Vector Control of Faulty Three-Phase Induction Motor with an Adaptive Sliding Mode Control

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1 oh JANNATI Al ONADI Nk Ruz NIK IDRIS oh Jun ABDU AI Ah Ah OHD FAUDI UT-PROTON Fuu D ooy Fculy o lccl ngnng Un Tknolog ly Joho Bhu AAYSIA () Cn o Acl Inllgnc n Rooc (CAIRO) Un Tknolog ly Joho Bhu AAYSIA () Vco Conol o Fuly Th-Ph Inucon oo wh n Ap Slng o Conol Ac. Th pp pn n p lng o conol wh n p wchng gn n o o co conol o Th-Ph Inucon oo (TPI) on Roo Flux On Conol (RFOC) ho un opn-ph ul (uly TPI). Th ho cn ulz o conol o I n o ccl pplcon whch u ul-oln ch. To con h goo ponc o h popo ho ulon ul h n pn. Th Sulon ul con coplly coy cn o h popo ho. Szczn. W ykul zpznowno pcyn own ślzgow ózowgo lnk nukcyngo zuąc n oz RFOC w pzypku gy n z z wykzu łą. (Apcyn ślzgow Sown wkoow ózowgo lnk nukcyngo z łę zy) Kywo: p lng o conol uly h-ph nucon oo oo lux on conol. Słow kluczow: own ślzgow own pcyn lnk nukcyny ózowy. Inoucon Inucon oo (I) coonly ploy n nul pplcon uch Hng Vnlon n A Cononng (HVAC) copo n n c. In h n y Fl On Conol (FOC) on o h o coon ppoch o conol o I. Opn-ph ul on o uul lu n h I o wnng [ ]. Th ul cu y lown u chncl hkng o h chn n c. Sl chnu h n popo o con o h ul n lccl oo [ ]. A opn-ph ul gno cn ch y chnu on hgh-uncy low-plu gnl ncon []. Tho o uh conon n h pp u h h ul con pocu. Ful-oln opon ung opn-ccu ul o h I gncn n pcul n o ccl pplcon uch lwy o pc chnology. Th ol ucu o h uly TPI l o lnc TPI ol po n [5]. To on ul-oln conol ch o h I h clcl FOC ho houl o. In h pp nw conol chnu o uly TPI on FOC pn. In h popo FOC gy o uly TPI on uln ccu o Sngl-Ph Inucon oo (SPI) unlnc oonl noon ulz. I po y ung o h oonl noon h uon o h unlnc TPI (uly TPI) co lk h lnc TPI uon. A ul y ung popo oonl noon nw FOC y lop o TPI un opn-ph ul o h connonl co conol. I hown n h pn conol y o uly TPI conol h p PI conoll h o uu y n p lng o conoll. Th ponc o h clcl FOC ucu (wh PI conoll) o oh lnc n unlnc TPI (uch [ 5]) ongly pn on uncn whch uully u o unknown p xnl lo unc p on nonln ync n c [6]. ny u h n pn o poc h ponc o h y un xnl lo unc n p on (uch : gnc lgoh [7] uzzy conol [8] nul conol [9] n p conol []). Bcu o ync pon nny o on o p goo ponc gn unoll n nonln ync con o xnl lo unc n c h lng o conol cn u n h p conol o lcc []. In h pp o copn h y uncn n p lng o conol wh on-ln lng gn on popo. Th p lng o conol ly h n lo po hough ypuno ly hoy. ol o uly TPI Th uon o uly TPI n h ony nc (upcp ) cn hown ollow [5]: So n oo olg uon: () So n oo lux uon: () lcognc ou uon: Pol ( ) () Pol l J F wh l l oo λ λ λ n λ h - x olg cun n lux o h o n oo n h o nc. n no h o n oo nc. n no h o n h oo l n uul nucnc. h chn p. τ τ l J n F lcognc ou lo ou n n cou con cocn. I hown n [5] n h uly o h nolz noon x (nolz noon x h x o noon o 6 PRGĄD KTROTCHNICNY ISSN -97 R. 89 NR /

