Inernonl Conference on Advnces n Energy nd Envronmenl Scence (ICAEES 5) Elecromgnec Trnsen Smulon of rge Power Trnsformer Inernl Ful Jun u,, Shwu Xo,, Qngsen Sun,c, Huxng Wng,d nd e Yng,e School of Elecrcl & Elecronc Engneerng, Norh Chn Elecrcl Power Unversy, Chngpn, Bejng, Chn Se Grd Shndong Elecrc Power Compny T n Power Supply Compny, T n, Shndong, Chn ljncepu@.com, xoshwu@.ne Keywords: prmeers of rnsformer; nernl ful; smulon; mhemcl model. Asrc. In hs pper, n he neglec of he core of he mgnec hyseress, eddy curren effec nd he core sn effec nd sed on he nlyss nd summry of prevous experence, n nlycl mehod o deermne he prmeers of he rnsformer's urn o urn shor crcu ful s mproved nd perfeced n order o deermne he prmeers of he rnsformer when he urn-o-urn ful nd urn-o-ground ful hppens ny poson of he rnsformer. Through he mhemcl model of rnsformer fer ful, we cn on he node volge equon of he smulon newor. And hen we dop hree prncples o clcule he unnown prmeers n he node volge equon we oned efore. Smulon resuls verfy he effecveness of he proposed lgorhm. Inroducon For rnsformer nernl ful model, here re wo mehods for clculng he prmeers: dvde he col no severl uns ccordng o he srucure of rnsformer col nd ful ypes, nd clcule he nducnce prmeers eween hese un cols drecly; regrd he nducnce prmeer of he norml operon of he rnsformer s he nown quny, nd he nducnce prmeers of he ful rnsformer re deermned y solvng he equons. The frs mehod requres o clcule he dsruon of lege mgnec feld n rnsformer nernl ful, s very complex o clcule, so hs pper uses he second mehod[]. In hs pper, due o he need for prolem we sudy, he ppropre smplfcon cn e doped. In he neglec of he core of he mgnec hyseress, eddy curren effec nd he core sn effec nd sed on he nlyss nd summry of prevous experence, n nlycl mehod o deermne he prmeers of he rnsformer's urn o urn shor crcu ful s mproved nd perfeced n order o deermne he prmeers of he rnsformer when he urn-o-urn ful nd urn-o-ground ful hppens ny poson. Through he mhemcl model of rnsformer fer ful, we cn on he node volge equon of he smulon newor. Smulon resuls verfy he effecveness of he proposed lgorhm. hemcl odel of Trnsformer Inernl Ful Smulon The smulon model of he rnsformer mus e le o smule ll he operng condons for he lgorhm, nd he nernl ful smulon of he rnsformer cn e performed prculrly. ETP provdes he self nducnce nd muul nducnce of he smulon lgorhm nd he rnch numer s no resrced, so we cn regrd he rnsformer s he self nducnce nd muul nducnce rnch composed of he cols. So he muul couplng rnch model n he ATP cn e used o smule rnsformer. The norml rnsformer cn e regrded s comnon of severl muul mgnec couplng rnches[]. If he urn-o-urn ful or urn-o-ground ful n cern col of he rnsformer occurs, hen col n whch he urn-o-urn ful occurs cn e vewed s wo couplng cols seprely, nd he rnsformer n whch he urn-o-ground ful occurs cn e consdered s hree muul couplng ndependen cols. 5. The uhors - Pulshed y Alns Press 7
