ARCHIVES OF EECRICA ENGINEERING VO. 61(3), pp. 41-438 (01) DOI 10.478/v10171-01-0033-z Analy and contol of dual tato wndng nducton oto KRZYSZOF PIEŃKOWSKI Inttut of Elctcal Machn, Dv and Maunt Woclaw Unvty of chnology Wybzż Wypańkgo 7, 50-370 Wocław, Poland -al: kzyztof.pnkowk@pw.woc.pl (Rcvd: 08.0.01, vd: 1.03.01) Abtact: h pap pnt th athatcal odl of dual tato qul-cag nducton oto, foulatd n pha coodnat yt and n gnal tanfod pac vcto fo. h two typ of odl of dual tato nducton oto a condd. h contol yt of fld-ontd contol (IFOC and DFOC) and dct toqu contol (DC) of th dual tato nducton oto hav bn dcbd and dcud. Ky wod: dual tato nducton oto, athatcal odl, analy, IFOC, DFOC and DC contol. 1. Intoducton Nowaday, th u of lctcal dv yt wth ultpha qul cag nducton oto n vaou ndutal applcaton ncang. It caud by th dvlopnt of pow lctonc fquncy convt that can gnat ult-pha yt of voltag and cunt. Multpha qul cag nducton oto a anly ud n hgh pow lctcal dv o dv wth pcfc qunt fo contol. h an advantag of th typ of oto a th hgh toqu dnty, hgh ffcncy, ducd toqu pulaton, gat fault tolant and a ducton n th qud atng p nvt lg. h poblty of pow dtbuton aong a gat nub of pha ak t pobl to obtan a ducton of cunt of oto ccut and pow convt ccut. Aong th dffnt ultpha dv oluton, on of th ot nttng and wdly appld th dual th-pha tato wndng qul cag nducton oto. h dual tato nducton oto (DSIM) ha two paat th-pha tato wndng, hang th a achn co and th coon qul cag oto wndng. Accodng to th layout of th tato wndng n th oto co th dual tato nducton oto can b dvdd nto two bac goup. h ft on cop th contucton n whch two paat th-pha tato wndng a locatd quntally along th tato co. In th ca th no agntc couplng btwn th tato wndng, but ach of tato wndng agntcally coupld wth th Unauthntcatd
4 K. Pńkowk Ach. Elct. Eng. oto cag wndng. h two tato wndng can b uppld fo th a o paat AC voltag ouc of th a fquncy. h typ of oto contucton wa condd and dcbd n any pap wttn by th autho and oth [4, 7]. h fo typ of dual tato contucton cop th oto wth two tato wndng, that a patally hftd and a tuatd n th a tato co. h tud pt th tatnt that th pong contucton. h analy of th typ of oto ha bn pfod n o pap [1-3, 5, 6, 8] and th ubjct of th atcl. h pap pnt th gnal appoach to th analy and contol of dual tato nducton oto. h athatcal odl of DSIM oto hav bn dcbd and th pncpl and thod of vcto contol, ung oto fld-ontd contol (FOC) and dct toqu contol (DC) hav bn dcud.. h odl of dual tato nducton oto.1. h plfd aupton In th athatcal dcpton of dual tato nducton oto t aud that th DSIM oto condd a an lctochancal yt contng of two th-pha tato wndng, dnotd a tato 1 and tato and th coon qul-cag oto wndng. h cag oto wndng placd by an quvalnt th-pha wndng. Fgu 1 how th pntaton of th tato and oto wndng of dual tato nducton oto. Fg. 1. Schatc pntaton of oto wndng of dual tato nducton oto (DSIM) It aud that th oto wndng a nuodally dtbutd aound th a gap. h two t of tato wndng a dgnd wth olatd nutal pont and a patally hftd by an lctcal angl of π/6 dg. h yty of th pha oto wndng and th lnaty of oto agntc ccut