CO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS

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1 CO-ORDINATION OF FAST NUMERICAL RELAYS AND CURRENT TRANSFORMERS OVERDIMENSIONING FACTORS AND INFLUENCING PARAMETERS Stig Holst ABB Automation Products Swdn Bapuji S Palki ABB Utilitis India This papr rports on som of th rsults of th working group WG 3.0, stablishd by th Study Committ 3 to study and invstigat co-ordination of rlays and convntional currnt transformrs (CT). Th objctiv of th WG 3.0 work is to suggst common rcommndations on how th manufacturrs should spcify th CT rquirmnts and also suggst a guidlin for co-ordination of rlays and currnt transformrs. Th papr will show and discuss a mor ralistic and corrct mthod of calculating th ovrdimnsioning factor of currnt transformrs whn co-ordinating fast numrical rlays and currnt transformrs, than what has normally bn th common practic.. Introduction Corrct opration of most protctiv rlays is dpndnt on th rlays bing supplid with sufficint information from th high voltag systm. Th fault currnt is on of th most important quantitis for th opration of th rlay. Th fault currnt has a stady stat and a transint componnt. Th DC transint part has a major rol in th currnt transformr rrors. Th rror of a convntional currnt transformr is dpndnt on, whthr th cor is saturatd or not. Whn th cor is saturatd th magntizing currnt is larg compard to th scondary currnt and th rror is high. Th dgr of saturation dpnds on th magnitud of fault currnt, primary tim constant, scondary tim constant of th currnt transformr and th magnitud of th DC componnt. Th rmannc of th cor will also influnc th saturation. Currnt transformr saturation can caus both failur to oprat and unwantd opration of th protction dpnding on th masuring principl. Thortically th saturation and th malopration of th protction can b avoidd by considring all th ngativ factors whn sizing th currnt transformr. In practic this will oftn rsult in unralistically larg and xpnsiv currnt transformrs. On th othr hand it is not ncssary that currnt transformrs ar totally fr from saturation, bcaus protctiv rlays can tolrat a crtain amount of masuring rrors and still maintain accptabl opration. Diffrnt rlays can allow th currnt transformrs to go into saturation aftr a crtain tim and still prform corrctly. To achiv spcifid tim to saturation th currnt transformr will hav to b ovrdimnsiond. Th ovrdimnsioning is influncd by th primary tim constant, th scondary tim constant of th currnt transformr and th magnitud of th DC componnt. Th rmannc also has impact on th ovrdimnsioning. Th commonly usd formula for calculation of th ovrdimnsioning factor ar oftn simplifid considring th primary tim constant and always th maximum DC componnt. Ths formula will not giv optimum dimnsioning in th co-ordination of currnt transformrs and modrn numrical rlays that somtims rquir just vry short tim to saturation for corrct opration. Oftn th ovrdimnsioning factor is too pssimistic. In som cass it is also important to considr th cas without any DC componnt. Th papr dscribs th basic thortical quations for th transint dimnsioning of currnt transformrs considring th impact of diffrnt dgrs of DC componnt. Th ffcts of various paramtrs on th ovrdimnsioning factor ar discussd and rcommndations on how to calculat mor rlvant ovrdimnsioning factors ar includd.. Basic thory for dimnsioning of currnt transformrs Th basic thortical quations for th transint dimnsioning of th currnt transformr considring th impact of switching angl as wll as othr factors ar dscribd in this chaptr. Th quations may b takn as xtnsion to th thortical quations givn in IEC Short circuit currnt Th quivalnt circuit of a typical fault loop can b rprsntd by an inductanc and a rsistanc in sris (S Figur). Assuming a sinusoidal.m.f.

