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Proceedingsof the 3rd I nternati onal Conference onPropert i es and Appl i cati onsof De ectric Materi al sJu ly 8-12, 1991 Tokyo, J apan

MODELLING OF ARC EXTINCTION I N A I R I N S U L A T I O NC.M . P o r t e l a N. H. C. Santiago

Corona and P a r ti 1 D i s c h a r g e Labor to ryF e d e r a l University of Rio d e JaneiroP . O . Box 68504A b s t r a c t : I he corr ect know edoe ot t he behavi our ot df iel ectr i c arc i n ai r has oreat i mpor t ance under t heaspect ot i nsul ati on di st ances sel ecti on in powersvs t ems.Many model s have been el abor at ed duri no t he l astdecades to si mul at e such behavl our b u t , u p t o nowt hese model s were not abl e t o r epr esent w t h oreataccuracy t he t ests result s. No qeneral aqreement on t heti el d of appl i cati on of t hese model s has al so beenachi eved vet .The mai n q o a l ot t hi s paper i s to present ar easonabl y si mpl e composed model w t h t wo t her m c t i meconst ant s w ch avoi d some of t he i nconsi st enci es a tsi mpl e t i me const ant model s curr ent l v used.The er oposed model i s compar ed w t h t ne mostusual model s and i s shown t o r each more accur at e arcsi mu1 at o r i s .One appl i cati on exampl e i s used to show t hedi f f er ences bet ween t wo Rode15 and how a model can hel pi r i eval uat i on of a rc sel t - ex t i nc t i on l i m ts i n at r ansmss i on or di s t r i but i on I i ne. These l i m ts a rei mport ant f or proper choi ce ot compensati on r eact ors.s i nql e-phase successtul l operat i on, neutra l qroundi nqcr i te r i a. pro tect i on sel ec t i on. and l nsul dt i on(1oor d1 nat on.

Introduction

Taki ng i nto account that ai r i nsulat i on i sregenerat i ve, t he hvpot hesi s of f l ashover i s consi deredi n several appl i cati ons, namel y i n power systems. atl east f or smal l probabi l i t v overvol t ages, f o l l owed by apower ar c and a current i nterr upt i on near a nat uralzero cur r ent . at power f r equencv.A reasonabl y accurate defi nit i on of arc ext i nct i oni s qui t e i mport ant f or an adequat e i nsul ati onsel ecti on. Ther ef ore, an accur ate know edge of smal lcurrent a r c behavi our i s necessary, as success of arcext i ncti on near a z e r o cur r ent depends upon arc -network i nter acti on, i ncl udi nq f ast phenomena I l l .The t i me const ant s i nvol ved i n such i nteracti on aretvpi cal l v i n the range of 0.1 t o 100 p5 corr espondi nqto f requenci es f rom k H z t o MHz.The experi ment al work necessary t o the studi es ofa r c behavi our presents pract i cal di f i cul t i es to beper f ormed i n actual condi t i ons. I n order t o becomef easi bl e t o perf orm a great number of experi ment sre l ated to the arc behavi our, a s i mpl i f i ed test c i rcui twas devel oped s o a s to generate s tabl e e l ect r i c a rcsi i nder l ow DC curr ent condi t i ons. An i mpul se cur r entgenerat or was al so provi ded to di st urb t he el ectr i c arcw th t he i nj ect i on of very smal l i mpul se curr snts .A systemati c t est procedure, i n stati c and dvnam ccondit i ons, f or l ow curr ent arcs was then carr i ed out,coveri ng a reasonabl e range of condi t i ons. The resul t sof t hese t ests were then used to i nvest i qat e arc model sand their suit abi l i ty f or arc s i mulat i on.I t was observed t hat s ome usual ar c model s ar e not

abl e t o represent, w th acceptabl e accuracy, t hemeasured ar c behavi our. . b more consi st ent composed ar cmodel i s t hen proposed and checked agai nst t hemeasurement s. The i dea of t hi s model i s t o consi dert he el ectr i c arc composed bv two axi a l regi ons i nser i es w th d i f f erent behavi ours a s f ar a s thei r t i meconst ant s ar e concer ned. The proposed model showedpract i cal advant aqes and may be used as a basi s f or a r cbehavi our st udi es and adequat e def i ni t i on of arcext i nct i on condi t i ons.