2 l o --c o - ) o o l ollow: () ul T In h oo lux on conol ho h uon o h chn n o h oo lux on nc. Fo h pupo oonl noon (connonl oonl noon) u ppl o h I uon ollow: (5) co n T n co In uon (5) θ n h ngl wn h ony nc n h ong nc. By ployng o connonl oonl noon h uly TPI uon on ow n ckw coponn (Th ckw coponn gn cu o unul nucnc; n n h uly TPI uon). In h ch p o nouc nol noon x o h uly TPI uon whch gun lnc o h y. RFOC o uly TPI Th n o ung noon x gn o h y- uln ccu o h SPI. Fg. how h y uln ccu o SPI. Fg.. Sy uln ccu o SPI In h gu V V I n I h n n uxly olg n cun "α" h un o (α = N / N ) n "" h u oo o "-". n h ow n ckw olg o gnzng nch o h n n uxly wnng. R R X n X h ow n ckw o nc n nucnc n n wnng. R l R l X l n X l h lkg nc n nucnc o h n n uxly wnng. B on Fg. h oo n n uxly wnng olg cn wn ollow: (6) V li V I wh l I I I I R l Rl X l By ollowng uuon: X l R R X l X l (7) I ( I I) I ( I I) (8) V V V uln ccu o SPI (Fg.) cn pl Fg.. In uon (7) n (8) n h uncon n o nucnc. By lcng y lu o n Fg. cn pl lnc ccu. ( l ) ( l ) ( ) (9) ( ) l l l l ( ) Fg.. Spl uln ccu o SPI A cn n y ung uon (7) n (8) h uln ccu o SPI chng no lnc ccu. uon (7) n (8) cn wn : N () V V I N I V N V I I N uon () h noon x o chngng l o unlnc o o h lnc o. Wh ollowng chng o l: N N n co N N () V V V V I I I I An wh uon o uon () n uon () h popo oonl noon o o olg n cun l on ollowng uon: Roonl noon o o olg l: () co n T n co Roonl noon o o cun l: () co n T n co I xpc y ung pn oonl noon (uon () n ()) h uon o uly TPI co l o h lnc oo uon. By ployng () n () o h uly TPI uon (uon ()-()) n plyng w h: Roo olg uon: () Roo lux uon: (5) PRGĄD KTROTCHNICNY ISSN -97 R. 89 NR / 7

3 lcognc ou uon: (6) Pol ( ) In uon () ω h ngul locy o h Roo Flux On nc. A cn n y pplyng popo oonl noon uon o oo olg oo lux n lcognc ou on lk lnc uon (h only nc wn h uon n lnc TPI uon h n h uon on: = = / u n h lnc TPI uon w h: =/ ). In h RFOC chnu h oo lux co lgn wh -x (λ = λ n λ = ). Wh h upon n o uon ()-(6) uon o RFOC o TPI un opn-ph ul on ollow: (7) T T In uon (7) T oo conn. A non o h oonl noon o o l cn con ollowng uon: co n (8) T n co c By ployng uon () n (8) n plyng / / n h uon o n / / n h uon o wll pp. Fo gnng o / / n h uon o n / / n h uon o PI conoll n. Ung o h PI conoll cu h conollng y o coplx. Fo olng o h pol h cocn o / / n h uon o n h cocn o / / n h uon o con ul o zo. Tho w h: (9).co c.. n. 5 5 wh: 5 Wh uppoon = -co θ n c = n θ n on : ( )n () ( ) co Tho uon (8) cn -wn : () co ( )n T n ( )co By conng o / = ( / ) (n h uly TPI: = / = / = l + / = l + / l ) h popo oonl noon o o olg l on ollowng uon: Roonl noon o o olg l: () co n T n co Pol By pplyng uon () n () n plyng RFOC uon o o olg on ollowng uon: ( ) ( ) () () ( ) ( )( ) T ( ) ( ) ( ) wh co n n co A you cn h ucu o uon () n () lk h ucu o lnc TPI uon ( on () n () h only nc wn h uon n lnc TPI uon h n h uon on: =(( + )/ ) ); = = / ; - - = = l +/ ; n o u n h lnc TPI uon w h: =/ ; = l +/ ). In uy nl ocon on h connonl co conol o k ul o conol o uly TPI uz n Tl. Fo plyng plnon o popo ho n h wok h cun conol loop wh n hy conoll u. Ap lng o conol In h conollng uly TPI h cocn o PI conoll n o oy o lnc o o uly o. Fo h pupo n h pp n p lng o plc n o p PI conoll. uon () cn hown : (5) c wh: F Pol l c Pol J J uon (5) cn con wh uncn ollow: (6) c c wh h n c no h uncn o h n c whch h uncn unknown n clculon o n upp oun h cul o on. Th p o cn pn : * (7) wh ω *() h nc p. Tkng o uon (7) yl: (8) u wh u * * c c Th wchng uc wh ngl coponn o h lng o p conol con : (9) S k wh k conn gn. In h wok h p conoll con ollow: 8 PRGĄD KTROTCHNICNY ISSN -97 R. 89 NR /

