Grounding Resistance 3

8/14/2019 Grounding Resistance 3

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IEEE Transactions on Power A p p a r a t u s and S y s t e m s , V o l . P A S - 9 8 , N ; o . 3 M a y / J u n e 1 9 7 9COMPUTER SIMULATION FO R DETERMININGSTEP A ND T OU CH POTENTIALS RESULTING FROMFA UL TS O R O P E N NEUTRALS I N URD CABLE

H . N. Nunnally, Member I E E EE. B . Joy, Member I E E E R . P . Webb, Member IEEEA . P . Meliopoulos, Member I E E E

Georgia In s t i tut e o f TechnologySchool of E l e c t r i c a l E n g i n e e r i n gAtlan t a, Georgia 30332

Abstr a c t - A c o m p u t e r s imulat i o n i s d e s c r i b e dwh i c h e n a b l e s the d e t e r m i n a t i o n o f voltages on t he sur-face a n d w i t h i n the e ar th c au se d by : ( 1 ) a phas e-to-n e u t r a l fault, ( 2 ) a fault w i t h s i m u l t a n e o u s open neu-t r als on ei ther s i d e , a n d ( 3 ) an open n e ut r al. T heb u r i e d c able a n d a s s o c i a t e d ground r o d s are m o d e l e d asa s e t o f i n t e r c o n n e c t e d cylin d r i c al s e gm en t s s i t ua t e di n a t h re e - di m en s i o na l , t w o -l a ye r e d e a r t h mo d e l. Si-multaneous s oluti o n of the i n t e r c o n n e c t e d s e g m e n t c i r -cui t a n d e l e c t r o m ag n e t o s t a t i c equat i o n s yi eld s thed e s i r e d solution. Output f r o m the computer s imulat i o ni s shown to m a t c h clo s ely t he d a t a f ro m f ie ld t e s t s offaulted c ables a n d o ther r e s ul t s f r o m t he literature.W o r k s up po rt ed by E PRI c o n t r a c t RP797-1.

INTRODUCTIONThe m a i n t e n a n c e o f a c c ept able s t e p a n d t o u c h po-t en t i als i n t he presence o f unusual o p e r a t i n g c o n d i -t i o n s w i t h und ergroun d d i s t r i b u t i o n systems is a v i t a l

concern i n the u t i l i t y i n dus t ry today. T h e s e cables,usually c o n t a i n i n g a concentr-ic neutral, are subjec t t ofaults f r o m a c ci d en t al d i g- in s or t o opens from corro-s i o n of the n e u t r a l c o n d uc t o r s . Su c h c o nd it io ns pro-d u c e t ouc h a nd s t e p p o t e n t i a l s on the earth's surfaceas d e f i n e d i n Figure 1 . In thi s fi gur e, V RG is t hevoltage (ref erenced t o r e m o t e ground) a t t he p o i n t o ffault; VT is the "touch pot en t i al" d i f f e r e n c e b e t w e e nt he fault p o i n t a n d t he e a r t h s ur fa ce a bo ve t he cable;a n d V S l , V S 2 , a n d V S 3 are s t ep p ot e nt i al s.

A n u m b e r o f f i e l d t e s t i n g programs d e s i g n e d t omeasure the s e p o t e n t i a l s un de r f a ult c o n d i t i o n s haveb e e n c o n d u c t e d [ 1 - 4 ] , t he m o s t r e c e n t being t h a t per-f o r m e d a t Franksville, W i s c o n s i n u nd er E PRI c on tr ac tRP-671 [ 5 ] . However, r es ul ts f r om e a c h o f t h e s e

6 ' L - - 3 ' - 3 'V s 3 V s 2 V 5

V6 3/ )VTV12\ V G / > F a u l t e d

Cable

R e m o t e gr oun d VRGF i g u r e 1 . D e f i n i t i o n o f F a u l t , t o u c h and step p o t e n t i a l s .

F 7 8 694-2. A pap er r e c a m u r n d e d and a p p r o v e d byt h e IEEE I n s u l a t e d C o n d u c t o r s C a m m i t t e e of t h e IEEEPower E n g i n e e r i n g S o c i e t y f o r p r e s e n t a t i o n a t t h eIEEE PES S u i l m r M e e t i n g , L o s A n g e l e s , C A , J u l y 1 6 -2 1 , 1 9 7 8 . M a n u s c r i p t s u b m i t t e d Ja n u a r y 27 , 1978;m a d e av a i l abl e for p r i n t i ng April 2 5 , 1978.

programs are valid o n l y fo r t he p a r t i c ul a r cables a n dcircuits use d an d the so il in w h i c h t he t e s t e d c a b l e swere buried. P a r t i c u l a r n u m e r i c a l results c o u l d bed i f f e r e n t i f t he cable c o n s t r u c t i o n or s o i l c o n d u c t i v i t yan d g e o m e t r y were changed. I t i s impos s ible t o fieldt e s t all p o ss i bl e c o mb in a ti o ns o f c ab le a n d s o i l c o n d u c -t i v i t y , and even i f th i s w e r e r , o s s i b l e , it is n o t c l e a r ho wone might extr apolat e t he t e s t d a t a t o p r e d i c t r e s u l t sin a c tual d i s t r i b u t i o n s y s t e m s u n d e r fault.

This paper d e s c r i b e s a c o m p u t e r program, e n t i t l e dBCAB, which c a l c ul a t e s t ouc h a nd s t e p voltages p r o d u c e dwhen a b u r i e d cable undergoes a fault or open n eu t r a l ora c ombin a t i o n fault a n d open n e ut r al. T he program ex-ists i n t w o vers i o n s, one for execution on a large com-put e r, a n d a n o t h e r w h i c h can be run w i t h a suitablemini c omputer .

