Accurate Computation of the Prospective Short Circuit Currents in Low Voltage Electric Installations

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1 EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 1 Accure Comuon of he Prosecve Shor Crcu Currens n ow Volge Elecrc Insllons Eml CAZACU, Iosf Vsle NEMOIANU, Mr-Crsn CONSANIN Absrc Shor crcu s n bnorml oerng regme of elecrc nsllons nd, by s consequences, reresens he mos serous mlfuncon h cn occur n n elecrc newor hus, he rosecve shor crcu curren s en s reference for seres of elecrc equmen ess nd bsed on s vlue he rgh choce for elecrc swchng devces re ccomlshed hs er ccurely redc he mxml rosecve shor crcu curren n rculr elecrc sysem he nlycl nd numercl roch relys on he exc soluons of he me dfferenl equons whch model he dynmc rocess Keywords: rosecve shor-crcu vlue, bng-ccy, coeffcen of mc 1 Inroducon he er resens he mehod of clculng he shor crcu curren vlues nd he shor crcu regme rmeers usng n nlycl nd numercl roch nd lso underlyng he mornce of nowng hese vlues he nlycl nd numercl clculus wll be ccomlshed hrough comuer rogrm whch comues he resul of he dfferenl equons h model hs rocess (MAPE or MAAB ) Also, hs er follows he nlyss of shor crcu mode rmeer vron, deendng on he nl hse ϕ, he ower generor volge nd lso he lne rmeers, exressed qunvely by he me consn he fnl urose of hs er s o ln cern chrcerscs of uomc breers (men o roec he nsllon from shor crcu nd overlod) o he elecrc rmeers of he shor crcu regme, hus esblshng beer selecvy n he nsllon of hese rmeers Modelng he shor crcu regme For hs er, we wll sudy he mono hse shor crcu, whch es lce due o n nsulon flw, n ccdenl mneuver n he newor or when conducor n mono hse newor s grounded [1, ] Fgure 1 Eml CAZACU, reder; Iosf-Vsle NEMOIANU, lecurer; Mr-Crsn CONSANIN, suden; Polehnc Unversy of Buchres Fgure 1 Modelng he shor crcu henomenon Nex, n order o be ble o resen some hyscl nd echncl secs of shor crcus, we wll consder h he curren s suled by ower source of nfne elecrc ower [3, 4] A ower source of n nfne elecrc ower s hyohecl nd s chrcerzed by he fc h s own mednce s consdered roxmely null hus, consn frequency, he volge he ermnls hs consn mlude In hese condons, he henomen deermned by he mgnec coulng beween he crcus of he sor nd he roor of he generng mchne, nd he demgnezon effec of he mchne, cused by he consn recon o he shor crcu, re neglgble [1] Becuse of hs, he rnsen rocess n he dmged crcu wll be chrcerzed by shor crcu curren wh wo comonens: erodc comonen (), of consn mlude, he crcu s consn rmeers, whch reresen snusodl lernng curren wh s cul vlue deendng only on he dmged re s mednce, nd n erodc comonen () h dms wh he me consn