a aud. h hyt phnona and ddy cunt Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 43 a nglctd. It wa aud that th agntc couplng btwn tato wndng 1 and occu only though th an flux, th couplng btwn th wndng though th lakag flux nglctd. All th lctoagntc vaabl and paat of quvalnt th-pha oto wndng hav bn tanfd to th tato d. In th pap, two odlng appoach and gnal thod of analy of dual tato qul-cag nducton oto hav bn condd: $ Modl I th DSIM oto tatd a two ndpndnt th-pha oto coupld togth by a coon oto wndng. h appoach bad on odlng pncpl ud fo clacal th-pha nducton achn. $ Modl II th DSIM oto condd a a x-pha nducton oto. h appoach bad on odlng pncpl ud fo ult-pha nducton achn. h both athatcal odl of DSIM wll b ft foulatd n pha vaabl fo. h odl a thn tanfod to abtay coon fnc fa n od to obtan o uful gnal fo... h quaton fo th Modl I of th DSIM oto Gnal voltag and flux quaton fo tato and oto ccut fo Modl I of th DSIM oto hav th followng atx fo: [ u1] [ R1][ 1] p[ ψ 1] [ u ] [ R ][ ] p[ ψ ] 0 [ R ][ ] p[ ψ ], (1) wh: [ ψ ] [ ][ ] [ ][ ] [ ][ ] 1 [ ψ ] [ ] [ ] [ ][ ] [ ][ ] 1 1, [ ψ ] [ ] [ ] [ ] [ ] [ ][ ]. 1, 1 1 1 1,, 1,, () Fo th Modl I th lctoagntc toqu of th oto can b xpd a th u of two coponnt caud by th lctoagntc ntacton btwn th tato 1 and th oto and th ntacton btwn th tato and th oto: M M M p [ ] [ ] [ ] p [ ] [ ] [ ]. 1 b 1 1, b, ϕ ϕ (3) h ndvdual atc of lctoagntc pha vaabl n Equaton (1)-(3) hav th followng fo: [ w ] [ w w w ] 1, [ w ] [ w w w ], w u,, ψ. a, a, b, b, c c, (4) Unauthntcatd
44 K. Pńkowk Ach. Elct. Eng. h ybol ud n th abov quaton hav th followng anng: ubcpt, ndcat th vaabl and paat of tato and oto, pctvly; ubcpt a, b, c ndcat pha vaabl and paat pctvly and ubcpt 1, dnot vaabl and paat of tato 1 and pctvly; th ybol of atx tanpoton; u voltag, cunt, ψ flux lnkag; [R 1 ], [R ], [R ] and [ 1 ], [ ], [ ] tanc and nductanc atc of tato 1, tato and oto, pctvly; [ 1, ], [ 1, ], [, ] atc of utual nductanc btwn tato 1 and, tato 1 and oto, tato and oto, pctvly; φ lctcal angl of oto otaton; p b th nub of oto pol pa, p d/dt th dffntal opato. h dtald fo of atc of pha tanc and nductanc of condd dual tato oto gvn n [3, 6, 8]. h utual nductanc btwn tato and oto pha wndng of DSIM hav podc vaaton wth th chang of th angl of oto otaton. h cau that th coffcnt n Equaton (1)-(3) a t dpndnt and th ak th quaton dffcult fo analy. In od to obtan th contant coffcnt th tanfoaton of oto pha vaabl to th coon, ctangula fnc fa (x, y, 0) appld. It aud that th fnc fa otat latv to tato yt wth any abtay angula pd ω k. h appld gnal fo of tanfoaton atx dnotd a [ ] ak th tanfoaton of pha vaabl of 3-pha tato 1, and oto to th ctangula coponnt n th yt (x, y) and to th zo coponnt: wh: [ ] [ D ] [ ], (5a) 3 coθ 0 nθ 0 0 1 1 1/ 1/ 3 1/ 1/ 1/ [ D ] nθ coθ 0 ; 1,, ; [ ] 0 3/ 3/, 3 (5b) θ 1 θ k ; θ θ k π / 6 ; θ θ k ϕ ; θ k ω k dt. (5c) 1 th angl btwn th x-ax of th coon fnc fa and th a1-ax of tato 1; th angl btwn th x-ax of th coon fnc fa and th a-ax of tato ; th angl btwn th x-ax of th coon fnc fa and th a-ax of oto. h fo of tanfoaton [ ] dpndnt on whth th tanfoaton appld to th pha vaabl of tato 1, tato and oto, pctvly. h oto tanfod vaabl can b tatd a th pojcton of th lctoagntc pac vcto on th ax of th coon fnc fa. Hnc th Equaton (1)-(3) can b xpd n th vcto fo. h vcto voltag quaton a: u u 1 R R 1 1 pψ pψ 1 jω ψ k 1 jω ψ k (6) 0 R pψ ( ω ω ) ψ, j k Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 45 h vcto flux lnkag quaton a:. 