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IEE Transactions on Power ApparatusandSystems,Vol. PAS-95, no. 1, JanuaryfFebruary 1976

OPTIMIZED GROUNDING GRID DESIGN USING VARIABLESPACING TECHNIQUEJ . G. Sverak, Member IEEE

ABSTRACTThe envelope of eart h urfac epotent ia lcurves i s dis-ti nc t ly convex fo r grounding mats with many meshes.Such a condition i s di f f ic u l t oa na lyz ewi th hees t-ablishedmethods,whichar eprimarilydevised orcal-culating the orner mesh voltage.Forhis eason, alarge, qually pacedgr id may be verdesignedowardth e cen ter and underdesigned oward the perimeter. Aim-ingo remedy such roblems, thi s ape r nal yze s andmodifies heexi sti ng method of IEEE Guide No. 80, t oallow a recursi ve point by point ntegration of surfacegradient s hrough onsecutiv e meshes. A computer ro-gram for ptimized rid esign i s described and th eef fe ct of pacing eometry i s documented .b y computerplot ted vol tage prof i les .INTRODUCTIONFollowing i t s publ ica t i on n 1961, I EEE Guide No. 801has rovedo e a very opular uide or ubstationgroundingapplications.The abi l i ty o prov ide a simple, yetconceptually sol idapproach to groundingyste m nalys is, and even moreimpo rtan tly, a method forobta ining a reasonable ol-ut io n by pen cil and .paper, ave een ndoubtedlyhemostppreciatedeatures. I t s proceduresor eter-mining he afe angeof tep, ouch and mesh vo lt ag esar egenerallyaccepted by the ndus try.However, i f compared wi th more rigoro usmethods,an un-res tra ined applica t ion of the present IEEE method occa-sional ly may pr oduce nconsi stent esult s or a l a rgegroundinggrid.Inpar t icula r , heequ ati on or he mesh voltageof arectangular, qually pacedgrid, oncerning he irstmesh from t he per im et er s :

h s h ( 1 ) =Km K i l ? I / L (1 )where Km i s a sur fa c e po te n t ia l c oe f f ide n t a k ing n -toaccount heeffectof number n,spacing D ,diameter, and depth of bu ri al , fhegrid conductors, which are mutu ally para llel ,ca lcula ted as:

mittee of th e IEEE Power Engineering Society for presentation at th e IEEE PESPaper F 75 526-4, recommendedand approved by the IEEE SubstationsCorn-Summer Meeting, San Francisco, Calif., July 20-25, 1975. Manwript submittedFebruary 5,1975; made available for printingMay 5,1975.

and K i l

L

I

United Engineers & Constructors Inc.Philadelphia,Pennsylvania

i s an i r r e gu la r i ty o r re c t ion a c to r o l lowfo rnon-uniformityofgroundcurrent low romd i f f e r e n tpa r t s o f hegrid,determinedempir-i c a l l y as:K i l = 0.65 +0.172 n ; ( 3 )

i s theo ta lengt h of buried onductors,nmeters;i s the maxmum t o t a l rms current, lowingbe-tween ground grid and earth, as adjust ed by thef ib r i l l a t io n de cre me nt ac tor o r a possibledcc ur re n t of fs et , n amperes;

0 i s the verage es is t ivi ty of the round, i nmeter-ohms.Thisequation 1)gi ves somewhat lo we rvalues orgr idswith more thanou rmeshes, i n comparisonwithhevaluesobtained from exper imental result s or calcula tedby o the r a na ly t ic a l me th0ds? , ~*7Also, a contradictingesignequirement may re su ltf rom the use of he equa t ion for s tep vol tage , given as

where Ksl i s the s te p po te n t ia l c oe f f ic ie n t , c a lc u la te dinsimplified form, as

when att emp tin g o sati sfy bot h he step and mesh vo lt -age l imits i n a rectang ular area which i s not oowide,and ifh eo i le s i s t i v i t y i s high.ornstance,when the number ofconductors i s inc reased norder tolower mesh pot ent ia ls, he combined eff ec t of highe r K iand Ks can offse t he nf luence of he ncreased engthL i n ( 4 ) , so th at an increase, a ther han heexpectedsimultaneous decrease of calculated step voltageasults .For c l a r i t y , l e t i t be noted hat:

1. Touch voltane i s theDotential difference between

2.

3.

Ithe ground el ectr ode pot enti al r i se and the earthsur fa c e o te n t ia l a t the oint where a man i sstanding on his feet, while simultaneously havinghi s hands inc on ta c twi th a grounded structure,during a f a u l t ;

Mesh voltage i s theworstpossiblevalueof ouchvol tag e o be found withi n a mesh of a groundinggr id , sua l ly f t a nd ing a t , or earhe en-t e r of he mesh;Stepvoltage is hed i f f e re nc e nsur fa c epo te n-t i a l s of two points a t one meter istance, x-perienced by a man bridging his is tancewithhis ee t ,withoutcontac t inganythinge ise .

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-COPEThe in t ent of h is pap er i s t o shopr that the pr inc ipa lproceduresof IEE No. 80 can be asily xtended andimproved t o compare fa vo rab lywith he more accurate,bu t a l so more elaborate methods,basedon a non-uniformcurrent densi ty pr inciple .

refo re, he well-known fundam entalequationsof hecurrentdens ity method and th e ro le of he i r -egu la r i t yo r r ec t ionac to r are br i e f lyi scussedf i r s t .Subsequently, a fornula i s developed t o allow a recur-sive, point by point n tegrat ionof u r f acegrad ien t sthrough a l l pa r a l l e l gridontbctors,or 'o thhequal and unequalspacings.The re la ti on between the envelope of surface ouch pot-n t i a lcu rves and spacinggeometry i s demonstrated byomputer plottedpo ten t i a lprof i les ofg round ing elec-trodes,usingvariousdegreesofprogressively educedspacing oward perimeter.Fina lly , he computerprogram i s described and severalof the program are l i s t ed to show iq l emen t ing o fthe method in For tra n,

EXISTING EQUATIONSerr ing o he Appendix I of he Guide', th eanalyt -i c a l l y most s ign i f i can tequa t ionso f he ZEE gradientnalysis method, are:

d

ere, in ad di t i on to th e symbols alreadymentioned,E y i s t h ev o l t a g ed i f f e r e n c e nv e r t i c a lplane be-tween a horizontally uried onductor and t hepoint on the earth surface nmediately above i t ;Ex i s the relative vo l t age d i f f e r ence nhor i zon ta lplane between any two points on theear th ur -face ,denot ing hei rdis tances XI, X2 from t heperimeter with a p lus s ign in an outward direct-ion from t he g r id , and with a minus sig n for thepo in t s n s ide he g r id area;i i s theur rentlowingnt o ground pe rn i tlength of conductor.a rectangular gr id , consis t ing of n x m conductors,t least a set of n para l l e l onduc to r s a so e

i t i s u s e f u l o a n t i c i p a t e h a t h e n t e g r a l(6) and (7) ca normally e xpected as= F(y) + Cy and Ex = P(x) + Cx, where Cy, Q are un-ntegral terms, which may fu rt he r ef le ctf ac to r o fn-conductor g e m t r y .