Te hree-phse doule-wndng rnsformer s n exmple o descre he ove prncples n del. Under norml crcumsnces he hree-phse doule-wndng rnsformer cn e regrded s sx rnches n whch muul nducnce exss, s s shown n Fg.. Ths wy, hree-phse wo-wndng rnsformer cn e expressed y he sxh-order rnch ressnce mrx [] nd he sxh-order rnch nducnce mrx [], s s shown n equon (). Prmry Secondry Phse I Phse II 5 Phse III [ ] = 5 Fg.. mul-phse coupled rnch model of rnsformer [ ] 5 5 () 5 5 5 5 5 5 5 s he self-nducnce of he col, 5 = 5 Among hem, s he ressnce of ech col n Fg., nd j s he muul nducnce eween col nd j( = (,,,,5,), j = (,,,,5,), j). We dvde he nernl ful of rnsformer no wo ypes: urn-o-urn ful nd urn-o-ground ful, Fg. s schemc dgrm of hree-phse doule-wndng rnsformer when urn-o-ground ful occurs. I cn e consdered s seven rnches n whch muul nducnce exss, nd cn e represened y sevenh-order rnch ressnce mrx [] nd sevenh-order rnch nducnce mrx [], s s shown n equon(). Prmry Secondry Phse I Phse II 5 Phse III Fg.. dgrm of hree-phse wo-wndng rnsformer when urn-o-ground ful occurs [ ] = 5 7 7 [ ] 5 5 5 = 5 5 5 5 5 5 5 5 5 5 7 7 () 77
Among hem, s he ressnce of ech col n Fg., s he self-nducnce of ech col, j s he muul nducnce eween he col nd j( = (,,,,,5,), j = (,,,,,5,), j). Fg. s schemc dgrm of he rnsformer when urn-o-urn ful occurs. Smlrly, he rnsformer cn e seen hs me s egh muul nducnce rnches, nd represened y eghh-order nducnce mrx nd eghh-order ressnce mrx. Prmry Secondry Phse I Phse II 5 Phse III Fg.. dgrm of hree-phse doule-wndng rnsformer when urn-o-urn ful occurs The * mrx [] nd [] of he rnsformer when urn-o-urn ful occurs cn lso e oned y usng he sme nlycl mehod ove. The mn purpose of hs pper s o deermne he prmeers of correspondng [] nd [] n he sevenh-order mrx or eghh-order mrx when urn-o-urn ful or urn-o-ground ful occurs y usng he nlyc mehod, nd he use ETP o smule he curren when urn-o-urn ful or urn-o-ground ful occurs. Shor Crcu eween Turns nd Ground When he rnsformer urn-o-ground shor crcu occurs, s equvlen h p s exrced from cern col, s s shown n Fg.. The prmeers n mrx [] nd [] of he rnsformer chnges no sevenh-order mrx respecvely, s s shown n formul (). In vew of he convenence of prolem nlyss nd prccl needs of he projec, n he mrx (), he prmeers of he non-ful col cn e consdered s he sme efore nd fer he ful []. For exmple,,, 5 nd, unnown prmeers re nd, hey cn e expressed s n n = = () n n In mrx [], Some prmeers ssoced wh he non-ful col cn e consdered o e pproxmely consn, for exmple, 5,, nd so on. And some prmeers reled o he ful col s chnged efore nd fer he ful, for exmple,,, nd so on. Therefore, we need o deermne he chnges of he prmeers of he rnsformer fer he ful. For he clculon of he ful prmeers of he rnsformer fer ful, he followng hree prncples re used n hs pper. () he prncple of conssency When usng he 7 * 7 mrx o nlyze urn-o-ground ful, seres connecon of he col nd he col s equvlen o * mrx, s s shown n Fg.. Fg.. seres equvlen crcu of ful col when urn-o-ground ful occurs 7
Assumng h he col nd he col re conneced n seres nd he curren flowng n hem s, nd oher cols hve no lod, ccordng o Fg., flux equon cn e lsed s follows[]: Φ = ( + ) Φ = ( + ) Before he ful, he mgnec flux n wndng s () Φ = (5) Inducor formul when he wo wndngs re conneced n seres cn e drwn from he ove wo expressons, nmely: + + = () Here, nd re he elemens of he 7 * 7 order mrx represened y he formul (). () lege coeffcen The rnsformer curren when urn-o-ground ful occurs lrgely depends on he sze of he mgnec flux lege, herefore, he mgnec flux lege fcor eween col nd col mus e consdered[5]. gnec flux lege fcor cn e expressed s: σ = (7) () proporonly I cn e pproxmed h self-nducor of wngdngs s proporonl o he squre of numer of urns. Ths cn mee he requremens of ccurcy n he cse of very smll lege coeffcen. n = () n Consder he ove hree equons. represens where he locon of he ful s sd o occur. n nd n cn e used s he nown quny n he ful rnsen smulon sofwre, herefore, we cn use equon(), (7) nd () o on, nd, her expressons re: = σ + + (9) = σ + + () σ = () ( + ) + σ The mehod of solvng he muul nducnce eween col nd he oher cols s dscussed elow. Generlly speng, muul nducon efore nd fer he ful comples wh followng equon: = + () In generl, he muul nducnce of he wndng s proporonl o he numer of urns[], h s: n n = = () 79
