Tertiary Windings in Transformers: Engineering Report Citation St. Clair, Harry Prentice and Smith, Donald DeWitt (1920) Tertiary Windings in Transformers: Engineering Report. Bachelor's thesis, California Institute of Technology. doi:10.7907/8s4e-fw97. https://resolver.caltech.edu/CaltechTHESIS:07262024-201453670 Abstract No abstract. Item Type: Thesis (Bachelor's thesis) Subject Keywords: (Electrical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1920 Record Number: CaltechTHESIS:07262024-201453670 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:07262024-201453670 DOI: 10.7907/8s4e-fw97 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16596 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 29 Jul 2024 17:39 Last Modified: 29 Jul 2024 17:39 Thesis Files PDF - Final Version See Usage Policy. 3MB Repository Staff Only: item control page

EHGilTEERilTG REPORT TE.l~TI.ARY WINDINGS IN TRAllSFOBl'1IBRS by Harry P. St. Clair Donald D. Smith Class of Nineteen Hundred Twenty Department of Electrical }tngineering CALIFORNIA IlTSTITUTJ~ OF TECffHOLOGY PasaclencL, California 1920 l I }TTRDDUCTIOlJ ?urpose 'l'he purpose o;f this report ir1 to oxpLtin the ui;rn of the terti..u-y vlinding i n tr ,.insforn1e1·s connoctod in Y-Y; to prosent ,l;J.ta rcsultin~; fro .m simple tosts; ..:.nd to st:ite tho conditions undor which it is -lcuirable to uBe the terti.1ry. I r.. modern rr .J.Ctice > st::)p-up or sto1-, -down tr,.1nsfo:r.1ner bd.:nks (.i.re ordi narily connected Delta.-Y> with tho Delta. on the low·-volt.;..fJO r;;ido of tho tr ,J.nsfor£;,0r. Howev e r, ther e exist Y-Y comiected °tJ.:..inhJ of trw-1s f urmers that for ma.ny rc~ons cunnot be conve1ti entl,'f ch,::,i,ngcd. The -t .es.ts he1.'ein de~_,c:cibed, r.10.de on a 1Jo..nk of three trouble with the Y-·Y c orm.ec'Gio n . Th e r crnults of t he f;hell t yp e tr.:i..nsformor. .' ertLi.ry rinding The tertL.:.ry wi nding i n a b~..nk of Y-Y. cormocted ent wi ndhi r::s connected in DcJ.t;.,1,. one wi1,;iir:.c; on t he core of each tr,1.nsformor. (See Jrig. G}. '.l'hese windii,gs mu.J bo ..i. 2 The pu.rpose of the te:ctiw.ry m:.:;,y ·bo to correct the w:kVe ful.'rn, the sa;i.ne time elimin.1.tlng dangerous ,:;,t pea.ks in the volt~1.iges, by providing d. pa.th for circulating cur:cent; t}1e to limit shur"t-circui t cl.U'ronts; or to supply a.n d,uxili<.il'y load. TlDWRY <.l. wJ transf orma:t', the flux t}u;t induces it must ch . .i.ngo .,:, sine :f'uxw tion. seen fron ,:h The porme'":.bili ty of trd.n;.:3forntcr study o:e the hystorotic loop of tlw iron; hencet the ra.tc of ·~n~ri.,:,tion of th.o flux density is difforent from tho r,.,ta of v:;.rL:.i.tion of tho nu.gnot;izThe::eofore, if the flux densi ty clu1n;:;es -~.u c1 sino f'urwt~ion, the ma.,:;netizing cur- rent CD. :n.not be sinu:,;oid.J..1. The nu,gnetizinc; current muot cont,;.ln som.o h.J.r1;10:nic or harmonics. in f 1ux den£:d. ty, ,.:i. Jurnu:rning th ..J.·~. due to tho clu.w1.ge m,k.W.le:r ru.,gnetizj_ng currcn t ia re- quired in one 1;a:t't o.t' th,J cycle t11su1 in u.110the:r 1.,,zt, the B"li..l.