4 ~ () u k gns wh ~ S S gns S oo ρ() wchng gn n α po conn. Tl. Copon wn wo co conol ho Connonl co conol o h lnc TPI Popo o co conol o h uly TPI o noon o h o cun: o noon o h o cun ccong o (): c Blnc oonl Unlnc oonl noon o h o cun ccong o (5): noon o h o cun ccong o (): co n co n n co n co In o lnc oonl In o unlnc noon o h o olg ccong o (5): oonl noon o h o olg ccong o (): co n n co o noon o h o olg: c So l nucnc: l So n oo uul nucnc: So nc: co n n co o noon o h o olg ccong o (): So l nucnc ccong o () n (): l So n oo uul nucnc ccong o (7) () n (): So nc ccong o () n (): So ckw coponn ccong o () n (): co n n co ocon o p PI conoll cocn ccong o Fg. Tho. Th p ucu p conoll wh h pon lgoh () k h conoll y congn o h wchng uc S() = n h ly o h p conol cn gun. Poo: Choong ypuno uncon cn: V S ˆ () wh ˆ ~ Tkng h o h ypuno uncon: V S S ˆ ˆ S k ˆ ~ S u k ˆ S S u k ~ S () S ~ gns ~ S S ~ S ~ S S S S S Aupon : ρ x Tho o uon (): S S S () x S S Aupon : α Tho o uon (): () S x Ung ypuno ho h conoll y l. Snc S() oun () lo oun. Fo uon (9): S S k k (5) Aupon : + k Fo uon (5) n Aupon I oou h ckng o () cong o zo. Tho o uon (8) n (): * * ( ) k ~ gn S c (6) B on uon (6) h lock g o h p conol wh p lng o cn pn lk n Fg.. Fg.. Sch o h p conoll wh p lng o Rul n ulon A oo whch o SPW (Sn Pul Wh oulon) Volg Souc In (VSI) w ul ung l. oo h n gn ollow: Volg:5V = 5Hz no. o pol = Pow = 75W =.6 = 9.5 l = l =.8H =.85H J =.8kg. Th conoll whch h n ploy o h p conol o I connonl RFOC. To y h cn o h popo conol y o uly TPI co conol y on Tl n Fg. lo ul. Fo howng h ponc o h popo y n uncny oun 5% ul occunc uppo. Fg. how h ulon ul o h connonl RFO conoll. In ng n long h oo hlhy. A =. h lo ou p o N. o N. n o uppo h h n uncny oun 5% ul occunc n h lo ou (In TPI n un opn ph ul h xu pl ou ou % o h oo ou non n []). A = n opn-ph ul occu n h oo co unlnc. Rul how x PRGĄD KTROTCHNICNY ISSN -97 R. 89 NR / 9

h h connonl conoll cn no conol h uly oo ppoply. pclly w cn conl ocllon n h ou n p o oo ul. Fg.. Sulon ul o h connonl conoll (Roo -x cun So -x cun Roo p lcognc ou) In Fg.

5 p oo p o 5 p). Fg.5. Sulon ul o h popo o conoll (Roo -x cun So -x cun Roo p lcognc ou) Ung lng o conol n h popo uly TPI h conoll p nn o on n h lo ou unc n p o oo.

I cn n o pn ul h ync ponc o h popo ppoch o co conol o uly TPI xly ccpl. Th ho cn u o hgh ccl nul pplcon wh w n o h ul-oln y n lo cn ulz o co conol o SPI cu SPI wh wo n n uxly wnng lk n unlnc I.

