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C H A P T D R V
Principles o f Circuit-breaking
N the occurrence of a short-circuit within a system, a particularbreaka in the aftected line will l* ttippud oB.6n automatically
fuaction of this breaker is to carrse the fault curreirt to oease flowingas soon as possible, and to dp so without harmful effeqtgeitlier to thesystem or to itsdfi It was shown in Cbapter IV that contact separa-tion merely creates an arc discharge i'ithofit caueing appreciable
'
altercion oJ the current initially. This is perfectly desiaSle becagseany suCden cut-off of the current at that stage might give rise toharmful induecd voltages in the circuit.
The function of the breaker is tihen, more epecificalln to intro-duce a high impedance into the circuit in such a rnanner as to force,or allow, tte current to reach zero without possibility of the arc beingres'truck thereafter, and without causing the current to r€ach anabnorsral rate of decrase. The possibility of daoage to thb breakerhas been mentioned because, as well as being subjected to hatingand electromagaetic force in common with the other components ofthe alfected line, the breaker is also the 'nain receptacle of ttre shoft-cirnrit energy because of the resistive nature of the discharge withinit A primary factor in high power circuit-breaker design is thePrwision of mechanical strength sufrcient ts withstand the sudden
Qeleasc of large quantities of eiergr of the order of, say 500 kilopatt-eeconds (i.e. more than 100,000 calories). Early extinction of thearc helps to keep tlis eneg5r release ie 3 minimum.
D.G" Circuit-brea&lng. Fig 5.1c rqrresents a eimple d.c.
*.u! *-prising a'geneoior, rdi"tor, teacior and circuit-breaker.t-he latter is assuued to break the lmd curreotr I - ElR. -ladiagram b, the line t is the currenf-voltage characteri*ic.'bJ-the arcu'hen'its current is decreasing; line 2 is a resistance line and repre-seilq.lhe voltage E-;& thai, is, tlrc: e.m.t'. remaining when therestgljV-_q drop is:heducted. . 5he initial current at contart'$:innrtiol
. r riJ l
IIl,II
76 sWtTCg€BAB PRINCTPLES
ir thc frrll velue r, and it is clear from thc diagram'l thst thc src buostablc d qtrrents betw.ccn r an{ 11 ei"ce tni voitages ",
,.q;rd:: 11:ijg TTj qr greater than the amounts.iil.ui" (.4_r").11-T,:""9 -!tb !:: howcver, tte arc current tdnds to i"cre"s;rmce this section of Iine ! lics -berow rine 2, and in ruch conditionr
tJ"ryp":l of thc fault current is not possible. UnAercircuit-hhing oonditions, howcycr, ttc arc is bciig tengtncnJ titihe scparetioa of tlrc contacrs, and tlc ecot'is;d;,fr;*;;,:voltagc cts*crsistic so ttst it lies abovd thc !*istanac ti;Thl
ctr(a ) .
Fig.5.l. D.C. qc choactsisth-+otatt deaca4nEprogrcssive lengthening, yh$ qly be assisrcd by etectromagnaicforce in cstain designg, is.a basic'r.equircment oi th" d";;il|r.breater. Ncverthelds-ti i; th" t;;rA;;;iA;G* ;;;;;nalntain th9, arc whish resutts in the rai-sing .f til';h;;illtlrnr{any adon which brings this about ,*} i_pro*;;;;;performance. Thus, any m-eans',r'hi"h in"""a.e thc.r.ate of enercytry. pg unir'teFth of'gc'arc' cotumn nay-uc a""l*uu=io-.id#ito thc lengthpning. -.
. -..--.
The grnerar cfi.ect of thc circuit inducrancc during thc inter.nrption ie of spccial imeresr. While the *I"1, i"j"-iir";;;l:to d whcre thc zolace-.a--r,R ir ress d ,"L bahncb of voltsge irgdl up by c, - fup,doo..hi" -q,r;ftb
iil nqativc with dc.crc$ng curEcnt an4 in a@rdance '*frti;r,; I;;A;;;qcnd to. 4fnrain tlrs o'rcnt Til ;Jrt"gaa.b";'"ti.fiJ.rsis6 ia istcrrustion, but ir ad G'to increasc ite indudvolagee hthc u;bblerangce
"f .u-*l--l dcarfron diaeranC.Morcovcr, m ec'ount d ol s.t *t-.t"F"io. .r"*iffiTi#
frl1#,ntnt_o *rr*o.[J"* r6i-o "*y high vetucr
g.D.
T( -
*Idcaun thc d.c" u'.,r", g"rrJ g.p*# iiln ;tri"HJ.f, Xfll#:frF rlrilcdl elcar of tho scristrnc! tiilil";dt* oo ,qioo bcrpca
Il t '
P R I N C I P L E S O P C I R C U I T . B N E A K I N O 7 i
L and f" should vanish, and such that induced toltagesjust prior to
*tinaio" are g Einimum. Note that alteration of the generator
Ir.f. giuo a correponding elteration of the positioi of the reietancc
tine 2 iho"e slope, however, remains fixed by the circuit resistance'
iii* ,ft" hish;r-the circuii e.m.f. the morl eficient'must be the
iJoi.f thelreaker in lengthcning and de-ionizing the arc to raiee
ths charactsistic above thc resistance line.
Fig.5.2. D.C. oc cnaactl**laawt dadc&h'g 6td I^Suarralc&n rg
[ig. 5.?.a shows the arc characteristic 6E it might bc- whennodified by lengthening during the brarLing-opgetign- .fh9 orcvoltagc ie
"i At piiou greatcr than the ahount-E+? anC thc batancc
!r grveu Vy t. il4at wnicn i" proPortignal t9 lhc gradie$ o{ theorrenrtirie curvc. Thie curvc msy therefore be deduccd, elrhown in.fig. 5.?,h, and prondes thc totd arcing timcr '-fhir
Pgibdney b€ an-appreciable-fraction of the total time of bhort-circuitcrrrrent flow and must be kept as ehort ss possibla Fig. 542 showBthar tlu arcing time may be reduced by incrcasiog thc retes of Gurrentfrlt but this i;volve nigber ralues of tlhc indued voltagec, ca, and aorrcapondingly highcr-poaition of thc chrracteri*ic" - In thc- typicelcase i[uatratcd-by fig. 5.2t thc e*tincion voltage of th. arc h ebcuttnicc the generaior-voltagq ehowing that thc dielectric etrcngth ofthe contact q'ap at ertinction has rcached an adequate levcl
' Summiizing, euccessful d.c. circuit-prca&'in! must-involve sostrin amount of-compromise. 'fhe nccessriry function of th9 9t q.til to raise the arc' charasteristic iufficiently to avoid rtability. - Dyincreasing ihe e$gctubeyond the minimtrm neccssary, a shot!3r-Iri.rg :ii". and,-tieiefoie less. lcverc heating and eleetronnsg3t€Bic'
' r '
af
('
78 swrrcucgaR pn.tNctplEs
. str6scr' will bcobained fthough the rikefihood of ovcrvortagcs ua!a.isa In goeral tlre minimumir-ciog e-e p.r_ioi[i. -*ti"p*iupon the 2r''ount of inductancc in tf,c circiia: A.C Circuit-brea&ing. In atternatiai_curlent cy*erns tfuwhole probtem.of circuir.f,seakiog i" difiHt-i;
-.1* io GsFtems. This is becar.se o.6. ..h"nEes directico t"ice l"-;"G;;and is therdore insangleoylf zdo twice p*.y"d l" i,nort, tilac" circuit-brealer gdoits th6 poperty bi pd;ddttre c'rrcnfrom rising again afti d ?Ero &"i.. It i,l.neithcr i"""o"ry ,i,desirablc to crrt ofi the anrrcot at any otherpoint"" trr" Jrr"i",{' wave because such a distoriion of the nattrrar--"o"1i*"*"a a*produce orervoltages. Idealy, tn" *tre"t.sni rru u"-"ri*"a to r.unormally to zero, at which iiiant Oe aiU""t lirt
""gO;ilh;;;between' the circuit-breaker contacts rnourJ rapiary"il""o*" *cprever:t re-striking of the ar',c" The aim of desigtrerj tni"*."", i, ibrea&er wriich cao-invariably accomplish tni" "t
irr" cirt *rredt zcmafter contast separation, "t "ny
c,r.,ent *i$hi' t" ,d;?;Icaplgiry' and without harur to it"er. rn" pfid;;"" ;fihiproblern in design is srtremely difr"olq;A-;;" lf ;;y;[rdwould not probably be economicalEfucts gf.pouer-Futot. The ac. circuit-breaker atte'pts bpreve-nt re-striking of the arc after the fault curcnt it"u
"'orqand the contacr gap must theiefore ;h;;-.h",'ctJuit vorag.appearing there at the" zcro instlnl This instantaneous vortagedcpends opg1 tl" po\rer factor of the circuii "f-."
