Approaches of Vector Control of a Linear Induction Motor Considering End Effects

Transcription

1 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: 5 Approachs of Vctor Control of a nar Inducton Motor Consdrng End Effcts Hajj Mansour, Barhou El Manâa, Bn Salah Boujâa Abstract In ths work, th da conssts to nz and copnsat th nd ffcts n a lnar nducton achn. To nz ths ffcts a nw ordr s dlopd. Ths control conssts n posng a prar flu so as to ha nal losss. For copnsaton, th aratons du to th nd ffcts ar calculatd b a nural ntwork. Th us of ths aratons aks t possbl to oprat th ctor control to orco ths ffcts. Th dlopd stratgs of ctor control ar snst to th scondar paratrs araton. To cur ths nsuffcnc, anothr approach wll b dlopd. Ind Tr nar Inducton Motor, End Effcts, Vctor Control, Mnzaton, Copnsaton. I. INTRODUCTION nar Inducton Motor (IM) has attractd uch ntrst n sral ndustral applcatons such as th lctrc tracton, ttl ndustrs, autonoous ong robotcs and partcularl n th fld of hgh loct anufacturng that appard rcntl [], []. Th us of thos actuators rprsnts a sutabl choc copard to th altrnats utlzng th rotar achns assocatd to ont transforaton ssts. Th an adantag of th nar Inducton Motor (IM) s th absnc of gars of rotar-to-lnar conrts. Two tps of th otor ar found, sngl-sdd and doublsdd. Sngl-sdd nducton otor (SIMs) ar usd or bcaus of thr spl structur. Th scondar of a SIM conssts of conductng plat backd b a frroagntc atral (back ron) [3], [4], [5]. To analz IMs, w us qualnt crcut odl. Th classcal qualnt crcut dos not allow stung th prforancs of a SIM, bcaus of thr spcfc phnona. Ths work was supportd b th aborator of Analss and Control of Ssts. Dpartnt of Elctrcal Engnrng, Natonal Engnrng School of Tuns, Tuns El Manar Unrst. Mansour Hajj s wth th Natonal Engnrng School of Tuns, Tuns El Manar Unrst. BP 37 l Béldar Tuns, Tunsa (-al: hajj_ansour@ ahoo.fr). El Manâa Barhou s wth th Natonal Engnrng School of Tuns, Tuns El Manar Unrst. BP 37 l Béldar Tuns, Tunsa (phon: ; -al: barhou.anaa@ gal.co). Boujâa Bn Salah s wth th Natonal Engnrng School of Tuns, Tuns El Manar Unrst. BP 37 l Béldar Tuns, Tunsa (-al: boujaa.bnsalah@ nt.rnu.tn). To quantf th phnona calld nd ffct, an rsarchrs ha drd pr-phas qualnt crcut. Duncan [6] dlopd th pr-phas qualnt crcut b odfng th agntzng branch of th qualnt crcut of th rotar nducton otor. Th rlat oton btwn a prar of fnt lngth and an nfnt long scondar causs th nd ffct, whch producs brakng forcs and an adonal loss. Duncan usd th paratr Q to sulat ths ffct [6]. Q R Not that Q s dnsonlss but rprsnts th otor lngth on th noralzd t scal. On ths bass, th otor lngth s clarl dpndnt on th otor loct so that at zro loct, th otor lngth s nfntl long. As th loct rss, th otor lngth wll ffctl shrnk. Th total agntzng nductanc n Duncan s odl s: pq ( Q) Q Notc that, as th loct tnds to zro, or th otor lngth tnds to nfnt, th agntzng branch nductanc bcos and th lnar nducton otor s dntcal to th rotar otor as th nd ffct dsappars. Th powr loss du to th nd ffct can b rprsntd as a srall connctd rsstor n th agntzng branch. pq R( Q) R Q II. MODE OF THE INEAR INDUCTION MOTOR Th (q) as qualnt crcut of th IM s dntcal to th (q) as qualnt crcut of th rotar nducton otor (RIM),.. th paratrs do not ar wth th nd ffcts. Howr, th (d) as ntr scondar currnts affct th ar gap flu b dcrasng ( ). Thrfor, th (d) as qualnt crcut of th RIM cannot b usd n th IM analss whn th nd ffcts ar consdrd. Fro th qualnt crcut of th IM (Fg.), th prar and scondar oltags quaton n a snchronous rfrnc sst algnd wth th scondar flu ar gn b []-[]: d R R ( Q) (4) () () (3) IJET-IJENS Aprl 3 IJENS