By he formul () nd () we cn on: = + () = + By usng he smlr mehod, he prmeers of [] nd [] n he * order mrx correspondng o he urn-o-urn shor crcu cn lso e oned. Inernl Ful Smulon of Trnsformer In hs pper, he correcness of he lgorhm s verfed y he exmple of he Dy connecon of rnsformer. The power supply prmeer: mplude of red volge s V, frequency s 5 Hz, n ernl ressnce s. ohm, recnce s. ohm; lne prmeer: ressnce s. ohm, rec nce s.9 ohm; The prmeers of hree-phse rnsformer re s follows: red volge U = 5/±.5% V ; wndng ressnce =./.Ω; lege recnce: =./.H. In Fg.5, he ful occurs on he A phse wndng of he hgh volge col, nd he shor crcu oc curs he pon of % of he wndng. The A,B,C hree-phse curren, s shown n Fg., re o ned y usng he ove smulon mehod: E E T f f E c Fg.5. Dgrm of rnsformer usng Dy connecon form when urn-o-ground ful occurs..5. - - - -..... c - - - -..... c.5. -.5 -. -.5 -...... c The prmry phse currens The prmry lne curren Secondry lne curren Fg.. Three phse curren wveforms In Fg.7, he ful occurs on he A phse wndng of he hgh volge col. The wndng urns ro s ::5 fer he urn-o-urn shor crcu. The A,B,C hree-phse curren, s shown n Fg., re oned y usng he ove smulon mehod. f E E T f f E c Fg.7. Schemc dgrm of rnsformer usng Dy connecon form when urn-o-urn ful occurs 7
c.5..5..5 - - - c. -.5 c - - -. - - -.5 - -..... - -..... -. -.5..... Concluson The prmry phse currens The prmry lne curren Secondry lne curren Fg. Three phse curren wveforms Due o he developmen of ful dgnoss nd rely proecon echnology for elecrcl equpmen, hgher requremens for he undersndng of he ful mechnsm of he mn elecrcl equpmen re pu forwrd. Especlly for lrge rnsformer rely proecon, only ccure nlyss of he chnges of he physcl qunes n he rnsen nd sedy se of he rnsformer ful operon s crred ou, nd dsruon nd lws of he rnsformer curren, volge nd oher elecrcl quny fer ful s reveled, so h we cn fnd ou he mesurle ful chrcersc moun nd use hese chrcerscs or derved qunes o form prccl creron for rely proecon o cheve he mprovemen of he exsng proecon scheme or o propose new proecon prncple nd scheme. In hs pper, due o he need for prolem we sudy, he ppropre smplfcon cn e doped. In he neglec of he core of he mgnec hyseress, eddy curren effec nd he core sn effec nd sed on he nlyss nd summry of prevous experence, n nlycl mehod o deermne he prmeers of he rnsformer's urn-o-urn shor crcu ful s mproved nd perfeced. Smulon resuls verfy he effecveness of he proposed lgorhm. eferences [] Y Zhu, Dzhong Fng, Power Sysem Technology, J. () -. [] Bohu Zhng, Xnggen Yn, Power Sysem Proecve elyng, second ed., Bejng,. [] chng Q, Power Trnsformer, frs ed., Bejng,. [] Xue Wng, Zengpng Wng, Sudy of smulon of rnsformer wh nernl fuls, J. Power Sysem Technology. () 5-5 (n Chnese). [5] Yongrong Hung, Qunzhn, Smulon for mgnec nrush nd ful curren of hree phse rnsformer sed on ETDC, J. ely. 5 (7) - (n Chnese). [] Zey Zho, Zhzo Feng, Dgl rel me smulon model nd dgl negrl of uornsformer, J. Journl of Tongj Unversy. 9 () - (n Chnese). 7