(~notizing-curreL t 'Vd,Ve will be ped.ked. the flux donaity in the iron ir; low, ~1.t When 'the first 1, c..l.rt 3 of the half-cycle, a frn1;,;i.llor current, co:mi;:J..ratively, will be re ,iui:t'e :1 tha.n in the lu.t·ter ~ nt.1rt ~ o:f: tho huJ.f- It is evident, C\cle, when the flux. derrni ty is high. then, th ,:,,t one pe ,1..1' po:r: half-eye lo is ret:luirad, ,i.n,l tir:1of;1 that of the f'u.nd0.n~ental, ion. :;1.-.l,tisfi0s thiG condi t- O·Ning to the fu.ct th;_;:,t the halv0n oi' t,lw c;:rcle of the Lt.J,Gncti.zing currer,:t rntwt bo iclentic,.w., no even l1;.i.r:rnonic~1 can exist. If the magnetizing cur:1:ent doos not c0nta.in ·tlw neccsBcil',I third h.-.:i..rmonic ccmpo:uent, the induced volt~d,e;e wi.11 not lie o.. sine wo.vo. In d, ba.nk of throe singlc-ph;;.se t1',..1.nsfo:cmers, the peaks of the thi1'd h;;i.r:monic vL,.:vos occur .:.t the fr0 ,1uenoy oircuL1:ting cu;c:cerJ.t. vided foi· tho flow oi' tho circul,),,tinc current, the line -to neutral (seG li'ig. 4). 'l'ho resulting volt- P ,;l,ths for t l w ci1.·culu.tin0 third h<-1.:r:-rnonic .Jore rrovidod in t l,e :following c,.1.n0s: 4 ~2. Y-Y oornrnc -ted banks when neu:tr ....ls of' gonorc:.tor a,nd tra.nsf'ormer prima.ry o..ro grm.mded.. J. Y -:{ connoc tod. b<;1,nke when t.he Del ta-con- nected. tertiu.ry winding is used. Tb.ree-phw.3e coro-ty-iJe tr,>..nsfor1n01·s aro not a:f:'fccted because the r:u.;_?,11etic cJ.rcuitB, being rm;.t- ually interconnected, i.U'G supplied w1th 1nagnetort1otive forces neceuso.l.':f to 1-,roducc a, sine w.;.ve by &1 interclrn,nge of r:1L;<;~netornoti ve f'crcos frorn one p.hd.f.rn to ;_;l.¥,J.o ther. APP AHArrUS General I]loctric Oscillogr-J.ph, 'l'ype E-H, J?o:rm C, lTo. 18191G. Thr.Jo Wostin:;lwlurn 10-kv-a. '.l.'r,;W:mformel'S, N-0 .. 3:,9489. YJestinghouee Al torrw.ting-Cu:r:r::mt G:.n,e:r ,,1.to:c, 30 kv-::;:i,., 2200 volts, 60 cycles, Scri0.l lTo. 1616116, 5 PROCI!DlTirn .AlID DISCUSSIOlr 1<:ach of 'tl:w three ti·aJ:rn.formnr }3 cont,:.1.irwd four low-tension coils which could he connec·ted in a.I1y way desired. ]?or this work, two of these coils, connect(;d in parallel, formed the f,ccond,_;. ry w1nding; v;hile the remuining two coils, also connected in i,~u.llel, .formed the tert Li.ry winding. 1"he p rinkU'.I u,.nd. s o conJ. ..;,J.' J o;f tho tr .;.ns:fo:cncr bci...<1k we:ce both coxm0ctad in Y, while tho terth.i.ry Wi.:l.S ccnrwct0d in Del ta. The primary H<.1U supplied with ex.citation from tho ;l~~oo-vol·t, three-phaso, altorm:l.ting-ou.rrer,t gonei.·u~tor. In series with the t -.J rtid.J.'y w.tu pl a..ced a.n :. 11. ,u-,1,~t ,:; r -J..rd ;.J, nwi tch, hi. ordux thc;i.t the conditions, with anJ v1ithout the tertid.ry ci:r-cuit, rni e;ht; be st~ud.ir;d; Ll.l1d th.1.t tho c i::ccul....ttir;.g ctu:·ront, flowing in the tertiary, might be me,.tSu:r:od. 1'he.n, ·by· rnc;i;J.JH:3 or th0 oscillo,,_;ru.ph, the w,.1 ve for1nH of tho volt, , ;cm fro rr: line to line a.nd front line to n eutru.li on the: seccnld...l'Y, vrith ,.md ¥✓ :i.thout, the tertiary , were obs.orved c..1.nd ro :".:Ord ed. by tra.eing. Th(: valuae of tho current flovling in the t0rtL.:1.ry when IJ.l volt- 6 u..ges :from line to lino u.ncl from lino to noutra.1. -.vere moasu.r :.:d with an orjina.xy al.tern0.ti:ng-curi·ant volt- meter• while t h e vol t,,Lgef~ from noutrJ..1 to e:rouml d,n.d. fro:cn ca.ch line to ,s ~:round v:ere mcL ..uu:ced, r: i th d. s ta.tic voltmeter. Roaiings v1ore -t ,~:e.n 'Ni th tho neutra.ls of tho trS1.nsformer hoth g1·otm.ded and floil.ting. J..S ahov1n on the dd.t,.i sheet. 