Cy doesnot epresent any problem. The l e f tsideofequation (6 ) exp l i c i t l yr e f l ec t s heassumpt ionha twi th in he n t eg ra t ionpa th f roma conductor ot s image, proc eed ing n vert ical plane, heef fectof

ohe early

equidistantposit ionof uch a planewith espect oan y o the r real conduc to r sor he ir images. Sinc ehhisc o n s t i t u t e s a geometric ndependence oreachconductoqthe CJt term can be se t equal t o ze ro , and t h e i g h ts ideof (6 ) i s per f ec t lyval id . F ig . la.

A ' B'Dab,h.d j h IG .IG . l ab belowe f t ,

IHowever, t his nde pen den ce- canneith er be declared folCx when analyzing ( 7 ) , nororhe quation (11, i nwhich t he acto r Km i s a directoutgrowthofusing (6)and ( 7 ) together.Sinceherregulari ty actor K i i sfur ther added as a s imple mul t ip l ie r af ter n tegrat ion,i . e .after computing P ( x ) from thedistance X1 = 0, tothecen te rof he ir st mesh inward, to X2 = -D/2, heoriginal components of (1 ) can no longer be re tre ive dfor cor rect ion s on the ndividualbasisof re la t ive dis-tance.Considering (l), th enextquestion hen, i s :

Can themutualnfluence fhendividual r idelements be sufficiently covered by t he fac tor K i ,as simply as app l i ed n l ) ,e l imi nat in g he needfo r non-zero erm Cx e n t i r e l y ?No i s the answer. For i n s t ance , f heoppos i t e weretrue,hen, ollowinghe r inciple f uperposit ion,i t shouldbepossible :1) o a lcula te hevol tage nthe enter f he i r s t meshy (1); 2) to ontinuefrom thisvalu e by Pntegra tingpoint by point towardthe en te ro f hegr id ; 3) t o t op a t thepoint ex-a c t l yabove , the most centra lconductor ; 4 ) t o estimatethevo l t age a t t h i sp o i n td i r e c t l y as E y by ( 6 ) ; and5) toget a i r agreementof esults, ince, n uch asymnetricalrlmostynmetricalonfiguration, a l lthe superimposed Ex terms canceleachother. Fig. b.)A substant ia l d isagreement resul ts n pract ice .Interestingly,Sctw artz 3 as een ery much aware fs o m i d i f f i c u l t i e s as ea r ly as 1957,mentioning i t a l s oin h i sdisc ussi on on the AIEE ConmitteeReport?Paper58-98, which had prece ede d he pub lic ati on of Guide No.80.Withoutelaborating urther , heequation (1)had bestnotbe nterpreted as givin g he orner mesh volt ageestimate. nstead, or easonswhich w i l l follow,heequa tion may serve as a f a i r estimate for he per ipher -a l meshes i nc e n t r a l axis, provided hegriddoesnotcons i s t o f many meshes, or to pro vid e a reasonable avepageestimate oranygrid - i fanoptimized, al lyspaced p at te rn of conductors i s ant ic ipated.DISCUSSIONSimple rectangular g r i d s i n u n i f o r m s o i l were r igorous-l y examined by E. T. B. Gross e t al. , during heyears

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1953-56.Using Maxwells method ofsubareas, hegrounde lec trode was di vid ed in to a gre at number of elementarysub-conductors, o btain a s imultaneous olut ion ort h e n d i v i d u a le l e m e n t sw i t h i n e a rc h a r g ed e n ~ i t y . ~ , s

Recently,Dawalibi nd Mukhedkar rep ort ed lY8 9 b e t t e rthan 90% agreemen twithexperimental esults or heirin te gr at io n mekhod, whichcombines the prin cipl e of in-f ini tes imal subdividing with a family of s inple correc-t ive c oe f f ic i e n t s to s imula te the e f fe c t o f non-un iformcurrent dens i ty , ncreas ing from the gri d cen ter towardperimeter. I n comparisonwithothermethods, heycon-cluded that:

1. I fonlyuniform urrentdens i ty i s assumed, anin te gra t ion method g ive s s a t i s f a c to ry r e su l t s fo rper iph era l meshes, but an ove r lys te e ppo te n t ia lpyramid r es ul ts in th e area of inn er meshes.2. I f h eco me r mesh voltage i s ca lcula ted by t heIEEE method, eitherwi th o rwi thou t some correc-t ion o rc ur re n t r r e gu la r i ty , heob ta ine dva l -ues rencreas ingly pt imis t ic or r idswi thmore thanfourmeshes,and hecalculatedvoltage

may erroneously f a l l t oz e r o o r h eg r i d sw i t hmore than 40 meshes.Both thesepointshave merit, de sp i te he f a c t that t h esecondconclusion i s ra ther mis lead ing and require6 hefol lowing qua l if ica t ion:

The Dawalibiand Mukhedkar c alc ul ati ons app ear to bebased on thedimensionsof a scaled-down laboratoryd e l , c har ac ter iz ed by a 16m x 16m gr id frame, bur-ied 0.6m below earth urfac e,with100amperes as-sumed to flow i n t o 200 ohm-meter eart h. And, if h emodel data arebe l ieved,conduc torsof a r e l a t i v e l ymonstrous si ze wereused,with O.lm (i.e. 3.937 incljdiameter.A check with he simplified equations of IEEE methodapp li ed n camputer series, Table I , seems t o con-fir m his dat a , though.Were th e model con si der ed as a 113 representa t ion ofa p r a c t i c a l i n s t a l l a t i o n , a 0.01111 l u e o f c onductordiameter i s more appropriate.Comparativeesultsfor such a rep res ent ati on and fo r a 48m x 48m, f u l ls ize gr id ca rrying 10 kA, ar e shown i n Tables I1 and111.