O.B. O l i v e i r a C. J. DupontCEPEL

Contro de Pesquisas de E n e r g i a E l l t r i c aP.O. Box 27154E x p e r i m e n t a l Work

T e s t s Set-upThe experi mental work was perf ormed i n as i mpl i f i ed test c i rcui t which was developed so a s t oqener ate st abl e el ectr i c arcs under l ow DC currentcondi t i ons. An i mpul se curr ent gener ator was d l 50provi ded to di s turb the e lec t r i c arc w th t he i nj ec t i onof very smal l i mpul se curr ent s.The mai n components of t hi s si mpl i f i ed t estc i rcui t are shown i n F i qure 1 .

F i s u r e 1 - Si mpl i f i e d t e st c i r c ui t us edt o perf orm t he experi ment s.

wher e: kc = charge res i storkd = r e s i s t i v e di v i d er , 1HR. 1OOO:ikCU = RC- ser i es di v i der , 112:lkL C = smal l i mpul se cur r ent generat orksh = shunt l ow i nduct i ve res i st ance

Much care was t aken w t h t he measuri ng ci r cui t ,mai nly w th t he scal e f act or determ nati on and t headj ustment of t he dynam c behavi our , t aki ng i ntoaccount t he ranqe of si gnal s t o be measured.

G = rod- rod e l ectr odes

E x p e r i m e n t sThe experi ment s wer e perf ormed i n order t o getresul t s w th i nformati on about the etat i c and dvnamccharacte r i s t i cs of e lec t r i c arcs .Arcs w t h di f f er e nt l engt hs ( f r o m5 t o 2Omm wer eqener ated under DC condi t i ons and t hei r st ati cc har a ct e r i s t i c s ( Y x I cur ves) wer e measur ed. For eacharc l enqth t he Y x I cur ve was measured and t he r esul t swere used to get t he arc vol t age per uni t of l ength andt he anodi c- cathodi c vol tage.Two el ectr ode materi al s ( brass and t ungsteni umand t wo el ect r ode shapes (r ounded r od- r od and needl erod- rod) were i nit i a l l y used i n t he exper i ments. knvs i gnif i cant i nf l uency of t hese parameters i n t he a rcchar acter i st i cs wa5 observed. The needl e r ad- rad

el ect r odes of brass wer e then used because they pr ovi debett er arc stabi l i tv condi t i ons and are e a s y t omanuf act ure.The arc dynam c behavi our was eval uated i npr a ct i c e b v measuri ng t he a rc vol t age change dur i ngvery small i mpul se curr ent i nj ecti on, I mpul se curr ent sw th d i f f erent wave shapes, d i f f erent ampl i t udes andboth pol ar i t i es were i njected i n st abl e arcs.Di f f erent i ni t i a l condi t i ons of t he a rc . ( DC V x I l evel s )were al so consi der ed.-381-

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The measur ed V x I curves obt ai ned f or each a rcl ength are shown i n Fi gur e 2. The arc vol t age peruni t of l ength ( Vl a) and t he anodi c- cathodi c vol t age!Vac) , deri ved tr om t hese measurements by cal cul ati on.are shown i n F i gure 3 . Thi s cal cul ati on was per f ormedt aki ng i nto account the l i near i ty of t he arc vol tage(Va ) w t h i t s l engt h, as s hown by t he measur ementr e sul t s i n F i gure 4 . l hen t he arc vol t age i s gi ven by:

Va = Vl axLa + Vac (1 )wher e Va = arc vol t age ( V i :V l a = a r c vol t age p e r uni t o f l ength ! V/ mm :Vac = anodi c- cathodi c vol t age I V ) ;La = arc l engt h (mm).B y us i ng curve f i t t i ng techniques. the f o l l ow ngequat i ons were deri ved f r om t he measurement r esul t s:

Vi a = a ( l a ) 'Vac = y + r ) i l awhere I a = arc curr ent i n m A

+or 100 I a 5 380 m A

f or 3 8 0 5 l a I 0 9 m A

a = 3.54Yx1Usp = - v . 9 3 9 7y = 70.92r) = 6 . 1 8 8 ~1 0 ~I5 . a b x io2y = 37 . 59 _jf3 -0.6357r) = 1 8 . 9 6 2 ~ 1 0 ~

1 I'J IOU '00 3C0 400 500 6U0 700

I iirrenttmY 1Fi qure 2 - S ta t i c characte r i s t i cs obta i ned fo r eacharc l enqht . ( so l i d l i nes = measur ed,dot t ed l i nes = cal cul ated