T he c able a n d any a s s o c i a t e d groun d r o d s are repre-s e n t e d as a s e t of i n t e r c o n n e c t e d s e g m e n t s , e a c h ofwh i c h is d e s c r i b e d by c e r ta i n e l e ct r ic a l a n d g e o m e t r i cp a r a m e t e r s . By sui t ably s el e c t i n g the p a r a m e t e r s , agiven segment may s imulat e a length o f gr ou nd r o d or alength of c able w it h e it he r a b ar e n eu tr al , an i n s u l a t e dneutral, or a n eu t r a l c o v e r e d w i t h s e mi c on d uc t in g ma-t e r i al. Other p a r a m e t e r s el e c t i o n s cause an open ors h o r t e d length of c able to be s i mulat e d . T he s u r r o u n d -ing s o il i s r e p r e s e n t e d as t w o homogen eous layers, t het o p layer having var i able thickness. Thus, the programcan p r e d i c t r esults w h i c h w o ul d be ex p e c t e d i n any geo-graphic al r egio n fo r wh i c h a soil m o d el is known, fo r al ar ge c la ss of cable/soil c ombin a t i o n s . T he program,w r i t t e n primarily in suppor t o f t he RP-671 t e s t program,i n c l u d e s t he c apability of including, i n detail, t hec omplet e c i rc ui t u ti li ze d i n t h o s e exper imen t s, but w i t hs u i t a b l e values i n s e r t e d fo r c i r c u i t p a r a m e t e r s i t cansimulate f aults a n d opens in a g e n e r a l d i s t r i b u t i o nsystem.

THE C OM P UT E R P R OG RA MG e n e r a l De s c r i p t i o n

T he a n al ys i s p r oc e d ur e u s e d i n t he program is b a s e don mod eli ng a short length (typically less tha n 50me t e r s ) of the bu r i e d c abl e n e ut r al a n d jacket a n d anyground r o d s as a s e t o f 22 i n t e r c o n n e c t e d s egmen t s lo -c a t e d i n the earth, w i t h t he e a r t h i t s e l f r e p r e s e n t e dby t w o homogen eous layer s o f k n o w n c o n duc t ivity. Be -cause of the short lengths s imulat ed, an e l e c t r o s t a t i ca n a l y s i s is s u f f i c i e n t in s olving fo r t he s egmen t v o l t -ages a n d c u r r e n t s [ 6 ] . T he s egmen t s are c o n n e c t e d t oan e x t e r n a l driving c i r c u i t d e s c r i b e d l a t e r . E a c h s e g -m e n t is of k n o w n length a n d o ut s id e d i am et e r a n d ha s ak n o w n p o s i t i o n i n t he p r o b l e m c o o r d i n a t e system.

Figure 2 d e p i c t s a typic al s egmen t c r o s s - s e c t i o n a sm o d e l e d . T h i s s h o w s t he n e u t r a l c o n d u c t o r i s treated asa u n i f o r m she ll o f c o n d u c t o r . T h e s e g m e n t p a r a m e t e r sn e e d e d fo r t he program are t he s egmen t o u t e r d i amet er,DIA, t he jacket t h i c k n e s s T J , t he jacket c o n duc t ivity,a j , a n d t he length L. P h a s e conductor p a r a m e t e r s aren o t n e e d e d , s i n c e they are i n c o r p o r a t e d i n t o t h e imped-ance of t he source d r i v i n g t he p o i n t o f f a u l t . B a s e d on

0018-9510/79/0500-1130$00.75 1979 I E E E

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thorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.


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P h a s eC o n d u c t o r

S h e l l r e p r e s e n t a t i o no f n e u t r a lJ a c k e t ,C o n d u c t i v i t y a j

F i g u r e 2 . C a b l e s e g m e n t c r o s s - s e c t i o nt h e s e p a r a m e t e r s , t he e l e c t r i c a l b e h a v i o r o f t he segmentis r e p r e s e n t e d by a longitudinal i mp ed an ce (assume dnegligible fo r the shor t c a b l e s egmen t s normally mod eled),a n d a r a d i a l imped a n c e, ZR' w h i c h d ef in es t he r e s i s t a n c et o r a d i a l c ur r en t f lo w in g from the n eu t r a l i n t o t heearth. T he expression fo r Z R is

1 l DIAR 2 i r L a J DIA-2 T JN o t e that by p r o p e r l y s el e c t i n g aj a n d T j , the s egmen tm a y in fac t r e p r e s e n t a p o r t i o n of bar e or jacketedcable. Also, a s e c t i o n w i t h open n e u t r a l is m o d e l e d byset t i ng very large v a l u e s fo r Z R a n d fo r longitud i n alimped a n c e.

Groun d r o d s a n d arcs are r e p r e s e n t e d by segmen t sw i t h zero r a d i a l imped a n c e. If no r o d s are d e s i r e d int he s imulat i o n, the r a d i a l imped a n c e o f r o d segments iss imply s e t large enough t o " i n s u l a t e " t he r o ds f r o m t heproblem.T he program p r o vi d e s s i m u l a t i o n s fo r t h r e e opera-t i n g c o n d i t i o n s . T h e s e are:C o n d i t i o n 1 - A single phase-to-neutral f a u l tC o n d i t i o n 2 - A single phase-to-neutral f a u l taccompanied by simultaneous openn eu t r a l s t o e i t h e r s i d e o f t hefaultC o n d i t i o n 3 - A single o p e n n e u t r a l

Fo r e a c h of these, an a p p r o p r i a t e arrangement o fs egmen t s ha s b e e n d e f i n e d t o s i m u l a t e t he c o nd i ti o n.These i n c l u d e lo a d imped a n c es Z L O A D l a n d Z L O A D 2 a t t a c h e da t t he c a b l e e n d s t o a ll o w t he p r o g r a m t o incorporate ane x t e r n a l c i r c u i t .Fo r t he fi rs t t w o c o n d i t i o n s, t he c i r c u i t ' s egmen tm od el s ol ve d is s h o w n i n Figure 3 . Here, a length, L C ,o f c able is buriedata d e p t h dc. T he s u r f a c e s o i l layeri s o f d e p t h D a n d c o n d u c t i v i t y a2, w h i l e t he l o w e r(semi-infinite) layer ha s c o n d u c t i v i t y a l . Bu s voltage,V S , i s c o n n e c t e d t o t he p o i n t o f fault, w i t h p o t e n t i a lVRG, through a high-side imped a n c e Z H I Fa ul t c ur r en tI F T f l o w s t o t he f a u l t a nd r et ur ns t o t he supply bus i nt w o c ompon en t s : I 2 , t he n e u t r a l r e t u r n c u r r e n t (throughl o w - s i d e impedance Z L O ) a n d I G , t he c u r r e n t e n t e r i n g t hee a r t h d i r e c t l y f r o m c a b l e a n d ground s egmen t s (indicated

F i g u r e 3 . C i r c u i t s e g m e n t model f o r conditions 1 a n d 2 .by t he arrows in the figure) an d r e t u r n i n g throughstation ground imped a n c e Z S G . N e ut r al v ol ta ge i s VN .As indicated, tw o ground r o d s may als o be i n c l u d e d insimulation.