2 L R whr G (L 0 L )/R L 0 /R is th scondary tim constant of th CT q L /(L 0 L ) L /L 0 is th ratio of inductancs. L 0 is th main inductanc L is th total inductanc of th scondary circuit R is th total rsistanc of th scondary circuit Figur : Equivalnt circuit of a short circuit loop. i i ( ω φ) v Vm cos t () U L Th short circuit currnt (i) may b writtn as i I ( ) ( ) cos φ α cos ωt φ α () U L 0 L R U R whr φ Angl of switching on th voltag curv V m is th r.m.s. valu of th gnrator.m.f. I V m / (R ω L ) ½ is th r.m.s. valu of primary symmtrical short circuit currnt L/R is th primary tim constant α tan - (ωl/r) is th phas angl diffrnc btwn voltag and currnt Substituting θ for (φ - α) th xprssion () can b writtn as i I ( ) cos θ cos ωt θ (3) Th scond trm in this xprssion is th stady stat sinusoidal variation and th first trm is th transint part, which thortically vanishs aftr infinit tim. At t 0 it can b sn that th transint componnt quals th stady stat componnt and sinc both hav opposing polaritis th currnt is zro at t 0. Th transint componnt will b zro whn θ ± π/ and will hav maximum valu whn θ 0. Making an assumption that th ntwork is prdominantly inductiv this corrsponds to switching taking plac on th voltag wav whn it is passing through maximum and zro rspctivly.. Transmission of asymmtrical short circuit currnt through a CT A CT can b rprsntd by th quivalnt circuit shown in Figur. From this circuit w can driv th following diffrntial quation. di0 di i0 q i () dt dt Figur : Equivalnt circuit of a currnt transformr By substituting th asymmtrical short circuit currnt in th systm quation for i, w obtain th following quation for th magntizing currnt i 0 for th cas. (5) i 0 I I [( q) ω sin θ ( qω ) cos θ] I æ q ç cos θ ç è ω ω [( q) ω sin θ) ( qω ) cos θ) ] In th abov quation substituting, g (qω )/(ω ) and assuming ω ω Equation (5) can b simplifid as ö ø

3 i 0 I I I q cos θ ( q) sin ω q q g cos θ sin θ cos θ ω θ) g cos θ) Th flux in th CT cor is dirctly proportional to i 0 and th proportionality constant is dpndnt upon th dimnsions of th cor and its prmability. From th quation abov it can b sn that th magntizing currnt consists of a DC componnt (7) i 0 I I and an AC componnt q cos θ q q g cos θ sin θ cos θ ω ( q) θ) g cos( ω θ) i0 ~ I sin t (8) ω Th maximum valu of th AC componnt i 0~max can b givn by i æ q ö 0~max I ç g ç (9) è ω ø.3 Symmtrical short circuit currnt factor Th.m.f. to b dvlopd by th CT to pass th scondary currnt I sn through a CT can b givn by (R ct R b ) I sn whr R ct is th CT scondary winding rsistanc and R b is th burdn of th rlay and th lads. If a short circuit currnt I is to pass through th CT th CT nds to b ovrdimnsiond. Purly on th symmtrical short circuit basis, without any transint componnt, th ovrdimnsioning factor of th CT dpnds on th magnitud of th symmtrical short circuit currnt and th ratd primary currnt I pn. Th symmtrical short circuit currnt factor ssc is dfind as th ratio of th r.m.s. valu of th short circuit currnt I and th ratd primary currnt I pn. I I (0) ssc pn. Transint dimnsioning factor If th short circuit currnt is asymmtrical compard to th cas of symmtrical short circuit currnt, and du to th DC componnt, saturation in th cor will b rachd much arlir. If saturation must not occur during th priod a protctiv rlay is carrying out th masurmnt, th transformr will hav to b ovr dimnsiond. This ovrdimnsioning factor is dfind by. Th transint dimnsioning factor is th ratio of th thortical total scondary linkd flux to th pak instantanous valu of th AC componnt flux. Sinc flux valus ar proportional to th corrsponding magntizing currnts can b givn by i i () 0 0~max Substituting xprssions for i 0 and i 0~max th transint dimnsioning factor can b writtn as q cos θ [( q ω) g ] ( q) ω sin q q g cos θ sin θ cos θ ω [( q ω) g ] θ) g cos θ) [( q ω) g ] () If th burdn is purly rsistiv as in th cas of static or numrical protction, L 0 and thus q 0 and g can b ignord. Thrfor quation () can b simplifid and th transint dimnsioning factor bcoms (3) æ ω ç cos θ ç è ö θ sin ø sin θ) For calculating th transint factor ncssary for dimnsioning purpos, quation (3) can b simplifid by writing sin (ωt θ) -. Th transint dimnsioning factor will thn bcom æ ö ω ç cos sin θ θ ç è ø () 3