2 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: 53 d R (5) d R R Q (6) q Rq sl (7) Whr: ( Q) ( Q) (8) (9) q ( Q) ( Q) () () q q Whl rfrrng to th prcdng quatons, th prar and scondar currnts ar gn b: q ( Q) ( Q) ( Q) ( Q) ( Q) q ( Q) ( Q) ( Q) ( Q) ( Q) q Fro (7) and () th slp frqunc s obtand as followd: () (3) (4) (5) R q sl T (6) Th slp frqunc quaton sl s th sa as that of th conntonal nducton otor. Th an dffrnc s th charactrstc. R R ω ϕ ω ϕ a. q-as qualnt crcut b. d-as qualnt crcut Fg.. dq-qualnt crcut of th IM wth nd ffcts Fro (6) and (), w obtand: l l l + + R f Q f Q l ω sl ϕ q ω sl ϕ R q R q R f Q s f Q R f Q Th thrust forc s gn b: (7) 3 F p (8) Aftr a long anpulaton of th quaton (8), w obtan: F p l f Q 3 ( Q) f Q f Q (9) Th scondar slf nductanc l, bcaus th lakag nductanc l. In ths cas, th thrust forc F dos not drctl dpnd on Q. For that, th dpndnc of F to th spd appars not to b as sgnfcant as s kpt constant. Thraftr, t wll b shown, b sulaton, that th dpndnc of to Q s larg. Thrfor, th thrust forc F bcos: f Q F p l f Q F F 3 () Startng fro th prcdng quaton, th thrust forc s not proportonal to, du to th stnc of th scond tr n (9) whch s producd b th d currnt loss. Th scond tr alwas has th oppost sgn, thus s calld nac brakng forc [5]. In an tr cas such that rgnc stop s ncssar; th nac brakng forc a b usd to assst th otor to stop. But, th nac brakng forc should b copnsatd to ach a lnar rlatonshp btwn F and. III. ORIENTED VECTOR CONTRO WITH MINIMIZATION OF END EFFECTS In conntonal ctor control (wthout nzaton), th nd ffcts g rs to a araton of th prar currnts and, thrfor b ncras of losss n ths tp of actuator. To dlop an ordr wth nzaton of nd ffcts, suons us brought to pos a arabl scondar flu accordng to th opratng conons. Th alu of ths flu s calculatd b nzaton th losss n ths tp of otor. For th sta stat, quaton (4)-(7) can b transfor to ()-(4) R R f Q () d R () R R f Q (3) q Rq sl (4) A. Assssnt of th losss Iron losss ar gn b th followng prsson: P R Q (5) F IJET-IJENS Aprl 3 IJENS

3 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: 54 Prar coppr losss ar gn b: c P R (6) Scondar coppr losss ar prssd b th followng quaton: c q P R (7) Total losss n a lnar nducton otor ar obtand startng fro th quatons (5)-(7): Pt PF Pc Pc (8) Th nd ffcts caus a araton of th prar currnts; thrfor w calculatd th total losss accordng to ths currnts. W prssd th scondar currnts accordng to th prar currnt n th followng quatons: f( Q) (9) f( Q) q (3) r Fro (5)-(3), total losss ar gn b []: P R R (3) Whr: t d ds q qs f( Q) Rd R R f( Q) Rq R R Spd controllr flu IP staton F ϕ F ϕ F ϕ (3) (33) 3 P π (Q) ϕ τ f Q R f Q s f Q +R +f Q dq abc θ f( Q) f ( Q) Th forc s prssd b: r (34) F p p p (35) Fro (3)-(33), t follows, q q q f( Q F t d q f ( Q) 3 p P R R Whr: F A B f( Q) A Rd f ( Q ) B Rq 3 p (36) (37) (38) If w want to gan th nu P t (nu nd ffcts), thn Pt F A B As a consqunc a b c a Currnt controllr b dq c abc a b c a b 3 IM E c (39) qs l qs f Q f Q ϕ R ϕ ω sl ω ω θ π τ Fg.. Block dagra of th proposd ctor control sch consdrng th nd ffcts W not that f (Q) R f (Q) rprsnts th losss du to th nds ffcts. Prar currnt can b prssd accordng to as follows: * B 4 F (4) A IJET-IJENS Aprl 3 IJENS