Fo r simulationsof t he RP-671 field tests, the c i r-c ui t s ho wn i n F igu r e 3 s imulat es all significant elementsof t he circuit. That i s , the buried t e s t cables were off i ni t e l e n gt h a n d a t t a c h e d t o a specified supply bus w i t ha high-side impedance composed of t he bu s imped a n c e, ahigh-side c u r r e n t limit i ng imped a n c e an d the supply cableimpedance. Also, the low-si d e c o n s i s t e d of the r e t ur nc ab le i mp ed a nc e and a low-si d e current-limiting impe-d a n c e . Some t e s t s included t w o ground rods, while o t h e r si n clud ed none. Also, a fe w t e s t s i n c o r p o r a t e d an a d d i-tional "syst em groun d" consisting of a group of groundr o d s installed a t a location removed f r o m the t e s t i n garea. This i s n o t sho wn in Figure 3 , but t he programt r e a t s it as an a d d i t i o n a l impedance c o n n e c t e d b e t w e e nthe p o i n t a t w h i c h VN i s d e f i n e d a nd r e m o t e ground. I na d d i t i o n, BCAB t r ea t s generalized d istribution c i r c u i t sw i t h physical dimensions much g r e a t e r t ha n t ho se asso-c i a t e d w i t h a field t e s t . Fo r such simulat i o n s, the ap-p r o a c h i s t o s imulat e in d e t a i l o nly a finite length,Lc , of t he c able near the fault. T he region a r o u n d thiss e c t i o n is c a l l e d the "Problem Spac e." T he p o r t i o n oft he s y s t em outs i d e the p roblem space is r e p r e s e n t e d ast he lumped elements ZHI, Z LO a n d ZSG' This p r o c e d u r ere sults in some errors near th e pr ob l e m space boundaries,bu t if t he s p a c e i s large, t he voltages p re dicte d nearthe f au lt i ts el f w i ll be a c c u r a t e .

It is n o t e w o r t h y that a c c u r a t e r e p r e s e n t a t i o n o f t hesystem e x t e r n a l t o the problem space is necessary o n lyfo r t he computation of t he absolute f a u l t voltage VRG.Step a n d t o u c h p o t e n t i a l s n o rmalized t o a t -f a u l t voltagea r e-almos t i n d e p e n d e n t of e xt e rn al s ys te m parameters.Thus, a bs ol ut e v ol ta ge s c alculat ed f r o m a given Z HI a n dZ L O can be a djust ed t o a c o u n t f o r expected t o l e r a n c e si n tho s e values.

I n a general utility circuit, the system impedancesw i l l normally be k n o w n in t e r m s of p o s i t i v e - a n d zero-s e q u e n c e impedances. Ther efo r e, BCAB s e t s

Z =ZHI POSZERO POSLO 3

w h e r e Z and Z are t he t o t a l p o s i t i v e a n d zero-PoS ZERO

Z H I1 1 3 1



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1 1 3 2sequence impedances from the ref e re nce bu s to the p ointof fault. These ma y be e xp re ss ed as the sum of the im-p e d a n c e s of the various d istribution links between r e-f e r e n c e bus a n d fa ult point.

T he ge ne ra l p roce dure fo r s o lv in g C o nd i t i o n 1 andC ondition 2 problems i s n o w outlin ed . Since the problemi s assumed l i n e a r , i t ispossible t o consider the Figure3 buried cable portion as a two-port n e t w o r k with inputat the fault point and output a t N , the point o f j u n c -tion of the neutral e n d s , as i n d i c a t e d , in the s i m p l i f i e dcircuit of Figure 4 . The Z a , Z b an d Z c i m p e d a n c e s ofthis figure ar e obtained in a conv e ntional m a n n e r bysolving j u s t the buried cable portion of Figure 3 twice:once w it h p oi nt N open-circuited, and o n c e w ith po i n t Nshorted to r em o t e ground. T hes e solutions r e p r e s e n t as imu lt a n e o us s o lu t io n of the s egmen t n e t w o r k e q u a t i o n s( c o m p o s e d o f terms formed from the radial and longitu-dinal impedances o f each s e g m e n t ) an d the sys t em electro-static equations d e s c r i b i n g the segment interactionsthrough a conducting earth. T he l a t t e r , i n turn, r e q u i r ethe calculation o f t he mu tua l impedances through thee a r t h between the segments, and the s e l f - i m p e d a n c e s ofe a c h segment. These i m p e d a n c e s , functions o f the s o i lelectrical p a r a m e t e r s and s egmen t geometric p a r a m e t e r s , -a re computed from a series o f formulas e m b o d y i n g theanalytic solution of the voltages a t a ny point in a t w o -layered e ar th d ue t o a uniform c u r r e n t l e a v i n g a s i n g l evertical o r horizontal s egmen t lo ca te d a ls o i n the t w o-layered model [ 6 ] . With Z a , Zb and Zc d e t e r m i n e d , VRG,VN and I 2 a r e e a s i l y f o u n d . F i n a l l y , the buried cableportion o f Figure 3 i s again s o l v e d , this time w ith VR Gspecified and point N conne cte d t o r emot e g r o u n d t h r o u g ha n impedance equal t o the ratio of VN and I 2 a s pre-viously determined.