TBBLE I (256m2 gr id a re a, 0.lm ca bl edia . ; 0.1 ld)

8.00 108.07* 126.01 78.254.00 31.95* 48.25 79.392.67 5.83* 10.82 88.682.00 -4.88* -10.74 100.90

TABLE I1 (256m2 g ri d ar ea , 0.01m cabledia.; 0.1 U)

TABLE I11 (1904m2 grid area, 0.03m cabledia. ;10 kA)MESH STEPOm MESH VOLTAGEPACINGSUM (v)v) (v )

416 21.82362553.84 9171.1865.52*2240.44 3497.7886.61*.27642245.79305.18513.37*0.91

5.45 1121.85* 2465.83 2339.70100144 4.36 698.0W 1774.32 2489.36196 3.64 438.34* 1265.06 2668.19256 3.12 268.18* 866.23 2866.05324 2.73 151.17*

3764.31179.9739.07*.983528.328.40.66*

4842.18 3298.8665.527.77*.42400

3077.3840.29

*) ind ic a te s va lue s fo r he r r e gu la r i ty f a c to r K i = 1.See al so Appendix fo r aFortran ormulationof heappliedequaticms.Obviously,not heul tim ate number ofmeshes,bu tspac-ing and depth of bur ia l lcodu c tor ra t io a re the fac torsundermining app li cab il it y of th e method.Fora major i ty of prac t i ca l cases , typi ca l ly with in the0.25m - lm depth angean dconductorsizesusuallynotexceeding00 M a , i.e.withominaliameterf0 . 025~1or ess , hecr i t ica ldec li ne of th e mesh w l t -agesoccurs or he a ther mprac t ica l pac ingva luesbetween 1 - 2.5 meters.Fur theranalysis of these and similarcomputer eries,as we l las comparisonwith healternate esults fromjthersources ,support he ollovi ng resume:

a. The simpl ifie d quat ions 11,2), 31 ,41, (5)of I EE method p rov ide sat isf act ory means of es t-irmting hegroundingperformanceofsmaller s y s -tems, typ ica lly up t o 138 kV cla ss , if th e groundgridca nbeapproximated by a ectangularsystemofeveralarallelonductors,quallypacedmore than4 - 5m (15 ft. ) a pa r t .b. For ph ys ic al ly la rg e gr id s wi th many meshes, yp-

i c a l of many out doo r ns ta l la t io ns n he 230 t o765 kV cla sses , he qu ati ons l) , 2), (3 ) maygive10 - 40% loir ervalu es or he orne r meshvoltage.C. The step oltage quations4) and (5) t e ndoproducepessimisticvalues.Since he tepvolt-ag e i s ca lcula ted by extrapola t in ghe maxiaumgradientverne meter dis tance ,ns teadffind ing he volt age diff erence between tw o poin t sby inte grat ion fhe urface radients i th int h ed i s t a n c e , n some cases heerrorcanbeashighas 1009..d. A l l the implif ied qua t ions re ill su i te d o rtreatment f ense umts, par t i cul a r l y when the

numerical value of spacing between he conductorsapproachesthe order of he conductor diameter andof the bur ia l depth va lues .

SUM4163664100144196256

2.001.601.331.14

(v)184.41*77.76*38.55*20.56*10.83*5.01*1 . 2 9-1.19

(9215.02117.4171.4745.1927.5214.454.18-4.25

r STEP(v)78.2579.3988.68100.90114.62129.30144.66160.55

However, in consider ing he a rgegr ids ,anaddit iona lpoint should b e emphasized:e. A s th ed i f f e re nc e n u r re n tde ns i tyva lues be-tween the nner and the peri pher al meshes in cr ea sswith an in cr ea se in th e number ofmeshes,anysin-gle calc ula tio n of the com er mesh volt age becomesi r r e l e v a n t o a p r ac t i ca lde si gn . Economizing bya separat e subdi visio n of few per iph era l meshes i sa ule .Furtherevaluationof nner mesh vol tag esbecomes thennecessary.

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METHODexperimental evidence' s 8 s 9 i t i s as-that th envelope froundurfaceotentiali s rather convex forequal ly pacedgr idswi thmeshes.

reason, t h e b i l i t y o v a l u a t e h e n t i r eesh vol t age prof i le of a l a rge g r id , from per imeter toa design necessity.

f o r h e ~ame eason,anunequally pacedgridde-to be he super ior al ternat ive t o t h a t o fspacing, oavoid he c m roblemofoverde-ing oward he cen ter, when th e number of grid sub-i s high.

o he equa t ion (7), the gra die nt G(x) ofnx midD(l), D(2),D(3) ,......,D(n-l),canbe ex-as

D()+X D(l)+D(2)+x+ +] 8)x2+h2D(1)+x)2+h2D(1)+D(2)+x)*+h2

ormally D(0) = 0, the equat ion for he vol t -two po in t s on ground sur face, n

d i r ec t ion , n s ide hegr id , i s

n i s t he d e r fparal le lconductorswhich areplaneof he a lcu la tedvol tageon t hebas i so f equal currentdensi ty , heequa-f o r t e p and touchpote ntial s of the nequallycomputerized.

hen the ef fec t of cur r bnt i r reg ular i ty ente rs the p ic-a problem arises. Impl i c i t l y , nyr r egu la r i t ys i m i l a r o K i of ( I ) , i s a two-coordinateaffair,that t he r e sen t IEEE Guide No. 80onlyn-con ducto rs from ,th e n x rn grid con-set, n e g l e c t i n g h ee f f e c t of cross-connectionsheemainingm-conductors. %ere i s l i t t l e ex-vidence 1, avai lableo rny attempt t oa s u i t a b l e f o n u u l a f o r h e r r e g u l a r i t y e f f e c t snn er meshes.

a s u b s t i t u t es o l u t i o n i s possible .i t has been already ndicated , he ntegratio n meth-ds t e n d op i l ee x c e s s i v e l y h ev o l t a g ed i f f e r e n t i a l sarea of inner meshes, i f a uniformcurrent den-i s assumed.

has found that, i n h ep a r t i c u l a r case ofEE method, t h i s phenomenon ca n be uti li ze d to a g r e a te l im inat ing he need for any pecia l ir-

acrif icinghe onceptual sinpl ici ty ofheIEEmethod, the ollowingsequenceof comput-will r e s u l t n a gradual , bui l t -

in" ompensation or urrent irregularities. Using anequa lspacing i r s t , i t i s possible o :1. calcula te he ent i re vol tage prof i le , using an ar-

b i t r a r y v o l t a g e level as t he n t eg ra t ion cons t an t ,2. fi nd he pr of il e maxlmun)which usu all ycorrespondst o h ep o i n t di r ect ly above theconductor ocatedclose o he geometr ic center of he gr id ,3. assume t he true v o l t a g eo f h i sp a r t i c u l a rp o i n tequa l o he g r id po ten t i a l r i se minus the vol tag e

drop in ver t ica l plane, calcula ted by (6),4. r e c u r s i v e l y r e c a l c u l a t e t h e e n t i r e v o l t a g e p r o f i l eto matchhe ssumption 3 , obtaining a so lu t ionwhich cor re la tes well withother , more soph i s t i -ca te d methods, fo r hepe ri ph er al mesh rows.

Fig. 2 i l l u s t r a t e s h i s conc ept , and he ol lowing partofcomputerprogram l i s t i ng , wr i t t en in th e Kronos ver -sionof FORTRAN Fig. 3, providesdetailed nformationon therocedure, as implemented i nhe sub-programPROFIL(JN) where sJN i s a number ofons ecu tiv e meshes throughwhich the vol t age prof i le i s taken,P(1) i s a so i l es is t i v i ty , n kohm-meters ,P(3) i s a ground 'faultc u r r e n t , n kA,P(8) i s a depthofbur ia l , n meters,P(17) i s a t o t a l g r i d p o t e n t i a l rise, i n kV,S(1) i s the per imeter - to-per imeteris tancenthe g iven p ro f i l e p l ane , i n meters,S(8) i s a to ta l ength f ur ied onductors , nmeters,Q(15) i s a diameterfheridonductor ,nmeters.