tn" i"-"fa f tnis relativery rigt, tLetreaker -"y r,""" a aJ-""1v,lii.ome natulof voltjrgc appreciably tess ttai .h" ;-J;,-t""".lrr"r,r, ono.Nevert'eless, in setecing a breaker r*'" o"*r*iar";'* possibh,fzults and associated poier f"d; n r"t i" "Uor"Ji* "nd,,
in anyevent, it should be rimeurbered o", O" a"*rl-ii*l", gap ms..contend iT,t\.p*t volage *.n" oni**iiiii", intemrsr tion, if not
".tra$, d +hst ii*""t (rssuming, of course, the 50 c./r\ &equeocy 1f *ppti). t -*y et"u.,-breakec locations on h.v.se'Erstems, the poira factor under f""tt *;Jttdd-#;;iearty.zao;grvi"g virt'a,Iy pcak vorage J*r*a zero.s; this is.beca'sc of tro
tr Hf.ry *. olaiin, c"Eciary-"uirl.lTgl"ilt"g *,**"* ., "ffu?"ffi llf*il:ffi ffi$?r#"TiHcase of aslmnetdcal *d;-R"f;;;-d:%:"rn ,"1"and uninor lco-ps .f q pyrg.t i""r currcnt on 50 c/s sgcms lgrci ....Y*o* gsears aaa ie.ilGfriffiu[i*-fir$, aqd thr,
i , , i , j - - - ' - : _ : : '
P R I N C I P I , . E S O F C I R C U I T . B R E A K I N C 7 9
.cur€nt zeros do not therefore coincide with p&ks of vottage. Thisphase disptacement dccrcases, of cource, as ihe d.c. comp-onent ofthc. asrynmetrical current decays. The apparent phase shiftassociated with asymmctrical current tends
-to give an easier
inrcmrption and breaker duiy. illuch of this benefit-man however,bc lost-bgcauy the asymmetry decays appreciably during ihe openingtime of the circuit-breaker. Even with ; power factor Is low as'0.1,for-examplg most of the asymmetrydies away dudng the 6rst q or L' g!!o: and this irrterval may be ehort comparad rpith that ffom fr.rltinitiation to contact separation. Much depends, howevei upon theipfting characteristics of the protectivl scheme, and-uiorn tfiebreaker mechanism and gontact d*ign, and partially asym-metrielcurrents oftcn occur during arcing.
A circuit-breaker has to deal with normal load currents, as wellas faults, and since the former are generally aseociated.with highpower factors the interruption duty is then rit"tivety easy: The;.load-breaking srvitch dso always-benefits from tais condition, ofoourBe.
Current Zero Period. After contact eeparation in an ac.-circuit-breaker, an ars is drawn but and its curient alternates suchthat an instantaneous zero (rccurs periodicafly according to the .supply frequency. Final extinction ofthe arc is onty po*ib=l" at oneot theie current zeros and will occur if the volage availatle at Buchan instant is not enough to break dowa the de-iinizea i.esidual arccolumn. The possibilities of breakdown or final --xtinction occurringat any current zero depend upon the phyisical conditions cxistingthen. 'I'his does not mean tlat the ..cirtient zero period'; on Uurcgardetl as being independent of conditions existing prwiously.rYe.-nave already shown.tb* power loss and rate of current fall,IT:r_tg zero, have a marked efrect upon the t€mperaturc aird.degreeof ioniCation of the irc,at the z;C imt nL
'The all-imfortot
Plyt:g state of the contact g-ap at cun€fit zero thus depends upon:lho,l* been happcniag to tf,e'arc just pleviously and thus includes1! .T-.e" 9f grrryit conditions as well as de-baizing and ionizing**Tn#!lrffii*f;
or the'roiaoal"or,,mn in the contacrBap. erists when the current. reaches zero. 'f,he next stage is tho13irt rise of voltage from zero (at the cprrent zero inetant)t what3;el
vatug.is appropriate to the circuit'conditions. It is Ois rlSng:_":,"Cj whigh_nray or-inay not.break dowrr the gap and re-strike thiarc. Just as the p.re-zelo conrlitionc art inpoiant in determining
lt,-
g0 s lv tTcHcEAR PRINCTPLES
the conductivity state of tle column ̂ t ?.arc,, the very s$ort peridof rising voltage immediately aften'ards is widently equally cdticalThe general aature of arcing conditions in circuh-breakss has beendescribed in Chapter IV and we uray now prcaeed to a closer etrrdyof the relationship b'etween the arc aad the circuit conditions arounicurrent zero. This involves a consid€ratiorr of: (i) dre efrects ofanvob.rge onthe currentwave-form; (2) the efieoof circuit capacitanccin parallel t'ith the breaker gn'current wave-form; (3) .the nanncrin which the volage across t.he breaks dfes frdm ao to tte circuit
La,-L-cb
Anc wltagse,er*Idil,a
oB ac k wa r.d "e urne n t, i6
I'ig..5.3. Distortbn of A.C. currcn, ttax,c b1'urc evltuge
value appropriate to thc current zero instant; and (4) the currentzero period in relation ro sone of the physical lrrosesses occurringin the residual column in the contact gap.. Arc Vollage and Curreat \[ave-form. It is convenient to.think of the a.c. arc ail a circuit dement whose resistance generallyvaries in an inverse rnanner with the current during any half-cycliThus.the power factor of the circuit in which a Urdf,erib oper;tingmay change someqriat during any half-cycle of arcing. For instanrr;an arc of 1,000 A r.m.s., iri oil" several co in tength, iiU have a totalresistance of a fraction of an ohar.ovs moet oia naf-"yae p€rio4but as th:e qnreot falls towards zero, tbe resistance may'rise Lpidtyto sr,veral hun&eds or thcusands of ohms. The effects oi this deirmiv.erX -nuch_ upon circuit conditions. Coileiaer a sinple inductivcdrcuit as shown in 69. 53. Thd cirsrit-bree&sr ts elced and tb
II
i rI
PRINCI PLES Or CTRCUTT.DREAKINC 8t
(
{ r
currqrt is sinusoi&I, loqS,nq 90" electrically behind thc gcnerstore'.f. llthen the circuit-breatcr opcns and an arc is €stabtishcd thcarc voltage eo modifies.tr" pn u; rehtion .f;;;;;;ivoltaga The efiect is comparativety small while tbe *-";i,;li;;. rnd arc resistane is low, but a m"rked efiect can;;; ;;JJ"?;approache zergt An irnpott ot tourtl" tan" zero is ehiftcd fromits natural position in tirire and so coincides *ith
";;;;;;;lglta.ge less than + p*k This distortioo of thu *r-"r-;;;""jdisplacement of rhe
rcurrenl ?Ero,:n y b" 9f iittfi-p;;;;h.v. systems, but on l.v. s1'stems wheri the
"re"g "Jdg; ;i tcompamble with the supply
-"?lqg", the currerit _"y-b, J;;acrmpletely forced intg nhxe wittr th-e supptyr.rrg" ".-;;L,
oi.Thie condition considerabry eases the di..y ; th;;;;;;;;1't"voluge available t
"*,ro is-iclatively.v"ry r'_"[
""d;Ae;ffi;;lrc is the more readily achieved. -
. .Fr.orn-fig.. 53 the- true current during arcing may be esilvdcernined, giveathe circuit e.m.f. and th;r""d;;;U #a ilrrfrriea_arc voltage characteristic. -The actual current l. wilt be thedifrcrence betrveen the- no,rmal *o"rrt-r, which floil *t"i tfr".breaker-is closed, andthe .,backwarJi *iL*t ,;, *n "l-,'r"finliin tt e circuit if the arcingroltage ,"pro"oiJif,J ,.fi".*fi;;;
IT "yrt voltage and;'backJardit;;;-; rehted as indicated.in the diagram. Summarizing, we -"y oy tlrt t" g*;a;;;;;isgontroltedappreciabtyby.ihe;";iJ;h;""ild;fi
;ill:controlled over the.remainder of the half-cycl* Th;*"*, G;hhs leen exaggerared i, fic. t.tf";;tffi.-'-.^^_P_1ttr"J Cgac-itanJg. The *"airio* shown in fig.5.3 bavcoeen sontewha. ldrlized for simplicity; in practice tno?" fu;;cenain amount of c-Facrtance in parallel *irh.;r;id.;k;?;;i3.j.ej* to (a) the capacit"""Jt * iitt" mu and onnectionson the generator side of the brea&a when an eartl r""rt]ol*"- oilill3l ddu:"g (Dl tp *pu"l.** u"irlccnli sonact and the t"nkuntb an oil circub-brealcr.. Figa S.&rpro*t,
" "i-prkr*ltt*i.t +" capacrtaae c, tu "F;;; t'ilara stuh thGbrca&crque to the eanh frn* on the lmd side.i tff".ry i_**;ffi'ot parallet capacianci are its innuenl on the;vorage acrocc tac
I*:t gap aft r corrTt zero, with.wniin we shsll deal later on,.o S,lrltn:. "ry
th. "r" *ro"i j; b"f;r the zcro. is rcachcd.