F i gure 3

' , -~Vac- - L L - U I L5,.m 3m NO ein BUD 7m- Arc vol t age per uni t l ength - V Iand anodi c- chatodi c - Va c (

'I I

Current (irR> a ( V )V )

C ! ? ? 0.50 0.75 I U1 1.25 I .50 1.75 2.00Fr c Lrr1gt.h c c m lw th t he arc l engthF i gure 4 - L i near i t y o f t he arc vol t aae

The resul t s f r o m t he combi nat i on of equat i ons 1 , 2and 3 ar e a150 shown i n Fi gure 2 by t h e dott ed 1i nes. I nF i gure 5 some r esul t s of t he dvneni c arc behavi ourar e presented on t he stat i c Curve of a DC arc.t o r a compar i son w t n hi qher curr ent vai ues. t het neoreti cal model s of C I J and experi ment al r esul t sc i t ed b v 1 4 1 and r eproduced i n i l l wer e used. A

r easonabi e agr eement i s f ound. e. g. , for Curr ents i n t ner ange 2-41) A, resul ts o f Cb j corr espond t o f% - 0. 64 i ngood agreet cent w t h val ues i n our t est r anae.

2"10 \JI IBI0 .(

0 in, , , , , , , , , , , , , 1! 0 1 00 2 00 3 01 1 I 1 I 01 6 10 7 00 8 11 I0F i gure 5 - Exampl es of dynam c ar c behavi our ont he 5 mm a rc s t at i c c har a ct e r i s t i cA l l r esul t s obt ai ned were used in t hedet erm nat i on of a r c model par amet er s a s shown i n the

f o l 1 ow ng.Arc Modellina

From r esul t s of some t ests al ready perf ormed C21,i t was not i ced t hat i n order t o have a correctrcpresent ati on of tr ansi ent arc behavi our , i t must becnnsi dered t he f act that di f f erent phvsi cal mechani ses.w i t h at l east t wo di f f erent orders of magni t udes of"t l ee const ant s" are i nvol ved a s a c o n s e q u e n c e of :- Di f f erent I nca1 condi t i ons, as i s t he case ofanodi c- cathodi c r egi ons and r egi ons far f rom anode andcat hode i n arc col umn, o r di f f er e nt c ondi t i ons , e . g . ,due to ai r macroscopi c t urbul ence;- Di f f erent re l a t i ve e f f ects of rapi d changes i nwhat concerns gl obal t hermal and el ectr i cal arcpropert i es , as a consequence of heat t ransm ssi on, i nthe radi al d ir ect i on and e l ectr i c conducti on, i n t heat: i a1 di rect i on.Wt h some physi cal cons i st ency cr i t er i a , namel yarc par amet er s i ndependent o f part i cul ar shape of smallampl i t ude di st urbances ( al t hough dependent of a r copera t i ng poi nt ) ? and s ta t i c characte r i s t i c sat i s fy i ng

382 -

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dynamic model, i t was searched a reasonably simplemodel avo iding some incon s is tenc i es of s imple t imeconstant models . I t was found th at a model wi th twot ime cons tant s , each as soc ia t ed t o an equ iv a le n tsub -arc reg ion , w i t h t he t w o sub-arcs i n s e r i e s ,a l l ow ed a reasonab le accurat e a rc s imu la t i on ands a t i s f y i n g a l l c o n s i s te n c y c r i t e r i a . S uc h e q u i va l e n t" s e r i e s t y pe " g l o b a l mo de l i s n o t a s s o c i a te d w i t hd i f f e r e n t c o n d i t i o n s a l o n g a r c l e n g t h , b u t i t i s fo un dt o b e a na tura l and s imple way to cons ider and modelt he g loba l a rc behav iour .F or each of the two sub-arcs. a Mayr type modelmay be assumed. The par ame ters of each sub- arc may bedependent o f operat ing po in t , bu t not o f d i s t u rbanceshape.

