A Review on Direct Torque Control of Induction Motor

Transcription

1 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX A Rviw on Dict Toqu Contol of Induction Moto Jagan Mohana Rao Malla and Manti Maiya Da mallajagan@gmail.com Abtact: At pnt, induction moto a th dominant div in vaiou induti. It i quit cumbom to contol an induction moto (IM) bcau of it poo dynamic pon in compaion to th DC moto div. Th cntal thm of Vcto Contol (VC) i to dcoupl th tato cunt of th IM into two othogonal componnt and i to contol th two componnt individually o a to achiv an indpndnt contol of flux and toqu of th IM. VC i till vy complx to implmnt. Dict Toqu Contol (DTC) i an impovid VC mthod. With th DTC chm mploying a Voltag Souc Invt, it i poibl to contol dictly th tato flux linkag and th lctomagntic toqu by th optimum lction of invt witching vcto. Th modling of an IM div mploying DTC with application of fuzzy i pfomd in thi aticl, it i btt to unand th DTC and it difficulti. Th fnc voltag vcto i thn alizd uing a voltag vcto modulato. Sval vaiation of DTC-SVM hav bn popod and dicud in th litatu. Th wok of thi viw pap i to tudy, valuat and compa th vaiou tchniqu of th DTC-SVM applid to th Induction Moto. Kywod: Induction Moto Div, Modling of Induction Moto, Vcto Contol, Fild Oint Contol, Dict Toqu Contol, and Fuzzy Application. 1. INTRODUCTION Th hitoy of lctical moto go back a fa a 1820, whn Han Chitian Otd dicovd th magntic ffct of an lctic cunt. On ya lat, Michal Faaday dicovd th lctomagntic otation and built th fit pimitiv D.C. moto. Faaday wnt on to dicov lctomagntic induction in 1831, but it wa not until 1883 that la invntd th A.C. aynchonou moto [1]. Cuntly, th main typ of lctic moto a till th am, DC, AC aynchonou and ynchonou, all bad on Otd, Faaday and la thoi dvlopd and dicovd mo than a hundd ya ago. An IM i a typ of aynchonou AC moto wh pow i upplid to th otating dvic by man of lctomagntic induction [2-5]. Induction moto a widly ud, pcially polypha induction moto, which a fquntly ud in indutial div. Th fact a du to th induction moto advantag ov th t of th moto. Mot of th indutial moto application u AC induction moto. Th aon fo thi includ high obutn, liability, low pic and high fficincy [2-8]. 2. PRINCIPLE OF OPERATION AND COMPARISON TO SYNCHRONOUS MOTORS A 3-pha pow upply povid a otating magntic fild in an IM. Th baic diffnc btwn an IM and a ynchonou AC moto i that in th latt a cunt i upplid onto th oto. Thi thn cat a magntic fild which, though magntic intaction, link to th otating magntic fild in th tato which in tun cau th oto to tun. It i calld ynchonou bcau at tady tat th pd of th oto i th am a th pd of th otating magntic fild in th tato. By way of contat, th IM do not hav any dict upply onto th oto; intad, a conday cunt i inducd in th oto [2, 9]. Thi changing magntic fild pattn can induc cunt in th oto conducto. Th cunt intact with th otating magntic fild catd by th tato and th oto will tun [10]. Availabl 32

