Performance Evaluation of Wound Rotor (Slip Ring) Induction Motor with Leading Power Factor

Transcription

1 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 Pefance Evaluatn f Wund t (Sl ng) Inductn Mt th Leadng Pe Fact Uguda A.U., Oute K.C. Izh A.N, Ajak U.P.P Deatent f Electcal Engneeng, Nnad Azke Unvety, Aka, Anaa State, Ngea Deatent f Electnc and Cute Engneeng, Nnad Azke Unvety, Aka, Anaa State, Ngea Cendng auth Oute Kngley Chueze, Deatent f Electcal Engneeng, Nnad Azke Unvety, Aka, Anaa State, Ngea. Atact: h ae eent an analy f und t nductn t th leadng e fact. If t etance t duct f l and t eactance ( / ) at f an nductn t take negatve value, lyng eng tadtnally negatve (ue ynchnu eed f the t), the t ha cuent I, ll lag the aled vltage y an angle geate than 9. h ean negatve e fact ( C ) electc e fl ut f the achne f t t the tat eultng n geneatn eatn. In th ae, eatn f an nductn t th a leadng e fact taned y njectng caactance, c he agntude aately tce that f the leakage eactance ay, the veall eactance f the t ccut ece j even thugh tve. he effectve leakage eactance caactve uch that e fact f the achne ece leadng ntead f the uual nductve laggng e fact hch ll lead t electagnetc tque n the te dectn t the tatn f the t hch geneatn eatn Key d: Wund t nductn t; Leadng e fact; Inveted tque-eed chaactetc; Cuent lc; Inductn geneat.. Intductn he feld f alcatn f altenatng cuent (a.c) t ha nceaed cndealy th the adtn f a.c yte f dtutn f electc enegy f lght and e. he nductn t ued n a de vaety f alcatn a a ean f cnvetng electc e t echancal k. It thut dut the khe f electc e nduty [-]. he ean ae t l ct, le and ugged cntuctn, aence f cutat and gd eatng chaactetc. Inductn t can e clafed a quel cage und t nductn t. he quel cage t ndng ae efectly yetcal and have advantage f eng adatale t any nue f le a. Aut 9 ecent f nductn t ae quel cage tye, ecaue th tye f t ha the let and t ugged cntuctn agnale and alt ndetuctle eeach ha hn that the dtutn f cuent due t electagnetc nductn n the t a vae f a t a nudally and deend un the tn and te, aung nudal dtutn f adal flu denty n ace and al the aled vltage t e vayng nudally th te[-4]. hee n lty f addng any etenal etance n the t ccut nce the t ndng eanently ht-ccuted n cage cntuctn. In und t nductn t, the t und th an nulated ndng la t the tat ecet that the nue f lt alle and fee tun e hae f a heave cnduct ae ued. Se achne ae vded th uh lftng and l-ng ht-ccutng aangeent f unnng cndtn. Snce the cnnectn f the und ecnday t the etenal tenal ade thugh l-ng and uhe, und ecnday t ften ae called l-ng nductn t. In t nal kng ange, the eed f the nductn t ean eanaly cntant, vayng lghtly th lad. F th ean t egaded a a cntant eed t; the aj htcng f the nductn t the elatve l e fact hch alay laggng. Anthe dtnguhng featue f uch t that they ae ngly ected achne, althugh uch achne ae equed th th feld and aatue ndng. In uch a achne the feld ( tat) ndng cnnected t an ac uly and thee n electcal cnnectn f the aatue ( t) t any uce f uly. Cuent ae ade t fl n the aatue ( t) cnduct y nductn hch nteact th the feld duced y the feld ( tat) ndng and theey duce a net undectnal tque. Such t ae al called aynchnu t a they un at a eed the than the ynchnu eed f tatng feld develed y the tat cuent. Lke the electcal achne, the aynchnu achne evele,.e t can eate a th a t and a geneat. When un fate than t ynchnu eed, an nductn t un a an nductn P a g e.jed.c

2 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 geneat. It cnvet the echancal enegy t eceve nt electcal enegy and th enegy eleaed y the tat. Heve nductn t can e eveed thut unnng t fate than ynchnu eed y cnnectng caact hch ake t eate th leadng e fact[5].. Dynac Mdel f an Inductn Mt n Atay efeence Fae. Stat ltage Equatn q d q q q d t ltage Equatn q d q d q d d q q d Flu Lnkage q Ll L q L q Ll q L q q d Ll L d L d d d L l d L q Ll q L q q d Ll d L d d Ll Suttutng the value f flu f equatn () nt the t and tat vltage equatn () and (), q q d d q d q d d Ll q L ( q lq L L L L q L L l d L q l L l l d q d L d q d q d () () (4). Inductn Machne Equatn n Statnay efeence Fae By ettng eed, = n equatn () and () gve: P a g e.jed.c