2 EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 corresondng o he dmged crcu hereby, ( ) = ( ) ( ) + In he cse of shor crcung mono hse lne wh snusodl volge: u = U sn( ω + ϕ), ccordng o Fgure 1, by lyng Krchhoff s second heorem we ge he followng exresson of he volge d equon: u = U sn( ω + ϕ) = Rl + l, d whch hs he followng generl soluon: R U ( ) = sn( ω + ϕ ψ ) + Ke (1) Z where Z R + ( ω) = reresens he shor crcu mednce of he newor, n bsolue vlue, relve o he shor crcu re, ϕ volge nl hse ngle, ω ψ = rcn shor crcu mednce R rgumen, n comlex form, K negron consn whch s clculed usng he nl condons of he shor crcu he frs erm ( ) = R U + ( ω ) sn( ω + ϕ ψ ) () corresonds o he erodc comonen of he shor crcu curren nd reresens he rculr soluon for he dfferenl equon; s mlude s consn, becuse of he fc h he volge he ermnls of he ower source h rovdes curren for he shor crcu remns consn vlue even fer he effec hs occurred he second erm n he equon s R ( ) = Ke nd reresens he erodc comonen of he shor crcu curren, whch dmens fer he followng exonenl equon: ( ) R = Ke = I e 0 (3) where K = I 0 s he nl vlue, he momen he shor crcu occurs ( = 0) for hs comonen, nd = s he me consn R of he dmng, whose vlue s deermned by he shor crcued crcu s rmeers he nl vlue of he erodc comonen s clculed by consderng he fc h n n nducnce crcu, he curren remns unmodfed when dsurbnce occurs n he funconng regme Consderng hs hyscl sec nd he fc h n ermnen regme, he curren n he dmged crcu hs he followng vlue: = Iˆ sn( ω + ϕ ψ), resuls n he followng equly for n nl momen = 0 of he occurrnce of he shor crcu: = = + I (4) where: 0 = Iˆsn( ϕ ψ), nd = ˆ sn( ϕ ψ ) I 0 I Under hese condons, we ge: = ˆsn( ) ˆ o 0 = I ϕ ψ I sn( ϕ ψ ) nd 0 = Iˆ sn( ω + ϕ ψ + [ I ˆ sn( ϕ ψ ) Iˆ ) + sn( ϕ ψ )] e (5) he equons ndce h he erodc comonen s well s he ol shor crcu curren vlue deend on he followng wo fcors: he momen of he shor crcu occurrence, e he nsnneous vlue of he curren n he ermnen regme he momen = 0, nd he connecon hse ϕ of he volge Admng he cse, when he momen of he shor crcu occurrence concdes wh he momen h he ermnen regme curren vlue sses hrough zero, e: = Iˆsn( ω + ϕ ψ) 0 (6) 0 = we hve: I = ˆ sn( ϕ ψ ) = ˆ 0 I I sn α = I ˆ sn e = I α e 0, nd ˆ (7) = I [sn( ω α)] + sn α e where α = ψ ϕ In order o hghlgh he wveform of he shor crcu curren nd s erodc nd erodc comonen, we consder crcu n whch he lne mednce u o he on of shor crcu s gven by he followng rmeers: R l = 345 mω nd l = 013 mh (generl low volge cble []) he emorl

EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 3 vron of hese funcons s resened n Fgure for 0 Fgure Grhcl reresenon of he shor crcu curren (1), he erodc comonen (3) nd he erodc comonen () 0 In

3 EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 3 vron of hese funcons s resened n Fgure for 0 Fgure Grhcl reresenon of he shor crcu curren (1), he erodc comonen (3) nd he erodc comonen () 0 In Fgure 3, hese wveforms re reresened for dfferen vlues of he nl hse φ for he crcu s ower source 3 4 Fgure 3 Grhcl reresenons of (), () nd () for dfferen vlues of he nl hse φ for he crcu s ower source 4 In Fgure 4, we cn see he 3D vron of he shor crcu curren vlue nd s deendence on he φ rmeer nd me Fgure 4 3D reresenon of he shor crcu curren If α = 0, e ψ, we ge: = 0, nd = = Iˆ sn ω hs mens h he erodc comonen dsers If α = ψ, we ge he followng equons: I Iˆ 0 = nd = Iˆ sn( ω ) = Iˆ cos ω