This last solution also y i e l d s theradial c u r r e n t si k , k = 1 , 2 , . . . , 2 2 fo r each s e g m e n t . F r o m t h e s e , thevoltage V p ( x , y , z ) produced a t a ny point ( x , y , z ) in thetwo-layer earth i s computed from2 2V ( x , y , Z ) = I ik k ( x I y I z )k=l

o p e r a t i n g cur r en t, or the available fa ult c ur re nt i fthe effect of a fault occuring outsid e thep roblem spacei s t o be calculated. T he c u r r e n t Ir et i s re turne d inthe neutral to the p roblem spa c e at p oint A . P a r t ofit flows i n to the e a r t h a n d through the open s ec t i o n,gene rating st ep a nd touch potentials. From Carson'sformulas, Ir et ma y be computed from Io by [ 9 ] :z

I = SC Ir e t Z 0s ( 4 )where

DZ = r + jO.0229 en( )

DZ = R + r + jO.0229 Q n ( )s s g Dd s

( 5 )

( 6 )

a n dD = 2 1 6 0 i / / a fe 1d 5Dc s

the d ep th of the equivalente a r t h r e t u r n ( f t . )= shea th g e o me t r i c m e a n r a d i u s

( f t . )= d i s t a n c e fr om middle ofshea th to c o n d u c t o r c e n t e r( f t . )

r = 0 . 301f x 10 = the e a r t h r etur n r e s i s t a n c eg ~ ~ ~ ~ ( Q / 1 0 0 0 f t . )R s = sheath a c r e s i s t a n c e ( Q / 1 0 0 0f t . )f = frequency ( H z )

( 3 ) a 1 = conductiv ityof lower s o illayer ( U / m )where S 1 k ( x , y , z ) , the mutual i m p e d a n c e between the k t hsegment and the p o i n t of e v a l u a t i o n , i s found from thesame formulas mentioned above.

Fo r simulations o f the t hi rd c o nd i ti o n ( t h e s i n g l eopen n e u t r a l ) , the a p p l i c a b l e circuit segment i m p e d a n c e sa r e the same as i n the F i g u r e 3 circuit. I n this case,h o w e v e r , the cable excitation i s described i n t erms ofth e c u r r e n t s I o and I r e t . The phase conductor c u r r e n tI o leaves the problem spa c e a nd e n te r s t he external sys-tem. This c u r r e n t c a n be s p e c i f i e d a s ei ther t he n o rmalZ H I F a u l t T - e q u i v a l e n t f o r c a b l eZ H I P o i n t r c

f ~ ~~F RG l a b | Nv )j ~ ~ ~ ~ ~ 1 2

F i g u r e 4 . S i m p l i f i e d c i r c u i t m o d e l f o r c o n d i t i o n s 1 a n d 2 , w i t hc a b l e r e p l a c e d b y i t s T - e q u i v a l e n t .

The sys t em of Figure 5 i s solved by a s s u m i n g aparticular voltage a t point A a n d then s o l v i n g the si-multaneous s et s of e q u a t i o n s fo r this system t o findthe segment r a d i a l c u r r e n t s a n d I 2 ' T he s um of thes emust be the r e t u r n e d c ur re nt for the assumed i n p u t vol-tage. Actual s e gm en t c u rr e nt s fo r t he desired Ir et ofequation ( 4 ) a r e o b t a i n e d by s c a l i n g b y the ratio ofthe a ct ua l a nd computed Iret values. Equation ( 3 ) i sZ H I

-RemoteG r o u n d.. . . .;.%.

F i g u r e 5 . C i r c u i t s e g m e n t m o d e l f o rc o n d i t i o n 3 s i m u l a t i o n s .

* . , ; - . . - ; ., ; ,L i - i w I e t- - u a- - ., & . . p , ... . . ?U i



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then employed t o fin d t he r e su lt i ng voltage a t d e s i r e dp o i n t s in the two-layered earth. Comparison of Simulated a nd Exp e r i m e n t a l ResultsP r o g r a m Outputs

Results fr om the s imulat i o n program are availablein both t abular a n d graphical form. T he li st ed o ut put sare the f o ll o wi n g p o t e n ti a l s d e f i n e d in Figure 1 : VRG,VT, VG, V3, V6, V12, V S 1 , V S 2 a n d V S 3 . Graphic al o u t -put i s in the f o r m of t w o plots of equipotential con-t our s--on e showing c o n t o u r s on the e a r t h s ur fa c e c e nt e re dover the fault poi n t, a n d a n o t h e r sho wi ng c o n t o u r s on ap la ne n or ma l t o the c a ble a nd p a s s i n g through t he p r o b -lem space midpo i n t .Computer Requir emen t s

The large c o m p u t e r ve r s i o n of BCAB r equir es about20K, 36-bit w o r d s memory, an d execution t im e ( exc lu si veof plots) i s a bo ut t w el ve s e c o n d s using a CD C Cyber 7 4 .The minicomputer v e r s i o n r equir es about 6 0 K , 16-bitw o r d s of memory a n d e x e c u t e s on a NOVA 83 0 w i t h d i s k ina bo ut f ive minutes.RESULTS

