About the Coupling Factor Influence on the Ground Fault Current Distribution on Overhead Transmission Lines

Transcription

1 > REPLACE THS LNE WTH YOUR PAPER DENTFCATON NUMBER (DOUBLE-CLCK HERE TO EDT) < About th Couplg Factor fluc o th Grou Fault Currt Drbuto o Ovrha Trasmsso Ls Mara VNTAN Uvrsty L. Blaga of Sbu, Dpartmt of Elctrcal Egrg a Elctrocs E. Cora Str. No. 4, RO-555, Sbu mara.vta@ulbsbu.ro Abract A phas-to-grou fault occurrg o a trasmsso l vs th l to two sctos, ach xtg from th fault towars o of th l. Ths two sctos of th l may b cosr ft f som crta cotos ar mt; othrws, thy mu b rgar as ft. Ths papr trats th cas wh thos two sctos of th l ar both vry log a allows th trmato of th grou fault currt rbuto powr tworks. Th fluc of th couplg factor btw th fault phas a th grou wr o th grou fault currt rbuto s u. x Trms fault currts, powr twork, trasmsso ls H. NTRODUCTON GH-VOLTGAE syms hav a ffctvly grou utral. Wh a grou fault occurs o a ovrha trasmsso l a thr-phas powr twork wth grou utral, th fault currt rturs to th grou utral through th towrs, grou rtur path a grou wrs. Kowlg of fault currt rbuto s mportat for th sz slcto of a ovrha grou wr, a rspctvly for th valuato of th fault towr s voltag rs. lctromagtc trfrc problms, th b way to vgat th sol s bhavor as couctg ma s to trm th currt rbuto wth grou [6]. Th grou fault vs th l to two sctos, ach xtg from th fault towars o of th l. Dpg of th umbr of towrs btw th fault towr a th atos, rspctvly of th ac btw th towrs, ths two sctos of th l may b cosr Ths work was partally support by th Romaa Natoal Coucl of Acamc Rsarch CNCSS-UEFSCU through th rsarch Grat No. 485/8. ft, whch cas th grou fault currt rbuto s pt o th trmato of th twork; othrws, thy mu b rgar as ft, whch cas th grou fault currt rbuto may p gratly o th trmato of th twork. Bas o Krchoff s thorms a o som mthos prst by Rubrg [8], Vrma [9], Ery [4], Elma [3] a Dawalb [], a aalytcal mtho orr to trm th grou fault currt rbuto ffctvly grou powr twork, was alray prst prvous works []-[]. [] t was prst th cas wh th fault appars to th la towr of th trasmsso l, cosrg both ft a ft trasmsso l, rspctvly th cas wh th fault appars at ay towr of th trasmsso l, th two sctos of th l ar ft a t s assum that th fault s f from both rctos. Th mtho s appl to thr phas syms wth mutual couplg btw phas couctors a grou wr. ths papr t wll b vlop a aalyz th cas wh th fault appars at larg ac from both trmals, a th two sctos of th l btw th fault a th trmals coul b cosr ft. Th calculato mtho s bas o th followg assumptos: mpacs ar cosr as lump paramtrs ach spa of th trasmsso l, l capactacs ar glct; th cotact rsac btw th towr a th grou wr, a th towr rsac btw th grou wr a th fault phas ar glct; th twork s cosr lar th susoal ay-at. th followg scto t wll b show how mght b obta th xprssos of th currts flowg to grou through th towrs a th currts vry spa of th grou couctor. Furthrmor, th fluc of th couplg factor btw th fault phas a th grou wr o th grou fault currt rbuto s u, too. t s cosr a ovrha trasmsso l wth o grou wr, coct to th grou at vry towr of th l a th fault appars at o towr locat at vry larg