4 4 EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 hus, he shor crcu curren hs vlue of: ˆ = I ( e cos ω) If α = 0, e ψ, we ge: = 0 nd = = Iˆ sn ω hs mens h he erodc comonen dsers If α = ψ ϕ=, we ge he followng equons: I Iˆ 0 = nd = Iˆ sn( ω ) = Iˆ cosω hus, he shor crcu curren hs vlue of: ˆ = I ( e cos ω ) 3 Secfc roeres of he shor crcu regme We wll sudy he cse where α =, becuse, n hese condons, he hghes curren nensy vlues er, h sress he elecrc nsllons mechnclly, elecro-dynmclly nd hermlly I s becuse of hs, h we hve o deermne he mxmum mlude of he shor crcu curren nd s cul vlue: ( ) 1,6 Iˆ shoc = (10) where I reresens he cul vlue of he erodc comonen of he shor crcu curren, whose vlue s clculed wh he followng equon: I U med = I = (11) R + X where I s he ermnen shor crcu curren, U med medn ne volge of he rnsformer reled o he dmged re, Z = R + X, he shor crcu re mednce n bsolue vlue In Fgure 5, we cn see he vron of he coeffcen of mc, deendng on he me consn of he dmged elecrc curren oron mx = ( shoc = Iˆ [1 + e ) scc ] = Iˆ [ e cosω ] = (8) he mxmum vlue of he shor crcu curren ers fer sem erod ( = s) fer he mlfuncon occurs In he echncl lnguge, hs vlue s clled shor crcu shoc curren, whch s en no consderon for esng he elecrodynmc sress of he collecor rods, solors, breers, serors, ec he equon, h cn be wren: ˆ shoc = nd shoc [1 = + e ] (9) ( ) scc shoci s clled he shoc fcor shor crcu or coeffcen of mc [3,5] he vlue of he shoc fcor shor crcu deends on he me consn of he dmged crcu, e For norml low volge newor srucure, he me consn vres round he 005 s vlue, o whch shoc fcor of roxmely 16 corresonds hs resuls n curren of: Fgure 5 Vron of he coeffcen of mc, deendng on he me consn of he dmged elecrc curren oron he cul vlue of he shor crcu shoc curren s used n rccl clculons for esng he herml sress of he curren lnes nd elecrc equmens nd corresonds o he frs sem erod Usully, cn be comued wh he followng equon: + 1 I = d (1) In hs cse, he shor crcu curren reresens comlced funcon Becuse of hs, o smlfy, we consder h n he

5 EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 5 sem erod for whch he clculon s mde, boh comonens remn consn hs s vld only n he cse of he erodc comonen, whose mlude remns, n he gven condons, ermnenly consn, s consequence of he fc h he volge he ower source ermnls s consn he erodc comonen s no consn, bu for he consdered me vlues nd me consn = 0,05 s, vres from Î o Iˆ 0, 05 e = 0,8Iˆ, e decreses less hn 0 % of s nl vlue ng he rhmec verge of he wo vlues, durng he frs sem erod, we cn consder he erodc comonen s I = 0, 91 I In hese condons, for every momen whn he frs sem erod, he cul vlues Iˆ of he shor crcu curren re: I = = I ; =, nd he cul vlue of he curren s I I = I + I = I 1+ 0,8 1, 60I, where I s clculed usng he followng U med equon: I = R + X 4 he correlon of equmen wh he rmeers of shor crcu curren In he nex secon of hs er, we wll lso descrbe some of he fundmenl rmeers of uomc crcu-breers 41 Red curren ( I n ) hs s he mxmum vlue of he curren h crcu-breer, fed wh secfed overcurren rng rely, cn ndefnely crry n mben emerure sed by he mnufcurer, whou exceedng he secfed emerure lms of he curren crryng rs Anoher rmeer s he shor crcu rely r-curren seng ( I m ) he shor crcu rng relys (nsnneous or slghly me-delyed) re nended o r he crcu-breer rdly on he occurrence of hgh vlues of ful curren her rng hreshold I m s: eher fxed by sndrds for domesc ye CBs, eg IEC 60898, or ndced by he mnufcurer for ndusrl ye CBs ccordng o reled sndrds, nobly IEC [6] For he ler crcu-breers, here exss wde vrey of rng devces whch llow user o d he roecve erformnce of he crcu-breer o he rculr requremens of lod he roecve scheme erformnce curve comrson n he cse of clscl herml mgnec roecve breer nd n elecronc one re shown n Fgure 6 nd Fgure 7, resecvely, where he followng erms were used [6]: I r - overlod (herml or long-dely) rely r-curren seng, I m - shor crcu (mgnec or shordely) rely r-curren seng, I - shor crcu nsnneous rely r-curren seng, I cu - breng ccy Fgure 6 Performnce curve of crcu-breer herml-mgnec roecve scheme [6] Fgure 7 Performnce curve of crcu-breer elecronc roecve scheme [6] 4 Red shor crcu breng ccy ( I cu or I cn ) he shor crcu curren-breng rng of CB s he hghes (rosecve) vlue of curren h he CB s cble of breng whou beng dmged he vlue of curren