'I'hc w,:..vo form of the t e:rtLiry c ircuLi.ting cu1''rhis W.J,v c ) which is o:r tripl 0 fre .:uc:ncy, v1..:..B superimposed upon the ,':r.1ve of vol td.ge i'rox:L line to line b y opor,:i:'i:;- ing tl1.0 synchronous Hoto:r :.1.nd one element o:C the oscillo r;ra1,h :Crom th0J line volt..t.gc , w,:nd ;;t rrncornl <Jlemont fro m tho curr,.mt flowin ::; l.n the t0rtL1.ry . '.l'he result (Ing. 3) Bhovrn very nicely tho f,)~ct that the ci:rcu1 ,..:,t- inc~ current i~:, of triple fre quency, :...r..d, thcre.fo1:o, thu,t it; iB causeJ, .m.o..inly, by tho thi:r:l h a.rrnonic cor:1poncm t of the macnot iz inc cu1·ron t. The r<Li.son th 0.t th.id trip1e-:fre .;_n(n1oy ou:n:ent is u.tt:ributod to th.! third h~L onic ifJ ox. .,l ~:d.ned .;l.S folJ.owB: Since identioa.l points on tho t h ird harrnonj_c wave occur a.t tho r; ..w-rte time interval as t.he into:rv.J.1 7 botvreen the pha.scs, 1. ~J., 120 degr0es with respect to th.a f'unda.rnen ta.l frequency, it follows t h.at tho third harmonics in all three phu.seB must; combine to form a triple-fre ,1uenoy circul :),ting cttr:cent. whenever a pa.th for this current iu 1:,ro-r;idcd. ~Cho s ec crnlary of tlw txa.nsi'or.mcr b.;i.nk Y•hi,%J then loaded by m.J21.ns of a.n induction .moto:t', and rewling£3 l~ shown of vol t c:~::;eG a.nd currents taken u.s before. by the da,ta. sheet 1 no clw.nge in the alncunt of current 'l'hi S Vfo.[J t0 bo expected, sine(~ the circuL,.t.ing current is a. .v}wn- with the loud. The oscillo;:;r&!lS in Fig. 4 E'lhow the W,J;VeG of voltage from lin1.1 to neutral, ·:,rith J.nd. without tl10 torTho distortion of" this w-a.ve Yihei : the te:1:'tiaryis disconnected is evidont in Curve l. tJ.10 'tfo,VO also iniic . ;ites th~tt the d.isto:-ction is due largely to ~t t h i:cd h a.rn~O~ iiC CO fij; Orw n t . Curve 2 shv us It is obvlous t l w,t nuch listortion of the b :J liable to cuaa0 rupture of insulations. 8 aze of ;ertiary The size of the tertiary wind.in;; nocess,...ry to carry the third. ha.r.L1011ic co,mponent of tho f;t:J{;netL.;ing current in tho tru.nsformcJr:3 under test Wd$ fom1d to With ·tlte seconda..ry oo ils in :i;u.rallel be ·V'ery small. (sui;I)lie:l to sccond.~U'.;t}, or a.Lout l..6 per cent of the full- load cur:r:ent. The circul:.i.ting cu:r:rcnt w,.1,u .14 di.11por::rn, o:c about 10 1:;0r c ont of' the exciting curront . 'rherefore, tlle tei·ti1;1Xy noed h,:..ve .J, c ~-.yo.oi"Gy o:.C 011ly .lo x l.6 1 or ,.ibout .16 1-:,er cent of the cupd.city of tt,.e transformer. However, for tra..r1sformer~3 of lcU'g0r r-;ize for power work , tJ:le m.d,gnotizing currcmt, ,i,n.l con:;e yent1:r, t. ,o tertL:l..r;:,r cu:t·ront, iu L.Lrge:t' in fl.'Oportion. The Jw.rn.onio oor11,t:.ment of th.