4 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: 55 * Fro (4), th scondar agntc flu corrspondng to nu nd ffcts s dtrnd b forc F and spd. B. Sulaton rsults Th tp of tst s achn that s consdrd n ths work s lnar nducton otor wth spl prar. Its prar s thr phas connctd n star. It s charactrzd b th paratrs prsntd n tabl I. Th bloc dagra of th proposd ctor control consdrng th nd ffct s gn b Fg.. Th al of ths control approach, laboratd to rgulat th scondar spd, s ralzd b nurc sulaton usng th Sulnk ntrfac of th Matlab nronnt. At no load, th rsults obtand b th two thods ar dntcal. Ths da nabls us to ha a good flung of th achn. At load, th curs rprsntng th currnts and flu ar dffrnt. Indd, currnt s qual to 36.3A for conntonal thod and qual to 66.A for th proposd thod. f (Q) f (Q) f (Q) f (Q) (4) f Q f Q t(s).5.5 a- Prar currnt d- Prar flu ϕ 5 5 t(s).5.5 b- Prar currnt t(s).5.5 c- Scondar flu ϕ f- Forcs du to th nd ffcts Spd Fg. 3. Rspons of loct control wth nd ffcts (: wthout nzaton; : wth nzaton) t(s) IV. SECONDARY FUX ORIENTED VECTOR CONTRO WITH COMPENSATION OF END EFFECTS In a IM, th nd ffcts ar prssd b both th gnraton and th dsapparanc of th fld that crat th d currnt n th racton ral. Th ar gap flu s or affctd b th d currnt. For ths rason, th lnkag flu ϕ s sparat n two portons: th frst s ndpndnt of th nd ffcts (.744Wb ), whl th scond dscrbs th lnkag flu that s du to th nd ffcts ( ). (4) A. Basc da for th copnsaton Th IM s prar currnts ar sparabl nto two portons. Th frst porton s th currnt n a conntonal achn and th scondar porton s a currnt du to th IM s nd ffcts. Basd on quaton (7), th prar currnt s []: For no load, scondar flu s fd at ts nonal alu (.744Wb ) to ha a good flung of th achn. For a gn load, flu ars accordng to ths load and spd forcd so as to ha a nal nd ffcts. Th rsults of sulaton show that th nflunc of th nd ffcts on currnt s or sgnfcant than that on currnt. Indd, for a spd of /s, th araton of s about 48A whras th araton of s approatl 5A. Whr: (43) f Q f Q Basd on quaton (8), th prar currnt s: F 3 P l f( Q) f( Q) Aftr a long anpulaton of th quaton (45), w obtand: F 3 P A F 3 P A (44) (45) (46) IJET-IJENS Aprl 3 IJENS

5 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: 56 Whr: A l f( Q) f ( Q ) (47) F (48) 3 P A F 3 p A (49) B. Nural Ntwork Th (d, q) currnts dpndnt of th nd ffcts ( ds and qs ) ar rlatd to. To calculat n ral t, a nuronal odl s usd. Th nputs of th Nural Ntwork (NN) ar th scondar spd and th load forc F l, th output of th NN s th araton of du to th nd ffcts. Th connct wghts and bass of th NN ar adjustd b a data bas to produc. Th nural ntwork undrstands thr lars; - Input lar: In th nput lar, th nput ctor of th NN s th scondar spd and th load forc: k k k, k fk k 6 (5) Wkk k f,, (5) Whr W k ar th conncts wghts btwn th nput and hddn lars; ar th thrshold alus for th unts n th k hddn lar; f s th actaton functon, whch s a sgod functon. - Output lar: j Wj k f j j j j j (53) Whr W j ar th connct wghts btwn th hddn and th output lars; θk C. Sulaton rsults Th stratg of control wth copnsaton conssts n actng on dffrnt rgulators to pos and such as arabls of control. Fg. 4 shows th sulaton rsults wth copnsaton of th nd ffcts. Indd, th scondar flu and th prar currnts ( and ) ar alost qual to thr rfrncs (.75Wb, = 85.3A, and = 4.3A). Wth ths stratg of control, th nd ffcts ar copnsatd. It s to b announcd that wth th copnsaton thod, th forc du to th nd ffcts s not copltl nutralzd. It s about (-47N) a- Prar currnt b- Prar currnt d- Prar flu ϕ Spd Fg. 4. Rsults obtand wth copnsaton of th nd ffcts.5.5 c- Scondar flu ϕ d- Forc du to th nd ffcts V.PRIMARY FUX ORIENTED VECTOR CONTRO Th control stratgs dlopd prousl ar r snst to th scondar paratrs araton. To cur ths nsuffcnc, anothr approach of ctor control basd on th prar flu orntd s dlopd. Whr: () t, F () t (5) - Hddn lar: l Th d currnt loss of th scondar conductor ust b to dscrb b a paralll rsstor, sa as th cor loss [4]. Howr, n Duncan s odl, th d currnt loss s dscrbd b a srs rsstor. In ths phas stu, w nglctd th d currnt loss (R.f(Q)). Howr, th ncluson of th loss branch ncrass th coplt of th quaton gratl, whlst th prsnc or absnc of th loss branch dos not ak a sgnfcant dffrnc n th currnt nacs unlss SIM s ong at a r hgh spd [4] IJET-IJENS Aprl 3 IJENS