2 > REPLACE THS LNE WTH YOUR PAPER DENTFCATON NUMBER (DOUBLE-CLCK HERE TO EDT) < ac from both trmals.. FAULTS ON OVERHEAD LNE Fgur prsts th cocto of a grou wr to arth through trasmsso towrs. t s assum that all th trasmsso towrs hav th sam grou mpac a th ac btw towrs s log ough to avo th fluc btw thr groug lctros. Th slf-mpac of th grou wr coct btw two grou towrs, call th slf-mpac pr spa, was ot wth cp. t was assum that th ac btw two coscutv towrs s th sam for vry spa. rprsts th cpm mutual-mpac btw th grou wr a th fault phas couctor, pr spa. As a fr p a wthout loosg th gralty, t s assum that th fault occurs at th la towr. Th half-l wll b u fr, a th th full-l aalyss wll b accomplsh by rgarg t as a compost of two half-ls. Wh th fault appars, part of th grou fault currt wll gt to th grou through th fault towr, a th r of th fault currt wll gt vrt to th grou wr a othr towrs. Fgur. Fault currt rbuto As t was alray prst [], th currt flowg to grou through th -th towr, cout from th trmal towr whr th fault s assum to tak plac, s qual wth th ffrc btw th currts a + : + () Th loop quato for th -th msh s gv by th xt xprsso: + cp ν cp () ν xprsso () rprsts th couplg factor btw m th ovrha phas a grou wr ( ν ). cp cp Th quato () coul b wrtt th xt form: ( ) + ν cp Smlarly: ( + ) + cp + ν Subtutg quatos (3) a (4) quato (), for th currt th fault towr wll b obta th xt quato, whch s a sco orr ffrc quato: cp + + (5) Accorg to [8], th solluto of ths quato s: A + B (6) Accorg wth th soluto (6) whch cotas th arbtrary paramtrs A a B, th currt flowg to grou through succssv towrs, has a xpotally varato. Th arbtrary paramtrs A a B coul b obta from th bouary cotos. Paramtr th soluto (6) coul b obta by subtutg th soluto (6) quato (5). Bcaus cp <<, t ca b wrtt: cp (7) By applyg quato () to th (-) towr, t wll b obta th followg xprsso: (8) By subtutg th quatos () a (8) quato (), t wll b obta th xt quato wth a coat trm: cp + + (3) (4) cp + ν (9) Smlar wth quato (5), th currt th grou wr s gv by th xt soluto:

3 > REPLACE THS LNE WTH YOUR PAPER DENTFCATON NUMBER (DOUBLE-CLCK HERE TO EDT) < 3 a + b + ν () xprsso (), a, b rprsts th arbtrary paramtrs. Bcaus of th lk btw currts a, th arbtrary paramtrs A, B a a, b ar ot pt. By subtutg th solutos (6) a () quato (), t wll b obta: A + B a ( ) + b ( ) () Bcaus ths rlatos ar th sam for vry valu of, t wll b obta th xt xprssos: A a( ) () B b( ) (3) Th currt th grou wr wll b th gv by th followg xprsso: A + B + ν (4) B ( ν )( ) () Th currt th fr spa, cout from th fault towr, wll b: [ + ν ( )] () Th voltag rs at th trmal towr s: U ( ν )( ) () A log l s o whch has a ml scto whr th l s v by ach towr to ft half-ls. Nxt, t s trat th cas wh thos two sctos of th l ar both log. fgur th fault occurs at larg ac from both trmals, at th towr umbr. Th fault vs th l to two sctos, ach xtg from th fault towars o of th l. Th bouary coto at th trmal towr of fgur s: + (5) That mas that th fault currt s gv by th sum btw th currt th fault towr a th currt th fr spa of th grou wr. cas that t s cosr that th l s suffctly log so that, aftr som ac, th varyg porto of th currt xpotally cays to zro, th th paramtr A. ths cas oly th paramtr B mu b fou from th bouary cotos [9]. Accorg to (6) a (4), rsults: B (6) B( / ) + ν (7) Subtutg ths xprssos (5), wth for a for, t wll b obta: B + B( / ) + ν (8) For B t wll b obta th xt xprsso: B ( ν )( ) (9) Th currt th fault towr wll gt th xprsso: Fgur. Fault currt rbuto Th bouary coto at th fault towr wll b: + (3) Subtutg xprssos (6) a (7) (3), wth for a for, t wll b obta: B + ( B + ν ) (4) Th, th currt th fault towr wll gt th xprsso: B ( ν ) (5) + Th currt th fr spa, cout from th fault towr, wll b th followg: (6)