1 1 1 1 1 ψ ψ ψ (7) h lctoagntc toqu can b xpd n th vcto fo a ( ) ( ). I I * * 1 1 ψ ψ b b p p M M M (8) h voltag quaton fo th zo coponnt of th tato 1, tato and oto a: ( ) ( ) ( ), 0 0 0 0 0 0 0 0 0 0 1 01 01 1 01 01 1 01 p R p R p R p R u p R p R u l l l ψ ψ ψ (9) wh: ( ). 3/ ; ; ; 1 1 l l l μ (10) 1,, th total nductanc of a tato 1, tato and oto pctvly; l1, l, l th lakag nductanc of tato 1, tato and oto pctvly; μ th an agntzng nductanc; ω lctcal angula pd of th oto. Fgu pnt th ccut pntaton of th tanfod quaton fo th Modl I of th DSIM. h ccut how th lctoagntc couplng btwn tato and oto quvalnt ccut and th pncpl of lctochancal ngy convon n th oto. h ccut n Fg.a an quvalnt ccut, whch how th agntc couplng btwn tato 1, tato and oto. Fgu b pnt th a ccut aft lnaton of agntc couplng and ntoducng galvanc conncton btwn ccut. In th Fg. c, d and th quvalnt ccut fo zo coponnt of tato 1, tato and oto, pctvly. h ccut a not coupld wth any oth ccut. Fo th condaton of th abov quaton and quvalnt ccut t can b tatd that th zo coponnt a not nvolvd n lctochancal ngy convon, but th pnc can cau addtonal pow lo n th oto. In typcal ca of th oto dgn wth pha wndng conncton n ta wthout nutal th coponnt a alway qual to zo and can b nglctd n futh analy. Unauthntcatd
46 K. Pńkowk Ach. Elct. Eng. Fg..h ccut pntaton of quaton n abtay fnc fa fo Modl I of dual tato nducton oto.3. h quaton fo th Modl II of th DSIM oto h analy of DSIM oto on th ba of Modl II qu an addtonal aupton of th pha yty of th both tato wndng 1 and. h two th-pha tato wndng can thn b condd a a ytcal x-pha yt. In th odlng th oto wndng can b condd a x-pha o th-pha wndng. Blow th oto wndng tatd a an quvalnt th-pha wndng. Gnal voltag and flux quaton fo Modl II xpd wth applcaton of tato and oto pha vaabl hav th followng atx fo: [ ] [ ] [ ] p[ ψ ] u R [] [ ][ ] p[ ψ ] 0 R. [ ψ ] [ ] [ ] [ ] [ ] [ ψ ] [ ] [ ] [ ][ ], h quaton of oto lctoagntc toqu :,. (11) (1) M p b, [ ] [ ] [ ], ϕ (13) wh: [R ], [ ] th atc of pha tanc and nductanc of x-pha tato wndng pctvly, [R ], [ ] th atc of pha tanc and nductanc of th-pha oto wndng pctvly, [, ] th atx of utual nductanc btwn th x-pha tato and th-pha oto wndng. h oth dgnaton ud abov a th a a fo th Modl I of DSIM. Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 47 h atc of lctoagntc pha vaabl occung n quaton (11)-(13) hav th followng gnal fo: [ ] [,,,, ] w a1, wb1 wc1 wa wb wc [ ] [,, ] w u,, ψ. w w w a w b w c h Equaton (11)-(13) conttut a yt of dffntal-algbac quaton wth o vaabl coffcnt caud by utual nductanc btwn tato and oto wndng, whch a n functon of th angl otaton of th oto. hu, n od to obtan th plfd athatcal odl th tanfoaton of oto vaabl hav bn ud. h tanfoaton of oto vaabl ha bn ad by ung th pntd abov tanfoaton atx [ 3 ]. h tanfoaton atx of x-pha tato vaabl, dnotd a [ 6 ] ha bn foulatd on th thoy of Vcto Spac Dcopoton, whch ha bn popod n [8]. h tanfoaton atx [ 6 ] ha th followng fo: (14) [ ] 6 1 co( γ ) co(γ ) co( α ) co( α γ ) co( α γ ) 0 n( γ ) n(γ ) n( α) n( α γ ) n( α γ ) 1 1 co(γ ) co( γ ) co( α γ ) co( α ) co( α γ ) 3 0 n(γ ) n( γ ) n( α γ ) n( α) n( α γ ) 1 1 1 0 0 0 0 0 0 1 1 1 (15) wh α π /6 lctcal angl of hft btwn th a-pha ax of th tato 1 and ; γ π/3. Applyng th tanfoaton [ 6 ] to th tato voltag and flux quaton, th ognal xdnonal tato yt can b dcopod nto th two-dnonal dcoupld yt: th bac yt (α, β) and th yt (z 1, z ) and (0 1, 0 ). h vaabl tanfod to th yt (α, β) can b condd a th lctoagntc coponnt dtnd n a tatonay coodnat yt fxd to th tato, wth th α-ax algnd wth th a-ax of th tato 1. o obtan th gnal analy th lctoagntc coponnt (α, β) hav bn futh tanfod to th fnc fa (x, y), otatng latv to th tato wth abtay angula pd ω k. Aft th anpulaton th gnal oto quaton can b pntd n vcto fo gvn blow: $ th vcto quaton fo th tanfod vaabl xpd n th gnal yt (x, y): u R pψ jω ψ ( ω ω ), 0 R pψ j k ψ ψ ψ k, (16) (17) Unauthntcatd
48 K. Pńkowk Ach. Elct. Eng. wh: * M 3 ( ) I p ψ b, (18) ; ; 3, (19) l l μ $ th vcto quaton fo th tato vaabl xpd n th yt (z 1, z ): u z R pψ ψ l, (0) z $ th vcto quaton fo th tato vaabl xpd n th yt (0 1, 0 ): z z u R p, ψ l. (1) 0 0 ψ 0 h vcto quaton fo th zo oto coponnt th a a fo Modl I. Fgu 3 pnt th ccut pntaton of th tanfod quaton fo th Modl II of th DSIM. h ccut dcb th lctoagntc couplng btwn tato and oto quvalnt ccut and th pncpl of lctochancal ngy convon n th oto. h ccut n Fg.3a an quvalnt ccut, whch how th agntc couplng btwn tato and oto. Fgu 3b pnt th a ccut aft lnaton of agntc couplng and ntoducng galvanc conncton btwn ccut. Fg.3c pnt th quvalnt ccut fo tato (z 1, z ) coponnt, Fgu 3d and 3 pnt th quvalnt ccut fo zo coponnt of x-pha tato and th-pha oto, pctvly. h ccut a not coupld wth any oth ccut. 0 z 0 Fg. 3. h ccut pntaton of vcto quaton fo Modl II of dual tato nducton oto h analy of Equaton (16)-(1) and ccut fo Fgu 3 how that only th vcto lctoagntc vaabl xpd n th bac yt (x, y) o (α, β) a aocatd wth th gnaton of th an flux lnkag and contbut to th lctochancal ngy convon n th oto. Hnc t follow that although th dual tato nducton oto pntd a a x-pha oto, only th two vcto coponnt can b ud fo contol of agntc flux and lctoagntc toqu of th oto. If th tato wndng of th DSIM a dgnd n th fo of two th-pha yt wth olatd nutal pont thn th (0 1, 0 )-coponnt of th tato lctoagntc va- Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 49 abl a alway qual to zo and can b ottd n futh analy. In contat, th pcfc fatu of th DSIM th poblty of occunc of lctoagntc coponnt n th yt (z 1, z ) [, 8]. h haonc voltag of od k 6n ± 1, (n 1, 3, 5,...) a tanfod to th coponnt, o n ult th haonc of od k 5, 7, 17, 19,... can xt. Haonc of th nub can b gnatd by th voltag vcto of pow lctonc nvt ud fo th contol of th oto. h tato cunt focd by th haonc can ach lag valu, bcau thy a ltd only by th low oto pdanc dtnd by th pha tanc and th pha lakag nductanc of th tato wndng. hu, dung th contol of dual tato nducton oto by x-pha pow lctonc nvt fo a lag nub of voltag vcto gnatd by an nvt, only th uch voltag vcto hould b chon, whch do not gnat lag valu of th coponnt dfnd n th yt (z 1, z ). 