4 .5 Effct of rmannt flux on transint dimnsioning factor In a currnt transformr with a closd grain orintd iron cor without any airgap, a rmannt flux will rmain aftr a currnt intrruption. An airgap in th cor will rduc th rmannc. Th amount of rmannt flux is dpndnt on th CT typ. Gnrally thr ar thr diffrnt typs of C: high rmannc typ CT low rmannc typ CT non rmannc typ CT Th high rmannc typ has no limit for th rmannt flux. This CT has a magntic cor without any airgap and a rmannt flux might rmain for almost infinit tim. In this typ of CT th rmannt flux can b up to % of th saturation flux. Typical xampls of high rmannc typ CT ar class P, TPS, TPX according to IEC, class P, X according to BS (British Standard) and nongappd class C, according to ANSI/IEEE. Th low rmannc typ has a spcifid limit for th rmannt flux. This CT is mad with a small airgap to rduc th rmannt flux to a lvl that dos not xcd 0 % of th saturation flux. Class TPY according to IEC is a low rmannc typ CT. Th non rmannc typ CT has practically ngligibl lvl of rmannt flux. This typ of CT has rlativly big airgaps in ordr to rduc th rmannt flux to practically zro lvl. Class TPZ according to IEC is a non rmannc typ CT. Onc th rmannt flux is stablishd vry littl of it is dissipatd undr srvic conditions and will rmain in th cor until it is dmagntizd. According to studis carrid out on C that had bn in srvic, th rmannc in practic can vary from 0-80 % of th saturation flux. Th rmannc will rduc th availabl margin for flux incras. This will naturally rduc th tim to saturation whn th rmannt flux is in th sam dirction as th flux incras rquird to rproduc th primary fault currnt. Th tim to saturation is prolongd whn th rmannt flux is in th opposit dirction. Th rmannc factor r is dfind as th ratio of ψ r /ψ s whr ψ r is th rmannt flux and ψ s is th saturation flux. If th rmannc factor is takn into account, th transint dimnsioning factor incrass by th rmannc dimnsioning factor rm whr ( ) (5) rm r Thus th total ovrdimnsioning factor tot can b dfind as tot (6) rm ssc 3. Effct of various paramtrs on th transint dimnsioning of currnt transformrs Th transint dimnsioning factor has traditionally bn calculatd according to th simplifid quation () and for th cas with maximum DC componnt, θ 0. Figur 3 shows th factor as a function of th tim and for som diffrnt valus of th scondary tim constant. Th primary tim constant is 60 ms in this xampl Tim in sconds Figur 3: as a function of th tim and 0 s 5 s 3 s s s 0.5 s Excpt for C with big airgaps, is oftn a fw or svral sconds and th influnc on is rlativly small and almost ngligibl during th first 00 ms. In th following diagrams is st to 3 s. Th incrass whn incrass. This is illustratd in Figur ms 00 ms.6 Th total ovrdimnsioning factor Th total ovrdimnsioning factor dpnds on th valu of th thr factors dscribd abov, namly th symmtrical short circuit factor ssc, th transint dimnsioning factor and th rmannc dimnsioning factor rm Tim in sconds 00 ms 50 ms 30 ms Figur : as a function of th tim and. 3 s.

5 To oprat corrctly ach spcific typ of protctiv rlay rquirs a crtain tim to saturation of th CT. In this cas it is possibl to draw th as a function of th primary tim constant. As an xampl Figur 5 shows th rquird for diffrnt valus of rquird tim to saturation. 0 t sat 70 ms Modrn numrical rlays ar oftn dsignd to b abl to oprat corrctly vn whn th CT saturats aftr a vry short tim. Th rquird minimum tim to saturation for ths rlays is oftn vry short. Somtims th rquird tim to saturation can b vn lss than ms. To gt th bnfit of th short rquird tim to saturation and b abl to rduc th siz of th CT w hav to considr th complt xprssion of th factor according to quation (3) ms 0 ms 6 θ 0 max DC 8 30 ms 0 ms θ in ms Figur 5: as a function of for diffrnt valus of th tim to saturation. 3 s. So far and in all figurs w hav considrd th factor according to th simplifid quation () and with maximum DC componnt. In Figur 6 w can s th diffrnc btwn th simplifid quation (), and th complt factor according to quation (3). Th ffct of th switching angl and diffrnt dgr of DC componnt on th factor is also shown Tim in ms θ 0 max DC θ 5 θ 90 no DC Figur 6: Th simplifid and complt as functions of th tim and diffrnt dgr of DC. 3 s. Th simplification is rlvant whn th tim is mor than 5 ms in a 50 Hz systm. Howvr, for shortr tim th simplifid formula for is too consrvativ and givs too larg valus of. S Figur Tim in ms θ 90 no DC Figur 7: Th factor as a function of th tim and diffrnt dgr of DC. 3 s. It is also important to notic that th cas with maximum DC componnt is not th most difficult cas for th tim shortr than 5 ms. For xampl, if th rquird tim to saturation is blow ms, th cas with almost no DC is th most difficult and has to b considrd whn calculating th rquird for th CT. For tim to saturation longr than around 5 ms, th cas with maximum DC must b considrd. In this cas it is also of intrst to stimat th probability of having a fault with maximum DC. In transmission systms, whr th fault currnt oftn is almost prdominantly inductiv, th incption of th fault has to tak plac on th voltag wav whn th voltag is clos to zro to giv maximum DC componnt. Th probability for this is normally small and it should oftn b possibl to rduc th rquird du to this rducd risk of maximum DC componnt. Th thory and stimation of th probability of having fault currnts with maximum DC componnt is outsid th scop of this papr. Howvr, it is important to notic that it is not possibl to rduc th calculatd in th sam way if th tim to saturation is shortr thn 5 ms. In this cas w hav to considr th switching angl that givs th largst. For ach valu of th rquird tim to saturation it is possibl to calculat th corrsponding valu of th switching angl, θ max, that givs th maximum valu of th factor. This rlation is shown in Figur 8. W can s that th primary tim constant has only a small influnc on th valu of th switching angl. 5

