Transient Analysis of Three-Phase Wound Rotor (Slip-Ring) Induction Motor under Operating Condition

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1 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- anent Analy f hee-phae Wund Rt (l-rng) Inductn Mt unde Oeatng Cndtn Oute K.C., Eneuh F.O. Deatent f Electcal Engneeng Nnad Azke Unvety Aka, Anaa tate Ngea Cendng Auth - Oute Kngley Chueze Deatent f Electcal Engneeng Nnad Azke Unvety Aka, Anaa tate Ngea Atact: h k nvetgate the tanent ehavu f a thee hae und t tye nductn t, unnng n lad. When tatng a t unde lad cndtn ece aaunt, vuly a und t (l ng) nductn ece the et chce f A.C. t. h ecaue au tque at tatng can e acheved y addng etenal etance t the t ccut thugh l-ng. Nally a face-late tye tate ued, and a the etance gadually educed, the t chaactetc at each tage change f the the (Jhn Bd ). Hence, the thee hae und t (l ng) nductn t cete favualy th the quel cage nductn t cunteat a the t dely ued thee-hae nductn t f ndutal alcatn. he ld-de ulaty and avalalty f th t tye ha attacted a dee lk and n-deth eeach ncludng t tanent ehav unde luggng (eatng) cndtn. h ae unvel, thugh atheatcal delng, flled y dynac ulatn, the tanent efance f th ecula achne, analyzed aed n Pak tanfatn technque. hat th dect-quadatue-ze (d-q-) a aed delng n tatnay efeence fae. Key Wd: anent Cndtn, d-q- efeence fae, a--c efeence fae, atay efeence fae, tatnay efeence fae, and und t nductn t etc. Intductn When a ccut e enegy-tng eleent uch a nductance and caactance, the enegy tate f the ccut can e dtued y changng the tn f the tch cnnectng the eleent t the uce. he ccut then ettle dn t anthe teady tate afte a cetan te. (aajt Ghh ). Inteetngly, the ehav f all electcal achne nly f nteet hen t n a teady-tate. hee et e cae, heve, hen the teay ene f a achne t a change n cndtn equed. F ntance, f a e uly n a achne tched n, thee ay e a uge, ly th cllatn efe a teady fl f cuent etalhed. h uge (ut f enegy) ht-lved and ntantnu, and caued y a udden change f tate f the achne. Ccut eht tanent hen they cntan actve cnent, that can te enegy, uch a tanfe and nductn t. anent henenn an aedc functn. he duatn f hch t lat vey ngnfcant a caed th the eatng te f the yte. Yet they ae vey tant ecaue, deendng un the evety f thee tanent, the yte ay eult nt hut dn f a lant etc. (Wadja 9). Evey electcal yte can e cndeed a ade u f lnea edance f eleent etance, nductance and caactance. F the l-ng nductn t unde dcun, t ccut nally enegzed and cae echancal lad, untl a fault uddenly ccu. he fault, then cend t the clng f a tch ( tche, deendng un the tye f fault). he clng f th/thee tch(e) chage() the ccut, that a ne dtutn f cuent and vltage ught aut. h edtutn accaned n geneal y a tanent ed dung hch the eultant cuent and vltage ay entaly e elatvely hgh. It ay t ealze that th edtutn f cuent and vltage cannt take lace ntantaneuly f the fllng ean: a) he electagnetc enegy ted y an nductance (L)(an cnent f evey electcal achne).5 LI, hee I the ntantaneu value f cuent. Aung nductance t e cntant, the change n agnetc enegy eque change n cuent hch an nduct ed y an e..f f agntude L di. dt In de t change the cuent ntatenuely dt = and theefe L di = (nfnty). h ugget that t O ng aut ntantaneu change n cuent the e..f. n the nduct huld ece nfnty hch actcally le. Hence the chage f enegy n an nduct gadual, and theefe the edtutn f enegy fllng a ccut change take a fnte te. 9 P a g e.jed.c

