Parameter Estimation for a Jiles-Atherton based Current Transformer core model

Transcription

1 Prmtr Etimtion for Jil-Athrton bd Currnt Trformr cor modl Y. Chn, D. S. Oulltt, P. A. Foryth, P.G. clrn, Yi Zhg Abtrct-- Th Jil-Athrton (J-A bd currnt trformr (CT cor modl provid ccurt modlling of hytri d turtion ffct d c ffctivly rprnt th rmnc flu in CT cor. Th didvtg of th J-A CT i th rlvt prmtr r not y to obtin. Thi ppr dvlop mthodology to timt th prmtr for J-A CT modl from B- loop. Th B- loop i rltivly y to gt from murmnt or c b gnrtd from ET digitl imultion of gnric CT modl uing B- curv d othr commonly vilbl dt. Vlidtion of th propod mthodology h bn prformd by compring th imultion rult of th J-A CT modl uing th timtd prmtr to th rult uing gnric CT modl uing th B- loop input. Kyword: Jil-Athrton hytri, B- loop, rmnc flu T I. INTRODUCTION h Jil-Athrton (J-A bd currnt trformr (CT cor modl ccurtly rprnt th rmnc flu [][], th ffct of which c b criticl to bhvior of protctiv rly. Th J-A CT modl c lo ccurtly rprnt long trm turtion d hytri ffct uch would occur with gomgntic inducd currnt (GIC ntring trformr []. Although it dvtg h bn wll rcognizd d it imultion modl h bn dvlopd in om imultion tool for ovr dcd, th J-A CT hn t bn widly ud in Elctromgntic Trint (ET bd imultion. Th min rtriction on th u of th J-A bd CT i tht th prmtr rquird by th modl r oftn not vilbl. Th prmtr r bd on th phyic of th cor d not on th lctricl chrctritic fmilir to th powr ytm nginr d th lctricl community whol. Th prmtr r lo intrlinkd in uch wy tht th t of poibl combintion c b quit lrg. Thu ignifict chg in th hp of th hytri loop my rult from mll prmtr vrition. Th gnric CT modl tht i widly ud in ET imultion tool i y to modl bcu it i not Y.Chn i with RTDS Tchnologi Inc., Winnipg, B RY 0B9, Cd (-mil: yuchn@rtd.com. D. S. Oulltt i with RTDS Tchnologi Inc., Winnipg, B RY 0B9, Cd (-mil of corrponding uthor: d@rtd.com.p. A. Foryth i with RTDS Tchnologi Inc., Winnipg, B RY 0B9, Cd (-mil: pf@rtd.com. P. G. clrn i with P.G. clrn Aocit, 09 Frmgh Dr., Tllh FL 09, USA (-mil: pgmcl7@gmil.com. Y. Zhg i with RTDS Tchnologi Inc., Winnipg, B RY 0B9, Cd (-mil: yzhg@rtd.com. Ppr ubmittd to th Intrntionl Confrnc on Powr Sytm Trint (IPST05 in Cvtt, Croti Jun 5-8, 05 computtionlly intniv d i y to u inc th input prmtr r mor commonly known. Th downid to thi modl i tht it my not b ccurt for vry low currnt, thr i no long-trm rmnc, d it w not dvlopd for th intrconnction of CT condri uch in bubr diffrntil protction chm. Thrfor thr i no poibility for intrction btwn multipl CT. Th J-A CT would b ud mor in ET imultion if th prmtr ndd by th modl could b timtd from om prmtr tht r ir to obtin, uch th B- or V-I curv for th cor. Th curv r normlly providd by th mufcturr or c b crtd uing murmnt normlly tkn during on-it fild commiioning. II. SUARY OF TE ANUSCRIPT Thi ppr dvlop mthodology to timt th J-A CT cor modl prmtr from murd B- loop. Th ET imultion of gnric CT modl, with B- or V-I curv input, r ud to produc th B- loop. Th B- loop i in turn ud input for lt qur lgorithm to timt th prmtr (including,,, d of th J-A CT. Th work in thi ppr w conductd on RTDS rl tim digitl imultor. Th ppr i orgizd follow: ction III brifly introduc th J-A CT modl on th RTDS Simultor. Sction IV prnt th dtild mthodology to timt th J-A CT prmtr bd on th B- loop. Sction V provid vlidtion of th mthodology. Finlly ction VI giv th concluion. Th propod mthod in thi ppr provid mthod to ily obtin prmtr for uprior CT modl, thu llowing imultion to b undrtkn which includ proprly modld long trm rmnc d intrction btwn CT. Th ufuln of thi c b pprcitd whn tting high impdc bu diffrntil protction chm which rquir proprly modld intrction btwn coupld CT [4]. Th vritor or OV plcd cro th nutrl brch of high impdc diffrntil chm c dd dditionl non-linr ffct. Th originl J-A CT modl i th on ud in rfrnc [4] d hown to giv cllnt grmnt with rcording (including rmnt flu ffct tkn from ynthtic tt bd. III. INTRODUCTION OF TE JILES-ATERTON CT ODEL Jil d Athrton ud phnomnologicl bd mthmticl rprnttion to ccurtly rprnt frromgntic mtril bhvior in oft mgntic mtril [][5]. Eqution ( rprnt th rltionhip btwn th - loop d B- loop.