3. Fld-ontd contol (FOC) of dual tato nducton oto h an goal of a fld-ontd contol (FOC) to obtan dcoupld contol of lctoagntc toqu and oto flux of th oto. It condd th FOC contol yt of DSIM wth applcaton of th oto flux vcto ontaton. h algoth of FOC contol bad on th athatcal quaton of DSIM foulatd n th coon fnc fa (x, y) wth th x-ax algnd wth th vcto of oto flux lnkag. Fo th oto flux ontaton th followng condton a t: ψ ψ ψ ; ψ 0; ω ω. () x Includng th condton () n th yt of quaton fo Modl I of DSIM w obtan: y k 1 pψ ψ ( 1x x), (3) M ψ p ( ) ψ ), (4) b ( 1y y ωl ωψ ω ( 1y y), (5) ψ wh: oto t contant; ω l oto lp pd, ω ψ angula pd of oto flux vcto, x, y ubcpt dnotng vcto coponnt n fld-ontd fnc fa (x, y). h Equaton (3)-(5) pnt th pncpl of FOC contol of DSIM bad on Modl I of th oto. h pncpl addtonally gaphcally llutatd n Fgu 4. Includng th condton () n th quaton of Modl II of DSIM t obtand: M 1 pψ ψ x, (6) ( ), 3p ψ (7) b y Unauthntcatd
430 K. Pńkowk Ach. Elct. Eng. ωl ωψ ω y. (8) ψ Fg. 4. Spac vcto daga of FOC contol bad on Modl I of DSIM h Equaton (6)-(8) pnt th pncpl of FOC contol of DSIM bad on Modl II of th oto. h pncpl addtonally gaphcally llutatd n Fgu5. Fg. 5. Spac vcto daga of FOC contol bad on Modl II of DSIM h abov quaton and Fgu how that whn th fld-ontd contol ud th a poblty of ndpndnt contol of th oto flux and th lctoagntc toqu of th oto. h followng concluon can b tatd fo pntd condaton: 1) Whn th FOC algoth bad on th Modl I of th oto two tato cunt vcto 1 and ut b paatly contolld n th contol yt. Fo th a th ndvdual tato of DSIM hould b contolld by two paat th-pha convt. ) Whn th FOC algoth bad on th Modl II of th oto only a ultant tato cunt vcto ut b contolld n a la ann a n convntonal th-pha oto. Fo th a th both tato of DSIM can b contolld by ngl x-pha convt. FOC ch can b clafd accodng to th thod on how th poton of oto flux vcto dtnd. h ndct IFOC thod and dct DFOC thod a dtnguhd. In th IFOC thod only th valu of angl poton of th oto flux vcto tatd. h Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 431 taton bad on calculaton of th ntgal of angula pd of oto flux vcto dfnd a th u of th aud oto angula pd and calculatd oto lp pd. In th DFOC thod both th agntud and angl poton of th oto flux vcto a dtnd. h valu can b obtand though taton wth ung th appopat cunt o voltag odl of th oto o by ung th oto flux obv bad on dct aunt of oto flux. h block ch of IFOC contol bad on Modl I of DSIM pntd n Fgu 4. Fg. 6. Sch of IFOC contol of DSIM bad on Modl I of th oto h a two an coand gnal n th contol yt: lctc angula oto pd ω z and agntud of oto flux vcto Ψ z. h pd contoll Rω dtn th u of coand coponnt of tato cunt vcto y y1 y whch popotonal to th ultant lctoagntc oto toqu. h flux poducng coand