6 6 EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 quoed n he sndrds s he rms vlue of he AC comonen of he ful curren, e he DC rnsen comonen (whch s lwys resen n he wors ossble cse of shor crcu) s ssumed o be zero for clculng he sndrdzed vlue hs red vlue ( I cu ) for ndusrl CBs nd ( I cn ) for domesc-ye CBs s normlly gven n A rms Currens I cu (red ulme sc breng ccy) nd I cs (red servce sc breng ccy) re defned n IEC ogeher wh ble relng I cs wh I cu for dfferen cegores of ulzon A (nsnneous rng) nd B (me-delyed rng) ess for rovng he red sc breng cces of CBs re governed by sndrds, nd nclude: oerng sequences, comrsng successon of oerons, e closng nd oenng on shor crcu; curren nd volge hse dslcemen When he curren s n hse wh he suly volge ( cos ϕ for he crcu = 1), nerruon of he curren s eser hn h ny oher ower fcor Breng curren low lggng vlues of cos ϕ s consderbly more dffcul o cheve; zero ower-fcor crcu beng (heoreclly) he mos onerous cse In rcce, ll ower-sysem shor crcu ful currens re (more or less) lggng ower fcors, nd sndrds re bsed on vlues commonly consdered o be reresenve of he mjory of ower sysems In generl, he greer he level of ful curren ( gven volge), he lower he ower fcor of he ful-curren loo, for exmle, close o generors or lrge rnsformers he ble below (ble 1) exrced from IEC reles sndrdzed vlues of cos ϕ o ndusrl crcu-breers ccordng o her red I cu Followng n oen-me dely-close/oen sequence o es he I cu ccy of CB, furher ess re mde o ensure h: he delecrc whsnd cbly, he dsconnecon (solon) erformnce nd he correc oeron of he overlod roecon hve no been mred by he es 43 Cegory (A or B) nd red shor me whsnd curren ( I cw ) here re wo cegores of V ndusrl swchger, A nd B, ccordng o IEC : hose of A cegory, for whch here s no delbere dely n he oeron of he nsnneous shor crcu mgnec rng devce (see Fgure 8), re generlly moulded-cse ye crcu-breers, nd Fgure 8 he A Cegory crcu-breer [6] hose of B cegory for whch, n order o dscrmne wh oher crcubreers on me bss, s ossble o dely he rng of he CB, where he ful-curren level s lower hn h of he shor-me whsnd curren rng ( I cw ) of he CB (see Fgure 9) ble 1 I cu reled o ower fcor (cos φ) of fulcurren crcu (IEC ) [6] I cu cos ϕ 6 A < I cu 10 A 0,5 10 A < I cu 0 A 0,3 0 A < I cu 50 A 0,5 50 A I cu 0, Fgure 9 he B Cegory crcu-breer [6]