6 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: 57 Th da rans unchangd; t s a quston of actng n nstantanous and ndpndnt annr on th phas and th apltud of th prar oltag, so as to rgulat currnt wthout odfng flu. A. Mathatcal quatons of th achn Th prar and scondar oltags quatons ar gn b [4], [3]: d R (54) R (55) R d (56) R dq (57) sl q q q sl Th dq-as flu lnkags of prar and scondar ar gn b: ( Q) ( Q) (58) ( Q) ( Q) (59) q ( Q) ( Q) (6) ( Q) ( Q) (6) q q q ( Q) ( Q) q Q Q Q ( ) ( ) ( Q) ( Q) ( Q) ( Q) ( Q) ( Q) q ( Q) ( Q) ( Q) ( Q) (63) (64) (65) Th prar quatons (54) and (55) consttut th stators hoologous wth thos of th control basd on scondar flu orntd. Indd, th spd rsults drctl fro th followng rlaton: R (66) And th flu s prssd drctl startng fro th followng forula: t R (67) IP Spd control ϕ F ϕ F ϕ sl σ(q) d = q = ϕ π τ π Q T Q σ Q τ g T Q +T Q σ Q d u u dq abc θ a b c E ϕ ϕ = ( R ) dq a b θ θ = R ϕ τ π du abc a b IM F F = π τ p ϕ R Q σ Q Q R + Q σ Q π τ g sl Estaton block Fg. 5. Block dagra of th prar flu orntd ctor control Ths two functons (66) and (67) show sgnfcant snstt to th aratons of prar rsstanc. To not that bcaus of th nd ffcts, th control of prar rsstanc s asr wth th oluton of scondar rsstanc. Whl rfrrng to th prcdng quatons, th prar and scondar currnts ar gn b: ( Q) ( Q) ( Q) ( Q) ( Q) (6) W show that thr s a slar proprt n th cas of prar flu orntd. Th scondar quatons (56) and (57) of th odl ar ntall transford to ral th scondar szs. Th scondar currnts rsult fro th prsson of prar flu. Q Q Q Q (68) q (69) IJET-IJENS Aprl 3 IJENS

7 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: 58 Undr ths conons, scondar flus ar wrttn: Q Q Q Q Q Q Q Q Q q Q (7) (7) What carrs out th nw sst of scondar quatons, ar: d d T ( Q) Q T QQ (7) T Q Q Q sl Q Q d T Q Q T Q (73) B cobnng ths two last quatons to lnat, w prss accordng to spd sl, t cos: T Q Q d Q T Q Q T QQ Th forula gng th forc bcos: (74) 3 3 F p p. TQ Q sl d Q T Q Q T QQ (75) In sta stat, th drat bcos null and, aftr hang prssd T (Q), th prsson (75) bcos: Ths last quaton assocatd wth th prsson (55) odls th lctrc part ss two ono-arabl procsss coupld b th arabls of dsturbanc d and q such as: Whr d T Q T Q Q T Q T Q d T Q QT Q d d (78) R q (79) d q Q QT Q d T Q Q T Q (8) B. Sulaton rsults For ths control, th adjustnt structur s gn b fg. 5. For th ctor control wth prar flu orntd, fg. 6, prar flu rans constant and qual to.4wb whras scondar flu dcrass accordng to spd. Currnt undrgos a wakr araton copard to th frst stratg. Th prar currnt dos not undrgo an araton. Th nd ffcts forc s about 7N for a spd qual to /s. 3 R Q Q F p sl (76) Q R Q In th quaton (54), w prss startng fro th prsson (7). It cos: d T Q R Q d QT Q R QTQ d d QT Q (77) IJET-IJENS Aprl 3 IJENS