. -8. ).) shosB ttre circuit_of !g. S.l in eimplified for*-T;;omple equations rqrresent the b€heviorr o{ t[c currcDts andvorqges" I.e*,;. .-,i. *r"o..i; t: ;6"; *rroo. (thlougb th3G
eC EwrrcgcEAR PRTNctPLBg
lnductang); l], - cafacitanoe curr?nt; c ' E sis, sa - arypttc.m.f., and c. - aie voltsge. Ttc arc dl instsatsrcou! velucs ofthe variablcs. Thc equetion of thc voluges is: c'- L "dinldt 1- c,The equation of currcnts is: i. 1- in .- l, The voltagc equafon nryslso b€ wittaz.ttri.ltlt - (c -. c.lfl.
(
F4.5.4. Capacitances h ?oalh, @irh c*adt-bteaha oc
Let us study the events occurring frgm the time when eo beginlto riee appreciably as tlrc current approaches zso. The current andvoltage curves in fig. 5.5 are shownn for clarity, on a somewhdexpanded time-scde. As in the previous simple exampl.e, the riein6arc voltage forces the main current t,o to collapse more quickly thmif the breaker had remained closed. This is clear also from tlcexprcs.sion tot di-ldt, as e at rtris period of the cqrrcnt cycle iincgative and the arc vohage e. is added to the generalor voltrgq dgiving a iorreslonding increase in the rate of current fall. Thlrising arc vottagi also causes a divcrsion of currcnt into the capach.ance, the value. o{ this current at any rnstant bcing given byrio - C . dc"lilt. 'This current is positive (clockwise in hg.-S.S1 d4sincc i - i- ; it is obtained at the expense ofthe arc currdwhich therefore starts to fdl more rapidly than does ,L. As th!instant a is approached the rce of fall of .li" diminishes eince i, itnowdecreasing with eo approaching ite pok value. At the instanta .*rle :0, r, - 0, and in - i-i this condition is illustratcd in 69;5.54. 'Immediately afterwards, the capaciance darts to discharsdgiving a negitive (anti-clocftnuise) currcnl: The 'nain and rrc,currens Tg "til
podtivc,s9 rtrat the ar! is eupplicil both by tho:ource Td. by the capacitahce, and ri is then gdi* than {,.. At t[crnstant , the main qrrrent r€ach€ zero and the arc is then eupplid.eolely by die'capacitance, nrr 6g. 5.i6.' Aftci thig iirsisnt td;d"
-.,i. .+r:{iz!a !
F R l N g I P L E S O F C I R C U I T - D R E A E T N G 83
)Current wftlrJ 6neeket, closcd\
( r
Arc caneatzeFo
Yoltoge zeroeo(pek)
Ln
"tl d(q) $)
FiS.55. Efrcat of palWcq.ibnt oruc aninail w!@ a.?o
84 switcl lcEAl PRTNcIPLEB
eir,en current rnoy bc much lcss w.hen tac eurrent has bccn decggasing
lpiafy ttran in the static casa Tbig is on ocoouttt of thcsmd
i-".t"roi, in tle arc and is obviously a disadvantage in circuit-
il;eakirg. Fhwever, the static condidon Tly--bo- a-pproeched.to ao
;.*, i"F"" Jing upon (") the actual rate of fall of the r.'trent bcforc
tf* io**. coti.iaite4 -and
(b) the el6ciency of dc-ionizCtio.nWe are here conccrned with'the erulent zcro insterg 88d ttre PgrSimmJat"ly afterwarris whcn $e gaP-ie subjectcd e qt cirsqitsoltage. Any mean" which cal bc e-iii'loyed to. pcrsuade *".*:.''.c,rch-as t ."ily
"" posible satic conditions at this stsge are deeirable"
The efect of parailel capaciance is evidendy favourablc, sincg-rt v!.{yrnuch reducesthe ratc oi fu11 of ar" c.trt"nt iW beforc zero, allowingthe arc temperatuie and conductivity morC time to accommodatcttemselvcs to the current zso condition
Note that it is the arc current thet is apprecirbly dtaed'in fotn,rather tfian the main cilrrent paneing through the series rgct{ce,and the questiou of high inductive voitageo does not neceaoarit-v-arise.Neverthcless, the riiversion of current from the arc increasee the arcvoltage (owing to tall of temPereture, ionization, etc.) eld its ratcof rii which in turn increases thc cepecitive current. The procmtlius terrds to become cumulativl, rail in oar1do circumstance' to bpsturtierl later, can tead to the production of ovcrmltrge. Thc extentto which current ie divcrted from t'he arc during this pre-zero perioddcpdnds upon the velue of rapritarcc ard tbe rate of rise of arc'ooit"go. Whcre thcs€ two hctors arc appreciable, the effect on tbearc tirnpcraturc and didectric *rength of tbe g{p 8t zGro may nrakecurrent intcrruption comparativdy cesy. The ratp of fdl pf surrentit zcro rvith asymmetrical currcnt ie generally lees thaa with thecquivalent q'rnmetrlcat current., and therdolg in accordancc u{thtte above principle, Bome casencnt of brcaker duty msy be obtaincd.wish the fcrmcr.
Re"etrikiog Vottago" Tte volagc available at thc circuit'breaker et a current zerodepends upon Powcr factor, aqd thcrdu€,has some finite nalue, unl€s8 tbc circoit is ri5tualy icaistivc. Ttcway in which the re*cri&in! volagc risec fron ztro (tnthc qrq€ntzcro instant) to the approprice tzlue it of thG gr€stcst importane"For instance, in o circuit sithout thir voltagc riec wouldbc instantaneol& snd therc would bc litdc chance of any circuit'breaker gap having aufficient'dielcc{ric ruength to witirstand itwithout breaking down. Forauratcly oucb conditione erc hypochcticatfior thse io alwaye eome capecitand.i piercnt in thc circuit" Thc
-::r\
)
-r':',. t , \
P R I N C I P T E S O F C I R C U I T - B R E A K I N C 8 '
cffcct of this is to modify the rate of rise of rLstriking voltage(R.R.R.V.) such that a few vital microsecends elapse between
",rrr.itzero and. the cstablishment of a voltage of any significance. Strictlyspeaking, there are two conditions to consider: (a) breaker andcapacitance in parallel, and (&) breaker and capacitance in series.11'e shall examine both, although the former is of much greaterimportance as it is nearly always associated with fault conditiong.Pnctical systems are usudly much more corrrplex than the basiccircuits referred to. in the following, although reasonable eimplifica-don of actual conditions may permit a rlseful mathematical treatmentusing the same principles. Alternatively, itudies of rate of rise ofrc-striking voltage may be carried out with the aid of a networkrnalyser.
A simple example of parallel capacitance is seen in fig. 5.4where the line fault places C1 effectively across the breaker. A pairof voltage equations is needed which, when sblved, will gi're thevoltage acro$ the breaker after current zero. Thus:
e : L d i ^ l d t + ' l ! C x ! i " . d t .and ll@ I i".dt : r (i* - i")
where a is the generator voltage and r the breaker resistance at z,ero.0n solving them we obtain three possible cases according to ihevalue assigned to a
l. If r is made infinitg and assuming no other resistance intlre circuig we have o (4cross breaker) :.e (l - cos {Ii@ . tl.In this hypotheticat instance the voltage rises-from zero to iwice thetnstananeorn circuit voltage and tlen returns to zero and continue.to ccillate in this way about the value e.
