NON-SYMMETRY POWER IN THREE-PHASE SYSTEMS

Transcription

1 O-YMMETRY OWER THREE-HAE YTEM Llana Marlna MATCA nvrsty of Orada, nvrstat str., no., 487, Orada; Abstract. For thr-phas lctrcal systms, n non-symmtrcal stuaton, an analyz mthod costs on quvalnt apparnt powr componnts computaton. uch a componnt s th non-symmtry powr, t may charactrz th non-symmtrcal stuato t has sgnfcant valu n thos stuato. For draw ths quvalnt apparnt powr componnt, th papr dscrb a graphcal modl ths modl rprsnts th mathmatcal rlatohps for non-symmtry powr. A nw ndcator, th non-symmtry factor s xplcatd non-symmtry powr vrsus quvalnt apparnt powr; t s smlar wth powr factor ractv powr vrsus apparnt powr. Also, th computaton procdur s dscrbd for th noymmtrcal and prodc non-snusodal stuato. ntroducton tartng wth 99 yar, th apparnt powr componnts problm was changd, ssntally, by prof. C.Budanu dfnton of dformant powr. cntfc thors wr dvlopd [5] for dfn othrs apparnt powr componnts, for xampl non-fundamntal powr. Rgardng noymmtry powr, codrng ts nam and computng formula, t s an apparnt powr componnt. Mostly, t s usful for non-symmtrcal stuato analyz, n dstrbuton lctrcal ntwors. Th coumrs whch ar not symmtrcal ar th caus [4] of non-symmtrcal stuato, n thr-phas systms. Th supply ffcncy of lctrcal nrgy s affctd. Th xplcato and computato of thos ffcts ar mportant for th lctrcal nrgy supplr, who must justfy th tchnologcal coumpton ncras. Th non-symmtry powr valu an apparnt powr componnt s n proporton wth non-symmtrcal stuaton, and t may b usful for thos stuato analyz. About non-symmtry powr n non-symmtrcal stuaton, thr-phas systms analyz [] s ralzd codrng thorm Fortsqu squnc componnts for currnt and voltag th postv squnc componnt ndxd by +, th ngatv squnc componnt ndxd by - and th zro squnc componnt ndxd by, accordng to th followng rlatohps: R T R T ; ndx R, and T codfy th thr phass n thr-phas systm. n non-symmtrcal stuaton, apparnt powr s computd wth rlatohp:

2 Codrng two apparnt powr componnts: actv powr of postv squnc + and ractv powr of postv squnc + dtrmnat conformng standard formula, t rsults th thrd componnt [], namly non-symmtry powr, notd : 4, whr + s apparnt powr of postv squnc. Th phas shft btwn voltag and currnt of postv squnc s notd wth φ +. Th prvous rlatohp may b xprssd as: sn cos 5 o, t rsults a formula for comput th non-symmtry powr: 6 Codrng only squnc componnts, t rsults nxt formula for comput th noymmtry powr: o o 7 Th non-symmtry may b charactrzd [] by svral coffcnts of rvrs noymmtry, of ant-symmtry, total coffcnt of non-symmtry or ratos of non-symmtry, dffrntal of symmtry. Ths papr dscrb a nw o: rato of mnm non-symmtry r mn, that codr th mnmum valu of th thr o, rportd to arthmtc avrag of thr phass valus and rato of maxm non-symmtry r max, that codr th maxm valu, rportd to sam arthmtc avrag for lctrcal currnt and voltag. Codrng voltag rvrs coffcnt of non-symmtry, -, currnt rvrs coffcnt of non-symmtry, - and voltag zro coffcnt of non-symmtry,, currnt zro coffcnt of non-symmtry,, th formula for comput th non-symmtry powr s: 8, b caus: 9 Clarly, rl.8 justfy th affrmaton that non-symmtry powr has sgnfcant valu only n noymmtrcal stuato, ts valu dpnds on ngatv and zro squnc componnts valus, so non-symmtrc powr may b assumd as an ndcator of non-symmtry. Th graphcal modl, for dscrb th non-symmtry powr, codrs axls systm Oxyz, th non-symmtrcal powr s drawn as a vctor, prpndcular on Oxy plan, s fg. t rsults th rlatohps for apparnt powr componnts, n accordanc wth tagora thorm. n th Oxy plan, t s drawn th standard graphcal modl and th apparnt powr has two componnts: actv and ractv powr all about postv squnc componnts.