P r o g r a m Verif icationT w o p r o c e d u r e s have b e e n employed t o e s t a b l i s h t hevalidity o f the equat i o n s u s e d in the p r o g r a m : comparisonof r e su lt s u si ng the p r o gr a m me d e qu a ti o n s fo r m u t u a l re-s i s t a n c e b e t w e e n c a b l e s egmen t s, w i t h r e s u l t s i n t helit er a tur e; a n d c o m p a r i s o n of s i m u l a t i o n outputs t o re-sults of f i e l d experiments. T he f i r s t p r o c e d u r e i n v o l -ve d s imulat i o n o f v a r i o u s configurations of c o n d u c t o r si n e a r t h a n d t he c a l c u l a t i o n o f t he r e s i s t a n c e t o r e m o t egr oun d of thos e c o n f igu r a t i o n s b a s e d on program r e sult s .Data fo r comparison came f r o m r e f e r e n c e s [ 7 1 a n d [ 8 ] ,b o t h of wh i c h give e m p i r i c a l r e s u l t s a n d analytical re-sults o b t a i n e d f r o m equations d i f f e r i n g f r o m t h o s e p r o -grammed i n BCAB. T he following c o m p a r i s o n r e s u l t s wereobta i n ed :1 . Single V e r t i c a l Ground Rod. Fo r a singler o d i n u n i f o r m soil, comparisons were per-formed fo r t e n d i f f e r e n t r o d lengths a n dthr ee d i a m e t e r s . Computed r e s i s t a n c e s t or e m o t e e a r t h were w i t h i n 3 per c e n t o fthos e given i n [ 8 ] .2 . T h r e e V er t i ca l Gr o un d Rods. Fo r t h r e er o d s in a t r e f o i l configuration, s i x d i f -f e r e n t t r i a ngle s i z e s w e r e employed . Com-puted r e m o t e e a r t h r e s i s t a n c e s were c l o s e rt o m e a s u r e d d a t a t h a n t he c a l c u l a t e dvalues given i n [ 7 ] .3 . H o r i z o n t a l W i r e . Fo r a single w i r e i n au n i f o r m earth, agreement w i t h [ 7 ] wasw i t h i n 1 per c e n t f o r t e n w i r e lengths a n dt w o depths.4 . V e r t i c a l Ro d i n Upper L ayer. Fora singler o d p o s i t i o n e d i n t he u p p e r layer o f a t w o -l ay er e ar th , comparisons were p e r f o r m e dfo r t e n r a t i o s o f s o il c o n d u c t i v i t i e s .Agreement o f p r o g r a m r e s u l t s w i t h [ 7 1 wasw i t h i n five p e r c e n t .5 . V e r t i c a l Ro d P e n e t r a t i n g T w o Layers. For

a r o d e x t e n d i n g f r o m ground s u r f a c e i n t othe l o w e r s o i l layer, comparisons werem a d e f o r t e n r o d lengths. Agreement w i t h[7 ] was w i t h i n five p e r c e n t .

P r o g r a m v a l i d a t i o n w i t h f i e l d t e s t data i s p r e s e n t e din t he n e x t s e c t i o n .

T he c able t e s t s c o n d u c t e d for E P R I P r o j e c t RP-671p r o vi d e t he field d a t a t o wh i c h t he program r e s u l t swere c ompar ed . I n that t e s t , s ev e r a l t y p e s of c ablewere us ed un de r various c o n d i t i o n s o f s up pl y v o lt a ge ,high an d lo w s i d e c u r r e n t l im it in g i mp ed an ce , a n dg r ou n d in g c o n fi gu r at i o ns . I n all, 114 t e s t s were con-ducted. The t e s t s were p e r f o r m e d in t w o m a i n groups:a 1 5K V s er ie s c o n d u c t e d in Fall 1975 a n d a 35KV s e r i e sd o n e i n Spring 1976. Fr o m all the field t e s t s , 18 weres el e c t e d fo r s i mu la t io n w i t h the BCAB. T h e s e span a l-mo s t all the t y p e s of t e s t c o nfigura t i o n s a nd c abletyp es.

The p a r a m e t e r s used fo r t he simulations were gene-r ally o bt ai ne d fr om r ea di ly available field t e s t d a t aa n d ~manufacturer's cable data. How eve r, the s o il para-m e t e r s required a more e l a b o r a t e pr o c edur e, i nvolvingt he m e as u re m e nt of the conductance from f aul t p oi n t t or emot e ground. This was necessary b e c a u s e we foundthat surfa c e layer s were so s ha ll ow t ha t r eli able mea-s u r e m e n t s of s u rf a ce c o n du c ti v it y , 02 , were n o t p ossi-ble usi ng st a n d a r d four-electrode techniques [ 7 ] .Furthermor e, 02 varied throughout the t o t a l t e s t p e r i o ddue t o changes in s ur fa ce l aye r m o i s t u r e c o n t e n t . Onthe o ther hand, the d e e p layer conductivity, 01, waskn ow n fr om me as ur eme nt s. T he re fo re , the following pro-c edur e was ad opt ed . The fi r s t s t ep was to establish as e t o f base value s. T o d o this, the 15K V bar e n e u t r a lt e s t s were s imulat ed w i t h 01 s e t equal t o t he valueactually measured a t the t e s t s i t e a t the t ime o f thetests. The upper layer conductivity, 02, an d d epth, D,were systematically varied unt il computed s t e p a n dt o uc h p o te n ti a ls matched as clo s ely as possible t o theexperimental data. T he conductivity a nd d e pt h v al ue so b t a i n e d by this process, n o t e d a s 01, 02 an d D, con-s t i t u t e d a bas e s e t of values for o ther t e s t s . T osimulate o ther p a r t i c u l a r tests, was always taken asthe me a sur e d va lue for the t e s t, a nd 02 was o b t a i n e df r o m 2a 2 =-a 29 1 ( 7 )wh e r e g 1 is the m e a s u r e d c o n d u c t a n c e f r o m t he p oint o ffault t o r e m o t e gr oun d t hr ough t he parallel paths o fbu r i e d c able and e ar th fo r the t e s t u n d e r s imulat i o n ;a nd gl i s t he m e a s u r e d p a r a l l e l c o n d u c t a n c e fo r t he bas eset. This process yielded 02 values w h i c h were f r o m 1t o 6 t imes t he a l values. In a ll cases, D was i n i t i a l-ly s e t a t X , but small (less than 20 per cent) adjust-m e n t s were o f t e n necessary t o yield a g r e em e n t b e t w e e nthe program a n d s imulat i o n r e sult s . This w o u l d s implyr ef l e c t the fa ct t ha t the e f f e c t i v e d ep th o f t he s u r f a c es o i l layer d e p e n d s on t he a c t u a l l o c a t i o n o f t he c a b l es ample i n t he t e s t plot. I n a ll c a s e s , D was b e t w e e n1 . 0 a n d 1. 2 meters.