6 θ max ms 30 ms th CT rquirmnts ar spcifid for dpndability rasons. Th risk of a short dlay on an opration is oftn accptabl. If th risk of a dlay is not accptabl th usr has to add an xtra margin to covr th rmannc. Howvr, for scurity rasons, it is ncssary to considr th rmannc whn dciding th CT rquirmnts. It is for xampl not accptabl to hav unwantd oprations from diffrntial rlays for xtrnal faults causd by rmannc and CT saturation t sat 0 ms Tim to saturation in ms Figur 8: Th switching angl, θ max, which givs th maximum valu of th factor as a function of tim to saturation. 3 s.. Rcommndations on how to dcid th ovrdimnsioning factor for currnt transformrs To b abl to spcify th CT rquirmnts and th rquird factor w must know th maximum tim to saturation rquird by th protctiv rlay. If th rquird tim to saturation is mor than 5 ms in a 50 Hz systm th simplifid quation () should b usd. Th for diffrnt tim to saturation is calculatd and can b shown as functions of th primary tim constant. (S Figur 5.) In this cas maximum DC componnt has bn assumd. Th working group WG 3.0 will giv rcommndations about th possibility to rduc th du to th low risk of having maximum DC componnt in th fault currnt in a high voltag transmission systm. Whn th rquird tim to saturation of th rlay is lss than 5 ms, th complt quation (3) shall b usd. Th switching angl θ max, which givs th maximum valu of th factor, is dtrmind for th spcific rquird tim to saturation according to Figur 8. With corrsponding valus of θ max and rquird tim to saturation, th can b calculatd as a function of th primary tim constant. Figur 9 shows th rsults for som diffrnt valus of th tim to saturation. W can s that th ncssary transint dimnsioning factor will b vry small if th rquird tim to saturation of th rlay is low. Th factor is almost indpndnt of th for vry low valu of th tim to saturation. This is bcaus th factor has its maximum valu for th cas whn th fault currnt has hardly any DC componnt. For highr valu of th tim to saturation thr is a highr dgr of DC in th dimnsioning cas, so th influnc of th primary tim constant on th factor will incras in this cas. For th total ovrdimnsioning factor w also hav to considr th rmannc. This is outsid th scop of this papr but w will suggst som gnral rcommndations. It should not b ncssary for th manufacturr to tak into account th rmannc whn in ms Figur 9: as a function of for diffrnt small valus of th tim to saturation. 3 s. 5. Conclusions 8 ms 6 ms ms ms Th papr has dscribd a mor complt basic thortical quation for th transint ovrdimnsioning factor than normally has bn publishd, or bn usd for spcifying of CT rquirmnts, and co-ordination of rlays and C. Th dscribd quation taks into considration th ffct on th factor for diffrnt dgr of DC in th fault currnt. Modrn numrical protctiv rlays oftn rquir only a vry short tim to saturation. If th rquird tim to saturation is lss than 5 ms th factor should b calculatd according to th mor complt quation. For this short tim to saturation it is also important to considr lss dgr of DC in th fault currnt. Th dimnsioning of th C will b mor corrct and th ovrdimnsioning will dcras. 6. Rfrncs N.E. orponay, Th Transint Bhaviour and Us of Currnt Transformrs, Brown Bovri Rv. vol. 6, pp. 55-6, Jun 975 N.E. orponay, Nongappd cors, Antirmannc Cors or Linar cors for Currnt Transformrs, IEEE Transactions on Powr Apparatus and Systms, vol. PAS-97, pp , March / April 978 IEC (99-03) Instrumnt transformrs- Part 6: Rquirmnts for protctiv currnt transformrs for transint prformanc. IEEE 76 CH 30- PWR Transint Rspons of Currnt Transformrs, January 976 6

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