2 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX Thi diffnc btwn th pd of th oto and pd of th otating magntic fild in th tato i calld lip. Th th pha AC IM and i th mot widly ud machin. Bcau it i having th chaactitic fatu Simpl and uggd contuction, Low cot and minimum maintnanc, High liability and ufficintly high fficincy, Nd no xta tating moto and nd not b ynchonizd, and an IM ha baically two pat: Stato and Roto [10] APPLICATIONS A wid vaity of induction moto a availabl and a cuntly in u thoughout a ang of indutial application. Singl pha induction moto a widly ud, du to thi implicity, tngth and high pfomanc. Thy a ud in houhold applianc, uch a figato, ai condition, hmtic compo, wahing machin, pump, fan, a wll a in om indutial application. Bfo th day of pow lctonic, a limitd pd contol of IM wa achivd by witching th th-tato winding fom dlta connction to ta connction, allowing th voltag at th moto winding to b ducd [1-20] VARIABLE-FREQUENCY DRIVES (VFD) A VFD can aily tat a moto at a low fquncy than th AC lin, a wll a a low voltag, o that th moto tat with full atd toqu and with no inuh of cunt. Th oto cicuit' impdanc inca with lip fquncy, which i qual to upply fquncy fo a tationay oto, o unning at a low fquncy actually inca toqu [21-23]. Induti hav many application, wh vaiabl opating pd i a pim quimnt. Pincipal bnfit of vaiabl pd div in indutial application a that thy allow th div pd and toqu to b adjutd to uit th poc quimnt. In many application, opating th plant at a ducd pd whn full output i not ndd poduc a futh impotant bnfit: ngy aving and ducd cot [21]. Wha infinitly vaiabl pd div with good pfomanc fo DC moto alady xitd. Th div not only pmittd th opation in fou quadant but alo covd a wid pow ang. Moov, thy had a good fficincy, and with a uitabl contol vn a good dynamic pon. It main dawback wa th compuloy quimnt of buh [10]. Th vaiou mthod of pd contol of quil cag IM though miconducto dvic a givn in [2, 9-20] a und: Scala contol, Vcto contol (Fild -Ointd Contol, FOC), Dict Toqu Contol (DTC) and DTC with SVM & Fuzzy bad contol. Th contoll a dpnd on how invt can b contolld, motly multilvl invt a uing in induti du to thi advantag [21-45]. Scala contoll: Dpit th fact that Voltag-Fquncy (V/F) i th implt contoll, it i th mot widpad, bing in th majoity of th indutial application [2]. It i known a a cala contol and act by impoing a contant lation btwn voltag and fquncy, o a to giv naly contant flux ov wid ang of pd vaiation [9]. Mo ov Contant voltag/htz contol kp th tato flux linkag contant in tady tat without maintaining dcoupling btwn th flux and toqu [2]. Howv, thi contoll do not achiv a good accuacy in both pd and toqu pon, mainly du to th fact that th tato flux and toqu a not dictly contolld. Evn though, a long a th paamt a idntifid, th accuacy in th pd can b 2% (xpct in a vy low pd), and th dynamic pon can b appoximatly aound 50m [2, 9]. Vcto contoll: In 1971, Blachk popo a chm which aim a th contol of an IM lik a paatly xcitd dc moto, calld fild ointd contol, VC, o Tan vcto contol [46-48]. In thi chm th IM analyzd fom a ynchonouly otating fnc fam wh all fundamntal vaiabl appa to b dc on. Th toqu and flux componnt of cunt a idntifid and contolld indpndntly to achiv good dynamic pon [46, 47]. Th mot widpad contoll of thi typ a th on that u vcto tanfom uch a ith Pak o Ku. Howv th i a ncity of tanfoming th vaiabl in th ynchonouly otating fnc fam to tato fnc fam to affct th contol of actual cunt/voltag [47]. Additionally th tanfomation alo nd th appoximat flux vcto angl, wh i ith calculatd lip angl o maud oto angl a indict VC o by timating th flux angl dictly by mploying a flux Availabl 33