2. "lf. r is less than infinity but greater than the quantity:-
! !4e (in-clr) - then the cosine term in the expreseion in ca6el. ts multiplied by a factor exponential decoy. Thislmply means th* the high-frgquency gecillation is gradually damped
row irnd the voltage rapidly setrl€o down to thc circuit rblue a. Thcfreqr5ncy of this edlation is giien by: f/(2zr) x {ire and ieusually puch greter than the normal 50 c/s altrirnation of thc
' - ' '!.ril'
86 SWITC 'TGEAR PRINCIPLT .S
Cun"entzeto
instant
,("
(e)
5O'c.p.s.G:Jt!{{}-_ _ _ _ s _ \ r
,(
zero'instant
ft)Fig. 5.6. Rllrfihiry aoh4c (a) aith ldgh-ttc'gercy &tin @d(blarfrcary detFl
voltrgg Lc. r feult bndition hving zcro Pows factor. The ftitpcet of tbo trrneicnt ccillrtion doeo nc qtdte rcach lpicc c onrccouat of tbc danping cfiect of bleakcr sesknca
3. Thc hst cssc iB that in which the breakcr resietancc r is lccrtm thc quaotiry * {Ti-C,eAqilth thir cqndition thc volagc ir notosAUstory but instcad dses loggithnicatly to the vdue c ar.rd Sgfollorrr tho normd 50 c/e veve-form. This is iltustrotcd in 69.5.6b andthc rc-otdking voitqgc is said to be logarithmi;a[y d+s,p"{
Now lct ue study an exanrplc where the caEaoanao ig tii scntwith thc brcakcr. Fig. 5.7 shourc asimplc circuit in whicb wp ns$Clc
i-!H;f;!i:i,"{o"
PntNctPLES O? clRcOrt-Bn8AB8N6 gt
no ftult' b't imagine thst thc brca&cc is to opca whilc the camcfuiveryt is flowing. We may faitly neglcc G,l thc rUetlvely maft
ridcrablc crpacitene to carth of e long tnusnisdon litia This lcavcrur sith e rinpte sc of inducanq-capacitencc and reristancc (ofthe brcalc^) in rccica Thc sppropristc voltegc cquation L:0 - L di@ + ,i + UC x t i.dt.- As bcfolc, tbr; cerer eroobtrind &on'thc rohfiion, but with r vcry inportrnt itiffcrcaco&om thc "pniall€1" ci!€:
e'
cr>c,Ffg. 5.7. Ccpacitaue oJ lng narlltt &rion fuu
sai6drhbcohah
l . I f rbserothcvoltageformie:o -a(1 -e.u@42. ll t is greetcr than zero but less than the i"*tity 2 {re
thcn the .cosine term is multiplied by an exponcntially doyingfr$df.
- 3, lf tiegeder than thc quantity Z @taf,n the volage ictogadthmicalty damped.
The foregoing discussion shoya that the form of volage rieodter zero ig infuenced by the value of the breikcr rcsiltance stzeioin rdatioa to the drcuii inducance and capacianca. Fdrthcr, inordcr to daop out the h.f. ccillation" a rninimum rralue of thcbtca&cr rcsistance is reqnired with mries capacitance and a rnoririumvduc with parallel capqcitance.- It will be secn tater that such$.pitg ie dnmt always deshable. When this is not pcsible wemut take account:of d most important factor, namety, the ratc atthigh the voltage rises up to its fiist peak; .This is clearly'depen-dent upon both e: and ihe natural froguency of the circui! which -
' ie vcry high for lorv'values of epacitance and inductance. 'fhe.
- + ,a . i-t
88 swtrcgcgAR pRrNcrpr.Es
rate of rise of volage may be high, thercfore, et e location ctce tot|re generator. t
The tcrm ..inherent restriking 'transient", often met witlr,
aimply mgry that volage trensient which. would bc obtaind on.c@unt of the
"it*i onln without nodification by the breker,
i.e. when r is infiirite with parallel capacitance, aod ;. with scriescapacitance. In practicg of coune, there is always 4 srnall esuruntof resisrance in the circuit itsdf and thus the inhgrent transient iB ofthc darnped occillatorytpe. For simpliciqf *tl";;;;G;i
""ofactor which b T-: lfllg u-gor, the vatue to whichihe "olggerises {fter zso. The initial.'anpfitude of thu t"""d;iil"lu.tio" i,not in fact e the circuit volage, but a + er.yherc c*(sie ig. S.A
is the pre-zerc arc voltage pe"k. This is realaity ""a6tA *i* iris remembered that the cciltations of tjre transient
"r a"" tiin,
rapid- interchapging of energy between thc ir-rductance *a- tuocapacitance, and that-this oscillation, therefgre,
"iontty u"Ein, ,"Lul
the ca_pacitance is charged to its.maximum just.UlforJ ,;;';;a in fig. 5.5. The amount of energy in,thJ op""itnn""
"i,U,instant'manifets itsgl.f a1 a vottageidditioo, ,; tb .h;*"r"foscillation initial amplitude a
f'he student ihould always appreciate the physical aspect ofeu-ch phenomena and nor be conteni with tt "
,nutir"i..ti""r;;;;^.-tration. In this way insight and intuition
"r" utti_otdJ-u"q;r"a
In the present instance, kiepin:g in mind tr,. iaqoi ii.eilnliii ro,energy intcrchange to occur between the circuit "t"-*t",
iii" Aityseen that, rvith series erpacitance the breaker reistance rr.iu; tf *ry- ltstr dircctlv absorb_ gncrgv to prevent
"-'"Jd';f-;il1;"sr.similurly, rvith para'et capacitance, a veryt tow bieokei ioi.ao*will prdvent sscillation by_-diversion of the €nergy.&ilical Resisttpzce. Wnh parallel capacita-rice the maximumvalue of breaker resiltance y[gb-will preveit *ell"tiool idr"gtry volage is givenby t {If1,pd inttre ecries case thc-nioinun
ralue.is ?1/L!C. These are termed criticalraistancq. A; b"*seen earlier, the series ryir genelfly -", *n* o$ir[;-d*-mission line wittr
"ppr"ciatrte-crpaatLl to carth. rn such en-ditions the criticar gi"tance lr ,i.tii. io*-r00 ohns or l€sc*ndg€n:rauy less than the curitnt "iio
roi*"o". of a circuit-breaka,so ttrat criticar &nnping is rrsuary pdseiure. rulr *liiitilF"uydesirable, however, sec page:l@, f"i "
-o* a.,"ff"a?t.fr" "f:apacitive-cu*enrT=nttr*.tr,*i{uiripal*[i#*.e,
ti:c brcaker is not alwave able to oni."a a"-fdJnii.uiJr-ra,
& '
PRTNCIPLES OF CTPCUTT-BNEAKINO 89
cxasrdle of a fault to earth on t&e line side of the b;caks in thcsnren shown in dg. 5.4, the paraltel capacitane is Cs whilh is.iudry small. The &itical resistance then may be of thc order of1.000 ohms. This may be more or less than tAe current zero resist-'ence of the breaker, depending upon the Erpe of breaker, t$e faultorrent magnitude and the circuit Paramet€rs.
(lrrrent Zero "Pause". Thc upp€r part of fig. 5.8 showt atypical record of arc current, arc voltage and cirorit voltage in whichtso current zeros occur. Thc first invoilves breakdown and re-suiking of the arc for a further half-qde atthe end of which the gapwithstands the rising voltage; this is seen to be of the.ccillatoryform.before following the'normal op-en-circuit voltage wavc. Withsuch a record the arc current aPPears to Pass straight through,erd it-, the lrreakdown case (a) and to cohe to an ab"rupt stoP atthe ctarance (&). The expanded records below show that theseimpressions may'be false. Just before zeto ardnrearc curreirt is forceddown abnormally due to the pardlel capacitance effest The arc'reshtence, although finite, is high enough irhmediately after zero forthe currcnt to remain very small-a frastion of an amperefor aperiod of microseconds, or even, tens of microseconds, bdore the ,breakdown at. which the curreat resum€s the normal sinusoi&l form. /This very small current existing between.zso and breakdown-'+ftentermed "pre-breakdov'n" surrsnt-may adopt various charagteristicforms. It may exhibit a small peak and thcn decreasc sliglrtly.beforeggg.rapi$y on b-reakdown of the gap. qis paniorlar form rnight
_ be'6btained wf,iri a powerful de-ionizing action exfuts bnt where thc. t,' rate of. rise'of re-.trikit g volage is v6y high. On the other hand,
vhere little de-ionization is achieved and a very high short-circuhctrrrent b involved, the current may pass more or less straightthroughzero with the breakdown occurring at a low point on the re-suiking.vokage wave Clearly it is not possible to generalize concerning pre.breakdown current form, but the idea of a errrent zgo pause istnownto be jusafied uodr q'any conditions.- 2e. zero E in fig. t.8 th" arc is successfutly internrpted aod in tho"lower diagram we see'ihat the current does not ceese abnrpdy butcontinues in the r&ersed direction'after zso fot a shon pciod ofeome inicroseconds beftlre frnally ceasing.. That "pet arc" .cuircntSoultt erist is only to be expecte-a since tEe asc resistance isrstill 6nitc8t crirr€st zeio.thougb'rapidly'increasing, and such cufrents can
- actually be of the order of an asrp&e in certain cirirrmstances. Noticc'thai tlt pre'zero arii vottbg" pJ"t.t zer6 g,-'.slp upper diagiaic-iir
I
90 SEI"CEGEAN PRINCTPLES
Anc curnent
'" Arc'twltsle
rAne \voltegg',v.ee6tt. \
, PEEKI CincuicI voltafe
ISreokdowi'
.IVormct s/t*r-tq/"to
Itcvoltaqepeok -
?,"9
t)showin$ successire
ca?"e n t -ze "os
le edind to- 6nea k{owh " e ny''cledronce"
(6)
\4rc cunnent
oPist-erc"
Expo n d e d ne cord s h ow in g c u rne nt Vffij,;;r,!i:W
Frg. 5.8. Cstat zoaoe-forns nca sero
smaller than the re-striking voltage peak This is a result of thlincreasing column resistance du:ing the zero period: Further, iq tsassrrmed that the de-ionizing effects have becone more pronounceCat zer.o D, and the arc voltage pak ju.t prior tg thig zerg is sho'i'n dis'tinctly higher than a1 zer6 a. Accordingln th9 pre-zero fcrcing dow
<, .i
P R I N C T P L E S O F C I R C U I T . B R E A K I N C 9 I
of arc current is shorvn to be more appreciabre at D in the cxpandcddiagram.