coponnt of tato cunt vcto x x1 x dtnd on th ba on fnc of oto flux. h tatd ntantanou valu of th angl poton γ ψ of th oto flux vcto ud n tanfoaton block fo utabl tanfoaton of oto vaabl. Coand cunt coponnt n th contol yt a copad wth th pctv cunt coponnt gnatd by tanfoaton block on th ba of aud valu of oto vaabl of tato 1 and. h pctv contol o gnat though PI contoll two t of fnc coponnt of tato voltag vcto dtnd n fld ontd coodnat yt. h voltag coand a thn tanfod nto two tatonay fnc fa, patally hftd by 30 lctcal d- Unauthntcatd
43 K. Pńkowk Ach. Elct. Eng. g and latd to tato 1 and. h valu a thn convtd by Modulato 1 and n od to gnat th wtch tgg gnal of ndvdual th-pha nvt. h block ch of DFOC contol bad on Modl II of DSIM pntd n Fgu 7. Fg. 7. Sch of DFOC contol of DSIM bad on Modl II of th oto h yt of DFOC contol of DSIM cont of two ovdng contol loop fo flux and pd gulaton. h actual agntud and angl poton of oto flux vcto a dtnd though an taton block o obv block. h flux contoll Rψ gnat th fnc of flux coponnt x of tato cunt vcto and th pd contoll Rω gnat th fnc of toqu coponnt y of tato cunt vcto. Coand coponnt of tato cunt vcto a copad wth th pctv actual coponnt of tato cunt vcto obtand by tanfoaton block on th ba of aud valu of oto vaabl. h ubodnat PI contoll gnat th fnc coponnt of tato voltag vcto dtnd n fld ontd yt. h voltag coand a thn tanfod nto tatonay fnc fa and nd to PWM Modulato, whch gnat th wtch tgg gnal fo x-pha nvt. 4. Dct toqu contol (DC) of dual tato nducton oto Dct toqu contol (DC) an altnatv to th fld-ontd contol (FOC) of nducton oto. h pncpl of DC dct contol of agntud of tato flux vcto and th Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 433 valu of lctoagntc toqu of nducton oto. h an fatu of DC contol a: th a no cunt contol loop, coodnat tanfoaton not qud, th no paat voltag PWM odulato. h DC thod of contol can b appld to dual tato nducton oto. h thod of DC contol of DSIM can b dvdd nto two bac typ, dpndng on whch odl of DSIM ncludd n contol algoth: 1) DC thod wth ndvdual tato flux contol of th oto th thod bad on Modl I of DSIM oto; ) DC thod wth ultant tato flux contol of th oto th thod bad on Modl II of DSIM oto; On th ba of quaton of Modl I of DSIM w obtan th followng t of vcto quaton dfnd n th coon tatonay fnc fa: M t ψ u R1 dt, 1 (9) 1 1 0 t ψ u R dt, (30) 0 1 ψ 1ψ n M M pb K δ ψ 1 pb K ψ ψ n δ ψ, (31) wh: ψ 1, ψ, ψ th agntud of flux vcto of tato 1, tato and oto, pctvly, Κ oto contant, δ Ψ1, δ Ψ th angl btwn tato1, tato and oto flux vcto pctvly. h Equaton (9)-(31) pnt th thotcal pncpl of DC thod wth ndvdual tato flux contol of DSIM oto. h pncpl addtonally llutatd gaphcally n Fgu 8. Fg. 8. Spac vcto daga of DC contol bad on Modl I of DSIM In od to apply th thod of DC contol th two tato of DSIM hould b uppld by two paat Voltag Souc Invt. Dcoupld contol of tato flux vcto and co- Unauthntcatd