3 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 P a g e.jed.c q q q q q q d d d q q q Whee 5 heefe, tat vltage equatn, 6 d d q q q t ltage Equatn. 7 d q q d d d q q Flu Lnkage Equatn. 8 d q d q L L L l l l d q d q que equatn, 9. N P P P e d q q d d q q d q d d

4 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4. Equatn f Sulatn f Inductn Mt n Statnay efeence Fae he del equatn 6, 7 and 8 ay e eaanged nt the fllng f f ulatn: ltage and flu lnkage equatn ae: q d LS ( q ( d ( l LS LS ( ( ) dt q d q)) dt d)) dt () q d L ( ( q d ( d d ) dt L L ( ( q d q)) dt d)) dt () q q q d q d Whee M and q ( q ( L, L, L M d L d q d q d ) ) q l d q, q, d d d M l he tque equatn l q l,,, d l d l q d q d q q q ( d L ( L L L d ) ) q q d () (4) (5) () e P ( q d q d ) N. P a g e.jed.c

5 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 he equatn f tn f the t taned y equatng the neta tque t the acceleatng tque, that, d N. (6) Whee dt e ech da ech = the etenally aled echancal tque n the dectn f the t eed. da = the dang tque n the dectn te t tatn. he e unt eed, / needed f Buldng the eed vltage te n the t vltage equatn, can e taned y ntegatng J P d / dt e ech da N. Equatn (6) 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 (8) S Eeed n e unt value f the achne n ae e and vltage, equatn (6) can e etten a (7) d / H e ech da n e unt dt he equatn f tanfng ac hae vltage t vltage gven a: v v v v q v v v d c ag a v g v ( vc v) ( vag vg) ( v v v ) ( v v v cg a c ag g cg cuent ack t hae cuent gven a: a c q q q d d c () () (9) ()) he equatn f tanfng f tat () (4) (5) he alanced uly vltage can e eeed a va v c( et) v v c( et ) (6) v v c( t 4 ) c e. Mdel Equatn f Caactve Inductn Mt. he tanfatn lke dq develed y ak can facltate the cutatn f the tanent lutn f the nductn achne del y tanfng the dffeental equatn th te-vayng nductance t dffeental equatn th cntant nductance[7-]. he tanfatn at, f tat f nductn achne 4 P a g e.jed.c

6 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP P a g e.jed.c ) (7 n n n c c c And t nvee (8) n c n c n c he tanfatn angle t the t hae quantte (Ѳ - Ѳ ). heefe (Ѳ - Ѳ ) the tanfatn angle. ) 9 ( n n n c c c () n c n c n c F tat ac q ac hee dt d q = quantty f chage. Alyng Pak tanfatn at equatn (7) and (8) t equatn (): a q h gve q q q q hee 4 q d q q q In eanded f

7 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 q q 5a q d ut q q q d q q cv q d c the caac tan ce thugh a. cv cv q d cv cv d q q cv F equatn 6 cv cv d d d q q vq vd dt c d vd vq dt 4 c F equatn 4 v dt 4 c F t 4 ac q ac he tanfatn angle t the t hae quantte ( the tanfatn angle. 6 P a g e.jed.c a a Suttutng equatn n equatn 8a F equatn 5 ). heefe Alyng the tanfatn at equatn (9) and () t equatn 4 n the ae anne a n that f tat, the equatn ll e taned a q q 4 In eanded f, cv q d d cv q 44 cvq cv d cv F equatn 4, cv q q q vq c F equatn 45 cv cv d q d q cv cv v dt 47 d d d cv q d vd q c 9 v dt 48

8 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 F equatn 46 v dt 49 c. Steady State Analy f Inductn Mt In a teady tate eatn, the devatve te n the vltage equatn ae ade ze. F equatn () 5. q q d Slaly f equatn (), q q 5 d Ung the tanfatn f d = j f q (nce q and d ae n ace quadatue). heefe, q q jq 5. q q j q F equatn (),Flu Lnkage Al L L L L q q q L l L q q L q 5 q L L q q L N uttutng (5) and (5) nt equatn (54) e have q q Al q q q q j L q L j L j L q q LS q L jl j q q q 54 q j, hee Sl L 55 q q q q q tan the teady-tate equvalent ccut, t aued that q-a algned th a hae f the achne uch that ; q q a a ; q q a ; a Equatn 57 ece j a a L a j Whle equatn 6 ece j j a a l a 56 a a 57 a a a Dvdng th de f equatn (57) y, e have j j 58 a l a a a 7 P a g e.jed.c