Both ther apezo ida l nd iqson ' sn t eg ra t ionu leswere t e s t e d , i v i n g r a c t i c a l l yd e n t i c a le s u l t sa0.3% differenceres s) . However, Simpson's rulehas been reta ined for he method as being heoret ical lymore adaptable o he character of calculated curves. A0 . b (10cm) in tegr at ion s tep i s used.

kV

I W1 7 )t o t a lp o t e n t i a lr i s e-1 0 dist.- meterI .TLegend: ADJV = an ad jusben t va lue

W R T = a voltagedrop i n v e r t i c a lplane, per th eEquation 6)

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I ~ ( I ~ P . G T . I ) GOTOIFCIKP.EP.0)LOOP-IWTO 34IF(IKP.Ee.2)KOX: IIP(IKP.EP.3)KOX:2

A spacingunction an-be eterndnedor obtaining apat ternofgr idconductors, which vi11 assu re a f a i r l yuniform level of maxinnnn mesh potenti als throughou t thegrid , ncwhere xceedinghe l lowabletep ndouchvoltages.For nstance, he Fig . 4b i l lu st ra te s the e f f e c t o f op-timized unequal spacing, in comparison with the equal lyspaceda l t e rna t ive of the same griddesign. Hg. 4a.

FIG. 3Depending on the np ut data sequence, i.e. i n w ha tor -de r hegr id ength andwidthparameters are entered,th ep o t e n t i a lp ro f i l e an be aken h rough he i r s tray of meshes, ei ther in t he onger ,o r n heshor t e rc u d s .Generally, heuse of unequal pacing echniquesdoesnotguarantee a re du ct io n n he number of grid con-duc to r s ,bu t a the rassu res he i rbe t t e ru t i l i za t ion .The b est pract ica l solu t ion i s usua lly achie ved by pro-granming t heop t imiz ingcr i t e r ion oex i t heunequa lspacing uild-upoop, as soon as the early ptimalba lance i s ach ieved fo r a l l but he cor ner meshes.In those aseswhere he orner mesh volta ge xceed ss i g n i f i c a n t l y h ep e r m i t t e d limits, i t i s more conom-ica l osubd iv idesuch meshes by additionalconductorson an i nd iv idua l bas i s , r a the r han o make a program-ming allayance fo r more conductors.

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MESH VOLTAGE COMPARI SON CHART CASE I8 Uni f orm soi l 30 ohm meter s, equal l y spaced gr i d of8 8 x 3 conduct ors , 161. 4m x 32. 5111 gr i d area, i ndi v-i dual mesh si ze 23. 05mx 16.275111, dept h of bur i al. 5m 25 k4 gr i d cur r ent , 0. 3 sec. faul t dur ati on' i me, si ze4/0 (211. 6 MU4) copper conduct or s.i

I EEEethod I Modi f i edethodMes h Unequal Spaci ng;qual Spaci ng

No SPACI NG SPACI NG IESHESHESHMETER METERvvv1Y7

32. 96 1.427 1. 2983. 06 27. 04. 371. 3773. 069521. 23. 398. 6263.06, 615. 91. 601 2. 099 1. 9023.06

Safel y t ol erabl e t ouch vol t ageimt.......1657 kVStat i on gr i d potent i al r i seal cul ated. . . . . 4. 522 kVSt at i on gri d t ot al esistance.............0.181 ohmMESH VOLTAGE COMPARI SONCHART - CASE I 1

w uni f orm soi l 165 ohmmeter s, equal l y spaced gr i d of2 9 x 7 conduct ors, 252. h x 22Cm gr i d area, i ndi v-i dual mesh si ze 31. 495mx 36. 667~1, depth of bur i al. 5m 30 kA gr i d cur r ent , 0-15 sec. f aul t durati on3 t i me, 500 MCM opper conduct ors.VJ

IEEE Met hod I Modi f i edethodMes h

MESH SPACI NGECHECH-PACI NGoUnequal Spaci ngqual Spaci ng

METER Kv ! METER ,Vv1,8

43. 14. 989. 8801.49Y5 35. 17 1.938. 0721. 49Y620. 33 2.298. 186 2. 848 31.492, 7 27. 34 2.002. 4801. 49

L

Safel y t ol er abl e t ouch vol t ageimt.......2 343 kVSt at i on gr i d potent i al ri se cal cul ated. . . . 10. 835 kVSt at i on gri d t ot al esistance.............O.361 ohmMESH VOLTAGE CWARI SON CHART - CASE I 11

Uni f orm soi l 165 ohm met ers, equal l y spaced gr i df15 x8 conduct or s, 290. 5~1 139m gri d ar ea, i ndi v-i dual mesh si ze 20. 747~1 x 19. 857111, depth of bur i alIrl . 5m 30 kA gr i d curr ent , 0. 15 sec. f aul t dur at i on3 t i me, 500 MCM copper conduct ors .

I EEE Met hod I Modi f i edethodMesh Unequal Spaci ngqual Spaci ng~ No MESH SPACI NGESHESHPACI NG, KV 1 METERVvETER1 1, 14 3.720 2. 393 20.75. 069

17. 06 1. 521. 3660. 753, 12 13. 70. 700 2.9300.752, 1310. 73

~ 4, 11 20. 75 - 1.952 1.453 20.665, l O 27. 80 1.503. 4720. 75, 9 24. 31 1.457. 6600. 751 798 30. 97.562 1.3790. 75

Safel y t ol erabl e t ouch vol t ageimt.......2343 kVStati on gri d pot enti al ri se cal cul at ed. . . , 11. 008kVSt at i on gr i d t ot alesistance..........,..O,367 ohm