<: 1w;.1.gn cJtizing current is d.lso la. rger, boing from ;}o 1; 01.'cent to 30 lJCl.' cent of the tot- i ty of .16 _p,-n' cont, the tertiary should h.wo _i, cur tl.Ci ty of :f';:;,>om 1 to 2 per cent of the tctaJ. lcv-a. ca.pu.city of the tra.nsl'orm0r. * )for grounded neutr,.u op erat i on, th t:: size of the t0rti.:u-y \'f ind in;~ is fixed. 'by tho '-, h o:rt-c ircui t oondi tion u , *J·. II. :eeto:cs, Electric .Journal, Vol. XVI~ n o . 11, PP. 4"17-.1:ao. 9 ra.thel' than by tho cond1 tiono ,ler,01.·ibod above. The t.he inte::cv--w. of time between tho occui'r,J:nce of tho ;;;hoxt ;:,w.d the opexa.tion of the c :i.:rcui t oncls. The a.rn.ount of tho short-circuit current in the tortL1.ry, well ,is in the :main winding, is dependent ~:i.s upon t.he impeda.nee betw:Jcn tho :mo.in uinding J.nd the ma.in winding. If In is the 110:i::rna.l ful1-lod.d cm·rent, Zt tho impedance b0tvrnon tho m.J.in vrinding u.nd the tertL.i.:cy, and Zo the imped,J.nce botwosn the primary Ll.rd second~:..:cy, the sh ·u :ct,-ciroui t curronta will be a.s follows: In the Od.rrn o:f c1. ;round 011 tho prinary Bide of' tJ:..:,;; trunsformer, tlie sho:rt-cirouit current will have i:J, value o:f In Z't ' in both the to:rtia.r:t und tho mu.in ~ 111indini;, with ea.ch of tho :following corui::;ction::i: prim- a:c:v a:nd scconda.:ry noutr<1ls grounded, sup p ly J.soL"ted; pri:ma.ry and supplJ nGut:r.•,-1.ls e;:r:otu1rL~,1, sooo:ndary isolu.tod. It if., evident, t.h<.L1, t}.1.~t for :t\iul ts on the prim.:.:i.ry side, 10 the short-oircui t cul.'r<:ut is limited. onti:c0l;7 by the In case of a grouml on tho l:)CJcond.:u-y sid.e, the short-ci.rouit current in tho tei-tiary will have the ··z1 ~In and in tho main ·uindinr~, •,;;- B 2 2'.o t it' '·· 2Zo + Zt/ with ea.ch of the follow'i ng corn1octions: grounded neu- V "'lue Yo ' tra.l on p:rima.ry ,,1nd socond.ary; on secondary a.nd supply. ;:_i,ry <'.l.lld ground ed neutral ~/hen f,;;,ul to on tho t,econd- occur, the short-circuit current iH limi t:::d L1rge- l y- b y the imp ed ance between tho mu.in vJindin.~ and the t o:rtiary . The impedance between tho tertiary ,ind the orJer th -..:.-t tho sho:rt-circui t current, u.nd 1 co:nne ,1uently, the ca.p ~;. .city cf the tertL-i.ry, m.J.;Y· l>e mni:111.i& ll COlTCI,USIOlTS As a result of these inveat1gi.:l.tions, it is evident tlw.t. vihei·0 oondi tions noo,;H:ssi ·t ,.ite the uee of the Y-Y connection, the ter·th.1.ry vtind.ing should be employed to take c u.re of the third ha.:rmonic compone.mt of the r;1agneti:;1.;ing aur:rent, which, if not providerJ. f ur, may c.;.;.use Jangerous paaJrn in the vol ta,£~e from line to :neutru.1, i:l.lld. hence to ,,-~round. :surthermore, BLw e the Y-Y con- used ·to l ir:1tt the slwrt-circui t cur r ents in c u.so of accidental grounding of a nJ of' the lines. I:n. some instu.llo.tionr;1, it might he ddvisd.ble to us8 the tcrtia.ry to carry .:;;J., a...11. ~,.u:-s:iJ.iary lo ,;1;:l , so tc 81im:inatc the necessity of having idls copper, to carry a 1a:rge. sho:rt-c iraui t current for period. ,1 sho1·t