2 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- ) Anthe cnent, the etance R (al tanale at the tat/t ndng) cnue enegy. At any te, the ncle f enegy cnevatn n an electcal ccut ale. hat the ate f geneatn f enegy equal t the ate f tage f enegy, lu the ate f enegy cnutn. In t uazed f, t ece clea that n any tatng achne; ) the cuent cannt change ntantaneuly thugh an nduct (ndng) ) the la f cnevatn f enegy ut hld gd, ae fundaental t the henenn f tanent n electc achne. Al f the ave elanatn, t can e ad that n de t have tanent n an electcal achne th ecal efeence t thee hae und t (l ng) nductn t, the fllng equeent huld e et. ) he nduct (ndng) huld e eent ) A udden change n the f f a fault any tchng eatn huld take lace. - HE RANIEN MAHEMAICAL MODELLING OF HE MOOR UING PARK RANFORMAION ECHNIQUE Unlke the teady tate atheatcal delng f nductn t, hch nt ne and ha eceved a cndeale attentn f eeache, the tanent atheatcal delng f nductn t cntnue t eceved uch attentn. h a a eult f the vtal effect the tanent ehav f the nductn t ha n the veall efance f the yte t hch t f a cnent at. anent delng f nductn t ve t e e dffcult th n the defntn f utale f f equatn and n the alcatn f aate nuecal ethd needed f the lutn f ae (Ok ). he thee hae und t (l-ng) nductn t deled ung Pak tanfatn technque (Dect-quadatue-ze (d-q-) a tanfatn they). In electcal engneeng, and the acated dclne, the analye f thee-hae ccut ae tly lfed ung d-q- tanfatn. It a e elale and accuate technque f nvetgatng the le f vltage d, cllaty tque and hanc n electcal yte, hch ae due t hgh cuent dan y all nductn t hen they ae tated and dung the the tanent eatn. he thee efeence fae nclude; ) tatnay efeence fae ) ) Rt efeence fae ynchnu efeence fae hee efeence fae ae ued t cnvet the a--c efeence fae (nut vltage) t the d-q- efeence fae, and/utut cuent (d-q- efeence fae) t the a--c efeence fae. Any ne f the afe-entned thee efeence fae can e ued t analyze the tanent dynac ehav f the thee hae t unde cndeatn, aed n the fllng cndtn; ) If the tat vltage unalanced and the t vltage ae alanced, the tatnay efeence fae ueful ) If the t vltage ae unalanced and tat vltage ae alanced, the t efeence fae ued ) If the tat and t vltage ae alanced and cntnuu, then ynchnu efeence fae ued. RANFORMAION OF a--c O d-q- REFERENCE FRAME he tanfatn lke d-q- develed y ak can facltate the cutatn f the tanent lutn f the thee-hae und t nductn t del y tanfng nductance t dffeental equatn th cntant nductance..- Equatn f Inductn Mt n Atay d-q- Refeence Fae he elatnh eteen the ac quantte and qd quantte f a efeence fae tatng at an angula eed,, hn n fgue el; P a g e.jed.c

3 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- q-a Ѳ W a-a C C Fgue - Relatnh eteen ac and atay d-q- d-a he tanfatn equatn f a--c t th d-q- efeence fae gven y: f q f a y: f d qd f... f f c Whee the vaale f can e the hae vltage, cuent flu lnkage f the achne. he ft quadant f the efeence fae tatng at an atay eed (t), n fgue hn a deacated. he tanfatn angle, (t), eteen the q-a f the efeence fae tatng at and the a-a f tatnay tat ndng ay e eeed a: t t t dt ( elect. ad... t Lkee, the t angle,, eteen the ae f the tat and the t a-hae f a t tatng th eed ay e eeed a t t t t dt ( elect. ad... he angle () and () ae the ntal value f the angle at the egnnng f te t. he qd tanfatn at, qd c n... 4 c c And t nvee qd n n c n c n qd...5 c n. d-q- ltage Equatn In at ntatn, the tat ndng a c vltage can e eeed a ac ac ac ac 6 Alyng the tanfatn t equatn (6), e tan P a g e.jed.c

4 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- P a g e.jed.c a qd qd ac qd qd qd qd qd ac ac qd ac qd ac qd c n c n c n n c n c n c qd qd qd qd qd uttutng equatn (8) ack nt equatn (7) gve: 9. c n c n c n qd qd qd qd qd qd Reaangng (9) ll gve:.... qd qd qd d q qd Whee, dt d, and... d d q d q q d q.4 q-d- anfatn Of he Rt... ac ac ac v he t quantte ut e tanfed n the ae d-q- fae. he tanfatn angle t the t hae quantte ( - ). heefe ( - ) the tanfatn angle.... n n n c c c...4 n c n c n c Alyng the tanfatn at t equatn 4 n the ae anne a n that f the tat, the equatn ll e taned a: (. aac et al ) a qd qd qd qd qd dt d qd