The compari son chart s at r i ght , CASES I, 11, 111, showt he di f f erence between therrvurimum sur f ace pot ent i al scal cul ated f or i ndi vi dual meshes al ong the l ongi t udi nalpr ofi l e, as obt ai ned for t he equal l y and t he unequal l yspaced gr i ds, i n three typi cal exampl es.Fi g. 5, f ur t her document s t he ef f ect of a gr adual l yi nt ensi f i ed spaci ng f uncti on. As shown, t he f uncti onbase i s one f or equal spaci ng, and ' gr eat er t han one unequal spaci ngs.DESCRI PTI ON OF OMPUTER PROGRAMGi ven the gr i d ar eadhns i ons , magni t ude and durat i onof gr ound f aul t cur r ent , pl us other desi gn parametersl i ke t he dept h f bur i al , average l engt hf ground r ods,soi l and surf ace l ayer resi sti vi t y dat a, etc. , t he pro-gr am f i r st eval uates si ze of t he mai n gr i d conduct ors.Si nce a ground gr i d shoul d w t hst and any t her mo- mechan-i cal abuse resul t i ng fr om t he pr ol onged fl ows of f aul tcurr ent , possi bl y caused by mal f unct i on of t he pr i maryr el ays, a Gui deNo. 80 r ecorrmended val ueof 4' seconddi s aut omati cal l y appl i ed i n t he cal cul at i on. However ,t he pr ogr am has a provi si on to over r i de such a nomnalt i me set t i ng, i f t he ef f ect of back- up r el ayi ng, or adel i berat e change of t he conduct or si ze, are requi r ed.Then, t he l kni t s f or t ol erabl e st ep and t ouch vol t agesdur i ng a gr ound f aul t ar e cal cul at ed, f ol l ow ng t hewel l - known f onuul i of I EEE Gui de, t r anscr i bed bel ow as

Etouch= (1+1. 5xP(2) ) xO l 65/ W (kV; kohmm A, sec) ( 11)wher e P(2) i s t he surf ace l ayer resi st i vi t y par ameter ,

P(4) i s t he ant i ci pated t i me f or cl ear i ng t heandf aul t.W t hi n a cer t ai n r ange of conductor t otal l engt h, aseri es of consecut i ve gr i d desi gns i s gener ated, r e-f l ecti ng t he const r ai nt s of appr oxi mat e gr i d w dt hndl engt h, i ndi vi dual mesh si de rat i o, m ni mum per m ssi bl edi st ance between groundi ng r ods, etc.The fi r st , equal l y spaced gr i d pat t er n i s det er m nedsem- empi r i cal l y, combi ni ng a comput er sel ect ed t otall engt h of hor i zont al l y bur i ed conductors w t h theo-t al l engt h of gr oundi ng rods, as r equi r ed by t he i nputdat a, Consequent l y, t he st ep and t ouch potenti al s arecal cul ated f or t he corner mesh, usi ng f he equati ons1)to (5), and the resul ts are compar ed w t h the per m s-i i bl e i mt s. Thencef ort h, corr ecti ons i n the t otall engt h est i mat es ar e made unt i l t he sol ut i on i s f oundf or a match bet ween t he cal cul atednd l i mt i ng vol tageval ues.Al t hough t hese si mpl i f i ed cal cul ati ons ar e not accur ateenough, i t i s expedi ent t o determ ne the basi c desi gnpat t er n, r esi stance and pot ent i al ri se of an equal l yspaced gr i d i nhat st age, and t hen t o pr oceed w t h t hemore accur ate, second par t of cal cul ati ons,ROFIL(JN),t o i mprove t he gri d desi gn by means of unequal spaci ngt echni que,Such an opt i m zed desi gn i s character i zed by a gr adual l ydecr easi ng spaci ng t oward t he per i meter , under t he con-st r ai nt of nrai ntai ni ng thesame number of conduct or s asdeter m ned by t he esti mati ng r out i ne.An exampl e of compl et e computerun i s shown n Fi g. 5.The pr i ntout , corr espondi ng t o t he al r eady tabul atedand pl ot t ed r esul t s of CASE I, i s sel f - expl anat or y t o al arge degr ee.

3 6 7

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1.657 kV limit twQ-m-(IDI*m SWUI m m r t v0 ;i:irM.............8 0..........143......... .t........la1........U

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....

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G?IDFVDED ARU Ifl III.................. 161.4 X 52.5W I D SPACIIICS LLEnElT SIZE lfl X R I . . . . . . . . 23.159 X 16.215...................T OT A L LERGTH O F BURIED COIDUCTORS I R I . . . . . . . . . . . . . 894.645

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3 69

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The pro gram ncludes an o p t i o n o bypass t h e t e r a t i v esubroutine foi: d etermining he otalconductor ength,and uch a length anbe nte reddirec t ly . % is pro-vis ion, oge ther with other nput data, permits a checkof the ina l ngineer ingdes ign,whichof tendiffe rsf r a u th eor ig ina l lyca lcul a ted one. The to ta l es is t -ance fhe round rid i s calcu late d by Schwartz 'smethod.3 Al so , he ff ectof ddi t iona l ubdivis ions ,a s nd iv idua l lya pp l ie d o r hecor ner meshes, anbeestimated.The program fi el d en gt h i s 0.043 KPR u n i t s . For com-parison,heieldength fhe rogram GRD 2, asl i s t ed in th e Appendix, i s 0.004 KPR uni t s .Uti l iz in g he computerim eharing ystem KRONOS ofthe Control Data Corpo ration , we use he memorg assign-ment of M A = 60,000 octalun it s. The average unningtime i s approximately15-20systemseconds.

CONCLUSIONSThe des cri bed method fo rsubs ta t iongroundingana lys iscombines a number of pra cti cal adva nta ges:

1.

2.

3.

4.

I t extends he presently well established conceptof I EE methodof calculating hedangerousstepand ouchvoltages,using a computerizedevalua-t io n o f the subs ta t ion po te n t ia l p ro f i l e h rough-out he ent i re grounding gr id .It rec t i f ies hose shor tcomings of he s implif iedapproach,which a r e no longer ole rable for a rgegr id c a lc u la t ions .An advanced onceptofoptimizedgroundinggridde s ign ,ut i l iz in g he echnique of progress iv e lyunequalspacings, i s implemented.The modest memory requirements make thecomputera p p l i c a t i o n s u i t a b l e f o r time s h a r i n g f a c i l i t i e s .

A(XNOWLEDGEMWTThe Authorwould l i ke to thank Mr. E.F. Jones,Chairmanof the I EE Task-Force P468.17 o f WorkingGroup 70.1,Groundingof Gas Insul ated Subst ation s," and Manager ofthe Substation Engineering Department, United Engineers6 Constructors,hiladelphia,orncouragementndsuppo rt of his work.Permiss ion i s grantedo eproduce r uote from thel i s t e d p a r t s of hecomputerprograms RENA 2 and GRD 2.However, credit should be given o United Engineers, asthesource.REFERENCES1.

2.

3.

LeEE No. 80fMarch 1961/71, "Guide f o rS a f e t y n Al -ternati ng Curren t Subst ation Grounding,"byAmericanI n s t i t u t e o fElec tr ica lEngineers , N e w York, 961,reaf finn ed 1971.AIEE CamitteeReport,VoltageGradientshroughthe Ground Under Fault Conditions,"AIEETransactionson Power Apparatus ndSystems, Vol. 79 , pp. 669 -692,October1958.S. J. Schwarz, "AnalyticalExpressions orhe Re-s i s ta nc e o fGroundingSystems, " bid., Vol. 73, pp.1011-1016,August 1954.

4.

5.

6.

7.

7a

8.

9.