9 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 N the teady tate equvalent ccut can e dan ung equatn (56) and (58) a hn el: a jl j l a a j a Fgue : Pe hae equvalent ccut f a ly-hae nductn t. a / In nductn achne, the t ndng ae nally ht-ccut and thu n vltage aled t the t. Hence a = and the equvalent ccut a hn n fgue. I a a j l I a j l Fgue : Pe-hae equvalent ccut f a ly-hae nductn t th t ht-ccuted.. Cuent Lc f Inductn Mt. he t ccut vltage equatn f an nductn t n ha f can e tten f t equvalent ccut f fgue [6] a E I jx 59 I X E / Fgue : t equvalent ccut f an nductn t. F equatn (59), the e-hae t cuent at any l gven y: I Whee E X Ac tan And the t cuent lag the t vltage E y Ө. he e nut t the t gven y: P g = E I cө (6) 6 8 P a g e.jed.c

10 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 e hae t e tan ce c e hae t edance he e fact cө ay e eeed a; Suttutng equatn (6) nt (6) gve: Pg E I I X 6 X P g actually the e tanfed f the tat t the t ac the a ga. F the ue f je X tanng the t lcu, (6) can e etten a: I ji 59a Equatn (66a) h that a cntant cuent cuent n the t ccut I lu vaale cnent X E X I laggng I y 9 a hn n fgue. X 6 laggng 9 ehnd E ade u f t cnent: the I E j X I ji X I X Fgue 4: Cuent lcu f nductve t ccut f nductn t. F the geety f the ha daga hn n fg 4, hee a ght-angled tangle fed ve a E cntant daete t can e een that the ha I tace ut e-ccle a vae f t. X If X take negatve value, lyng eng tadtnally negatve, (ue ynchnu eed f the je X t), equatn 59a dfe t: I ji 59 X he ha I ll tace ut e-ccle el the OA c-dnate, hch the negatve l egn. he ha I ll n lag the aled vltage y an angle geate than 9. h ean negatve e fact (c Ө ) that electc e fl ut f the achne f t t the tat eultng n geneat Oeatn Pg I, a eveal f e fl. Sue caactance njected nt the t ccut thugh the l-ng and f agntude tce that f the leakage eactance X ay, the veall eactance f the t ccut ece jx even thugh tve. Equatn 59a ll n e dfed t E j I ji 59c X X F equatn 59c), the lcu f I a vae f ze t hn n fg 4 el: 9 P a g e.jed.c X

11 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 E j E j X X I Ө Fgue 5: Cuent lcu f the caactve t ccut f nductn achne. It can e een f fgue 4 that the t cuent I lead t the aled vltage E y Ө >9. Cnequently, the leadng e fact C Ө negatve, hch ean that e fl ut f the achne f the t t the tat eultng n geneatng eatn geneatng eatn can e taned at t eed el ynchnu ( P g I X.heefe, the ) y caactve njectn nt the t ccut, uch that the veall eactance f the t ccut ece caactve (.e. njected caactve eactance X c geate than the leakage eactance X ).. Pefance Equatn f an Inductn Mt th Caact Injected at the t. If caact njected nt the t f an nductn t uch that the eactance f caact ( c ) e than the eactance f nduct, l ( c l ), the tque can e deved f the equvalent ccut f fgue 5 el. I a th j X th j X l -j X c th Z th th j j j j l j l Fgue 6:hevenn equvalent ccut f caactve nductn t l X a (64).74 hee th and Z th ae hevenn equvalent vltage and edance eectvely. I as th v j th th l he echancal e develed gven a P I a c 65 (66) Suttutng equatn (68) nt equatn (69) gve 4 P a g e.jed.c

12 Electagnetc que IJED Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 th P 67 th th l c he nut e f the caactve und t nductn t gven y P I a c 68 c = e fact. F caactve laded t, c negatve, and hence the e nut t the t negatve. he develed tque gven y P P (69) heefe uttutng equatn (67) n equatn 69, the develed tque, th 7 th th l c ale.: A 4-le und t nductn t aaete a 4.9 Ω. Ω. Ω X X.5 Ω X Xc 5 Ω.8 Ω F 5Hz ated e 78att P 4 le Ment f neta, J t.kg Dang ceffcent,.9 he value f aaete n tale. ee taned y cntantly changng the value n atla envnent untl aate tque eed cuve taned a hn n fgue 7.. que-seed Chaactetc f the 4-le Wund t Inductn Mt th Leadng Pe Fact. he tque eed chaactetc f the 4-le und t nductn t el (fgue 7 ) taned y uttutng the value f aaete n tale. nt equatn t eed Fgue 7: Inveted tque Seed chaactetc f the 4-le und t nductn t 4 P a g e.jed.c