De-ioaisation at Zoo paase. Any detailed consideration of theproccses T y"r\ Tti" the arc "residual corumn"
"t tn"
""ro p"ur"
3rc not onlv heyond the scope of this volume but are out of phl forthe very good reason thst much has still to be clarifiea o*iic t" th"glr€Te nmplexity of curent zero phenornena. Neverthel""* ,h;follo*ing broad outline should be useful, bearing i";;d th'i th;pfenymag vary widely, according to the type of 6roker, f"fi-";:ilo'de and qr€uit conditions. \4/ith any given circuit-breaker tf,cmost important factor at currcnt zero is proiabry tr," -o"l"o,pu*-ture of the residual columr\ since the amo"nt of lonir"tion"i;fi:;"wr,v critically d-ependent upon this. Agir, th" *or,t'""ro-tlro-per-sture generally depcnds upon the rate of current decrease iustbeforc zero an! r9eo3r the amount of cooring and de-io;i;ti;il ril;ti: rh9f period. Thus, at current zero we t uu" .ioiauJ;!";;still subjected to de-ionizing effects and possessi"g *
"ppr;;;li;core temperature-bdieved to approach r0.000.K ,ir,a.r rom" .on-ditions-and therefore co'tainirig- considerable densities or etect orpand positive and ncgr,'tive ions. The rising voltage after zero a""a" LilT.f.
the energy content.of the col.rmniy cfJetdng the i;;,;;,'*.l.oy tendrng to maintain the tempera.ture and ionization levels.^:1t.^p-y1may
eventually lead to breakdown anci re-establishment:t_1|t::*
'I he power inpuj !o the arc is, however, "ery
srnull at firet:31".n: :oltage is tow, and the continued cooling, by external meanssucn_rs uast, natural convection and conduction, may predominateand funher increase the corumn resistance ro it,'t it.#ilffi.g"l:::TTn""aiiqlv tess efiecr on the t -pl."r". Sirin"iiy, itGclt i: lt:ilg rapidly lengthened the rate'of energtr input 6er unitlcngth of thc cotumn duelo the ris11g vgltage *ttt#;ildrd;i;reduced- such conditions may we[ ieaa to'successru aea"ince iffilQer6'y losses continue to preiominata.. This is aot necessarilythe case, howwer, for we baveonlv con-sidered the immediate posr-zerc period r-.-t"-p'otffii#;otetgy content of the column It seems, very probabih th*;61";
L:fO*:* can still ocsur, evcn wn* tUe telipo"ture has fallen on-"rqcraDry-'oD account of energy losses, provided there is still somecegre of.ionization^rernaininf-when tt
" "oft"gu r;cilL-o ;;;:
:::l) ,,r{n lcvet. - The genernl proce$ of brskdonn in this
""ht i,
il'.i:rentti' one of rapid ioniration by collisions betneen eleGrons of..,8n crr€r6T and gas particles. . Little irj knorrn about the poeci;
9 2 s l v I T c T I c E A R l t R I N c r P L E s
rnechrnism h.t it seems likely that-it nray bc starterl by i,small num_ber of elccr.rns-ha'ing liigh vclocitie derived from ihe n"ri ii .i.gap- 'l'his may bc akin to 'f spar-k" type breakdown, as a;rti""iiroithe " thermal " qrpe rvhere the column iesistance falls coz t;""o"rti- irito in-creasing 9ne-qy content. Tlesetwo generar ror- or Crl"t-to-*-oare distingui$gd by the form of voltage-collapse, as seen;;;;much expandgd time scale(sea fig. 5.9). T'he ispark" ur*t.r"*ricxtreryely rapid and the voltage may collapse from several th.usarrds
taermol-hreal<down Spork"breakdownF;g.5.9, Eutr7bs of beahdozon at cTrtrent zero
of votts to atmost zero in_ ao more than a microsecond. The thermal94rc, on the other h** p generally ̂ very much slowe, oro&qlibiting a- quite rounded yhag" &ot
""i ;;;j#d^;;,misocconds. A^ *y be imagi-ned" i""tu""o appar to exist inwhich a prooess starts as a therial rF*a t" ;;d;-uyip*rformation" and vice versaBcsidcr the simple th€rmat and spark breakdown mechaniemsoutlincd it is orobalrc that
"*r"*-J,iiii"ty p-"o.o may bcimportant du;qg the cTrref zerg pcriod. For instancc, the cxistcnccof a high tempeiaturc in thc rcsiiual;;G; ;;;;ffi;;;riderabh photo-emission of cl"d;]";; .h. cathode if the radiationfroin thc gas to thc erectrodc t htgh l;;b .yp" "r
prfr"',il.cethodc itsdlf ma1' havc varying "ClJ ""riging b thc.state of io
(
'TVermol"6reo/<down
PRTNCIPLES OF CIRCUIT.BREAKTNG 93
gfaoe and the purity of rnetal. The attachment of elcctrons to atorns.o form neg'ative ions ocgtris in orylen and is, ih cfiecq virtualtv arbionization process since the mobility of such ions is relatively vervbv, Energy is given up when a gas reverts from the atomic io thl
.aolecular state with falling tempemture. This ..dissociative re-ccabination" may be occrirring to some extent during the zero per.iodmd the cnc.rgy given up ma5r contribute towards ionization. Ali theseprooerees, rind others, qrobably occur during the critical period, andoal4rge extcnt the problem is to decide which of them predominate'mder
epecifed conditions. Much research is being divoted to the.understanding of these phenomena
It is often stated that the outcome of any current zero perioddrp."d" upon thj "race" between the rising voltage and the'risingdidectricitrength of the residual column inthe breaker gap. This isin gentral tnre, but'may be wrongly interpreted. It should not beuten as meaninq ttrat the dielectric strength and appliei voltageincrease independently of each other. For insance, if the energ;,--'balance principle is applicable to the 6eturnn at ?.ero, the rate ofchange of tlielestric strength, or resistance, is ccrtainly very much "afrected by the rising voltage as well as by energy loss. It is useful to
:note the definition of dielectric strength of the residual column asgrven by Dr. J. Slepian: the dielectric strength is measured by thc
' roltage needed to maintain the reistance of the column constant.. Thus, if V, W, R arcthe dielectric strength, power loss and resistanccrspectively, IPIR-W. Thet is, the power input and loss are equa!and the resistance is steady, or V - (Wn'f'. 'fhis definition treats t'hecolumn as a simple variable resiqtor whose resistance is some functioncf the enerry content. It musl be emphasized however, that thcphenomena associated with the current zero period now appearto bcmuch too complex for simple mathematical.treatment
Although uncertainties exist about the precise nature of currentztro processis, we can be sure that time is always one vital factor inthe po*-zero period- Consequently, the rate o?.ise of the voltagclltcr z€ro aiross the gap may exercise a consid€rable influence upon
.the outcome of t.he zero period, and.it is b€ause"bf thii that somcrpace was devoted to rates of rise of re-striking voltage earlier.. Efieaioeness ol De-ionizatioz. l'here is an aspect of ac. circuit-ItTUing not.always fully apprepiated. I'he importanc€ of powerfulae'ionization action at, and immediately after, current zero is beyoad .
,. -.*-!.d.-+.--j
f '
94 swtrc l IGEAR : ' l t tNc lPr .gs
*'ell es unnecessar,v. Interruption of the arc current, arrd de-ionization, are not regriired at any other irntant er(cePt zero. ln mcrnodern circuit-breakers the de-ionizing mearur are neccrisarily appliecnoie or less continuously; hence, liberated from the arc are largrarnounts of energy which have liale efiest on the de-ionization azero. The state of afiairs at z"rc Ccpcnds generally on conditicns oveta very short priol period, because an arc is generally able to adju*itself to changing conditions extremely rapidly. A highly efrcient deionizing force applied, say in tbe middle of the current loop, merelymeans that more voltage is required to maintain the current theqwhile much mostly useless energf is ideased which must be safel;disposed of. Thus it is that de-ionizing means which arc a functioaoftlre currcnt, such as electromagnetic devices, are not necessarilyaeft'ective as might be supposed, for they have little br*rring on e"intet crtrrent zero, tlloi is, when most needdd. There are excepdonrhowever, where the energy liberated in the middle of the loup mayhave a residud effect at current zero, and these will be met later.