R e s u l t s f r o m the 18 s imulat i o n s are s h o w n i n T a b l e1 a n d Figures 6 , 7 a n d 8 . Table 1 shows the f a u l t v o l -t age VRG ( no r ma li ze d b y supply voltage) from b o t h mea-s u r e d r esults a nd f r o m BCAB simulat i o n results. Cablesare i d en t ifi ed by n e u t r a l m a t e r i a l ( A L = aluminum, CU =copper), n eu t r a l c o n s t r u c t i o n ( F S = flat strap, CT =c o n t i nuous tape, or "LC" t ype , CW = c o n c e n t r i c wi r e),a n d i n s ul a t i o n ( I = insulated, B = bare, SC = semi-c o n duc t i ng). Also s h o w n is t he n eu t r a l size a n d ground-ing a r r a ngemen t . Figure 6 sho ws m e a s u r e d a n d s i m u l a t e de a r t h s u r f a c e voltages n o r m a l i z e d by f a u l t voltage f o rt he 15KV cases of T able 1 . D a t a f o r the 35KV casesw i t h o u t "system ground" a p p e a r i n Figure 7 ; w h i l e F i g u r e8 sho ws r esults f r o m the 35KV cases w i t h "systemground ." E a c h of t he se f igu re s was d r a w n by c o n n e c t i n gt he m e a s u r e d or simulated values fo r VG, V3, V6 a n d V12( s e e Figure 1 ) w i t h s m o o t h li n e s . From t he figures a n d

1 1 3 3



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1 1 3 4table, it i s ap p are nt that the BCAB simulation r e s ul t sc omp ar e f avo ra bl y w i th experimental results.A dditional Examples

On e of the advantages o f a simultaneous p r o g r a msuch a s BCAB is that r es ult s fr o m a spe cific fi eldtest ma y be e a s i l y extended to other circuit o r soilconfigurations. Fo r e xa mp le , s u pp o se the 3 5 K V , CU-CW-B, full n e ut r al c a bl e of T able 1 w a s faulted andalso ha d 0.25-meter opens in the neutral, l o c a t e d 1meter to either side of the fault. This w ould be aCondition 2 operating condition. Table 2 shows theresults of such a simulation a n d compares the resultsw it h r es ul ts from t he fa ult w it ho ut opens (Condition 1 ) .Surface equipotential plots from both conditions a r eshown in Figures 9 a nd 1 0 . Not e the tabulated resultsshow step a n d touch potentials several times largerfo r the fault with o pe n n eu tr al as compared to the

T A B L E 1S I M U L A T E D A N D M E A S U R E D F A U L T V O L T A G E S - - 1 8 C A S E SS U P P L Y N E U - V R GV O L T A G E C A B L E T RAL GROUND S Y S T E M ( M E A S U R E D /( K V ) T Y P E S I Z E R O D S ? G R O U N D ? S I M U L A T I O N )1 5 C U - C W - B F U L L N O N O 0 . 4 4 / 0 . 4 41 5 C U - C W - I F U L L N O N O 0 . 4 5 / 0 . 4 51 5 C U - C T - S C F U L L N O N O 0 . 4 2 / 0 . 4 31 5 A L - F S - S C F U L L N O N O 0 . 4 4 / 0 . 4 3 61 5 A L - F S - I F U L L N O N O 0 . 4 8 / 0 . 4 71 5 A L - C T - I F U L L N O N O 0 . 4 8 / 0 . 4 71 5 C U - C T - I F U L L N O N O 0 . 4 5 / 0 . 4 23 5 C U - C W - B F U L L N O N O 0 . 2 8 5 / 0 . 2 7 43 5 C U - C W - I F U L L N O N O 0 . 3 9 5 / 0 . 3 9 33 5 C U - C T - S C F U L L N O N O 0 . 2 8 / 0 . 2 63 5 C U - C T - I F U L L N O N O 0 . 0 5 / 0 . 0 4 63 5 A L - F S - I F U L L N O N O 0 . 2 9 / 0 . 2 83 5 A L - F S - I F U L L N O N O 0 . 3 9 / 0 . 3 7 43 5 C U - C W - S C F U L L N O N O 0 . 2 9 / 0 . 2 8 33 5 A L - C T - S C 1 F U L L Y E S Y E S 0 . 2 3 / 0 . 2 23 5 A L - C T - S C F U L L Y E S Y E S O . 0 4 / o . 0 2 1 23 5 C U - C W - B A L F N O Y E S 0 . 2 3 / 0 . 1 9 43 5 C U - C W - I A L F N O Y E S 0 . 2 9 / 0 . 2 9I C u r r e n t l i m i t i n g i m g e d a n c e sL o w S i d e : 0 . 7 1 42 C u r r e n t l i m i t i n g i m p e d a n c e sL o w S i d e : 0 . 0 5 7 1 7 3 0

- High S i d e : 1 . 4 8 186- High S i d e : 1.98 7 1 ,

S U R F A C E V O L T A G E I V R g ST E S T R E S U L T--- S IMAT EDESLTS

0 , A L - C T - I A L - F S - IC U - C T - I C U - C T 4 IC U - E - 4 C U - C W -I --I -I I t

S U R F A C E V O L T A 6 E V n g *t o - t

I 3 gD I S T A N C E F R O M F A U L T E D B U R I E D C A B L E SFAC E ED

F I S I R E 1 . M E A S U R E O A N D S I M U L A T E D R E S U L l O F XK V C A S E SWTNOUT S Y S T E M B R O U N D F R O M T AK E I

a 2

S U R F A C E V O L T A S E I Y R S MI s 1m l

T E T R E U L T S--- S I M U L A T E D S U L T n

I - = ._3 5 1 2D I S T A N C E F R O M F A UL T EO B U R I E O C A U L E (UACE F E E D

F I G U R E L M E A S U R E D ANO S I U L A T E D RESUTS f f 2 5 K V C A S EW I T H S Y E M G R O U N F R O M T A K . E Lsimple fault case. Figure 10 cl e arly sho ws the d i s -torting effect o n the surface equipotential c o n t o u r s ofthe d i s c o n n e c t e d c able s ec t i o n s .