A5 f a r as poss ib le . t he chosen parameters mus thave a not so st rong dependence of operat ion point .The s imp les t model t o cons ider t wo t ime cons t ant si s t o a s s o c i a te th e tw o e q u i va l e n t s ub - ar cs i n s e r i e s ,on a composed type model.Being g the ar c conductance, i h e a r c c u r r e n t a ndui, u z . s u b- a rc v o l t a g e s a t ea ch r e g i o n r e l a t e d t o t h earc v o l t age U b y t h e c o o p l in g f a c t o r c , comes L41:U = U1 + U 2 = e . u t t 1 - c J . u

The Mayr model to r e a c h r e g i o n i s :

where: P o i = t .PoPo = uo . i oPm = ( 1 -C j . Po

Be ing t he not a t i on " 0" u s ed h e r e t o r e p r e s e n t t h ep o i n t a t t h e a r c s t a t i c c h a r a c t e r i s t i c i n w hi ch t h ec u r r e n t i m p u l s e i s a p p l ie d .D e r i v a t i n g t h e e x p re s s i o n ( 4 ) and cons ider ing (5 )and (6) i t comes:dg = F i . d g i 4. F 2 . 2 2 5d t d t d t

2where: F L =92qi+g212

o b ta i n e d t ro m t h e t e s t s r e s u l t s , i n c l u d i n g t h e s t a t i ccha rac t er i s t i c measurements and t h e impu l se cu r re n ti n j e c t i o n w i t h t h e r e s p e c t i v e a r c r es p on s e.Tab le I shows some of the obtaaned ar c parameters.I t i s c l ea r t h a t 81 i s of t he o rder of microsecondsand 82 i s o f t he o rder o f hundreds o f m ic roseconds . I nt h i s t a b l e d i s t h e d is t a n c e b etw ee n e l e c tr o d e s , t f a nd

t t a r e th e f r o n t a nd t a i l t im e s o f t h e i n i e c t e dimpu l s i v e cu r ren t .

Tab le I - R F C parame ters f o r th e Composed modeld = 5 m m

It must be emphas ized tha t models were adl uste dcov er ing a w ide range o t re la t i v e d i s t u rbance shapesand arc ope rat ing poin ts . The s epara te adjustment ofeach d i s t u rbance i s a lmos t meaningles s . It can be shown1 2 1 , t h a t f o r a s p e c i f i c d i s tu r b a n c e s e v e r a l t yp e s o farc models l i nc lu di ng the most common ones) , w i th thes ~me umber of adjus ted parameters , appear as almostequivale nt . The main po in t 1s t hat a con s i s t en t mode lmust be gen era l and must no t depend upon one re la t i veshape.

To v e r i f y t he adequation and cons i s t encv o f t heproposed model , th e obtained r es ul ts were compared withr e s u l t s o f th r e e o th e r mo de ls , p a r t i c u l a r l y t h e m od e lsof Mayr, C ass ie and Expanded Mayr. These models areshown i n [ ab le 11 . Some re su l t s f rom t hese s imu la t i ona r e p r e s e nt ed i n F i g u r e b f o r t he impu l se nb 9. I n t h i se xa mp le , a nd i n a l l o t h e r s i m u la t e d ca s es , t h e f i t t i n g 5of conduc tance curv es w ere b et t er f o r t he p roposedmodel.

I n p r i n c i p l e , P o i , P a , 81, 8 2 may depend upono p e r a t i n g p o i n t . A st ron g dependency , however, i s no td e s i r a b l e , a t l e a s t u nd er a p r a c t i c a l a p p l i c a t i o n p o i n to t v iew, and, als o, as an in di ca t iv e of h i g h e rd i f i c u l t y i n c o r r e c t p a ra me te r e s t i m a ti o n . Whenposs ib le, the s imp les t sub arc model ( i n what concernsdependence o f P o i , P a , 81, 2 upon operat ing po in t )must be considered.The parameter adiu stne nt must be done with s everaldis turbanc e shapes, and the parameter values must beIndependent of a spec i f i c shape .Using the equations showed above, a numericrou t ine was developed and th e arc parameters were

i 7 1Tab le 11 - Models compared with the Composed Model C3,41I Mode l E qua t ion Arc parameters I

I t must be po in t ed ou t t hat f o r o t her con d i t i onsd i f f e r e n t o f t h o s e c o n s i de r e d he r e , f o r i ns t ance :long er arc len gth and presence of w ind, some aspe ctsmust be a150 co nsi dere d 111. However, they do noti n v a l i d a t e t h e r e s u l t s h e r e s howe d. - 83-

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t Il l

F i gure 4 - Measured and aj ust ed Composed. Mayr. Lass i eand Expanded ar c c onduct ance - i mp. nb. 9E x a m l e of A ~ ~ l i c a t i o n

