environment and by redundacy of the fault currentpath from faulted equipment.The authors have prepared convenient charts to determine G and B

factors for overhead lines. Are the procedures used to determine thesecharts adaptable to hand-held programable calculators? Has the authorscalculated current division in the grounding complex been verified bystaged fault tests?

Manuscript received February 23, 1984.

B. Thapar and S. K. Madan: The authors wish to thank the discussersfor their interest and comments. The intent of our paper was to developa handy guide for determining the current to be used in evaluating thepotential gradiants in a high voltage substation. The value of ca obtain-ed from Figs. 3 to 6 is within 10 percent of more detailed and lengthycalculations. This has been checked and confirmed by Mr. Arnot andMr. Dick.We agree with Mr. Fortin that the grounding grid design must aim

to minimise the rebounding of the fault currents away form the station.The paper does not advocate the reduction of grounding conductor tothe extent that would increase the grounding resistance of the grid. Fora given substation switchyard area at a particular site the reduction inthe grounding resistance is very small if the number of meshes is increasedbeyond 64. However closer meshes in the grid may be needed to limitthe step and touch potentials to safe values. The step and touch poten-tials are directly proportional to the current IG flowing through thegrounding system at the station to the ground. If proper value of thecurrent is adopted for design, use of extra conductor which is requiredto limit the step and touch potential is reduced resulting in saving in thecost of the grounding system.The subject of protection of communication cables is beyond the scope

of the paper.Mr. White has pointed out that there are many additional pathways

that the fault current follows on return to the source. The considerationof the additional pathways will further reduce the current IG. Howeverbecause of the random nature of these pathways a general analysis can-not be made. The data presented in the paper is applicable only to thestation where the overhead groundwire is connected to the grounding grid.The procedure used to determine the graphs of Figs. 3 to 6 is adap-

table to hand held programable calculators.Attempts were made to verify the calculated current division in the

grounding complex at two locations. In both cases the actual value ofIG as obtained from the potential gradient on the earth was less thanthe calculated value indicating that the value of a obtained from Fig.6 can be safely used to determine the step and touch potentials. The twotypographical errors pointed out by Mr. Arnot and Mr. Dick are ob-vious. Only the numerical value of B is given in Figs. 5 and 6.

Manuscript received February 27, 1984. Manuscript received April 18, 1984.