8 Intrnatonal Journal of Engnrng & Tchnolog IJET-IJENS Vol:3 No: a- Prar currnt b- Prar currnt c- Scondar flu ϕ d- Prar flu ϕ - Spd f- Forc du to th nd ffcts Fg. 6. Rsults obtand b th scondar flu orntd ctor control VI. CONCUSION Th nzaton and copnsaton of th nd ffcts n a IM consttuts th prncpal th n ths papr. For that, an approach of odlng s dlopd to hold account th nd ffcts whch charactrz ths tp of achn. Th nzaton da conssts n forcng scondar flu ( ) so as to ha nal losss. Ths stratg shows that currnt dcrass whras currnt ncrass. Ths chang lad to good rsults. Th stratg of copnsaton conssts n statng th prar flu araton b a Nural Ntwork. Ths flu s usd to dtrn th scondar currnts dpndnt of th nd ffcts. Th copnsaton s nsurd b acton on th dffrnt rgulators. Th obtand sulaton rsults show that th nd ffcts can b copnsatd. Th control stratgs dlopd prousl ar r snst to th scondar paratrs araton. To cur ths nsuffcnc, anothr approach of ctor control basd on th prar flu orntd s dlopd. REFERENCES [] GIERAS, J. F., nar Inducton Drs, Oford, U. K. Clarndon Prss, 994. [] BHATIA, R. P. and SNIDER, D. R., Thrust Eprssons for Inducton Motors wth Thn Conductng Scondars, IEEE Trans. Magn., Vol. 6, No., pp. -6, March 99. [3] GIERAS, J. F., DAWSON, G. E. and EASTHAM, A. R., A nw longtudnal nd ffct factor for lnar nducton otors, IEEE Transacton on Enrg Conrson, Vol. EC-, No., pp. 5-59, March 987. [4] KAN, G. and NAM, K., Fld-orntd control sch for lnar nducton otor wth th nd ffct, IEE, Proc. Elctr. Powr Appl. Vol. 5, No. 6, pp , Nobr 5. [5] SUNG, J. H. and NAM, K., A Nw Approach to Vctor Control for nar Inducton Motor Consdrng End Effcts, IEEE IAS annual tng, Phon, Arzona, pp , Octobr 3-7, 999. [6] DUNCAN, J. and ENG, C., nar nducton otor-qualnt crcut odl, IEE Proc., Elctr. Powr Appl. Vol. 3, No., pp. 5-57, Januar 983. [7] DA SIVA, E. F., DOS SANTOS, E. B., MACHADO, P. C. M. and DE OIVEIRA, M. A. A., Dnac Modl for nar Inducton Motors, IEEE ICIT Confrnc, Marbor, Slona, pp , 3. [8] DA SIVA, E. F., DOS SANTOS, E. B., MACHADO, P. C. M. and DE OIVEIRA, M. A. A., Vctor Control for nar Inducton Motor, IEEE ICIT Confrnc, Marbor, Slona, pp , 3. [9] DA SIVA, E. F., DOS SANTOS, E. B. and DE NERYS, J. W.., Fld orntd Control for nar Inducton Motor Takng nto Account End ffcts, IEEE Intrnatonal workshop on Adancd Moton, Kawasak, Japan, pp , 4. [] HAJJI, M., NASR KHOIDJA, M. A. and BEN SAAH, B., Drct thrust control of a nar Inducton Motor wth nd ffcts, Intrnatonal Rw of Elctrcal Engnrng, Vol. 4, No. 4, pp , Jul- August 9. [] HAJJI, M., NASR KHOIDJA,M. A., BARHOUMI, E. M., and BEN SAAH, B., Vctor Control for nar Inducton Machn wth Mnzaton of th nd ffcts Th Frst Intrnatonal Confrnc on Rnwabl Enrg and Vhcular Tchnolog, REVET, March 6-8,, Haat-Tunsa. [] HAJJI, M., NASR KHOIDJA, M. A. and BEN SAAH, B., Vctor control for nar Inducton Motor wth Copnsaton of th nd ffct, Intrnatonal Rw on Modlng and Sulaton, Cod ISSN , Vol. 4, No., pp. -6, Fbruar. [3] HAJJI, M., NASR KHOIDJA, M. A. and BEN SAAH, B., Vctor Control for nar Inducton Machn Consdrng End Effcts th th Intrnatonal Confrnc on Scncs and Tchnqus of Autoatc Control and Coputr Engnrng, Dcbr 8-,, Souss, Tunsa. APPENDIX TABE I DESIGN DATA OF THE P ROPOSED SIM Sbol Quantt Valu τ Pol ptch 5 p Nubr of pols 6 Rsstanc of prar pr.968ω phas Rsstanc of scondar pr.56ω phas Slf nductanc of prar.64 H Slf nductanc of scondar.396 H Mutual nductanc.393 H IJET-IJENS Aprl 3 IJENS