434 K. Pńkowk Ach. Elct. Eng. ponnt of lctoagntc toqu achvd by focng lvant voltag vcto fo paat nvt, actng on ndvdual tato wndng. h block ch of DC contol of DSIM wth ndvdual tato flux contol of th oto hown n Fgu 9. Fg. 9. h ch of DC contol of DSIM wth ndvdual tato flux contol h contol yt u nonlna hyt contoll: th two-tat hyt contoll of flux agntud of tato 1 and tato and th th-tat hyt contoll of lctoagntc toqu of th oto. In th yt pha voltag and cunt of ndvdual tato wndng a aud. h aud valu a tanfod to ctangula coodnat yt (α1, β1) and (α, β) tatonay latv to th tato wndng. anfod valu a ud n taton block n od to dtn th ntantanou valu of lctoagntc toqu, th ntantanou valu of agntud of flux vcto of tato 1 and tato and th cto nub of ntantanou poton of tato flux vcto on th plan (α1, β1) and (α, β). h fnc valu of lctoagntc toqu and agntud of tato flux vcto a copad wth actual valu obtand fo taton block. Output gnal fo hyt contoll of toqu and flux wth gnal pcfyng th cto nub dtn though wtchng tabl P1 and P optal contol gnal fo contol of ndvdual 3-pha nvt. Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 435 On th ba of quaton of Modl II of DSIM w obtan th followng t of vcto quaton dfnd n th coon tatonay fnc fa: M t ψ u R dt, (3) 0 3pb ψ ψ nδψ, (33) σ wh: ψ agntud of tato flux vcto, σ oto total lakag facto; δ Ψ th angl btwn tato and oto flux vcto. h Equaton (3)-(33) pnt th thotcal pncpl of DC thod wth ultant tato flux contol of DSIM oto. h pncpl addtonally llutatd gaphcally n Fgu 10. Fg. 10. Spac vcto daga of DC contol bad on Modl II of DSIM In od to apply th thod of DC contol th two tato of DSIM hould b uppld by ngl x-pha Voltag Souc Invt. Dcoupld contol of tato flux vcto and lctoagntc toqu achvd by focng lvant voltag vcto fo nvt, actng on ndvdual tato wndng, condd a x-pha yt. h block ch of DC contol of DSIM wth ultant tato flux contol of th oto hown n Fgu 11. h contol yt u two nonlna hyt contoll: th two-tat contoll of ultant tato flux and th th-tat contoll of lctoagntc toqu. In th yt pha voltag and pha cunt of oto tato a aud, gadd a a 6-pha yt. h aud valu a tanfod to th tatonay ctangula coodnat yt (α, β). h tanfod valu a ud n taton block to calculat th ntantanou valu of lctoagntc toqu, agntud of ultant flux vcto and th cto nub of angl poton of th ultant tato flux vcto. h t gnal of lctoagntc toqu and tato ultant flux a copad wth actual valu obtand fo th taton block. Output gnal fo hyt contoll, and gnal wth nfoaton of cto nub of cunt poton of tato ultant flux vcto though th wtch tabl dt- Unauthntcatd
436 K. Pńkowk Ach. Elct. Eng. n th optal wtchng gnal fo th valv contol of x-pha voltag nvt. h nub of th nvt voltag vcto dctly nflunc th pfoanc of DC yt. Dffng fo th-pha yt, th a n th ca 64 pac voltag vcto fo th xpha voltag nvt. It vy cubo to choo th utabl vcto fo all th 64 vcto. In th dvlopd thod of contol th plan n whch tato flux vcto a condd dvdd nto twlv cto and only th lagt twlv voltag vcto of nvt a ud fo contol. Fg. 11. h ch of DC contol of DSIM wth ultant tato flux contol 5. Sulaton ult Sulaton tud of pntd FOC and DC thod ud fo contol of DSIM hav bn pfod. h tud w cad out fo 4-kW pototyp contucton of DSIM wth on pa of pol. h lctd ult of ulaton of DC contol of ndvdual tato flux contol a pntd n Fgu 1 and 13. Fgu 