7 EECROEHNICĂ, EECRONICĂ, AUOMAICĂ, 59 (011), nr 1 7 hs s generlly led o lrge oenye crcu-breers nd o cern hevyduy moulded-cse yes I cw s he mxmum curren h he B cegory CB cn whsnd, hermlly nd elecro-dynmclly, whou susnng dmge, for erod of me gven by he mnufcurer 44 Red mng ccy (I cm ) I cm s he hghes nsnneous vlue of curren h he crcu-breer cn esblsh red volge n secfed condons In AC sysems, hs nsnneous e vlue s reled o I cu (e o he red breng curren) by he fcor, whch deends on he ower fcor ( cos ϕ ) of he shor crcu curren loo (see ble ) ble Relon beween red breng ccy nd he red mng ccy dfferen ower-fcor vlues of shor crcu curren, s sndrdzed n IEC [6] I cm cos ϕ I cm = I cu 6 A < I cu 10 A 0,5 1,7 x I cu 10 A < I cu 0 A 0,3 x I cu 0 A < I cu 50 A 0,5,1 x I cu 50 A I cu 0,, x I cu 45 Red servce shor crcu breng ccy ( I cs ) he red breng ccy ( I cu ) or ( I cn ) s he mxmum ful-curren crcubreer cn successfully nerru whou beng dmged he robbly of such curren occurrng s exremely low, nd n norml crcumsnces he ful-currens re consderbly less hn he red breng ccy ( I cu ) of he CB On he oher hnd, s morn h hgh currens (of low robbly) be nerrued under good condons, so h he CB s mmedely vlble for reclosure, fer he fuly crcu hs been rered I s for hese resons, h new chrcersc ( I cs ) hs been creed, exressed s ercenge of I cu, s follows: 5, 50, 75, nd 100 % for ndusrl crcu-breers [7] In Euroe, s he ndusrl rcce o use fcor of 100 %, so h I cs = I cu 5 Conclusons he er hs ccomlshed qulve nd qunve nlyss of he mn elecrc rmeers of shor crcu henomen h occur n low volge elecrc newors hereby, hs documen roosed crcu model of he newor where he nlyzed mlfuncon ers hs model llowed n nlyc rese, srng wh he dfferenl equon h descrbes he vron n me of he elecrc curren nensy, of s mxmum nd cul vlues, nd lso of he rnsen comonens n cse of mlfuncon hese rmeers rove o be exremely useful, boh n recon of he newor elecro-dynmcl nd herml sresses n he on where he shor crcu occurs, s well s n he selecon of he roecon devces, h re men o sole he dmge reled o he usrem crcu In hs sense, he correlon beween d from vrous mnufcurers of elecrc roecon equmen nd he vlue of shor crcu curren rmeers clculed for newor wh nown rmeers ws nlyzed o now n del he chrcerscs of hese devces nd o correcly nerre hem, comred wh he nlyclly re-evlued shor crcu rmeers, llow beer choce of hese devces, resulng n beer roecon of he newor he sudy hs en no consderon he curren Euroen rules nd sndrds (CEI) h regule he oeron of low volge devces References [1] HOROPAN, G, Are elecrce de comuţe, vol1+, Edur ehncă, Bucureş, 000 [] DINCUESCU, P, Inslţ Elecrce ndusrle de josă ensune, Edur MrxRom, Bucureş, 003 [3] MIRCEA, I, Inslţ ş echmene elecrce Ghd eorec ş rcc (edţ dou), Edur Ddccă ş Pedgogcă, Bucureş, 00 [4] IGNA, J, CG Poovc, Reţele elecrce de josă ensune, Edur MrxRom, Bucureş, 003 [5] WAKINS, J, C Kcher, Elecrc nsllon clculons, vol 1 +, Elsever nd Newnes Publshng, 6h Edon, 006 [6] GROUP SCHNEIDER, Elecrc Insllon Gude, Schneder Elecrc, 007 [7] EECRICA SA, Normv rvnd meodolog de clcul l curenlor de scurcrcu în reelele elecrce cu ensune sub 1 V, NE 0006/06/00, 006

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