5 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- q d q q q F equatn 5a, the ak equatn ae: d d-q- Flu Lnkage Relatn he tat qd flu lnkage ae taned y alyng qd (Ѳ) t the tat ac flu lnkage f equatn (6), that : ac L L ac ac ac ac...6 Ung aate tanfatn, e tan: ac ac qd ac qd L L qd ac qd ac L L qd qd qd q d qd...7a qd qd...7 Equatn (7) gve e t: LL L L. qd qd qd LL L L... 7 L L laly, the qd t flu lnkage can e deved a, ac ac ac ac ac L L. Alyng the tanfatn: ac qd ac qd L L ac qd L qd... a qd qd qd qd 8 h gve: L LL L qd qd qd L LL L LL he tat and t flu lnkage elatnh n equatn (7 and 8) an e eeed cactly a q L L L L q d LL L L d LL...9 q L LL q L LL L d d LL Whee, N q q, d N N q q, d N L L N N L L N N N N d d d d P a g e.jed.c

6 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- N N And L, the agnetzng nductance n the tat de, : L L L L... N N F equatn () and equatn (5), F tat, F t Al, flu lnkage f equatn 9 can e tten a: q L d q d l L L q L l L l L l L l l l L L L d q d L L L q q d L L d q d q q d q d d...9 uttutng the value f flu n the t and tat vltage equatn () and (5) gve: q d q d q q d d q d q d q q In te f d Ll q L ( q lq L L L L d q d q L L q l d L q l d L q l l d q d d q L d q d q d q d 4, and, tat and t vltage equatn (.4) can e tten a: 4 P a g e.jed.c

7 IJRERD Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- v v v v v v q d q d Whee q l d q d Whee l d d q d l d q L q d d q q L d q d q d L q-d- que Equatn n Atay Refeence Fae he u f the ntantaneu nut e t all ndng f the tat and t gven y P...7 n a a c In te f q-d- quantte, the ntantaneu nut e Pn c... 8 q q d d q q d d uttutng the value f tan; Pn a a q, d, q, d q q d qd d q dd... 9 q q d d c c...6 f equatn () and (5a) nt the ght de f equatn (8), e q d F equatn (9), e tan knd f te:,, and te. he te ae ce le; the te eeent the ate f echange f agnetc feld enegy eteen ndng. he te eeent the ate f enegy cnveted t echancal k. hat e. d q q d d q q d But... P e d q q d d q q d uttutng value f,, f equatn (9) nt equatn, e have q, d q d..6 5 P a g e.jed.c

8 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- d q d q q d Ll d q L d q d q Ll Lq d L q d L q] L And q d q d d q h le that d heefe, q q d q d q d d q d L L q d q d q q d d q d d q d L... d q uttutng equatn () nt equatn () gve; q P e q P d P L d q d d q q q q d q d d q q d N. N. N.... Inductn Machne Equatn n tatnay Refeence Fae By ettng = n equatn () gve: q q q d d d... q Whee q q q heefe, f tat q d q q d q q F t et = n equatn (5): P a g e.jed.c

9 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9-7 P a g e.jed.c...5 d q q d d d q q...6 d q d q L L L l l l d q d q que equatn, N P P P e d q q d d q q d q d d. Equatn f ulatn f Inductn Mt n tatnay Refeence Fae

10 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- he del equatn f the nductn achne n the tatnay q-d- efeence fae ay e eaanged nt the fllng f f ulatn q d L ( q ( ( d l L L ( ( ) dt q d q)) dt d)) dt...8 q d L ( ( q d ( d d ) dt L L ( ( q d q d )) dt )) dt...9 q q ( ( q d q d ) )...4 q d q d M and L q, L L d, L q d d q, l q, d,,, l q d q d q q q ( d L ( L L d ) q q d L ) Whee q d M M l q l d he tque equatn d l d l P a g e.jed.c