3 Fg.. Graphcal modl about non-symmtry powr. Th ngatv and zro squnc componnts dtrmn th supplmntary tchnologcal coumpton of actv powr, comparng to symmtrcal stuato whn postv squnc componnt xst, only: Apparnt powr componnts n snusodal non-symmtrcal and prodcal nonusodal stuato n prodcal non-snusodal stuato, th analyz starts from fundamntal componnt valuaton, ndxd wth "", and harmonc componnts, ndxd wth "", for voltag and currnt. Thos componnts dtrmn th fundamntal componnt of apparnt powr,, and non-fundamntal componnt of apparnt powr, F, accordng to nxt rlatohp H s th gomtrcal mda of harmonc componnts for voltag and H for currnt: F H H n a thr-phas systm, analyz s dvlopd, startng wth th componnts of quvalnt apparnt powr, :,, H n prvous rlatohp rl., ndx "" codfy fundamntal componnt and s fundamntal componnt of quvalnt apparnt powr; ndx "H" codfy non-fundamntal componnt of quvalnt apparnt powr and H s non-fundamntal harmonc componnt of quvalnt apparnt powr; ndx ", codfy " harmonc quvalnt componnt for voltag or currnt. n snusodal non-symmtrcal and prodcal non-snusodal stuato, fundamntal quvalnt apparnt powr conta squnc componnts postv, ngatv and zro. Accordng to rl.5, ths fundamntal quvalnt apparnt powr conta th non-symmtry powr,. Th othr componnt s quvalnt apparnt powr of postv squnc, + and t has two componnts: actv powr of postv squnc, +, and ractv powr of postv squnc, +, accordng to analyz mthod of symmtrcal and snusodal stuato. t rsults nxt rlatohp: H H H

4 , b caus: mlar wth th powr factor n symmtrcal and snusodal stuato, w dfnd th noymmtry factor, p, accordng wth nxt rlatohp: p A formula of non-symmtry factor, codrng th postv squnc componnts fundamntal o, s: p Th " valu of non-symmtry factor s charactrstc of symmtry, about a thr-phas systm. 4 om xprmntal rsults An xprmnt dd comput non-symmtry factor valus, [] n svral nots of a thrphas systm. Thos nots wr: frst not, lctrcal traformr; scond not, noymmtrcal coumr, suppld wth an lctrcal ln typ ACYAbY, x of 5m lngth; thrd not, non-lnar coumr, placd aftr 75 m aftr th symmtrcal coumr, th sam typ of lctrcal ln. Th valus of non-symmtry factor wr computd wth pc softwar. Tabl. on-symmtry factor valus o.crt. not Valu of noymmtry factor rcntag of non-symmtry powr valu from fundamntal apparnt powr valu. Elctrcal traformr,864,6 %. on-symmtrcal coumr,65 4,7 %. on-lnar coumr,999, % t can b obsrvd th sgnfcant valu maxmum of non-symmtry powr, n th not scond of non-symmtrcal coumr. Th valu of non-symmtry factor charactrzs th non-symmtrcal stuato, codrng ngatv and zro squnc componnts. sually, th lmtato, about non-symmtrcal 4

5 stuato, analyz th ngatv squnc componnt, only. For dstrbuton lctrcal ntwors and mdum voltag lctrcal ntwors, th lmt of nvrs coffcnt s %. For hgh voltag lctrcal ntwors, th lmt s % [ 5 Concluso n thr-phas systms, non-symmtry powr s a componnt of fundamntal quvalnt apparnt powr rl.. Th non-symmtry powr valu may b an ndcator of non-symmtrcal stuato; f th thr-phas systm s non-symmtrcal, non-symmtry powr has a sgnfcant valu. Th non-symmtry powr valu and som computaton rlatohps may b xplcatd wth a graphcal modl, fg.. n non-symmtrcal and prodcal non-snusodal stuaton, non-symmtry factor stmats th proporton of apparnt powr of postv squnc valu or non-symmtry powr valu vrsus fundamntal quvalnt apparnt powr valu, rl.5. on-symmtry factor s smlar wth powr factor actv powr or ractv powr vrsus apparnt powr valus. Codrato Th author thans for study coordnaton, about ths subjct, rcvd from prof.dr.doc.ng. ora Cotantn. Rfrncs [].., Antonu, Chstun spcal d lctrothncă, Edtura Acadm, 956. [] ttutul d Crctar s Modrnzar Enrgtc CEMEERG.A., ormatv d ncrcar s masurator spcal n domnul nrgtc, Edtura CEMEERG, B ; B , 6. [] L.M., Matca, Contrbuţ prvnd analza sstmlor trfazat în rgmur snusodal mtrc ş prodc nusodal, Tză d doctorat, Tmşoara,. [4] A., Tugula, Codraţ prvnd fctl nrgtc în rgmur armonc mtrc al sstmlor trfazat, Rvsta Enrgtca, nr., pg., 986. [5] EEE Worng Group on onusodal tuaton, ractcal dfnton for owr n ystms wth onusodal Wafforms a nbalancd Loads: A Dscusson, EEE Traacton on owr Dlvry, Vol., o., January