The case of a t ransm ssi on o r di s t r i but i on l i newher e a f aul t ocurr ed and was cl eared b y aci rcui t - breaker, i s a pract i cal exampl e of ho w a modelwhi ch descr i bes t he behavi our of a t r e e el ec t r i c ar c i nair can i nfl uence an adequat e i nsul ati on sel ecti on.The success o f an aut omati c r ecl ose w l l depend ont he reqenerat i on of ai r i nsul at i on near t he f aul tpoi nt , and th i s i s rel ated to the shor t - c i r cu i t cur rentl evel , arc l enqth and arc i nteract i on w th the whol ec i r c ui t ,For t he m cr oseconds ri qht before and att er t hecurr ent zero cross i ng, whi ch determ ne t he s u c c e s s ofthe arc i nterr upt i on, the c i rcui t may be represented,i n f i rst approxi mati on, by an equival ent character i st i ci mpedance o f t ype Z C = f l . 51 .The equi val ent ci r cui t t o be consi dered i spresented i n F i qure 1 .

V a"

F i qure 7 - Equival ent c i rcui t used in s i mul at i onsUsi ng equat i ons ( I ) , r 2J and ( 3 ) w t h someeventual adi t i onal modi f i cat i ons. f or best est i mate t hedom nant r ange f or arc ext i ncti on near curr ent zer o,l i m t conecti ons may be obtai ned.Some prel i m nar t est s showed an i mpor t anti nf l uence ot arc model , and the j ust i f i cat i on tor us i nua composed mode!, w t h two t i me const ant s.Thi s approach al l ows a bet t er accuracy i n defi ni ngcondi t i ons f o r arc ext i nc t i on in ai r , and , s o , a m o r eopt m sed and confi dent use of natura l arc ext i nct i onand network concept i ons t aki ng advantage o t such fac t .ssi ch a s i n si ngl e phase sw t chi ng and opt m sed eart hi ngc i r c ui t s .

C o n c l u s i o n sThe most common us ed a r c moael s have not aeen abl e

t o r epr esent adequatel y t he arc dynam cbehavi our observed i n experi mental t ests.The composed code1 present ed her e, besi des bei ngphysi cal l y more consi st ent , has shown a aett er f i t t i ngo t t he si mul ated resul t s t o the experi ment al ones.Consi der i no that t hese resul t s were obta i ned f romexper i ment s pertormea i n s i epl i t i ed condi t i ons, f utureworks usi ng t he proposed composed model shal l be doneI n order t o take i nto account ot her f a c t o r s re l ated t oactual arcs , such as higher curr ent s , l onger arcl enaths, di tf et- ent el ectr ode shapes and envi r onment alcondi t l ons.

R e f e r e n c e sC I ~ PORTELA. C . " Some met hods t o anal yse t hebehavi our o t an el ect r i c arc i n ai r - Hopl i cat i onExampl es" . V I 1 SNPTEE - qrcup I V , S%o Paul o - S F ,Brazi l . 1 9 8 4 i i n port uquesel .12 1 - F' UHTELH C ., SANTI AGO. N H . L . . kt i rUHEWTE.J . . "Model I i nq a t Dynamc Ar c Behavi our tor Smal lCurr ent s". Report presented at t he Col l oqui um otCl GRE SC 13, Sarai evo, May 1?8O,.121 - Ci rLDHBU. R. , ' The El ectr i c Rrc and I t s Hodel l i nqi n Hi gh Vol t age Ci r cui t Br eakers" . Si emens Revi ewV I 1 4187 !in por t uguese~.t 4 1 - Wor ki ng Gr oup 1 S . u l . CI GHE, "Pract i calAppl i cat i on of Arc Phys i cs i n Ci rcui t Breakers .Survey of i al cul ati on Methods and Appl i cati onGui de". El ectr a nb. l l B, pp. 6 5 - 7 9 . mavl i 988.C ~ J PURTELA, C. . "Ueterm nati on ot Cr i t i cal condi t i onsi n c i r cui t breaker Sw tchinq f or Short - Li neF aul t s ' , I X SNPTEE, Belo Hori zont e - Bra:i l , 1987( i n port uquese).I 6 1 - I r I N G , L. H . H.. "El ectr i cal Research Hssoci at i onreport b i l l 17: