Itatioal Joual o Elctical Egiig ad Ifomatic - Volum 7, Numb 3, Sptmb 5 Faid Boumaaf, M.L. Bdaa, Rachid Abdmd, ad Sbti Blkacm LEB- Rach Laboatoy, Dpatmt of Elctical Egiig, Uivity of Bata Algia faidltb@yahoo.f Abtact: Th pt pap popo a ovl Doubly Fd Iductio Machi (DFIM) cotol tatgy uig Dict Toqu Cotol (DTC) likd with two Switchig Tabl i od to cotol lctomagtic toqu of DFIM via tato ad oto flux vcto. Th popod chm i dcibd claly ad imulatio ult a potd to dmotat it ffctiv. Th ti cotol chm i implmtd with Matlab/Simulik. Kywod: Dual dict toqu cotol, doubly fd iductio machi, witchig tabl.. Itoductio Du to it xcllt pd cotollability, ducd covt iz, high pfomac ad lativly low cot compad to oth machi []. Doubly-fd iductio machi hav b popod i th litatu, amog oth idutial applicatio a moto i high pow applicatio uch a tactio, mai populio o a gato i wid gy covio ytm lik wid tubi, o pumpd toag ytm. Sval mthod of cotol a ud to cotol th doubly fd iductio machi amog which th vcto cotol o fild oitatio cotol that allow a dcouplig btw th toqu ad th flux, i od to obtai a idpdt cotol of toqu ad th flux lik DC moto [3]. Thfo, dcouplig th cotol chm i quid by compatio of th couplig ffct btw q- axi ad d-axi cut dyamic. It i wll kow that vcto cotol d quit complicatd to o li coodiat tafom to dcoupl th itactio btw flux cotol ad toqu cotol i od to povid a fat toqu cotol. I ct ya a iovativ cotol mthod, calld dict toqu cotol ha gaid th attactio of ach. Dict toqu cotol (DTC) tatgy wa itoducd by Takahahi to giv a fat ad good dyamic pfomac ad ca b coidd a a altativ to th fild oitd cotol (FOC) tatgy [4]. Thfo, i ct ya th idutial applicatio aa of th high pfomac AC div bad o DTC tchiqu hav gadually icad du to th followig advatag ov th fild oitd cotol tchiqu, uch a Excllt dyamic pfomac, pci ad quick cotol of tato flux ad lctomagtic toqu, abc of co-odiat tafomatio, which duc th complxity of algoithm ivolvd i FOC, obut agait machi paamt vaiatio ad o cut cotol loop. I thi tudy a w Dual-Dict Toqu Cotol chm i dvlopd with flux modl of DFIM. Two Switchig Tabl (ST) likd to VSI a dfid fo tato ad oto flux vcto cotol. W popo paat cotol of tato ad oto flux. I fact, i od to applid DTC tatgy to thi cofiguatio, w dfi a fit witchig tabl to cotol th tato flux vcto, ad a cod witchig tabl to cotol th oto flux vcto. Th xt pat of th cotol tatgy mak poibl to cotol itactio btw both flux vcto. Coqutly, w a abl to cotol th lctomagtic toqu ad to gulat th mchaical pd [3]. Th pfomac of uch a chm dpd o th o bad t btw th did ad maud tato ad oto flux valu. I thi cotol chm, th tato ivt witchig fqucy i chagd accodig to th hyti badwidth of tato flux ad tato flux agula poitio, ad th oto ivt witchig fqucy i chagd accodig to th hyti badwidth of oto flux ad oto flux agula poitio. Rcivd: Novmb th, 3. Accptd: Sptmb t, 5 DOI:.5676/iji.5.7.3.5 54
Faid Boumaaf, t al.. Mathmatical modl of DFIM Th modl of th-pha doubly fd iductio machi i th laboatoy fam (α,β) i giv by th followig quatio (): d V RI dt d V RI () dt d V R I ω dt d V R I ω dt LI μi, LI μi () L I μi, L I μi R β S β I I Sβ I R α ω θ S α Figu. Two pha fc fam Ad th lctomagtic toqu of doubly fd iductio machi ca b xpd a: 3 N p.μ T. (3) σ.l.l Wh T i th lctomagtic toqu, Np i th umb of Pol pai, tato ad oto lf iductac, μ i th mutual iductac ad, oto flux pac vcto ad μ σ i th lakag cofficit. W ca u: L L γ L, L a th a th tato ad T K. i (4) I Sα γ i th agl btw tato ad oto flux a how i Fig. Thi agl i fd 3Npμ K a toqu agl. Th cotat K i dfid a blow: σσ L Y γ C X Z Figu. Flux Vcto Diagam of DFIM 54
Figu how thi fc fam wh I, I a th tato cut, ad I, I th oto cut. W ca xp th two-pha quatio dcibig th lctical bhavio a blow [3]: L μ(θ) α,β (5) T μ(θ) L α,β Wh: 4.π.π co(θ) co(θ+ ) co(θ+ ) 3 3.π 4.π μ θ =μ. co(θ+ ) co(θ) co(θ+ ) (6) 3 3 4.π.π co(θ+ ) co(θ+ ) co(θ) 3 3 W xp th Laplac opato a ad obtai om ditubac tm otd P,P,P, P dfid a follow: P P P μ σ.t.l μ σ.t.l μ σ.t.l ( ( ( iθ iθ iθ coθ) coθ) coθ) μ P ( iθ coθ) β α σ.t.l Wh: L L T,T R R Th tato ad oto tamittac tm a dfid a: σ.t T () σ.t. (8) σ.t T () σ.t. It ca b fom (5), (7) ad (8) that th DFIM i flux mod ca b ptd a how i figu 3. P (7) V P T () V P T () V P T () V T() Figu 3. Bloc diagam of DFIM flux modl. 543
Faid Boumaaf, t al. Th tato ad oto flux vcto,, a obtaid by itgatig th moto mf pac vcto, maud tato ad oto cut, tato ad oto itac. () () t t (V R (V R.I )dt.i )dt Duig th witchig itval,, T w hav: V >>R.I Et V >>R.I. W ca xp: (t) (t) V.T V.T W adopt a tadad aumptio fo th coidd fquci. It coit i glctig th itiv ffct i th widig compad with th iductiv ffct. W ca obv that thi aumptio i pcially valid fo high pow machi. Coqutly, w ca xp [3]: σt.s,fo : σt.s,fo : So: σ.t T () σ.t. σ.t T () σ.t.,, wh : wh : A cod aumptio i ud. It coit i glctig th couplig tm (9) () () () P,P,P, P Thi ca b do bcau th couplig tm a a low valu i latio to th omial valu of th voltag lvl V,V,V, V If w u th ig fo th omial valu of th coidd tm, thi aumptio ca b xpd a blow [3]: P V,P V P V,P V Accodig to th quatio (), that th flux xpio a th voltag itgal, ad by uig th two lut aumptio, w ca fomulat th DFIM global modl a how i Figu 4. (3) U U U 3 Stato V T T U U U 3 Roto V Figu 4. Block chm of VSI ad DFIM. 544
3. Dual dict toqu cotol tatgy Th baic ida of DTC dpd o th o bad t btw th did ad maud toqu ad flux valu, th ivt witchig fqucy i chagd accodig to th hyti badwidth of flux ad toqu cotoll ad th vaiatio of pd ad moto paamt. I thi pap; w popo paat cotol of tato ad oto flux. I fact, i od to applid dual DTC tatgy to thi cofiguatio, w dfi a fit witchig tabl to cotol th tato flux vcto with hi agula poitio, ad a cod witchig tabl to cotol th oto flux vcto with hi agula poitio. Th xt pat of th cotol tatgy mak poibl to cotol itactio btw both flux vcto. Coqutly, w a abl to cotol th lctomagtic toqu ad to gulat th mchaical pd [3]. 4. Dual DTC applid to th DFIM Fom quatio (4) it i cla that th DFIM toqu ca b vaid by chagig th oto o tato flux vcto. Th dual DTC u th hyti bad to dictly cotol th tato flux ad hi agula poitio ρ ad oto flux with hi agula poitio ρ of th DFIM. Wh th tato o oto flux fall out-id th hyti bad, th ivt witchig tato o oto i chagd o that th flux tak a optimal path towad. So VSI output (tato ad oto) ca b dducd fom two timatd ad two quid valu of tato ad oto flux. A. Vcto flux cotol Th quatio () ca b ay tafomd to: Δ () V.T Δ So: (t (t ) ) () V.T (t (t ) ) T.V T.V (t (t ) ) Th voltag vcto applicatio tim T qual to amplig tim).coqutly, mai cotat duig th itval T, T. Wh: T T T T.V T.V (4) (5) V, V (6) R β S β T.V T.V Compot Compo t fo flux R Figu 5. Stato ad oto flux vcto dviatio. S 545
Faid Boumaaf, t al. By glctig th tato ad oto itac, () impli that th d of th tato ad oto flux vcto will mov i th dictio of th applid voltag vcto a how i thi figu. Th appopiat voltag vcto o VSI output ca b dducd fom two timatd ad two quid valu of tato ad oto flux. To lct th voltag vcto fo cotollig th amplitud of th tato ad oto flux likag, th voltag vcto pla i dividd ito ix gio, a how i Figu.5. β α Figu 6. Applicabl voltag vcto fo tato ad oto flux vcto cotol. I ach gio, two adjact voltag vcto, which giv th miimum witchig fqucy, a lctd to ica o dca th flux amplitud. If V i applid, th magitud of, ica. Wh a th agula poitio ρ, of, dca. Wh a pcific voltag vcto i applid, th volutio of ρ, ad th magitud of, ca diff accodig to th ρ, iitial valu. Coqutly, if, i i th am cto, u of idtical voltag vcto lad to a imila pha ad magitud volutio of th flux vcto. W maag th oto flux vcto i th am way. Thu, th voltag vcto to apply dpd o: - Th cto umb (accodig to ρ, ), - Th quid flux agula poitio, - Th quid flux magitud volutio. β (,) T. (, ) T. V (,)4 V (,)3 T. T., V (,) T. V T. V (,)5 (, )6 V (,) 3 4, ρ, α 5 6 V,V7 Figu 7. Scto dfiitio i ( α,β) fc fam. 546
Fo itac, vcto a lctd to ica ad dca th amplitud of flux vcto ad ou agula poitio a: if V (,)i i lctd th, ica ad ρ, ica; if V (,)i i lctd th, ica ad ρ, dca; if V (,)i i lctd th, dca ad ρ, ica; if V (,)i i lctd th, dca ad ρ, dca. B. Stato ad oto flux timatio Th magitud of tato ad oto flux, which ca b timatd a followig t t (V (V R R.I.I )dt )dt (7) Th tato ad oto flux likag phao a giv by:, (8) Th tato ad oto flux likag phao poitio a: ρ ta,ρ ta (9) C. Flux cocto I thi dual DTC w a dd to u fou hyti compaato: two tato hyti compaato i od to cotol th tato flux magitud ad hi agula poitio.th output of th compaato a coctd to tato witchig tabl; ad two oto hyti compaato i od to cotol th oto flux magitud ad hi agula poitio ρ. Th output of th compaato a coctd to oto witchig tabl. Th iput of th fo compaato i th diffc btw fc valu ad timatd valu of flux magitud ad agula poitio; flux magitud fc valu ff ad ff a cotat ad qual to thi omial valu. Fo th tato flux fc ρ, th flux poitio valu dpd oly o maud mchaical pd. Fo th oto flux fc ff ρ ff th flux poitio valu dpd o toqu agl γ, oto poitio θ ad tato flux poitio fc ρ ff a how i (). Th output of th compaato with th umb of cto at which th tato ad oto flux pac vcto i locatd ( ρ, ) a fd to a witchig tabl to lct a appopiat ivt voltag vcto. Th lctd voltag vcto will b applid to th DFIM at th d of th ampl tim, a a how i (8) 547
Faid Boumaaf, t al. V V5 4 V 4 V 3 V 5 V 6 3 V 4 V 3 V 5 4 V V 6 5 6 V 3 V V V V 6 V V Figu 8. Fomig of th (tato ad oto) flux tajctoy by appopiat voltag vcto lctio. Δ, (,)ff Δ, Δ, Δ, Figu 9. Th hyti cotoll. D. Elaboatio of th witchig tabl (, )ff (,) Figu. Bloc diagam of th dual DTC of th DFIM Fo th tato ad oto flux vcto layig i cto (Figu 7) i od to ica it magitud th voltag vcto V, V6 ca b lctd. Covly, a dca ca b obtaid 548
Toqu(N.m) Spd(Rd/) by lctig V 3, V5. Fo th tato ad oto flux agula poitio ρ, i ud thfo, to ica it th voltag vcto V, V3 ca b lctd ad to dca V 6, V5. Th abov coidatio allow cotuctio of th lctio tabl a: Scto umb Toqu Flux volutio 3 4 5 6 T ρ Voltag vcto, V V3 V4 V5 V6 V V6 V V V3 V4 V5 V3 V4 V5 V6 V V V5 V6 V V V3 V4 Switchig tabl Th ovall tuctu of th popod cotol i how i figu. 5. Simulatio ult To vify th ffctiv of th popod dual DTC of th doubly fd iductio machi; th imulatio a pfomd by uig th MATLAB/Simulik. I th pfomd imulatio th pd, toqu, tato ad oto flux ad cut po ha b aalyzd i taitoi ad tady tat. A. Spd val 5 5-5 - -5.5.5.5 3 3.5 4 Tim() 5-5 -.5.5.5 3 3.5 4 Tim(S) 549
Faid Boumaaf, t al., (wb).5.5.5.5 Tim(S).5 3 3.5 4.5, (Wb).5 -.5 - -.5 -.5 - -.5,.5.5 (Wb) 5 I, I (A) I, I (A) 4 3 -.4.6 Tim(S).8 - -.5.5.5 3 3.5 4 Tim(S) I,I (A) 4 3 I,I (A) 5 -.4.6 Tim.8 - -.5.5.5 3 3.5 4 Tim Figu. Simulatio ult fo pd val Th DFIM fc pd i chagd fom ad/ to - ad/ at ad th agai, pd i chagd fom -d/ to d/ at ad th, pd i t to - ad/ at 3. without ay chag i paamt duig th opatig tim. Th pfomac of th popod cotoll fo uch kid of pd fc i how i Figu. Plot th fc pd ad, actual DFIM pd with pct to tim. It i obvd that th actual DFIM pd follow th fc with good accuacy. 55
I I (A) I I (A) (Wb) Spd(Rd/) Toqu(N.m) B. Vaiatio of th load toqu 8 6 4.5.5.5 3 3.5 4 Tim(S) 8 6 4 load toqu applid load toqu movd.5.5.5 3 3.5 4 Tim(S).5.5.5.5.5 3 3.5 4 Tim(S) 4 3 -..4.6.8 Tim(S) - -.5.5.5 3 3.5 4 Tim(S) Figu. Simulatio ult ud load toqu chag Figu dpict th imulatio ult aft th itoductio of load toqu of 8 Nm btw ad aft a ladl tatig. W ca th iibility of th cotol algoithm to load toqu vaiatio ad th tato ad oto flux po a l affctd by thi ptubatio. 55
Rfc of oto itac, (Wb) Spd(Rd/) Rfc of tato itac Faid Boumaaf, t al. C. Vaiatio i th tato itac.5.5.5.5.5 3 3.5 4 Tim(S) 8 6 4.5.5.5 3 3.5 4 Tim(S).5.5.5.5.5 3 3.5 4 Tim(S) Figu 3. Simulatio ult ud tato itac chag Th tt ivtigat th ifluc of th lctical paamt chag o th div pfomac. Figu3 dpict th div pfomac fo buqu chag i th tato itac. it ca b that th impact of th lctical paamt chag o th div pfomac i mo impotat. Howv, tho ult how alo that th div obut ad jctio of th ptubatio i igificatly hacd. D. Vaiatio i th oto itac.5.5.5.5.5.5 3 3.5 4 Tim(S) 55
, (Wb) Spd(Rd/) (Wb) Spd(Rd/) 8 6 4.5.5.5 3 3.5 4 Tim(S).5.5.5.5.5 3 3.5 4 Tim(S) Figu 4. Simulatio ult ud oto itac chag Figu 4 dpict th imulatio ult aft th itoductio of th oto itac chag btw ad 3. E. Vaiatio i th itia cofficit Figu5 how th div dyamic ud difft valu of itia with cotat pd fc. It i cla that th pd tackig i littl affctd by tho chag. 8 6 J=.5*J J=J J=*J 4.5.5.5 3 3.5 4 Tim(S).4..8.6.4..5.5.5 3 3.5 4 Tim(S) Figu 5. Simulatio ult ud difft itia valu 6. Cocluio A ovl doubly Fd Iductio Machi (DFIM) cotol tatgy uig Dual dict toqu cotol ha b ptd i thi pap. Two Voltag Souc Ivt (VSI) fd th tato 553
Faid Boumaaf, t al. ad oto widig, ad Two Switchig Tabl (ST) likd to VSI a dfid fo tato ad oto flux vcto cotol i od to cotol lctomagtic toqu of DFIM via tato ad oto flux vcto. Th complt dyamic modl of th dual DTC ytm i dvlopd ad imulatd by uig MATLAB-SIMULINK. Th coct flux vcto cotol bhavio, toqu ad pd tackig pfomac how i th imulatio ult cofim th fat ad good po of th popod div ytm ad thi obut to th vaiatio of moto mchaical ad lctical paamt vaiatio. Th majo diadvatag of dual DTC cotol i th tady tat ippl i toqu ad flux. To ovcom thi poblm w a goig to itoduc th itlligt tchiqu. 7. Rfc []. W. Chg, L. Xu Toqu ad Ractiv Pow Cotol of a Doubly-Fd Iductio Machi by Poitio Sol Schm, -783-993-94 $4. 994 IEEE. []. A. Faokh Payam A Adaptiv Backtppig Cotoll fo Doubly-Fd Iductio Machi Div,-783-977-X/6/$. 6 IEEE. [3]. F. Bot, P Vidal ad M pitzk-david, Dual Dict Toqu cotol Of Doubly fd Iductio Machi, IEEE Ta Idutial Elctoic, vol, 54, No, 5, Octob 7. [4]. B. Roby, B. Façoi, P. Dgobt t J. P. Hauti, Commad Vctoill d la Machi Aycho: Déibiliatio t Optimiatio pa la Logiqu flou, Editio Tchip, Pai, 7. [5]. J. Soltai, A. Faokh payam, M.A. Abbaia, Spd Sol Slidig-Mod cotoll Fo Doubly-Fd Iductio Machi Div Adaptiv Backtppig Obv", -444-76-5/6/.;6, IEEE. [6]. F. Zidai, D. Diallo, M. E. H. Bbouzid ad R. Na ıt-sa ıd, Dict Toqu Cotol of Iductio Moto with Fuzzy Stato Ritac Adaptatio, IEEE Taactio o Egy Covio, VOL., NO., JUNE 6 [7]. N.R.N. Idi, C.L. Toh ad M.E. Elbuluk, A Nw Toqu ad Flux Cotoll fo Dict Toqu Cotol of Iductio Machi, IEEE Taactio o Idutial Applicatio, Vol. 4, No. 6, pp. 358 366, Novmb- Dcmb 6. [8]. S. Baicha, R. Nait Said, F. Zidai ad M.S. Nait. Said Dict Toqu with Fuzzy Logic Toqu Rippl Rductio bad Stato Flux Vcto Cotol, Mdiamia Scic PuPlih, ACTA Elctotchica, Vol. 5, N, pp. 3-37, 9. [9]. R.Toufouti, S Mzia, H Balla dict toqu cotol of iductio moto uig fuzzy lgic, ACSE joual,vol.6, iu, ju 6. []. S.R.Kap, V.P. Dhot fuzzy logic bad dict toqu cotol of iductio moto, IJESAT, VOL, Iu 94,. []. J. Bcklig, Ed. Th Aalyi of Dictioal Tim Si: Applicatio to Wid Spd ad Dictio,. Lctu Not i Statitic. Bli, Gmay: Spig, 989, vol. 6. []. F. Bot, P. Vidal, ad M. Pitzak-David, Adaptiv vaiabl tuctu cotol of a doubly fd iductio machi, Poc. ofit. Cof. Plicc, Waaw, o CD (5). [3]. Y. Kawabata, E. Ejiogu, ad T. Kawabata, Vcto cotolld doubl ivt fd woud oto iductio moto uitabl fo high pow div, IEEE Ta. Iduty Appl. 35 (5), 58 66 (999). [4]. G.S. Buja ad M.P. Ka zmikowki, Dict toqu cotol of pwm ivt-fd ac moto a uvy, IEEE Ta. o Idutial Elctoic 5 (4), (4). [5]. P.E. Vidal ad M. Pitzak-David, Stato flux oitd cotol of a doubly fd iductio machi, Poc. EPE, Toulou, o CD (3). [6]. Hog-H L, H.M.N., Ta-Wo Chu ad Wo-Ho Choi. Implmtatio of Dict Toqu Cotol Mthod Uig Matix Covt Fd Iductio Moto. I IEEE, 7 [7]. D-Fa Ch, C.-W.L., Kai-Chao Yao. Dict Toqu Cotol fo a Matix Covt Bad o Iductio Moto Div Sytm i IEEE 7 554
Faid Boumaaf civd th Magitium Dg i Elctical Egiig fom Bata Uivity i 9. ad th Ph.D dg i 4 H i mmb i th Elctical Egiig Laboatoy (LEB). Hi ach itt, Fuzzy logic cotol, Wid gy ytm ad dict toqu cotol. Rachid Abdmd wa bo i Bata, Algia i 95. H civd th M.Sc. ad Ph.D. dg i Elctical Egiig fom Kiv Polytchic Ititut, Kiv, Ukai, i 978 ad 98, pctivly. H ha b wokig fo mo tha 8 ya with th Dpatmt of Elctical Egiig, Uivity of Bata, a a Pofo. Cutly, h i th dicto of th Elctical Egiig Laboatoy (LEB). Hi cut aa of ach iclud dig ad cotol of doubly fd iductio machi, liability, magtic baig, adaptiv cotol ad wabl gy. Sbti Blkacm wa bo i Bata, Algia i 976; H civd th Mat Dg i Elctical Egiig fom Bata Uivity i 5, ad Ph.D. dg i Elctical Egiig i. H i mmb i th Elctical Egiig Laboatoy (LEB). Hi ach itt, adaptiv cotol, olia cotol ad dict toqu cotol. 555