E.T.B. Gross, B.V. Chitnis , L.J. Stratton, ttGround-in gGrids orHigh-VoltageStations," bid.,Vol.72,pp. 799-810,August1953.E.T.B. Gross, R.B. Wise, "GroundingGrids orHigh-VoltageStations I1 - Resistance fLargeRectang-ula r la tes , "bi d. , Vol. 74, pp. 801-809October1955.E.T.B. Gross, R.S. Hollitch, "GroundingGridsorHigh-Voltage Stations I11 - ResistanceofRectang-ularGrids,"bid ., Vol. 75,p. 926-935,October1956.F. Dawalibi, D. Mukhedkar, "Optimum Design f Sub-st at io n Grounding i n a -0 LayerEarthStructure,P a r t 1 -.-AnalyticalStudy," I EE Trans ., Vol. PAS-94( to be p r in te d) .J. G. Sverak, Discussion fhe bove aper, I EEETrans., V O l . PAS 94, pp. ( t oer i n t e d ) .F. Dawalibi, D. Mukhedkar, "Optimum Design f Sub-st at io n Grounding i n a Two Lay erEarthStructure,P a r t I1 - Comparisonbetween theoretical and exper-ime ntal esu lts ," bid .,bl . PAS-94, (t o bepr inted) .F. Dawalibi, D. Mukhedkar, "Optimum Design f Sub-st at io n Grounding i n a Two LayerEarthStructure,Pa r t 111 - Studyofgroundinggridsperformance andnew electr odes onfi gurat ion, "bid ., Vol. PAS-94,( to be p r in te d) .

Listed below i s the program GRD 2,which hasbeenusedforeva lu ati on of IEEE si mpl if ied method.However, theFortran ormulationofequations l) , (2), (3), 4) nd(5), inc ludednhe ubroutines MESHC and STEPC, i sgenera l ly sableor any computerizedpplication fth e ex is ti ng IEEE method.mO GR AM CJ(D2CINPUT OUTPUT)READ,~R_EA_,S_O_fL,PP_TH,CDIA,C_UURRPRINT,*AREA,SOIL,D~PTH, IAMETER,CURRENT+,SIDE-SQRT(AREA)PRINT,*LOOP*, S READ,NN 1PRINT 18PRINT 19 in: [m2,0hm-m,m~m,A]W 1 1 I=l,ANNC: (NS+1)*2CTL=ROAT(NC)*SIDENM: NS**2SPACZSIDE/FLOAT(IS)

NSZ2* -S is n&nberfpacingsCI: .SS+. I?L*FLOAT(HS+OW E S H ~ C M * C I * S O I L * C U R ~ / C T LESTEP:CS*CI*S~IL;CURR~CTLCALL MESHC(CM, NS,SPAC, DPTH, CDIA)CALL STEPCCCS HS SPAC DPTH,CDIA)Er(FS@=EmFSH/CIPRINT 20,N?l,SPAC,~ESO,EW~H,ESTEP1 CONTINUE21 FCRWAT(/23X 3H*) *INDICATES VALUE*/26X *FOR KIRREG.:2E FORMAT(I4,4~,F5.2:2X.FR.2,2H* ,2(F8.2,2h) etc.-19 FORMAT(* NO. * , 3X , * [W1* , 3 ( 7X , * t V I * ) / )18 FORMAT(//* MEsH*,2X,*SPACING*,2X,*CORNER MESH VOLTAGE*PRINT 2 1 etc. APRINT,////STOP S ENDSUBROUTINE STEPCCCS, NS,SPAC,DPTH,CDIA)R:(1./(2*DPTH))+(l./(SPAC+DPTH))R= f S + ( I . / (FLOAT(I)*SPAC))2 CONTINUECS:FS/3.142RETURN f ENDFs=0.SUBROUTINE MESHC(CM,NS,SPAC,DPTH,CDIA)Fm:. 15DO 1 115 NF 2NF:2*NS- I1 COHTInUEC M Z ( A L O G ( S P AC * * ~ . / ( I ~ . * D PT H * C D I A ) ) ) / ~ . ~~ ~ + A L O G ( F ~ ~ ) /~ . I ~ ~

- -

Do 2 IZ2,NS, 1

F ~ : ~ * ~ ~ A T ~ I ) / F L o A T ( I + I )

RETURN S ENDFm: .

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Discussion 1:F. D a w a i (The Shawinigan Engineering Co., Montreal, Quebec) andD. Mukhedkar (Ecole Polytechnique Montreal, Quebec): Mr. Sverak isto be congratulated for a very timely paper. His efforts to improve andupdate the IEEE GuideNo 80 are welcome. t is unfortunate that in urdays where power systems are studied in increasingly greater detail byuse of sophisticated computer programs,grounding is sti l l looked at by 13semi-empirical methods.We agree with most of the conclusions of the paper. However anumber of points in thepaper are misleading and need to be clarified:- In his abstract and in the text the author states that "The en-velope of earth surface potentialcurves is distinctly convex for ground-ing mats with manymeshes. This is true when uniform current distribu-tion is assumed in the conductors of the mat. The use of an exact cur-rentdistribution n hemat will flatten th e envelopeand make itpractically horizontal. In order to illustrate ths point we have studiedwith our comuuter urogram case I11 of Mr. Sverak's uauer. The mid is 10shown in Figuk I of thediscussion. We have calculated b e earth &fac epotentials for the three directions shown and for both conditions ofuniform current distribution and exact current distribution. Howeveronly the results for direction 3 are shown in Figure 2 and 3. These lastfigures c o n f m that the convexity of the potential envelope is causedby a uniform current assumption in the grid, such a hypothesis s onlyjustified forgrids with small number of meshes,Mr. Sverak refers to our publication (7 ) in order to justify hisabove statement. The curves of our experimental measurements whichwere reported in the mentioned paper showclearly flat envelopes forthe experimental curves. Perhaps our labeling of the curves plotted wasnot clear enough or misleading.

Direc, Direc. Dlret.3 2 14 4 4I I I

+ x axisFig. 1. Grid configuration

Manuscript received August 29,1975.3 71

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his paper. The reducedmodelused could not have extremely mall- Mr. Sverak is right about the model data used in reference 7 f

conductor radius for obvious minimum mechanical rigidity needed forhandling and installation. Our opinion is that the results and conclusionsgiven in (7) are not nfluenced by the radius size selection. However wefor the case studied. Much more work is still needed in order to deter-emphasize again that the conclusions given in our paper were peculiarmine the influenceof all the parameters.ment in contradiction with the text content. Can the author elaborate- In page 3 of the discussed paper, paragraph d we find the state-more onths?- Attempts to develop methods for he calculations of currentnumber of publications are available (Reference (1) and (2) of the dis-distribution in grounding electrodes have been carried out recently. Acussion).- The method of compensation for current irregularities seemsvery interesting. Is it possible with this method to take into account thepresence, in close proximity of the main grid, of return grounds and/orburied metallic structures? Such close structures will obviously distortthe voltage profie.