-
"Cut:ent Chopping." The common phcnomenon knorryn as"current chopping" is an undesirable consequence of the genentirnperfection mentioned above, and is also a cause of overvottage. Ua brc:rker cxerts the same de-ionizing force for all currenB rvithin itshort-circuit capacitn then this force must be great enough, invariably, t9 givc intermption at the highet current ratin!. Ideally, irwo.uld be just sufficient for this but not high enough to iatrse uniucdistortion of the current wave. Ilou'ever, whcn such a brea&er !' called_upon to break, say thc normal road current, rvhich may be lesthan 5 pcr celq bf thc maximum breaking currcnt, this smali curredmay suffer such distortionastobeactuallyforccd straight dorvn t. zerofrom a relatively high value bdore tne nat'rat zera. l'his is termedyo-! chopping. The idea of :i breaker with a constant de-ionizingforce has bden invoked to illustrate this poasibitrty,.but typea wtticigrod119e_varying {egrees of this fqrce in tneir operation arilnerrertholess llabLe to "chop" when breaking "-roll cgrrents.. 'fhe bfiect of rpracicauy instrntaneous colrapse olthe arc cutrei,g.even ofonlyrfcw am:peres, is- potentiall-v very serious from the p"l*
"i"f.*'aovervoltages which may rcsult in the systern- An example will illus,trate this: a 220 kY oil circuit-breaklr.,internrpting ia tr-ansformctmaSnetizing current of ll A'r.m-s. chop.i this rinrrit ut.in i*t o.
. taneous value of ? A. The nalues of inductanc" u"a c"p""iun& iocirolit ye 35.2_H and,0.0023 pP;n4 ;"*t"c.d;U-.ilil;;enirgy is transferred to the cabacita*i
""roo :trrrb;;;; ;il;"d.
pRtNcl f r ,E8 0t r o tRcutT_DRSArrNO f.i
Curreot fiaollusuppnessed 66fonendtur ol zeno--.
Anccul.ent
Ancvoltoge
'ilbturol'carten€ zerv
-!..+r
_ . G l
trnreIIIIIIII
II
-.i
I
Recovetutaanshllt
Ancvoltogep?o*
i 1,,
i i i i ;iii#i i i , , t L_i;fbir;m$:"-rrl'*'f"/ choPPtng
. t&.sJe. Effsorexadcio4fuS
ffi;ffiffi;iffiffi*sffitrtclado 3e rh/q phcaomcnon ;"4 ;.fi" "id
of 6g. 5.fO, u,htch.no$s a sone*n"t "irnpunJ_ilrii"ililenent, wc mryrcc horto.
T*T:*g hgyo \Faen curr€nt chopprng scts rn.r"nil*"if ,:f#'#"T:lTiiffff Le*rlffiqrrreat' At a cenain "titi&i rarue;il;;;" *rrent, inrtab'ity rcr'!r on accouhr or-tn" aisptopoiioo't ri'i"?gl dc-ionizing forcc. and
c3.
96 swrrcrcEAR PRTNcTPLBS
there is a.l drnost instantarreous collapse to zero. This is ohown in thcdiagram a.s the lirst chop. The current in the arc at the tinre wrrflorving from the souree through the inductance to t[e brea].er. In-ductive curent cannot cease rnstantarreousln and the actual choppiagof the arc current is, therefore, acbompanied hy a simultaneouidiversion of the main current from the breaker to the capacitancc.Consid€f, what must be involved when such a rapid collapse of arccurent takes place. Ifthe current chopped is i. thin the voltage osthe gpacitance rises initially at a rate: doldt - i/C (neglecting any
'
small capacitance current existing befoge the chop). But this voltasiis also across the breaker and acis in the same way as the normal pte.zero rise of arc voltage in incresingthe rate of fall of the rzaft currentcorring from the source and through the inducance. The maxinrumpossible voltage across the cpacitance and breaks is thereforoobtairred whea the main current reachs zero; that is, when atl thcelectromagnetic energv associated with the chbpped current in thein<iucrance is tranqferred to the capacitance Thie .,prepective',
"oJ,"g is gryen by: o - it@ and may be estrenrety high io
relation to the normal system voltage. Fortunately the breaker,dthough the bulprit in this matter, is usually able-to relieve thisituation by re-striking a: . re point on the rising chop voltage. Justhorv far the voltage ray,n"g bdore re-striking dcpends upon-orionrfactors. Fbrcxample, the lower the rate of rise-of this voltage thcmore time thtre is for di-ionization of the breaka gap, and s 6rr€s"pondingly high overvolage may be reached.' sinilarly, the effectivc,lg*: of the de-iorrizing msns will. infuence the re-iriking voltagaSuch a re-strike draws the enprgiy oui from the capacitani and 6cvoltage ther_eon collapses; the first re-strike is ctlady seen in tho.diagmm both as a sudden rise of c.rrent toit" normal ialue (slighttyless than that of the first dop), and as a voltage co[rapse._ Th9 de-ionizing force is stil in action, [owwd and a second
ehoP takes place; this tiine the chopped ctrrrent is rather t€ss then .I'rcviously lqd accordingly the rise-of volage is somembst slower.'I'his may give the gap a chance to become iuttter de.ionized thaiTe"n?, a1a 1!!etter re-striking voltage uray resule This b nd:hoyl io !S1.5.10. Successrr." eop" ;y dxrq
"" *nowo urrtit e
M *9p btihgo rhc current io z zixo.pr6..turay *ith ;; i"nnoI!*l*fog since the gap is now,in an advance stag6 of de-ionizatioorE wtu be-appr€crated that surrent chopping is really an extreme foroor.thc nhenonenon ilustrated,ill .Fg. 5.5. The fottowiig genenlpoins should ben6ticcd: ' I "-
't l
a
( t
pnrNctpt.ns oF crRcutr-BREAKtNc 97l. Thc maximuin instantaoeous current whiqh can be ctropped
sith a given r.m.s. current by- I particular breaker is increased byincreasing thi amount of paralld capacitance, since this cnabtes ari.instability to set in at a higher crurent a ?*lro is approached.
2. The rise of voltage when the currcnt c6,ttap.es may bedamggd by the ellects of eddy currents a'ri hystercsirtm in sinaltransformer magnetizing currenL.
3. The risirig chop voltagg may be limited by.the circuit_brcakcrin two ways: (a) the breaker gap is generally abti to allow re-strikingbefore the pe.& of the prospective voltagi is reached: and (D) thl'rnode of operation of the breaker limits the instantaneous vatuc orcurent that it can chop.
4. \l-'her- the cap-acitance and inductance involved are fairlysnali, the rate of rise of volage is ftlst and re-strikine occun at quiiel,rn'ralues of the voltagg sin-e the time for further?e-ionizatiol oithe gap is correspondingly small. A consequence of this is tlut.thcrcsurrence flegucncl of successive chops may be veiy high, with thcpossibility-of a dangcrous resonanoe condition being sri up in thesystem. .This is often the most undesirable feature of current chop:ping, since although the prospective voltages as.sociated witt
-tf,e
choppr.ng are not generally reached, overvoltages rnay occur due tosuch iesonance-
^, Thg .yT"lt choppin-g phenomenon is an interesting aspect ofthe thcrmal hybteresis efl'ect in a.c. circuit-breaker arcs.'.Supposc,tor _irstance, tJrat therc were no such lag effec1 and thit in arccould adjust itself infinitely quickty to
",rrrJnt-"-n"ig* Til ili;
mern that a circriit-breaker with Lfficient de-ioniziig means wourdaluiys prodrrce chopping n€ar current zero, irrespecti-ve of tlre r.m.s.sal_ue o[ current being_broken In actual facq however, the ihenome-non is not obtained when the r.[Ls. current is increased ubov romccritical value depending upon therbraker and circuit. This shorv!Inrt $ such higher currents tlie tenp€rature and conductivity of thcarc rcmain too high for instability to occur near ?.sro.
{.lapacitive.currest Breaeing. There is another @rnmon1our5 of overvoltage which is dug-to
"n imp.rfecdo" j"E;i;:
I*|9r behaviour, and the conilitions here are'thd oUtairwa wnen::::"*i,lq capacitive.cuLeni a1 for erample, in the openingof a long
. uul.'adeil transmission fine- Sggh a lini, although lntoalea in thll"*t1l scnse, 'wili aduaty cairy
" ,;"tt- ii;;il &; i;;i
lill.llt". :urr.enr on a9c9u-nt9? t!" "ppieci"bte op-"cilnc. to card.ur rtte lrnG itself, even although it bb open at the far end.