As a fin al example, Figure 11 sho ws the resultof using BCAB fo r p aram e tric studies. T he figure plotsf a u l t , touch, an d three-foot step p ote ntials w h i c hw o ul d ha ve o cc ur e d i f the 3 5 K V , CU-CW-B t es t of Figure7 ha d b e e n conducted in s o ils w i t h a w i d e r a nge ofratios o f surface layer conductivity t o lower layerconductivity. T he s t r o ng dependence of the se p o t e n -tials o n relative c o n d u c t i vi t i e s is cle a r fr o m thef i g u r e . Through such s tud ies a s t h i s , BCAB c a n beused t o extrapolate field results obtained u n d e r o n es e t o f s o il conditions t o predict d a t a w h i c h wouldc o m e from the s ame t es t s c o n d u c t e d els ewher e.

CONCLUSIONSW i th the development of the s imulat i o n p r o g r a mBCAB, the distribution engineer n o w has a va ila ble at ool for the e stim ation o f t ouc h an d step p ote ntialsresulting from several types of URD c able faults. T hea c c u r a c y of the computed r e s ul t s d o e s depend o n the

4.

D I S T A N C E F R O M F A U L T J E S B U R E D C A L I I S U R F A C E F E E TF I G U R E l . M E A S U R E S A S I M U L A T E R E S U L T S O F 1 S K V CA S FM T A B K E 1 .



6/7

1 1 3 5T A B L E 2

F A U L T , T O U C H , S U R F A C E A N D S T E P P O T E N T I A L S F O R C A B L E W I T HF A U L T O N L Y A N D F A U L T C O M B I N E D W I T H O P E N S I N N E U T R A L

z 4 0 . 0 M E T E R S

F i g u r e 9 . S u r f a c e e q u i p o t e n t i a l s n o r m a l i z e d to F a u l tv o l t a g e f o r 3 5 K V , CU-CW-B c a b l e o fT a b l e 1 w i t h s i n g l e F a u l t a t m i d p o i n t .B u r i e d c a b l e l e n g t h 2 7 . 4 3 m e t e r s ( 9 0 f e e t ) .accuracy of t he d a t a u s e d i n t he computer m o d e l .F r o m a pr a c t i c a l standpoint, t h i s means that r e a l i s t i cvalues must be supplied f o r a ll required input p a r a -m e t e r s . This i s straightforward fo r m o s t o f them, bu tthe v a lu e s n e e d e d f o r a2 a n d D a r e , i n general, mored iff icult t o f ind. However, w i t h t h e s e specified,the p r o g r a m w i l l accurately s o l v e t he problem s i n c eit in effect s o l v e s simultaneously t he system circuita n d electromagnetostatic equations. T he only simpli-fying assump tion u s e d is t he representation of t hec able an d ground r o d s as a s e t o f segments fo r whiche a c h ha s a uniformly d i s t r i b u t e d r a d i a l c u r r e n t .

Complete d o c um e n t a t i o n a n d F o r t r a n I V lis t i ngsof the p r o g r a m ma y be o b t a i n e d f r om t he E l e c t r i c PowerIn s t i tut e.

T h i s w o r k was supported by E P R I c o n t r a c t RP797-1.Programming a s s i s t a n c e was provided by D. Rudolf.

4 0 . 0 METERS

F i g u r e 1 0 . S u r f a c e e q u i p o t e n t i a l s n o r m a l i z e d t o f a u l tv o l t a g e f o r 3 5 K V CU-CW-B c a b l e o fT a b l e 1 w i t h s i n g l e f a u l t a n d s i m u l t a n e o u sop en n e u t r a l s on e i t h e r s i d e . B u r i e dc a b l e l e n g t h 2 7 . 4 3 meters ( 9 0 f e e t ) .

VRGV T

V s l

. 5. 4c o *> . 2

.1e n

0 .t . 0 30 -.03z. . 0 2C00 .

An.

.1 .2 . 3. 4. 5 1 2 3 4 5F i g u r e 1 1 . F a u l t v o l t a g e , VRG, t o uc h voltage, VT,and

3 - f t . S t e p p o t e n t i a l , V . 1 , v e r s us s o i l l a y e rc o n d u c t i v i t y r a t i o .I n d u s t r y p a r t i c i p a n t s were M. A. Martin, Georgia PowerCompa ny; and N. E. P i c c i o n e , Long Island Lighting Com-pany. We a l s o a c k n o w l e d g e the contributions of G.Bah d e r a n d D. A. S ilver, G e n e r a l Cable Co r p o r a t i o n ;a n d J. B. P r ime , Florida Power and Light Company.

REFERENCES1. C r o n i n , L. D. and S e s s l e r , L. H. , "Random S ep a r a -ti o n--Developmen t a n d Exper i en c e," I E E E Trans Power

App. Sys t . , 89:673-680, 1 9 7 0 .

V O L T A G E N O R M A L I Z E D T O S U P P L Y V O L T A G EF A U L T O N L Y F A U L T W I T H O P E N S

V R G 0 . 2 7 3 0 . 9 6 7V T 0 . 0 8 3 0 . 5 8 5V G 0 . 1 9 0 0 . 3 8 2V 3 0 . 1 6 1 0 . 2 3 5V 6 0 . 1 3 5 0 . 1 4 0V 1 2 0 . 1 0 4 0 . 0 7 0 1V S 1 0 . 0 2 9 0 . 1 4 7 2V S 2 0 . 0 2 6 0 . 0 9 5V S 3 0 . 0 3 1 0 . 0 7 0

. 0 1

II

I .