5 h h connonl conoll cn no conol h uly oo ppoply. pclly w cn conl ocllon n h ou n p o oo ul. Fg.. Sulon ul o h connonl conoll (Roo -x cun So -x cun Roo p lcognc ou) In Fg.5 h ncl pocu on gn u h h opn-ph ul h popo o conoll ppl. Sulon ul how h h popo y uc h ou n oo p ocllon nocly (.g. oo p ocllon y ung connonl RFO conoll opn-ph ul n y ~ 8 p u y ung popo o RFO conoll h p ocllon c ounngly ~.5 p oo p o 5 p). Fg.5. Sulon ul o h popo o conoll (Roo -x cun So -x cun Roo p lcognc ou) Ung lng o conol n h popo uly TPI h conoll p nn o on n h lo ou unc n p o oo. Du o h l ucu conol nu h popo conol y ou un uncn cu y chng n h lo n p o. Concluon Th wok how co conol o uly TPI wh n p lng o conol B on RFOC. Th hoy n nly o h popo co conol pocu h n xpln o. I cn n o pn ul h ync ponc o h popo ppoch o co conol o uly TPI xly ccpl. Th ho cn u o hgh ccl nul pplcon wh w n o h ul-oln y n lo cn ulz o co conol o SPI cu SPI wh wo n n uxly wnng lk n unlnc I. RFRNCS [].Jnn.Fllh olng n Vco Conol o Unlnc nucon oo (uly h ph o ngl ph nucon oo). Connc on Pow lconc & D Sy & Tchnolog (PDSTC) pp. 8 y. []. S. Blll D.. Blll H.. Suywnh n. Ku h Wng Tchnu: A Nol Appoch o h Dcon o So Wnng In-Tun Sho Ccu n Opn Ccu Ful n Th Ph Inucon oo Jounl o Pow lconc Vol. No. pp. 8- Jnuy [] Ghzl. n J. Pohn Rou o wnng ul con n nucon oo In Pow lconc D Sy n Tchnolog Connc (PDSTC) n pp I [] Alo G Gcoo Scl n Alo Conol ollng n Conol o Th-Ph PS un Opn-Ph Ful I Tncon on In. Apl. Vol. 9 No. pp. 7-8 Jun/F [5]. Jnn N. R. N. I n. Sl A Nw ho o ollng n Vco Conol o Unlnc Inucon oo ngy Conon Cong n xpoon (CC) Sp [6] S. Jn n K. B. ohny ROBUST FID ORINTD INDUCTION ACHIN CONTRO USING SC Th 5 h PSU- UNS Innonl Connc on ngnng n Tchnology (ICT-) Phuk y - [7]. onz-gh A. Pou B. Ghlch Applcon o gnc lgoh o opzon o conol gy n plll hy lcc hcl Jounl o h Fnkln Inu (6) 5. [8].A. Fnch F. Bn G.A. Cpolno F. Fnch Fuzzy logc n lng-o conol ppl o x-ph nucon chn wh opn ph I Tncon on Inul lconc 57 () () 5 6. [9] T-J. Rn T-C. Chn Rou p-conoll nucon oo on cun nul nwok lcc Pow Sy Rch 76 (6) 6 7. [] R. no P. To C.. Vll An p ckng conol o cun un o nucon oo wh uncn lo ou n oo nc Auoc (8) [] V.I. Ukn Slng o conol gn pncpl n pplcon o lcc I Tncon on Inul lconc (99) 6 6. [] Slh A.; Pc.; Shlou A. "Ful Toln Fl On Conol o h Inucon oo o o o On In Ph I Inul lconc ICON 6 - n Annul Connc on ol. no. pp No. 6 oh Jnn UT-PROTON Fuu D ooy Fculy o lccl ngnng Un Tknolog ly Joho Bhu AAYSIA. -l: nn9@yhoo.co; Al on UT-PROTON Fuu D ooy Fculy o lccl ngnng Un Tknolog ly Joho Bhu AAYSIA. -l:.lon@gl.co; Nk Ruz Nk I UT-PROTON Fuu D ooy Fculy o lccl ngnng Un Tknolog ly Joho Bhu AAYSIA. -l: nkuz@k.u.y; oh Jun Aul Azz UT-PROTON Fuu D ooy Fculy o lccl ngnng Un Tknolog ly Joho Bhu AAYSIA. -l: un@k.u.y; Ah Ah oh Fuz Cn o Acl Inllgnc n Rooc (CAIRO) Un Tknolog ly Joho Bhu AAYSIA -l: h@k.u.y Th coponnc :h@k.u.y PRGĄD KTROTCHNICNY ISSN -97 R. 89 NR /

SYMMETRICAL COMPONENTS

SYMMETRICAL COMPONENTS SYMMETRCA COMPONENTS Syl oponn llow ph un of volg n un o pl y h p ln yl oponn Con h ph ln oponn wh Engy Convon o 4 o o wh o, 4 o, 6 o Engy Convon SYMMETRCA COMPONENTS Dfn h opo wh o Th o of pho : pov ph