98 srvrrelrcEAR PRINctPLeS
Fig. 5.lt shows the simple equivalent circuig and the voltage andqnrent.phenomena theoretically possible when breaking a smallcapacitance qrrrent The latter is assumed to be intemlpted cinstant a when the circuit volgge is at its peak value Zn, in the positivedir.edion..'This dfectivety separates the ge,netator side of thC'circuitfrom the line side and, since it is achieved while the common mltageis of .magnitude { Vrs, the unloaded line is isobted with this positivcvoltage upon ia The circuitvoltage cpntinues on its nor.mal sinusoidal oourse and tbese two difierem voltages exi;t at therespective contacts of tle breaker. Aftei in;stact a the breaker gap irtheiefore zubjectsd to the clifiaanceof
-the voltages V, ard% ti*,
aftcr one quaner-c,yde period from a, the circuitvoltage hae reac-hed,:"o -"od the voltage acroes the breaker is theo Zrr; thereeftcrthe circuit rcltage Z, increases in the negative direiiion and ticvoit4ge across r"he breaker gap becomes even greatcr und! at i isrziue is tvice (u. ,L.suae aow that this abnormally high irressingof the gap results in re-striring the arc. The two previously-ssparatedparts ot the circuit wilt now be joined effectively, b-v an arc of verylow resistancc. The liue capacitance discharges at once to reduce tliivottage across the breaker to its appropriarc i"gligiUl" value, and thisis accompanied by thc tamiliar h.f. ciscillation set up when.a capacitordisci'rarges in an inductive-capacitive circuit. It is most iriporant toapprecia!9 tha! the zero, aB it were; of the voltage swing isnot erthpotential but the circuit voltage at the iastant 9f discharge" l.lnrs scsee,tlt.p.yill swing right down to the value -3 Z*lbelow earthpotergtid), siace the arnplitude of the voltage swing is? i/,o, neglect-:ng damping efiects. l'he restrike crrreni quicHy ,octil it"-nstzero, since its pciodicity is in accordance with tire cltcuit oaturalfrlquepcy, 3"q-*iU prcbably cease after this one half-cy.cle. Thcvoltags on tAe llnc is noy -3 Ve nL once ag?in, the tsvi halves ofthe ciro-it are squ:zted and tlc"line is isolated a this poteotial.. Atthis stage-imarediately after L-the vbltage aaoss the'brea&er is, of@urse' only-twice z* since'the circuir votage is itsetf ai its instas-taneous maximum in tbc aegative direcrion" Tte poiential dificrencoacross the.breaker.gp *otii.*to increase, d;;, * I/, b"*;less nggative an{, aI the instant c, th:,e etressing reaches 4 f *. $,th,Sap shguld breakdown again at this point thd the events &*rrlog.one-half-qyde earlier areiepeated oo * eoeo -or" fo"-iarSi" Ji3s the voltage suriagnill_ now & I Ve ana tn" rine may tien Ue te$rsolercd at a potcntial 5 Z; abdve eai.h vlhFn the trans-ient ,e_eciilccuTclrtertiguisheqiustafterc.. - . .- . ':.-. . '."
( l
PRINC.IPLES OF CTBCUIT.ARAABTNOt
99
76xYgp
\II
\
/t'-iDze \ - r . r t
{ !\...-./
L:JCapocitive cunnent 6eforc inten uptionlnonsient curneot of resCrike
eE.asxTgpt
V. oltoge to eoeth on genewto" sr.de of ilrcokcr.v_Yoltoge to eort;h of trunsmission linervs
' (g) lnternuption of copocttire caF?qrt(b) firc ri*nikei"i sririili*;r" lUo. e*-n"orunl
r3. 5.ll. rrW ohen bicahhg
_-,^-1o 6-y $e nhenomcnon may procccd indef,nitctn lcevingYoltage on thc line of nagnitud€s i V*l V*nd - oo. Th-rirnd practice usually difierihoweve, aild diondb"=as hcrc. thlPTTcat fartors'which precludc a theorctically ixtsibic condition rrc1 utessilg. Thec limiting factrire arc asrociccd rrith catainsT{o* mads namely:
-
**ff 'l'.l"'ffi .H;!*",:ff*Jnf'[tfru":,Iflllll|n. is !'tFpp{'], it niy fd! quirc iapidty on aioum of tcri-ilffittona toq the lattc bcing Pard@lirly cficctivc rc vcry high
l0o swl rcHGEAR PRINCIPLSS
?- The instsnt of re;striking. From the point of view of voltagcguing amplitude the worst possibte instarts rpere chosen td show thc
".*ilifi iL of the sitgation- It should be remembered thag after the
il."k;|f of the capacitive surrent at a, the dielectric strength of the-
""" i" ii"n r"ing dt i rate which-ariy be comparable with the rate of
ilE* of the ioltage stressing of tbe gap after a. The variation of
s; di"f"cttic *t "gtn
attcr zctrrrent zero is subjec to.the influene
|i'"t"-"no of a nildom nafi''e an4 under these condition', a te-
&it" l" posible at rarious times after the normal interruption, and
not necessarily one half-cyde latet.Notwithstanding ttree pracical limitetions, howbver, serious
overvoltages catr occ,it in th" manner shown when breaking.caplgtivecurrents,;d the vdues obtained may amoustto as much as 3 Zrp ontL" tir," or on the breaker. The sole cause of this qpe of overvoltagg
G it noted, is the inability of the circuit-breaker to provide adbquate
dielectric strength in the contast gap after intemrpiion'In the simplified exaurple just given, fig. 5.Il' the voltage across
the breaker is'shown as zero u'hen the capacitive .:urrent is ex-
tincuishcd and tlrcn nses rclatirrly slowly, i.e. attlre supply frequency.A irore practical example would indude ttre reactance between thegeneratoi qnd the breaker; the lead.ing capacitive current qaus€s eioltage rui in this reactance. At the zeros of the -capacitive cu-rr-entthe vilage onthe supply side of the breaker therefore tends to fall tothe geneiator value and, ln doing so' sets up a transient re'strikingvoltige oscillation- T'his trairsient appears for the same basic rerlsortsas rviih the normal intemrtltion of short-circuit iaductive current but' .
whcreas the latter transient is bised on the pekof the firll recoveryvoltage, the capacitive current re-striking transient is a funstjon of thesmallir peak vollage a6o$s the serie$ reactance.. Fol this 1asolcapacitive current G rebtively. basy to internrpt Paradoxically s'rfhgood performance is undesirablg for h raeans that dre corditions fori"-"ttifir,g (and oven'ohages) tend to arise while the contact gap iosti[ shoft-an4 therefore, the srore likely to allow re-striking. Siuri'larln a fast rate of rise of re-srtriking voltage is'actually.desirable atthiJ stage. Preferably the breaker should clear the capryfive currentorily w[en a gap tength has be€n redhrd wirich will prevent subsequent re-striking.-
The .'Id€a!" Gircuit-Breaker. It is hdpful to have in mindthe conception of the ideal, or perfect, breaker from the intemrpdonpoint of viem. Impossible of ac.biervement ihough this nay b!' iodefinition is simple: tlu ?qfcc, t*dtit-bleafu ofrcts seto in?cd&re
I'
il.L-i]fiP
P R I N C T P T . E S ( , F C I R C U T T - B R E A K I i I C 101
(
&fna intantption and infnite impedancc thncaltet For an a-c.circuit-brcaker we_ ma-!r elaborate upon the dcftnition somewhat bylpcifying our perfect breaker as one that offers zero impedance untiiflcfirst curremt zero after contacr separation, at rrlrich instant infinitcimpdance !s ofrered, Coruider the implications of such nerfection.Zcro impedance before thc first current zero meerut: (a) no arcvoltagg q) ry getg)' releaeed within the breakcr, a featurc greetlyo bc dcsircd (c) no distortion of the current wavc. (d) no currerrtchopping. The instananeous change from zero to infinite impedanCn the 6nt qrrrent zao would ensure, (a) invadable clearencc at tte6nt zcro and (6) impcsibility of re-siriking, and conscqucntly noorcrvoltages.
It is interesting to note that in practice a circuit-breaker deaigrredto hsve a powerfrrl de-ionizing force to obviate re-stri&ing is, for ttatvcry reason, mor€ likdy to produce current chopping. This inustrates .ocll &c need for a complete-change of condltions at cu'rrent zero.Thc neard precticat e2proach to-the ideal breaker woutd be onecrpatlc of applp.g
" very powerful de-iouizing fore instantaneously
a the fitst currGnt zero after contact scparition- Such co-ordiaatiotbaween thc ncchanical and electrical aspects of circuit-breakcropntion b undoubtedty bcyond rcolization at presenl The ac.