3 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX obv a in dict VC [47]. It accuacy can ach valu uch a 0.5% gading th pd and 2% gading th toqu, vn whn at tanill. Th main diadvantag a th hug computational capability quid and th compuloy good idntification of th moto paamt. Rcntly advancd contol tatgi fo PWM invt fd IM div hav bn dvlopd bad on th pac vcto appoach, wh th IM can b dictly and indpndntly contolld without any co-odination tanfomation [48]. On of th mging mthod in thi ppctiv i th dict toqu and flux contol (DTFC). In DTFC, th moto toqu and th flux a calculatd fom th pimay vaiabl, and thy a contolld dictly and indpndntly by lcting optimum invt witch mod [2-52]. Thi contol ult in quick toqu pon in th tanint opation and impovmnt in th tady tat fficincy [14]. It main chaactitic i th good pfomanc, obtaining ult a good a th claical vcto contol but with val advantag bad on it impl tuctu and contol diagam. DTC i aid to b on of th futu way of contolling th IM in fou quadant. In DTC it i poibl to contol dictly th tato flux and th toqu by lcting th appopiat invt tat [46, 54]. DTC main fatu a dict contol of flux and toqu, indict contol of tato cunt and voltag, appoximatly inuoidal tato flux and tato cunt, and High dynamic pfomanc vn at tand till [53, 54]. DTC hav val advantag lik, Dcoupld contol of toqu and flux, Abnc of co-odinat tanfom, Abnc of voltag modula block, Abnc of mchanical tanduc, Cunt gulato, PWM pul gnation, PI contol of flux and toqu and co-odinat tanfomation i not quid, Vy impl contol chm and low computational tim, and Rducd paamt nitivity and Vy good dynamic popti a wll a oth contoll uch a PID fo moto flux and toqu, and Minimal toqu pon tim vn btt than th VC [53, 54]. Howv, om diadvantag a alo pnt uch a: Poibl poblm duing tating, Rquimnt of toqu and flux timato, implying th conqunt paamt idntification, and Inhnt toqu and tato flux ippl [53-54]. Although, om diadvantag a: High toqu ippl and cunt ditotion, Low witching fquncy of tanito with lation to computation tim, Contant o btwn fnc and al toqu [3]. Aft thi, compaion of vaiabl pd div i givn. Th aim bing to find vn impl mthod of pd contol fo induction machin on mthod, which i popula at th momnt, i DTC. Initially th thoy of induction machin modl i givn. Th unanding of thi modl i mandatoy to unand both th contol tatgi (i.. FOC and DTC). DTC div utilizing hyti compaato uff fom high toqu ippl and vaiabl witching fquncy. Staightly paking, Majo dawback of Claical DTC i high toqu & flux ippl. Th mot common olution to thi poblm i to u fuzzy application with Spac Vcto Modulation (SVM) o u ing multilvl invt [2, 3]. In thi Pap th autho bifly xplaind about two-fuzzy contoll along with th SVM tchniqu i applid to two lvl invt. Bfo going to DTC, fit w tudy about th mathmatical backgound of DTC. 3. INDUCTION MOTOR MATHEMATICAL MODEL Th tady-tat modl and quivalnt cicuit a uful fo tudying th pfomanc of machin in tady tat. Thi impli that all lctical tanint a nglctd duing load chang and tato fquncy vaiation. Th dynamic modl of IM i divd by uing a two-pha moto in dict and quadatu ax [55]. Thi appoach i diabl bcau of th concptual implicity obtaind with th two t of th winding, on on th tato and th oth on th oto. Th quivalnc btwn th th-pha and two-pha machin modl i divd fom th impl obvation. Th concpt of pow invaianc i intoducd [2, 3, 8]. Th fnc fam a chon to abitay and paticula ca uch a tationay, oto, and ynchonou fnc fam, a impl intanc of th gnal ca. Th pac-phao modl i divd fom th dynamic modl in dict and quadatu ax [55]. 3.1 DYNAMIC d-q MODEL Availabl 34

4 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX Th aumption a mad to div th dynamic modl a unifom ai gap, balancd oto and tato winding, with inuoidal ditibutd mmf, inductanc v. oto poition in inuoidal, and Satuation and paamt chang a nglctd. Th dynamic pfomanc of an AC machin i omwhat complx bcau th th-pha oto winding mov with pct to th th-pha tato winding a hown in Fig 1(a). Baically, it can b lookd on a a tanfom with a moving conday, wh th coupling cofficint btwn th tato and oto pha chang continuouly with th chang of oto poition copond to oto dict and quadatu ax [2-4, 7, 8]. Not that a th-pha machin can b pntd by an quivalnt two-pha machin a hown in Fig 1(b), wh d ~ q copond to tato dict and quadatu ax, and d ~q i coponding to oto. Fig 1: (a) Coupling ffct in th-pha tato and oto winding of moto; (b) Equivalnt two-pha machin. Although it i omwhat impl, th poblm of tim-vaying paamt till main. R.H. Pak, in th 1920, popod a nw thoy of lctic machin analyi to olv thi poblm. Entially, h tanfomd o fd, th tato vaiabl to a ynchonouly otating fnc fam fixd in th oto [56]. With uch a tanfomation (calld Pak tanfomation), h howd that all th tim-vaying inductanc that occu du to an lctic cicuit in lativ motion and lctic cicuit with vaying magntic luctanc can b liminatd [3,7]. Lat, in th 1930, H. C. Stanly howd that tim- vaying inductanc in th voltag quation of an induction machin du to lctic cicuit in lativ motion can b liminatd by tanfoming th oto vaiabl to vaiabl aociatd with fictitiou tationay winding. Lat, G. Kon popod a tanfomation of both tato and oto vaiabl to a ynchonouly otating fnc fam that mov with th otating magntic fild. D. S. Bton popod a tanfomation of tato vaiabl to a otating fnc fam that i fixd on th oto. In fact, it wa hown lat by Kau and Thoma that timvaying inductanc can b liminatd by fing th tato and oto vaiabl to a common fnc fam which may otat at any pd AXES TRANSFORMATION Conid a ymmtical th-pha induction machin with tationay a-b-c ax at 2π/3- angl apat, a hown in Fig 2. Ou goal i to tanfom th th-pha tationay fnc fam (a-b -c) vaiabl into two-pha tationay fnc fam (d ~q ) vaiabl and thn tanfom th to ynchonouly otating fnc fam (d ~ q ), and vic-va [3, 56]. Aum that th d q. Ax a ointd at angl, a hown in Fig 2. Th voltag and can b olvd into a-b-c componnt and can b pntd in th matix fom a V a co in 1 V q Vb = 0 0 co( 120 ) in( 120 ) 1 V d (1) 0 0 V c co( 120 ) in( 120 ) 1 V o V d V q Availabl 35