2 B0( ( whr B i mgntic flu dnity, i mgntiztion, i 7 N 0 4 *0 mgntic fild intnity, d A (th prmbility of fr pc. Th mgntiztion rltionhip btwn B d i rplcd by th hytrtic mgntiztion curv ( btwn d f ( Whr i ffctiv fild d dfind (, α i th intr-domin coupling, i th turtion mgntiztion. J-A modld th turtion chrctritic uing modifid Lgvin function to produc th fmilir igmoid typ curv for f (, giving th following qution. f ( coth( whr i hytrtic lo. Eqution ( d J-A thory produc trm in follow: irr rv 4 Th firt trm irr i du to th pinning of mgntic domin by dicontinuiti in th mtril tructur. Th cond trm rv i du to domin wll bnding in ltic mnr. J-A built upon th fundmntl rltionhip to rriv t th finl t of qution to contruct th B- d - loop in (5. d d ( c irr C 5 d k ( d irr whr k i irrvribl lo, c i rvribl/irrvribl d proportion, i ign of dt. Whn th J-A lgorithm w implmntd for CT modl, th CT cor chrctritic could not b ccurtly modld uing th Lgvin function []. Th J-A CT modl on th RTDS Simultor u improvd hytrtic function intd of th Lgvin function which ccurtly modl th houldr r of th hytrtic mgntiztion []. Th dtil of th improvd J-A modl qution ud in th RTDS Simultor r dcribd follow: d d = c d + d δk mod μ α ( 0 c αc d, if ( δ 0 ( d c d d αc d, othrwi (7 { d Whr i hytrtic mgntiztion, α d c r contt, kmod i dynmic djutmnt of th domin pining prmtr, δ d kmod r dfind follow: δ = ign( prv (8 k mod = { k ( β (, if δ 0 (9 k, othrwi Th improvd hytrtic mgntiztion function i givn by th following: ign( 0 Th improvd hytrtic mgntiztion function mut hv th following proprti d will b tifid, providd 0,, 0 tht. lim 0 d 0, lim 0, d Th drivtiv with rpct to i givn by th following: d d b ( IV. DETERINATION OF YSTERESIS PARAETERS Th objct in thi ppr i to trct th prmtr for J- A CT modl from B- loop. Th B- loop c b obtind from th mufcturr/fild murmnt or from digitl imultion of gnric CT modl uing B- curv input d plotting th B- loop. Fig. how th flowchrt of th timtion mthodology ud to obtin th J-A CT modl prmtr from picwi linr B- curv. Firt, th B- loop i obtind from th digitl imultion of gnric CT modl contining 4 point B- curv. Scond, th prmtr of th J-A CT r timtd with Lt Squr fitting lgorithm uing dt from th B- loop.

3 Gntiztion flu dnity, B(T Vrm-Irm Chrctritic Point of Ordinry CT Vrm-Irm pir of point of gnric CT Sving th - plot of th turtd dt in mpb formt U loop to pick up - dt Obtin th vd - loop point from th out fil uing th point lt qur To clcult th,, Clcult Output,, B- loop of th gnric CT A Clcult - Pir of point Etblih th J-A CT on RTDS clcult th vlu t th givn vlu B- loop of J-A CT B Vlidtion: compr A d B Fig.. Flowchrt of th timtion mthodology for prmtr of J-A CT modl. It hould b notd tht th lgorithm c lo b prformd uing th B- loop dt from fild murmnt or mufcturr dt. A. Obtining th B- Loop Prmtr In ordr to timt th prmtr for J-A CT, on nd to hv murd B- loop hown in Fig.. Idlly th B- loop c b obtind from fild murmnt. An ltrntiv wy to obtin th B- loop i from th digitl imultion. It i rltivly y to gt th point by point B- curv or V-I rfrnc curv from th mufcturr or by fild murmnt. Onc w hv th B- or V-I curv of th CT to b modlld, ET imultion c b co nductd uing th gnric CT modl. Th B- loop c b obtind rult of th imultion. In thi ppr, th B- loop i obtind by ET imultion of th gnric CT on th RTDS Simultor. Th cor turtion chrctritic i rprntd by th dynmic olution of intgr powr ri qution givn follow: 5 ( t B * B( t B * B ( t whr cofficint B d B r dtrmind from curv fitting tchniqu uing pir of point from th rfrnc curv. Fig.. B- loop B Br B c gntic fild intnity, [ka/m] B. Dtrmin th Sturtion gntiztion S Th it prmtr to obtin i th turtion prmtr S. It i oftn known for prticulr mtril, o c b tkn dirctly from th mtril dt ht. Thi prmtr c lo b obtind from th murd B- (- loop prmtr. Eqution ( i ud bi to convrt th B- loop dt to - loop dt with th following:

4 0 B S, turtion mgntiztion i th mimum vlu of hown in Fig.. gntiztion, (T gntic fild intnity, [ka/m] Fig.. - hytri loop C. Dtrmintion of,, Th mot importt procdur of th timtion i to clcult,, d ud in (0. In fct, th - curv c b dtrmind if,,, r known. From th - curv c b dtrmind hown in Fig. 4. Auming α i t dfult vlu, on c obtin th - curv, in which i th vrging point of th lft id d right id of curv in Eqution (4 d (5: 4 _ ( _ ( 0.5 * ( L n R n n 5 ( ( n n Whr (n i th vlu of hytrtic mgntiztion t point n; (n _R i th vlu of - curv(right id t point n; (n _L i th vlu of - curv(lft id t point n. gint (4_L, (4 (4_R, (4 (4, (4 gntiztion, (T Effctiv fild, [ka/m] Fig hytri loop (n=4 Eqution ( c b obtind from (0, with, d unknown, whn d i known: ( ign And in which th following rtriction nd to b tifid: 0,, 0. Now timt of, d r computd with lt qur mthod. Si mpl of d dt r ud to comput, d follow: Eqution (7 i tblihd with th i mpl of d in which thr r unknown but qution. 7 ( ( ( ( ( ( ign ign Th qution r dfind into d Y trm d th unknown r olvd uing th lt qur olution. Dfin d Y: ( ( ( ( ( ( ign ign Y W hv: * Y Uing th lt qur olution w hv: * * * Y T T

5 T * T * * Y (8 Th olution of (8 will b furthr chckd by th rtriction of 0,, 0. If thi rtriction i mt th olution i conidrd to b optiml. If th rtriction i not mt, nw pir of dt point r chon d qution 8 i olvd until th rtriction 0,, 0 i tifid. D. Dtrmintion of ytri Prmtr c, α, k Rfrnc [] providd dtild dcription on how to clcult th hytri prmtr c, α, k in qution (. According to [], th corcivity i dtrmind by th mount of pinning d hnc by th prmtr k. odifiction of th k prmtr will chg th corcivity point c (th width of th hytri loop. Figur 5 how th B- loop with diffrnt k prmtr vlu. Incring k vlu in ronbl rg rult in lrgr corcivity point. On c obtin th k vlu pproimtly by tril d rror bd on th comprion btwn th ET imultion rult of th J-A CT modl d th known B- loop. Fig.. - loop with diffrnt α vlu: Rd - - loop with α=.5*0-5, Blu - - loop with α=0.8*0-5 Th rvribl componnt of mgntiztion du to rvribl wll bnding d rvribl trltion i dtrmind in th modl by th cofficint c. Thi c b clcultd from th rtio of th initil norml ucptibility to th initil hytrtic ucptibility []. According to th tt rult, prmtr c do not contribut much to th B- loop whn th CT i turtd. So on c prform th bov tt d gt th,,, k d α with c t t th dfult vlu, thn djut th vlu of c by compring th known B- loop d B- loop from th imultion. Fig. 7 how th B- loop r lmot idnticl with diffrnt c vlu. Fig. 5. B- loopwith diffrnt k vlu: Blu B- loop with K=*0-5, Rd B- loop with K=5*0-5 According to [], th rmnc point r i dpndnt on α d othr prmtr. If th othr prmtr r known, th rmnc c b ud to clcult α []. odifiction of th prmtr α will chg th rmnc point d th inclintion of th hytri loop. Fig. how th - curv with diffrnt α vlu. Biclly lrgr α vlu corrpond to lrgr rmnc point. Similrly th vlu c b djutd ccording to th rmnc point of th hytri loop of th known - loop. Fig. 7 B- loop with diffrnt c vlu: Blu - B- loop with c=0., Rd - B- loop with c=0. V. VALIDATION Th propod mthodology i vlidtd by compring th RTDS imultion rult of J-A CT modl with th timtd prmtr (ction IV.A with th gnric CT (ction IV.B with th B- curv input. Th imultion rult dmontrtd tht th propod mthodology c ffctivly timt prmtr for J-A CT. A. Vlidt th clcultion with J-A bd CT Fig. 8 how th tt c ud for vlidtion coniting of ourc, bu, brkr, lod d two J-A CT modl ud for comprion. Th top J-A CT i ud with th originl dt d th bottom J-A CT modl i ud with th timtd dt. Th ph brkr currnt i ud th CT primry currnt.