II



7/7

1 1 3 62 . "Buried P o w e r a nd T e le ph on e Dist r ibuti o n Systems--A n a l y s i s o f P r i m a r y Cable Fa ul t T e s t s a n d Ev a l u a -t i o n o f E x p e r i e n c e w i t h Rad ome S e p a r a t i o n , " E E IP u b l i c a t i o n , 68-62, J u n e 1968.3 . Martin, M. A. , Silve r, D . A. , Lukac, R. G . a n dSua r ez, R. , "No rmal a n d S h o r t - C i r c u i t Op e r a t i n gC h a r a c t e r i s t i c s o f M e t a l l i c S h i e l d e d S o l i d D i e l e c -t r i c P ow e r Ca ble ," I E E E T r a n s . P o w e r Ap p. Sy st .,93:601-613, 1974 .4 . P i c c i o n e , N. E ., Fa ul t T e s t i n g o f V a r i o u s Co n c e n -t r i c Ne ut ra l Ca ble s W i t h a n d W it ho ut Co nd uc ti veJackets, P r el i m i n a r y Re p o r t t o ICC T a s k F o r c e 6-21.L o n g I s l a n d Lighting Compa ny, M a r c h 1 9 75.5 . Bahder, G. , Ma r t i n , M. A. , P i c c i o n e , N. , P r ime , J.B. , Jr., a n d Silve r, D. A. , O u t d o o r High V o l t a g ea n d High Cu r r e n t Sho r t Ci r c u i t T e s t s on SingleP ha s e E xt r ud ed Di e le c t r i c P r i m a r y D i s t r i b u t i o nCable s, P h a s e II . F i n a l Repo r t, E P R I P r o j e c t RP -671, Ma y 1977.6 . Webb, R . P ., Nunnally, H . N. , a n d Joy, E. B. ,Co m p u t e r P r o g r a m f o r D e t e r m i n a t i o n o f E ar t h P ot en -t i a l s Du e t o Faults or L o s s o f C o n c e n t r i c N e u t r a l

on URD Cable, Fi n a l Re p o r t EPRI P r o j e c t RP-797-1,Ma y 1977.7 . Tagg, G. F. , E a r t h R e s i s t a n c e , P i t t m a n P u b l i s h i n gCorp., New York, 1 9 6 4 .8. Sunde, E. D. , E a r t h C o n d u c t i o n E f f e c t s i n T r a n s m i s -s i o n Sys t ems, D o v e r P u b l i c a t i o n s , I nc., 1968.9 . A n d e r s o n , P. M. , A n a ly s i s o f Faulted P o w e r Sys t ems,I o w a S t a t e U n i v e r s i t y P r e s s, 1 9 73.

H . N . NUNNALLY (S'65-M'72) was b o r n i n Atlanta, GA, onDecember 2 8 , 19 4 4 . He r e c e i v e d t he BEE, MS E E and Ph .D.d e g r e e s f r o m Ge o rg ia I n st i tu te o f T e c h n o l o g y i n 1966,1968 a n d 1971, r e s p e c t i v e l y .I n 1971, he j o i n e d t he f a c u l t y o f t he S c h o o l o fE l e c t r i c a l E n g i n e e r i n g a t G e o r g i a I n s t i t u t e of Technolo-

gy, w h e r e he is an A s s i s t a n t P r o f e s s o r . I n addition tohi s w o r k i n t he power systems a r e a , he h a s been activein b i o e n g i n e e r i n g p r o j e c t s .Dr . Nu n n a lly i s a m e m b e r o f t he I E E E P o w e r E n g i n e -e ri ng So ci et y, E t a K a p p a Nu , Tau Beta Pi, and P hi K a p p aPhi. He i s a r egi st er e d p ro fe ss io na l e ngi ne er in t h es t a t e o f Ge o rg i a .

E . B . JOY ( S ' 6 7 - M ' 7 0 ) w a s bo r n in T ro y, Ne w Yo r k o nNovember 1 5 , 1 9 4 1 . He r e c e i v e d the BEE, MSEE a nd P h. D.degrees from Ge or gi a I n s t i t u t e of T e c h n o l o g y i n 19 63,1 9 6 7 , and 1 9 7 0 , respectively.I n 1 9 7 0 , he joined t he faculty of the School ofEl e c t r i c a l E ngine e ring a t Georgia I n s t i t u t e o f T e c h n o l o -gy , where he i s n o w a n A ssociate Professor. Dr . Jo y ha sinterests i n electromagnetics, p ow er t ra ns mi ss io n a n dgrounding, a n d c o m p u t e r graphics.Dr . Jo y i s a me mbe r of IEEE, URSI, Sigma Xi, a n dE t a K a p p a Nu .R . P . W EBB ( S ' 5 7 - M ' 6 0 ) w a s bo r n in Ce d a r City, Ut a h o nDecember 2 8 , 1936. He r e c e i v e d the BSE E d e g r e e f r o mt he University of U t a h i n 1957, t he MSE E d e gr e e f r o mthe University of S o u t h e r n Califor n i a in 1959, a n d thePh.D. degree from Georgia I n s t i t u t e of T e c h n o l o g y i n1 9 6 4 . Dr . Webb w orke d for t he Do ug la s A ir c ra f t Companyan d the S p e r r y Company b e f o r e join i ng the E l e c t r i c a lEngineering D ep a r t m e n t a t Ge o rg ia I ns t it ut e of T e c h n o -logy i n 1 9 6 1 , wh e r e he i s a Pr ofes s o r . Hi s fields ofinterest a r e electric p o w e r sys t e ms, instrumentationan d control sys t e ms .Dr . Webb i s a member of the I E E E P o w e r E n g i n e e r i n gSociety, E t a K a p p a Nu , T a u Be t a Pi a n d i s a r eg i s t e r e dp r of es s io n al e n gi n ee r in t he s t a t e of Georgia.A . P . MELIOPOULOS ( S ' 6 9 - M ' 7 6 ) w a s born i n Katerini,G r e e c e o n Ma r c h 1 9 , 1 9 4 9 . He received the ME and E EDiplomas from the N ational Technical University ofAthens, G r e e c e i n 1 9 7 2 , a nd the MSEE a nd Ph.D. degreesfrom Georgia Institute of Technology i n 1974 an d 1 9 7 6 ,respectively.I n 1 9 7 6 , he joined the faculty o f the Georgia I n -stitute of Technologywherehe i s a n A s s i s t a n t P rof e ssori n Electrical E n g i n e e r i n g . Hi s i nt er es ts l i e i n the a p-plication of systems t h e o r y a nd op e rations r e s e a r c h t ol ar ge s ca le systems w ith emphasis o n p o w e r sy stem s.Dr . Meliopoulos i s a member o f the I E E E P o w e rEngineering Society a nd t he He ll en i c S oc i et y o f P r o f e s -sional Engineers.

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