1 pnt th wavfo of fnc angula vlocty of th oto and al tac of oto angula vlocty. It ha bn ulatd that th fnc pd at ft lna vu t, thn ha th contant valu and aft that vng. h pfod ulaton conf that th actual oto vlocty ha pactcal th a wavfo a th fnc pd. Fgu 13 pnt th wavfo of lctoagntc toqu coponnt and th ultant lctoagntc toqu. h obtand ulaton ult conf th good contol fatu and quck acton of DC thod of DSIM contol. It ha bn povd that th condd DC contol povd fat toqu pon fo th fnc gnal. Unauthntcatd
Vol. 61(01) Analy and contol of dual tato wndng nducton oto 437 Fg. 1. h t wavfo of fnc angula pd (oga z ) and actual angula pd (oga z ) of th DSIM oto fo DC contol wth ndvdual tato flux contol Fg. 13. h t wavfo of toqu coponnt and th ultant lctoagntc toqu fo DC contol of DSIM wth ndvdual tato flux contol (Fo top to th botto: lctoagntc toqu coponnt M 1 and M, ultant lctoagntc toqu M ) 6. Suay Analy of dual tato nducton oto ay b pfod on th ba of two quvalnt athatcal odl of th oto. h Modl I of th oto condd a a yt of two 3-pha oto wth a coon oto. h advantag of th odl th ablty to analyz oto wth pobl ayt of lctoagntc paat of two tato wndng. Unauthntcatd
438 K. Pńkowk Ach. Elct. Eng. h Modl II of th oto condd a a 6-pha yt. A ltaton of th thod of analy th poblty of t applcaton only to th oto wth two dntcal tato wndng. h advantag of th thod th poblty of atonal choc vcto of th nvt output voltag fo ducng xcv valu of tato cunt and pow lo n th oto. h conductd analy allow to daw th concluon that, dpndng on th choc of oto odl dffnt algoth and contol ch a obtand. h DSIM oto can b contolld by applcaton FOC o DC thod of contol. Contol algoth and contol ch bad on th Modl I a to o xtnt o coplx and qu a lag nub of gnal pocng block and contol block n copaon to ch bad on Modl II. Rfnc [1] Bojo R., azza M., Pofuo F., ncon A., Dgtal Fld Ontd Contol fo Dual h-pha Inducton Moto Dv. IEEE an. on Induty Appl. 39(3): 75-760 (003). [] Bojo R., Fana F., Fva G. t al., Dct oqu Contol fo Dual h-pha Inducton Moto Dv. IEEE an. on Induty Appl. 41(6): 167-1636 (005). [3] Fgna W., Pńkowk K., Stowan wktoow lnk ndukcyjny z dwoa uzwojna tojana (Vcto contol of dual tato nducton oto), Mazyny Elktyczn. Zzyty Poblow 86: 65-70 (010) (n Polh). [4] Han B., Kawack W., owk J., t al., Dwutwonkowy lnk aynchonczny klatkowy do napędu aggatów popowych o gulowanj wydajnośc (Squl-cag aynchonou oto wth doubl tato wndng fo th dv of pup yt wth contolld flow). Zzyt Spcjalny, Wyd. Rdakcja Gónctwa Odkywkowgo, Wocław (000), (n Polh). [5] Khoud H., Maou A., Moufl A., Dual Sta Inducton Moto Dv: Modllng, Supplyng and Contol. Intnatonal Jounal of Elctcal and Pow Engnng 5: 8-34 (011). [6] Muňoz A.R., po.a., Dual Stato Wndng Inducton Machn Dv. IEEE an. on Induty Appl. 36(5): 1369-1379 (000). [7] Pnkowk, K., Analy of qul cag nducton oto wth dual tato wndng. Poc. of Int. Conf. on Elctcal Machn ICEM, Bug, Blgu, CD-ROM Pap 518 (00). [8] Zhao Y., po.a., Spac Vcto PWM Contol of Dual h-pha Inducton Machn Ung Vcto Spac Dcopoton. IEEE an. on Induty Appl. 31(5): 1100-1108 (1995). Unauthntcatd