6 Fig. 8. Tt c for prmtr Comprion On c gt th timtd hytri prmtr through RTDS RunTim Script progrmmd with th timtion lgorithm. (Othr pltform will hv to progrm th timtion lgorithm. Tbl I how th comprion btwn th originl prmtr d timtd prmtr. TABLE I COPARISON BETWEEN ORIGINAL PARAETERS AND ESTIATED PARAETERS Originl Etimt It i obviou tht th clcultion rult i vry clo to th originl dt. Th imultion rult of CT with th originl dt d th timtd dt in tbl I r comprd. Fig. 9 d Fig. 0 how th wvform comprion of originl J-A CT modl gint tt J-A CT modl uing timtd prmtr drivd by th propod mthod. Th blck curv i th originl J-A CT modl d th rd curv i th timtd J-A CT modl. Th B- loop, condry currnt (I, B(t d (t r lmot idnticl in th comprion. Fig. 9. Zoomd Simultd B- Loop Comprion

7 Fig. 0. Wvform Comprion of J-A CT with timtd prmtr d Originl J-A CT B. Vlidt th clcultion with th Gnric CT Th tt c hown in Fig. i imilr to th tt c hown in Fig. 8. Th only diffrnc btwn Fig. 8 d Fig. i th top CT i gnric CT with B-/V rm -I rm dt intd of th J-A CT with originl dt. Fig.. Tt c for prmtr Comprion with Gnric CT On c gt th timtd hytri prmtr through RTDS RunTim Script progrmmd with th timtion lgorithm. Prmtr k, αd c r dtrmind ccording to

8 ction IV.D (i.., th corcivity, rmnc point d B- loop. Tbl II how timtd J-A prmtr with k=5.80-5, α=.50 5, d c=0.. TABLE II ESTIATED J-A YSTERESIS PARAETERS OF GENERIC CT Etimt Fig. d Fig. how th wvform comprion of gnric CT modl d th tt J-A CT modl uing timtd prmtr drivd from th B- curv of th gnric CT modl. Th blck curv i th gnric CT modl d th rd curv i th tt J-A CT modl. Th B- loop i lmot idnticl cpt t th houldr (kn point whr improvd hytrtic function i ud in RTDS J-A CT modl. Th B- loop, condry currnt (I, B(t d (t r lmot idnticl in comprion. Fig.. Zoomd Simultd B- Loop Comprion of Gnric CT Fig.. Wvform Comprion of J-A CT with timtd prmtr d Gnric CT VI. CONCLUSIONS A nw mthodology h bn dvlopd to timt th prmtr for J-A CT modl. Th mthod driv th prmtr of J-A CT bd on om commonly vilbl B- or V-I curv. Th mthod h bn implmntd on th RTDS Simultor but c b implmntd on othr pltform. Th imultion rult dmontrtd th propod timtion lgorithm giv ccurt rult, thu mking it poibl for th J-A CT to b mor widly ud in tudi d imultion involving CT [4] or othr typ of trformr []. VII. REFERENCES [] D.C. Jil, D.L. Athrton. Thory of Frromgntic ytri. Journl of gntim d gntic tril, vol., 98. p48. [] U. D. Annkkg, P. G. clrn, E. Dirk, R. P. Jyingh d A. D. Prkr, A Currnt Trformr odl Bd on th Jil-Athrton Thory of Frromgntic ytri, IEEE Trction On Powr Dlivry, vol. 5, No., pp. 57-, J 000. [] W. Chdrn, P. G. clrn, U.D. Annkkg, R.P. Jyingh, An Improvd Low Frquncy Trformr odl for u in GIC tudi. IEEE Trction on Powr Dlivry, Vol.9, No., April 004, p4. [4] W Chdrn, P G clrn, R. P. Jyingh, D. uthumuni, E. Dirk, A. Prkr Simultion of diffrntil currnt protction chm involving multipl currnt trformr d vritor." IEEE Powr Enginring Socity Summr Powr ting, Vcouvr, 00, Vol., 00, pp [5] D. C. Jil d D. L. Athrton, Frromgntic hytri, IEEE Tr. gn., vol. 9, No. 5, pp. 8 85, Sp. 98. [] D. C. Jil, J. B. Tholk, d. Dvin, Numricl dtrmintion of hytri prmtr uing th thory of frromgntic hytri, IEEE Trction on gntic, vol. 8, pp. 7 5, 99.