5 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX Th coponding inv lation i. 0 0 V q co co( 120 ) co( 120 ) V a = V d (2) 3 in in( 120 ) in( 120 ) Vb V o V c Wh V o i addd a th zo qunc componnt, which may o may not b pnt. Th cunt and flux linkag can b tanfomd by imila quation. It i convnint to t = 0, o that th q axi i alignd with th a-axi, th tanfomation lation can b implifid by ignoing zo qunc. Fig 3 how th ynchonouly otating d - q, which otat at ynchonou pd with pct to th d -q ax and th angl th two-pha d - q t. winding a tanfomd into th hypothtical winding mountd on th d -q ax [3]. Th voltag on th d -q ax can b convtd (o olvd) into th d -q fam a follow: V V co V in (3) V Fo convninc, th upcipt ha bn doppd fom now on fom th ynchonouly otating fam paamt. Again, olving th otating fam paamt into a tationay fam, th lation a. V V co V in (5) V Th q -d componnt can alo b combind into a vcto fom: V V jv ( V co V in ) j( V in O invly V q d q d qd ( V V q q q V q q q in V q jv d d co d in V d ) d d j d q V q co j V jv ( V jv ) d Not that th vcto magnitud in tationay and otating fam a qual, that i, 2 2 V Vˆ V V (9) m q d j d (4) (6) (8) q V d co ) (7) Fig 2. Stationay fam a~b~c to d ~q ax tanfomation. Availabl 36

6 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX j In Equation (7), i dfind a th inv vcto otato that convt d -q vaiabl into d - q vaiabl. Th vcto V and it componnt pojctd on otating and tationay ax a hown in Fig 3. Th a-b-c vaiabl can alo b xpd in vcto fom. And alo: V V jv q d Va Vb Vc j Vb Vc (10) V a avb a Vc 3 Wh a= j 2 / 3. Th paamt a and a 2 can b intptd a unit vcto. Simila tanfomation can b mad fo oto cicuit vaiabl alo [3, 8, 17] SYNCHRONOUSLY ROTATING REFERENCE FRAME - DYNAMIC MODEL. Fo th two-pha machin hown in Fig 3, w nd to pnt both d -q and d q cicuit and thi vaiabl in a ynchonouly otating d -q fam. W can wit th following tato cicuit quation: d Vq R I q q (11) d Vd R I d d (12) Wh and a q- axi and d-axi tato flux linkag, pctivly. Whn th q d quation a convtd to d -q fam, th following quation can b wittn: d Vq R I q q d (13) d Vd R I d d q (14) Fig.3: (a) Stationay fam d - q to otating fam d - q ; (b) Flux and cunt vcto d - q. If th oto i not moving, that i, 0, th oto quation fo a doubly fd wound-oto machin will b imila to Equation (13) - (14): Availabl 37

7 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX d Vq R iq q d (15) d Vd R id d q (16) Th oto actually mov at pd, th d - q ax fixd on th oto mov at a pd - lativ to th ynchonouly otating fam. Thfo, oto quation hould b modifid a. d Vq R iq q ( ) d d Vd R id d ( ) q (17) (18) Th d -q dynamic modl quivalnt cicuit that atify Equation (13), (14) and (17), (18). A pcial advantag of th d -q dynamic modl of th machin i that all th inuoidal vaiabl in tationay fam appa a dc quantiti in ynchonou fam. Th flux linkag xpion in tm of th cunt can b wittn fom Fig 3(b) a follow: L i L i i ) (19) L i L i i ) (20) q l q m ( q q L i i ) (21) qm m ( q q L i L i i ) (22) d l d m ( d d l d m ( id id m ( id id ) L i L ) (23) d q m ( q q dm L (24) Combining th abov xpion with Equation (13), (14), (17) and (18 ), th lctical tanint modl in tm of voltag and cunt can b givn in matix fom a V R SL L SLm Lm i q q V L R SL Lm SLm i d d (25). V SL m ( ) Lm R SL ( ) L i q q V ( ) Lm SLm ( ) L R SL d id Wh S i Laplac opato. Fo a cag moto, V q =V d = 0. If th pd i conidd contant. Thn, knowing th input V q, V d and l q Equation (25 ). If th machin i fd by cunt ouc, i q, i d and, th cunt i q, i d, i q and i d can b olvd fom a indpndnt. Thn th dpndnt vaiabl V q,v d, i q and i d can b olvd fom Equation (25). Th pd in Equation (25) cannot nomally b tatd a a contant. It can b latd to th toqu a dm 2 d T (26) TL J TL J P Wh T L = load toqu, J = oto intia, and m = mchanical pd. Oftn, fo compact pntation, th machin modl and quivalnt cicuit a xpd in complx fom [3]. Multiplying Equation (14) by j and adding with Equation (13) giv. d Vq jvd R ( iq jid ) ( q j d ) j ( q j d ) (27) d O Vqd Riqd qd j( ) qd (28) Similaly, th oto quation (17)-(18) can b combind to pnt d Vqd Riqd qd j( ) qd (29) Availabl 38