_ brca&,cr b, in eomc forms ar lang nearer the idesl thgn thc d"c. typc. rhich, by io very sstion in mbing the rclagc of ttrc erc to achieitdnctioq.is a looi way indeed from thc of ao arcroltrge prior to intcrruption
rl.C Gtrcuit-breeecr Rstinp fucahing Capacity. \ige hrvcrccn thet thc r.m.r. vdue of Lrrrent rcsulting frorh a shbrt-cirodt naytrry epprcciebly rrith tine oa aeount of dccrcncnt and.erymmgtry,nd tturt a cirerit-trealcr ie q*liad with having broken tli vt"c iiry cxirting d thG cottracr spparation imr.at This is-drryaldcd ss en r.m.s. vrluc eod ie cr[cd 6e brcnling crncat. If thc we;o .bailt aqynmcrrical ccoatect acparrtion it ir nJorrc rnually canea tmFt,rctricol bcahdrg qra& T\c sywical braHng cEtat iB tlNltm-givco to ths r.o.r. veftre of tbe as (tc. symadcat) c@(afiS:22) of thc sByGat @ntee ecparition
Ttg paformane of g brcelrcr in dcating with a given bru&in6clltrent'elsii dcpcnda ee wc hgvc soen, upon the voltage anilable tCtscrikc the arc gt caeh eutlsrt zcrb. Now thie particnlar reluc:tqrdr nqontyuponthcr.n-r. trluo olvoltage availablc but upolrr:-Polcr fs6or of rhe feultcd cirbrG,.-For the prceent purpcc h ilebdoruty be* o rrsunc zeo powc fector rinci this gi;'c.ihc tld
- a r :
ro2 gwtrcrrcEAR pRrNcrpLEB
5
scvene bTaFng-duty. The arailable volage is subjcct gsteraly toeome variation duririg short-circuig and the am-e. valuJof intric*regardiqg tbc U le,,ttlg gnfty is t.hat of the
"ccotlc?tt voltagq which
ig that acoss the circuit-breaker contasrs iineaLtay "ita
fi-lcxtiastion oftf,e arcs. The pcfoloance of a circrrh-bieafcr oo
"hiottcircuit test is assessed by t tring account of various hitori in iilitidonto the breaki4g curr€ut aad recoverlr volagg but these lmcr are t*-gro quanthies of imnediate coqcern in the considerdion ofe bttatdfqr a-giveofadt le'eL -The bre&a copacitl of a citodt-breaka,is,thereforg,the current that it can brea&-at a-stated ruoov€rJr *rtrdaad thisagzia is- genaally expressed more coopletely in 6s of ftsynnctr;c( aot-d. osytmnetrical capacities, i.e.
-the {1--etfot ani
asyryet$cal-b.reaking currents respectively "t " "t"[ed
vOliage_The breaking apacity rctittggiven to a circuit-bftaker is s&€ralrt
one of a set of standards and is usudiy txpressed in ter-"-or ltti1nd kV. Thuc tbe breakiry gpacity rating of a single_phasedA;is g!l'en, icr accordar.ce vath British coo"ritior,, as iolious: . --
Rated brlking cafalg @\r4) - rated.s1,mmefiicalbrealcingcurrent ([A) x rated service volage (kV).
F-o; a 3-piase brcaker the raled x{vA is similarly obtained bynulti-plyrag the product of rated breaking current
""a "o"i"" ,'oiug" I
€;.flb fago-r appgars here, as.in any 3-phase circuig whea $wer,or VA, is calculated ia tc.rms of line *.rer,t and voltage 56;""F"3 ,f"! by_means of suitable tests it has been pro""t.fut
"-fio"i3-phzsc. break." can iovariably interrupt "
.ym-t ic"l.SrdUnfcurrent of 13.5 kA r.m.s, with a tesr recovery voluge of fZ tl..-iis)ometrical breaking capaclty is, therefore:
13-5 (kA) x 12 (kv) x 6 _ 280.5 (Mva)The uearesr *andard ratilg lelow this is 250 MVA at lI kV, wtri.S:^ITp"l * p a syurnetilcal breakiog c.urr€rt of 13.1 irA, ;J$iir:ung mrgEttrerefore be assigned to the bresker. rn facg as we shen:fjl $1fT_:t cTam gtrer test reqrdents nust usuallyte fut-uued ,'etor-e ary snch ratiag can be giVur. The above state'meat of,"I*TC c".pagty nting rs a British one, taken from the g.S. tfO:-.-:.11t. otl.otTit-breaken, and,. it will be noted, is in terrns ofs]Enmetrical brq,king current. Noir since tbe lattcr may onlv be t$c?c- con.Itonent of a short-circuit current wave, ..Au
"tut.fo*Jt_;f*.that a-breaker rated at, for instancs zSO ftAdfl il kV;;"#ersa8 irn aqfonetrical of Otd r.n.s. value great€f rr."n.l3.l
..
(
- a.-
1 l
FRTNCTPLES oF CrtCUlT-D'RBtKtNo 103
tA. This is indeed so, and the mattsr ie taten carl of in the proyingtests which ensure thaq before beiag allotted the ratiog, the Lreakeican internrpt currents having tAe rated symmetrical value togetherwith at least as rnqch asymm€try as might occur in senrice.
In America it is the practice to give circrrit-breakers asynmetricalbrcaking capacity ratingr. That is, the rating is in terms of aq";m-rnetrical breaking and the servie vottage; any particularbreaker would thus be given a higher rating in America than inBritain The rdative merits of the two methods of rating have'beenthe subja t of no litdc discussion and argument, for the matter isfairly complex. An outline of thie question is, however, included in '
Chapter X.A(ak'ng Capaqity. The possibility of a circuit-breaker com-
pleting a gull short circuit on being clgsed must be taken account of,and it nrust therefore be tested and proved ig this respegt. la mahingclt acity is thereby -assessgd a1d a coiresponding rating gir.en-. Nowthe capacity of a circuit-breaker te "make" cutrents depends verymuch_upon its ability to withstand, and to close eucceisfuily againsi,the effects of electromagnetic forces. The maximura force in'unyplurse is a function of the square of the maximum instantaneou'scurrent occurring in that phase on dosing. .We thdrbforg-find thatnaking capacity is stated in tcrms of apeak value of currcnt insteacl ofen r.m.s. value. The making cunent is thus the pedk value of theyalmu1 clrrent loop, induding d.c.n component, in any pha.seduring the first cycle of current when the circuit-breaker is ciosed.The making capacity is, accordingly, the making current it can make*1 -qrty instantaneously at the rated senrice voltage. Thesedefinitions, from B.S. 116:1952, are oonaerned only wiih the firstcycle of current on closing the breakbr. This is clear'when it ie .rcmembered that the maximum peak currem possible occurs in theIto-"yA-" only, wheir marirnum aslnmmetrJr **r" in any phase oftbe breaker. The miaking of a breaker intended for a givenfault level must therefor"-ne at least equal to the first peaf of aTuiyaslmmetrical current wave whose as. comp?tcnt has.an r.nus. valuicqual to the grmrerrfraf fauh lwel To calculatc thi" pon, we there-'fore
multipty the symmetrical breaking current by {irceonverr thirt19m r,yt.s. to peak, and thcn by 1.8 to indude tte .. doubling effgct,'or maximum asymmery, thb total multiplicrtion factor being 2.55.llottcc tlut the closing duty o! the breaks qrnnot be lessened by$rrtm decrement and decai of the d.c. cornponent es rray occur i;tlc breaking duty.
a
tOl swrrcncsAn PRrNctpLEs
fffrl/.-era Mg. Fault occrrrrd oftca iavolvor thc'florof hcavy qrrrcut tlrtough a sircuit-brca&cr not rcquirpd to opco.This neans thst circuil-breakcrs generally shorld bc ablc to carrvhigh crrrcnt eafdy frr eome specified short pcriod whilo remaiainrcJccdi that rs, thcy shorrld hsve a prov€o elu*erc airy. Nehott-time ctrlcnt, which is $ocrelly not tess than rhe sydtctricetbreaAing currerit, is uqgly requfrcd to be carried for'g f;iod of uoto 3 eernnd+acordingtg thc protecive schemc rcquir;co6. Tdshort-frtrre reting wS+ go F gr"* depcnds upon thc ability of thcbreakerto witbstand (a) the electronegnetic force erficct, end (r) thtcmpcrature rise. Ihe greatp4 dectrooagaaiclorcc billosedfirr isthe making capacity mting, bot th" efiees of szsrairadvibrrrtions'einbe:rwealed only-in-a test for ghoit-time rating. The questioa oftemperatlrre rise is also very important, as this riie may bc sdde4 hservice, to tbat already exisdng due to frrll load currqit
Nonnal Ct reTt Rdilng. This is the curr.,ntshic& cao be.csnicdcontinuously by a circuit-breakea The only limiatioa in t}ir caociathe Gmperature rise of the current-carrying priits.
A circuit-brenter is genbrally rderred to tnief,y in terns of ir