13 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4. Sulatn eult f the 4-le und t nductn t. he aaete f ulatn f the 4-le und t nductn t ae hn n tale.: he echancal tque the etenally aled tque n the dectn f the t eed. he te and value aay f the echancal tque, ech eeatng equence uce gnal f ulatn f the 4-le und t nductn t hn el: ech _ te = [ ] ech _value = [ ] he ulatn eult f the 4-le und t nductn t ae hn el: Mechancal que e 5 Q-A-ltage D-A ltage e Fgue 8: Sulatn gah f the 4-le und t nductn t 4. Dcun f eult If a caact he eactance tce that f the veall nductn eactance cnnected ac the l-ng f the 4-le und t nductn t uch that the e fact leadng, the t eate th nveted tque aut the eed a. Fgue 6 h the nveted tque-eed chaactetc f an nductn t. he nveted tque a a a eult negatve e taned nce e fact leadng. Ung a t te f ecnd, the 4-le und t nductn t a ulated tatng f et th ated vltage aled and th echancal lad tque f t 9N. t. F the ulatn eult, a the echancal tque change thee a cendng change n eed and electagnetc tque. he d-a vltage and q-a vltage ae nudal. Snce e negatve, the cuted neta cntant negatve. A a eult, the eed nveted a hn n fgue 7. Inductn t tng hen echancal tque negatve and geneatng hen echancal tque tve. 4. Cnclun Wund t nductn t th leadng e fact ha een analyzed. If caact cnnected t the t ndng f the 4-le und t nductn t thugh l ng uch that the eactance caactve (caactve eactance e than veall nductve eactance), the cuent n the ndng ll then e 4 P a g e.jed.c

14 Intenatnal Junal f ecent Engneeng eeach and Develent (IJED) ISSN: jed.c lue Iue 9 Setee 7 PP. -4 leadng the vltage and hence the cuent dectn ll e eveed. h eveal f the cuent ll lead t electagnetc tque n the te dectn t the tatn f the t, hch geneatn eatn. he develed e ece negatve. heefe, the geneatng eatn can e taned at t eed el ynchnu ( ccut ece caactve. ) y caactve njectn nt the t ccut, uch that the veall eactance f the t 5. Acknledgeent he auth jyuly acknledge Gd f H nfnte ecy and kndne dung the eeach k. Gd, We thank yu. efeence []. Chee-un ng,( 997) Dynanac Sulatnlatn f Electc Machney ung Matla/Sulnk Pentce Hall P Ue Saddle ve, Ne Jeey, 7458) PP67. []. P.C Kaue, (98) Analy f Electc Machney, (Pudue Unvety Schl f Electcal Engneeng, Lafayette, Indan 4797:) []. J.B Guta, (9) hey and Pefance f Electcal Machne, (S.K Kataa and Cany, 4446 Guu Nanak Maket, Na Saak Delh-6:) 58, 7 [4]. B.L heaja and K.A, heaja, () Electcal echnlgy,(s. Chand and Cany anaga, Ne Delh-55:)8 [5]. L.U Anh, E.S Oe, E.O Agach,( ) Analytc Synthe f Hytee Mt, Enegy Cnven and Manageent, l.5, 9-96, Junal He Page:.eleve.c/lcate/encnan [6]. A.U Uguda, L.U Anh,( 4) Inductn Mt Baed-ynthe f Hytee Mt,(Electcal Engneeng Nnad Azke Unvety, Aka:)49-5 [7]. G.J ge; J.D Mann and..h Alden (984), An aggegate nductn t del f ndutal lant, IEEE an. Pe aaatu and yte, l. N [8]. J. Wll, G.J Bck and J.S Ednd,(989), Devatn f nductn t del f tandtll fequency ene tet, IEEE an. n enegy cnven, l.4 N [9]. G.J ge, (965), Lneazed analy f nductn t tanent, Pc. Iee, l, []. D.W Nvnty and J.H Wutee, (976), Inductn Machne tanfe functn and cle te vaale,ieee an. Pe aaatu and yte, vl 95 N []. G. Mchen, (98), An ntductn t Electcal Machne and anfe, Jhn Wlley and n, Ne Yk. P P a g e.jed.c