4 > REPLACE THS LNE WTH YOUR PAPER DENTFCATON NUMBER (DOUBLE-CLCK HERE TO EDT) < 4 Th voltag at th fault towr wll b: U ( ν ) th (7) f th th couplg factor btw th ovrha phas a grou wr s glct, th th currt th fault towr wll gt th followg xprsso: B th (8) Th voltag at th fault towr wll b: U th (9) Wth xprsso (9) was ot th quvalt mpac of th twork lookg back from th fault.. RESULTS orr to llurat th thortcal approach outl scto abov, t s cosrg that th l who cocts two atos s a kv trasmsso l wth alumum-l 85/3mm a o alumum-l grou wr 95/55mm (fgur 3) [5]. phas couctor, bcaus t coul ot b assum that a l scto of a fw spas s traspos. Th fault was assum to occur o th phas whch s th furth from th grou couctors, bcaus th low couplg btw th phas a grou wr wll prouc th hgh towr voltag. Th total fault currt from both atos was assum to b 5A. Thos valus ar val for a sol rsvty of Ω m. t was assum that th fault appars at th ml towr of th l, so thr ar N towrs btw th fault towr a ach of th trmals. All th furthr prst quattatv rsults ar bas o th thortcal approachs vlop urg th prvous scto. orr to o ths thr wr vlop som umrcal tsv programs wrtt Matlab 7. softwar fram. Fgur 4 shows th currts flowg th trasmsso l towrs ( 4 Ω ), fr cosrg th mutual couplg btw th fault phas a th grou couctor, tha glctg that mutual couplg. Currts towrs [A] glctg couplg factor Fgur 3. Dsposto of l couctors Th l mpacs pr o spa ar trm o th bass of th followg assumptos: th avrag spa s lgth s 5m; th rsacs pr ut lgth of grou wr s.3 Ω / km a t s amtr s 6mm. Grou wr mpac pr o spa cp a th mutual mpac btw th grou wr a th fault phas m ar calculat for ffrt valus of th sol rsvty ρ wth formulas bas o Carso s thory of th grou rtur path []. mpac s calculat oly rlato to th fault m cosrg couplg factor Towrs o lft s Fault towr Towrs o rght s Fgur 4. Currts flowg through th trasmsso l towrs t ca b s that th absc of mutual couplg, th fault currt wll flow through th grou through a smallr umbr of towrs tha th mutual couplg prsc. Fgur 5 shows th currts flowg th grou wr for 4 Ω, fr cosrg th mutual couplg btw th fault phas a th grou couctor, tha glctg that mutual couplg. t ca b s that th absc of couplg btw th ovrha phas a grou wr, th total fault currt wll graually flow to th grou through th towrs, a, f th l s log ough, o currt rmas th ovrha wr. cotra, th prsc of couplg factor a porto of th currt wll ay th ovrha wr.

5 > REPLACE THS LNE WTH YOUR PAPER DENTFCATON NUMBER (DOUBLE-CLCK HERE TO EDT) < 5 Currts grou wr [A] cosrg couplg factor glctg couplg factor ft l mpac [ Ω] glctg couplg factor Spas o lft s Fault towr Spas o rght s Fgur 5. Currts flowg th grou wr Th voltag rs of th fault towr ps of a umbr of factors. Som of th mo mportat factors ar: magtus of fault currts o both ss of th fault locato, fault locato wth rspct to th l trmals, couctor arragmt o th towr a th locato of th fault phas, th grou rsac of th fault towr, sol rsvty, umbr, matral a sz of grou wrs. Fgur 6 shows th fluc of th mutual mpac btw th fault phas a th grou wr o th voltag rs of fault towr. t was cosr that th grou wr mpac s cp. 9Ω. Voltag rs of fault towr [V].5 x cosrg couplg factor glctg couplg factor [Ω] Fgur 6. Voltag rs of th fault towr as a fucto of th towr grou mpac orr to s th fct of th mutual couplg btw th fault phas a th grou wr, fgur 7 s rprst th mpac of th ft l from quato (9), for a grou wr mpac cp. 9Ω, as a fucto of th towr grou mpac, cosrg, rspctv glctg th couplg factor cosrg couplg factor [Ω] Fgur 7. Equvalt mpac of th ft orr to valat th propos aalytcal xprssos thr rsults wr compar wth thos masur smlar cotos usg ral fault ts []. Also th vlop aalytcal mthos wr compar wth othr rcogz aalytcal mthos [7]. both cass th obta rsults wr vry smlarly wth thos obta by othr rsarchrs. For xampl, th fault towr s voltag rs rror s always smallr tha 5%. As mportat avatags, th prst mtho s smplr a far lss tm cosumg tha othrs. V. CONCLUSON A paramtrc aalyss s o orr to uy th ffcts of th couplg factor btw th fault phas a th grou wr o th grou fault currt rbuto powr tworks. t was cosr a ovrha trasmsso l wth o grou wr, coct to th grou at vry towr of th l. t was assum that th fault occurs at larg ac from both trmals. Thr wr prst th xprssos of th currts flowg to grou through th towrs a th currts vry spa of th grou couctor. Ths currts ar varyg xpotally a thr xprssos cota arbtrary paramtrs whch coul b obta from th bouary cotos. For th log ls cas, o of ths paramtrs coul b zro. t s appart that th absc of couplg btw th ovrha phas a grou wr th total fault currt wll graually flow to th grou through th towrs, a, f th l s log ough, o currt rmas th ovrha wr; whras th prsc of couplg factor a porto of th currt wll ay th ovrha wr. Th mutual mpac btw th grou couctor a th fault phas couctor rucs th total crcut mpac. Nglctg ths mutual mpac th fault currt woul b sgfcatly hghr. From th mol prst abov, t ca b s that u to th mutual couplg, th fault currt s ruc wth ( ν ) factor. t also ca b s that th absc of mutual couplg, th fault currt wll flow through th grou