REFERENCEST. N. Ciao, M. P. Sarma Effect of two ayer earth on the electricNovember 1972 pp 2356-65.fieldsnear HVDC electrodes IEEE Transactions, PAS,Vol. 91F. Dawalibi, D. Mukhedkar. MultiStep Analysis of nterconnectedelectrodesIEEE Summer Power Meeting, San Francisco, 1975paperNo F75 522-3.

A. B. Purdy (AppalachianPower Company, Roanoke, Virginia): Mr.Sverakand his company are to becommended for theirefforts npresenting a paper that is both educational and useful. The author hasdeveloped a needed computer program for solving the longexistingproblem of calculating surface potentials nd gradients in electric powerstations when the system is faulted.The basic principles n IEEE Guide No.80 for Safety in AlternatingCurrent Substation Grounding are modified and further developed andsome of the simplifying assumptions are analyzed. Many of the short-comings of the Guide result from the simplifications.Equation (2 ) of thi s paper is Equation ( 6 6 ) n IEEE Guide No.80neither of the assumptions is valid and calculations may show meshsimplified for X=D/2 and D>>h. As the numberof meshesis increasedvoltages less han zero.mesh. Guide No. 80 states that Ki is the Non-Uniformity Factor toEquation ( 3 ) isof dubious value except forsquaregrids with squaretake into account the higher gradients at corners. The empirical equa-tion is based only on ground conductor distribution.tion of this paper.The latter partof statement c s not so evident.The above facts justify statements , b and d in theDiscussion sec-Equation (8 ) is valid only for conductors of infrnite length.Whenthe distance from the conductor to the point under investigation a pproaches the length of the conductor the value obtained is very pes s i -mistic.The final computerprintoutshould be made to adjust all theconductors t o one voltage level and the surface potential outside thegrid shown for at least one half the spacing of the two outside con-ductors.This paper shows the great importance of IEEE GuideNo. 80 andat the same time makes parts of the Guide obsolete.

Manuscript received August 14,1975.

George L. Finley (Duke Power Company, Charlotte, N.C.): Mr. Sverakis to be congratulated for his fine contributiono the state of the art ofsubstation grounding.This paper shows that by the use of modem tools, such as thecomputer, one can accomplish safer andbetter grounding grid results inyears of our industry,and with less grounding material.large substations than could possibly have been achieved in the earlierIt would be interesting to makeacomparison of thecost ofgrounding two identical substations by using the former uniform gridmethod and the method outlined in this paper, as well as the safetycomparison described in the paper. Also, I believe it would be valuablet o make field voltage readings of step, touch, and mesh voltages withtypical fault current values introduced into these grids at realistic faultentry ocations, such as at breakers,ransformers, and groundingswitches.

Manuscript received September , 19 75 .

The concentration and varying depth of ground rods at criticallocations in the substationare not described at any length in the paper.I would appreciate the authors comments regarding the use of longground rods in soil layers with varying degrees of resistivity, also, withgroundmg material installed in deep wells or in adjacent lakes and alsohow thi s could affect he step, ouch, andmeshvoltages in his cal-culations.Finally, I would appreciate the authors comments concerning isfeeling about not connecting the substation ground to the substationfence ground in ordero reduce faultvoltage on the fence to theeneralpublic.

In reply to Mr.A. B. Purdy; we are in agreement with most of hisconcise comments. With regard to the profde printout, the suggestionneglect the rregularity problem entirely and to align all theprofdeto adjust all theconductors to one voltage evelwouldmean topeaks to the P(1O)UVERT voltage level. If his is what Mr.Purdy hadin mind, the result ould be as follows:With the exception of peripheral meshes, such a rectified prof ieshould come close to a true representationof the centralvoltage profiein Direction 4, Fig. 7. Thus, from the practical point ofview, onewould be able to obtain two imiting profdes from ach computer run.The best one, corresponding o the central row line, and the worstone, asumed tobe taken through the peripheral esh rows,as describedbefore.face potentials outside the grid, is valid. In fact, we neglected to showThe remark that the final computer printout should show the sur-this part of the curve only for the rather petty technicaleason that thepotential profie reduces very sharply outside the perimeter, nd so thescale of the computer plot would have to be drastically compressed.But, we agree that it is essential to show the outside surface potentialdata, and we intend to accomplish that with an additional, separateprintout.

J. G . S v d : First, I would like to thank al l discussers for their valuablecomments and for their interest inhi s paper.The described program represents nothing more than an adequateengineering tool for specific design purposes. There are, nd have been,several other methods which may offer solutions analytically superiorto thatof RENA 2. In Mis respect, our goals were more utilitarian.Gross andhis students, and tried to benefit fromsome of their advancedFor instance, we looked into the earlier work done by Professorcalculations. Yet, it soon became obvious that for large grids, the re-quirements on the computer memory tendo skyrocket.the quality of soil sampling in the field. In practice, this fact acts as aThe final worth of any grounding calculation depends largely ondeterrent against the use of more-precise, but elaborate methods.Veryoften the mean value of soil resistivity readings has such a wide marginof confidence limits hat its statistical value is only a bit better than anarbitrary guess. So , we felt that if there is any positive way to extendthe relativelysimpleIEEE method, hat this would be of a generaladvantage.

Fg .

Manuscript received September 6,1975.372

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integration process is appliedOf course, certain problems result from the uniform current con-is that the voltage differentialspiled excessively towards the center of the grid, i.ei in comparisonwhat would be the cumulative value of voltage differentials propor-true, non-uniform current distribution.resulting curve by adjusting all the grid conductors to one voltageIn terms of the voltage profile, any additional attempt to correctwould not help much. In order to compensate for the effects ofges would have to be obtained with the help of some correctivedistribution, either the inner or the peripheral meshfact, much in the same way as in the original IEEE method.

as it results from the equal current distribution. Instead ofHowever, the Authors method retains the shape of voltage profileng to adjust the profile voltage at the perimeter, the whole curve issingle peak. The point to be made is that by adjusting thetermined voltage level, which applies only to thethis least dangerouserent effect, that of averaged unequal distributio n, is achievedFigure 6 shows a comparison of.the typical charge density curvese qu ar e loop6, and of the center and outermost profiles of a, versus an estimated segment of averaged density curvesting from the analysis of computer runs for square grids with fromto 64 meshes.Since these last curveshavesomewhat ess than ideal character-simulation, the final outcome is a small mesh voltagehe central area of the grid, educinggradually into a fairation of mesh voltages, in the critical parts close to the peri-

pessimistic values, as pointed out by Mr. Purdy, but the erromWith most errors on the conservative side, the approximation eans

significant only for very large grids with many meshes. In thisuse of theunequal spacing technique acts as a partialThis result is rather logical, considering that the total sum of allto be the same for any distribution. Thus, for aconsisting of n-elements, the total ground current I=I]+Iz+ ...+In

resistance are determined. All the individual conductor cur-..., n must satisfy the equationsvo=r1111+r1212+ ...+l n I n

rij represents the mutual resistance between elements i and j for# , rd =rji; or the self-resistance for i= .Smilarly, once a certain potential level is predetermined correctlyths ort the earth surface, it follows from the super-positionon the earth surface, and for the related current. Therefore, the individual currents, their mutual ratios and thebe determined by simultaneous solu-f such equationsets, step by step.Dr . Mukhedkar and Mr. Dawalibi have indicated that the introduc-statements concerning the convexity of thepotential curve en-be misleading since the convexity results from the particular- hat is, from a ufiform current assumption. It is furtherted that the use of an exact current distribution in the mat wouldthe envelope and make it practically horizontal. If the Discusserspe of the profile peaks, they are right. However,the envelope of valleys is concerned, as originally shown in Fig. 4a,problem is more complex.