11 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- e P ( q d q d ) N. he equatn f tn f the t taned y equatng the neta tque t the acceleatng tque, that, d dt e ech da N Whee ech = the etenally aled echancal tque n the dectn f the t eed. da = the dang tque n the dectn te t tatn. When equatn (44) ued n cnjunctn th equatn (8) and (9), the e unt eed, / needed f uldng the eed vltage te n the t vltage equatn, can e taned y ntegatng J P d dt / e ech da N Equatn (45) can e tten n te f the neta cntant, H, defned a the at f the knetc enegy f the tatng a at ae eed t the ated e, that J H n e. unt...46 Eeed n e unt value f the achne n ae e and vltage, equatn (45) can e etten a d / H e ech da n e unt dt IMULAION REUL he efeence del e dcued ehautvely ave, a teted n a thee hae und t (lng) nductn t, th atng taulated n tale el, t analyze the dynac ehav f the achne. ale Ccut Paaete alue and cntant f the dynac ulatn f the thee-hae und t (l-ng) nductn t (Eleanya 5), Ccut aaete alue Pe atng 5h ltage (Lne t lne) () 45v Fequency (f) 5Hz N f le ( P n ) 4 tat etance ( ).Ω tat nducdance (L ).45H Rt etnace.9ω Rt nductn L.4H Magnetzng nductance L.4H Ment f neta f t J.4kg Wth value f tale and ung equatn 8 thugh equatn 47, the dynac ulatn lt f the achne a hn n fg thugh fg 4 Fg : he Electagnetc gue, e agant 9 P a g e t eed f the thee-hae und t Inductn Mt (IM).jed.c

12 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- Fg : he Electagnetc gue, e agant te f the thee-hae und t Inductn Fg : Rt agant te f thee-hae und t nductn Mt P a g e.jed.c

13 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9- Fg 4: Plttng f hae A cuent f tat and t ndng f the nductn t 5 PERFORMANCE ANALYI OF HE MACHINE UNDER RANIEN CONDIION F the gah ltted, and eectve f the efeence fae chen f the t, the ateal nductance f achne deend n the t tn hch vae th te. Due t tanent cndtn, the tque eed lttng ehted chaactetc la t that tanale unde teady-tate cndtn. he achne cllated and ettled at a t eed f 4 ad - hat at ynchnu eed. he lttng hn n fg. When the achne a ulated t tat n n lad, t acceleated feely, and afte e daed cllatn, ettle at a ynchnu eed, = = 4 ad - at a te f.6 ecnd. ee fg a On the the und, hen t a ulated th lad tque f.5n, the t eed dd nt acceleate feely a t dd unde n-lad; athe t ha fe ecnd f delayed acceleatn, cllated vey efly and ettle at le than the ynchnu eed ( = ad - ), at cllatn te f. ecnd. h hn n fg. Me-tll, the ulatn tudy al unvel that the achne cannt actually tleate a lnge tatng te th ut undue dtuance t the uly, due t t hgh tatng cuent chaactetc, eecally unde lcked t cndtn. he lttng llutated n fg 4a/. On n-lad and fnal eatng eed, the cuent cculatng n the t ndng f the achne ze. Futhe tll, the electagnetc tque f the achne, agant te deately hgh at tat, and aued a teady cndtn afte.8 ecnd. h llutated n fg. P a g e.jed.c

14 Intenatnal Junal f Recent Engneeng Reeach and Develent (IJRERD) IN: jed.c lue Iue 7 July 7 PP. 9-6 Cnclun h k ha eented vvdly a le ethd f analyzng and ulatng the tanent tate efance f thee-hae und t (l-ng) nductn t unde eatng cndtn. he ulatn eult eented n th et ae ndeed ndenale and edctale tl t Electcal Machne Engnee ve the t efance t the degn and cntuctn. Acknledgeent he auth acknledge Gd Alghty f h tectn and the fale f the enduance, tleance and ut dung the eeach k. Refeence []. O. I. Ok teady-tate and tanent analy f nductn t dvng a u lad. Ngean Junal f echnlgy, vl, N, Mach. Page 46-5 [].. aac, G. Cvetkvk -anent analy f nductn t ung dffeent ulatn del. Acta echnca Junena l 6, N.. age 69-7 []. Mukeh Kua Aya, D. ulchana Wadhan anent analy f thee hae quel cage nductn achne ung atla. Intenatnal Junal f Engneeng Reeach and Alcatn (IJERA), l. I Iue, Page [4]. Jhn Bd Electcal Ccut hey and echnlgy Pulhed y Eleve Ltd age [5]. Elanya M.N. 5 Caatve Analy f a anfe feld Machne and an nductn achne An unulhed the utted t the Deatent f Electcal Engneeng, Unvety f Ngea age [6]. aajt Ghh -Netk they (Analy and ynthe). Pulhed y Ake K. Ghh Page 94 P a g e.jed.c