6 > REPLACE THS LNE WTH YOUR PAPER DENTFCATON NUMBER (DOUBLE-CLCK HERE TO EDT) < 6 through a smallr umbr of towrs tha th mutual couplg prsc. As a cosquc, ths cas th fault towr s voltag rs a also ts ghbours voltag rss wll b hghr a artfcal mar. cocluso our vlop mol volvs mor accurat ralc aalyss of th powr trasmsso tworks. Th papr prsts a practcal mtho for grou fault aalyss bg xtrmly usful sgg groug syms. Th mtho ca b also us for th sg of w trasmsso ls orr to slct th sz of th grou wr a for valuatg safty cotos ar trasmsso towrs. ACKNOWLEDGMENT Ths work was support by th CNCSS-UEFSCU through th rsarch Grat No. 485 / 8. REFERENCES [] Carso J. R. - Wav propagato Ovrha Wrs wth Grou Rtur, Bll Sym Tch., vol. 5, 96 [] Dawalb F., Nls G. B. Masurmts a Computatos of Fault Currt Drbuto o Ovrha Trasmsso Ls, EEE Trasactos o Powr Apparatus a Syms, Vol. PAS-3, No. 3, March 984 [3] Elma H. Elctrcal Calculus of trcoct Ntworks, Publshg Tchcal Hous, Buchar, 966 ( Romaa) [4] Ery J. Aalyss of Trasmsso Towr Pottals urg Grou Faults, EEE Trasactos o Powr Apparatus a Syms, Vol.PAS- 86, No., Octobr 967 [5] *** - Mthoology of Currt Fault Calculus Elctrcal Ntworks - PE 34/984, Elctrcal Rsarch a Dvlopmt - CEMENERG, Buchar 993 ( Romaa) [6] Mcu D., Mutau R., t. al.- Orgal Approachs for Solvg Elctromagtc trfrc Problms, Avacs Elctrcal a Computr Egrg, vol. 9, Numbr, 9 [7] Popovc L. M. - Practcal Mtho for Evaluatg Grou Fault Currt Drbuto Stato, Towrs a Grou Wr, EEE Trasactos o Powr Dlvry, Vol.3, No., Jauary 998 [8] Rubrg R. Trast Prformac of Elctrc Powr Syms, Publshg Tchcal Hous, 959, (traslat to Romaa) [9] Vrma R., Mukhkar D. - Grou Fault Currt Drbuto Sub- Stato, Towrs a Grou Wr, EEE Trasactos o Powr Apparatus a Syms, Vol.PAS-98, No.3, May/Ju 979 [] Vta M., Buta A. Grou fault currt rbuto o ovrha trasmsso ls, FACTA UNVERSTATS (NS), SSN: , sr.: Elctrocs a Ergtcs, vol.9, No., Aprl 6, Srba [] Vta M. - Evaluatg trasmsso towrs pottals urg grou faults, Joural of hjag Uvrsty SCENCE A, hjag Uvrsty Prss, co-publsh wth Sprgr-Vrlag GmbH, Volum 9, Numbr /Fbruary, 8, pp. 8-89, SSN X (Prt); SSN (Ol), Cha, 8