of current density within the last two or threeIn large grids, thegeometry of the gradient field produces a rela-eral mesh rows, while the large area of inner meshes remains at aUsing a 1 to 5 intensity scale, Figure 7 illustrates the usual spatialof grid segments with high current densities. The grid configura-meshes in Direction 3, arebound to have their valleys moreIt is apparent that at east six peripheral meshes in Direction 1, andmeshes, even with the exact current distribu-From this point of view, it is somewhat unfortunate that the Dis-s opted to show the profile curve n Direction 3, instead of 1 .Figure 3 of this discussionstillseems to offer enoughthe existing convexity.

beviewed as taken through the peripheral rows. ThisFor the same eason, the voitageprofilesproducedbyRENA2of averaged distribution curves,shown in Fig. 6, than from the method. The basic concept of the

Profile directions*\ 4 ,-v t t tD # *

Fg 7.

IEEE method makes the terms like central profile or peripheralprofile irrelevant to the calculation.To the other points:- Paragraph d relates more to the equations (1 ) to ( 5 ) and less tothe equations ( 6 ) to (9). Yet, as this is a matter of degree, there ishardly any contradiction.-The addition of recent references is welcomed.-The problem of separate conductive objects buried near the gridis the intricate one, as they disturb the ground field and alter the pathof ground currents emanating from the grid. Without going into detail,the m e b d cannot take into account uch effects, and no modificationshort of writing a new program would do.In reply to Mr . A . B. Purdy; we are in agreement with most of hisconcise comments. With regard to the profile printout, the suggestionto adjust all the conductors to one voltage level would mean to neg-lect the irregularity problem entirely and to align all the profile peaksto the P(I0)-UVERT voltage evel. If this is what Mr. Purdy had inmind, the result would be as follows:With the exception of peripheral meshes, such a rectified profileshould come close to a true representation of the central voltage profilein Direction 4, Fig. 7 . Thus, from he practical point of view, onewould be able to obtain two limiting profiles from each computer run.The best one, corresponding to the central row line, and the worstone, assumed to be taken through the peripheral mesh ows, as de-scribed before.The remark that he final computerprintout should show thesurface potentials outside he grid, isvalid. In fact, weneglected toshow this part of the curve only for the rather pet ty technical reasonthat the potential profile reduces very sharply outside the perimeter,

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and so the scale of the computer plotwould have to be drastically com-pressed. But, we agree that it is essential to show the outside surface po-tential data, and we intend to accomplish that with an additional, sepa-rate printout.use of ground rods in the computerized design: The program can handleResponding to Mr. George L. Finleys questions concerning theonly ground rods of uniformly prescribed length. The other parameterwhich can be prescribed is the minimum spacing between the individualrods. Depending on the final grid design selected by the computer, therods are placed either at each crossing point, o r if the grid spacing isis smaller than the required rod distance, then the rods are placed in asort of checker board pattern.

Concerning the use of deep wells, or adjacent ground electrodesgenerally useful in conditions where the soil resistivity is high,but onetied over some distance to the grounding grid, such an application ismay encounter the problem of transferred potentials. However, thsparticular program is not equipped for this type of consideration. As amatter of fact, we have developed another program, named PUGY, fortha t purpose. The program provides modeling of a distributed parameterlattice network system to evaluate the transfer of ground potentialsalongburiedong metallic electrodes, like cable shielding sheaths,counterpoise, water pipes, etc. We hope to describe the specific model

representations used in PUGY, and the experience gained with its appli-cation, on some other occasion.substation ground to the substation fence, the choice depends mostlyFinally, to the question about connecting or not connecting theon local circumstances. When the fence is not connected t o the ground-ing grid, the arrangement will be safe for all ground faults within thestation except when there is a direct feeding of the fault current intothe fence. In such a case, there might be extremely steep voltage gradi-ents around the fence which may constitute a danger for both tep andtouch. For other faults, the fence remains at the same potential as thesurrounding soil.On the other hand,when the fence isconnected to the ground grid,rise will be transferred to the fence and therefore it is rather mandatorythen during every fault within the substation, the ground grid potentialto provide some kind of potential ramp in the vicinity of the fence, byburying one or two loopsof ground conductor outside the perimeter.tageous in cases where the danger of a fallen overhead wire is low. TheSo, in summary, the separately grounded fence mg ht be advan-tied-in fence seems to be he preferable arrangement for substationswith many incoming overhead lines, or where the outer loops outsidethe fence may favorably contribute in lowering the total resistance ofthe system.

CORRECTION TO A SIMULATION TECHNIQUE FOR STUDYING REAL AND REAC-TIVE POWER FLOW PAITERNSI AND AN APPROACH FOR PREVENTING SYSTEMINSECURITIESARISING FROM LINE AND TRANSFORMER OUTAGES~

M. S.Sachdev and S. A. IbrahimPower Systems ResearchGroup

University of SaskatchewanSaskatoon. Canada

In the above papers the first pages and corresponding discussions were interchanged. Thecorrect order for A Simulation Technique for Studying Real andReactivePowerFlowPatterns1is page 2092,2102-2109,2100. The correct order forAn Approach for PreventingSystem Insecurities Arising from Line and Transformer Outages2 is page 2101, 2093-2099,21 I@-2114

lM. . Sachdev and S . A. Ibrahim, IEEE T m ct io n s on Power Appmafur and Systems, vol. PAS-94, Novem-2M . S.Sachdev an d S. A. IbrahimJEEE Tmnracr ions onPowerAppamtusand Systems, vol. PAS-94,Novem-ber/December 1975, p. 2092.ber/ 1975 ,p .2101 .

lM. . Sachdev and S . A. Ibrahim, IEEE T m ct io n s on Power Appmafur and Systems, vol. PAS-94, Novem-2M . S.Sachdev an d S. A. IbrahimJEEE Tmnracr ions onPowerAppamtusand Systems, vol. PAS-94,Novem-ber/December 1975, p. 2092.ber/ 1975 ,p .2101 .

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