8 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX Wh V qd =0. Thfo, th tady-tat quation can b divd a V R I j (30) R 0 I j (31) S If th paamt R m i nglctd. W know that 3 P mi in (32) 2 2 Fom Equation (32), th toqu can b gnally xpd in th vcto fom a 3 P m xi (33) P dmiq qmi d (34) 2 2 Som oth toqu xpion can b divd aily a follow: 3 P dmiq qmi d (35) P diq qi d (36) P Lm ( iqid idiq ) (37) P ( diq q I d ) (38) 2 2 Equation (25), (26), and (37) giv th complt modl of th lcto-mchanical dynamic of an IM in ynchonou fam. Fig 4 how th block diagam of th machin modl along with input voltag & output cunt tanfomation [2, 8] and olving vaiabl into dq componnt. Rnwabl ngy bad wat upply ytm i on of th application [57-74]. In iigation and dinking wat upply, motly w a uing induction moto; hnc tudy of contol of induction moto i ncay. Availabl 39

9 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX Fig 4. Synchonouly otating fam machin modl with input voltag and output cunt tanfomation. 4. CONTROL METHODS Stato flux linkag i timatd by intgating th tato voltag. Toqu i timatd a a co poduct of timatd tato flux linkag vcto and maud moto cunt vcto [75, 76]. Th timatd flux magnitud and toqu a thn compad with thi fnc valu. If ith th timatd flux o toqu dviat fom th fnc mo than allowd tolanc, th GTO of th vaiabl fquncy div a tund off and on in uch a way that th flux and toqu will tun in thi tolanc band a fat a poibl. Thu DTC i on fom of th hyti o bang-bang contol. Thi contol mthod impli th popti of th contol: Toqu and flux can b changd vy fat by changing th fnc, Th tp pon ha no ovhoot, No coodinat tanfom a ndd, all calculation a don in tationay coodinat ytm, No paat modulato i ndd, th hyti contol dfin th witch contol ignal dictly [3, 75, 76], and Th a no PI cunt contoll. Thu no tuning of th PI i quid. Howv, by contolling th wih of th tolanc band th avag witching fquncy can b kpt oughly at it fnc valu [2, 3]. Thi alo kp th cunt and toqu ippl mall. Thu th toqu and cunt ippl a of th am magnitud than with vcto contolld div with th am witching fquncy. Du to th hyti contol th witching poc i andom by natu. Synchonization to otating machin i taightfowad du to th fat contol; jut mak th toqu fnc zo and tat th invt [2, 3, 75, 76]. Th flux will b idntifid by th fit cunt pul. Typically th contol algoithm ha to b pfomd with micocond o hot intval bcau of th implicity of th algoithm. Th DTC mthod pfom vy wll vn without pd no [3]. Howv, th flux timation i uually bad on th intgation of th moto pha voltag [75, 76]. Du to th invitabl o in th voltag maumnt and tato itanc timat th intgal tnd to bcom onou at low pd. Thu it i not poibl to contol th moto if th output fquncy of th vaiabl fquncy div i zo. Howv, by caful dign of th contol ytm it i poibl to hav th minimum fquncy in th ang 0.5 Hz to 1 Hz that i nough to mak poibl to tat an IM with full toqu fom a tanill ituation. A val of th otation diction i poibl too if Availabl 40

10 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX th pd i paing though th zo ang apidly nough to pvnt xciv flux timat dviation [77, 78]. If continuou opation at low pd including zo fquncy opation i quid, a poition no can b addd to th DTC ytm [77-79]. Fig 5: Block diagam of th induction moto div ytm bad on DTC chm VIEW OF DIRECT TORQUE CONTROL In pincipl th DTC mthod lct on of th ix nonzo and two zo voltag vcto of th invt on th bai of th intantanou o in toqu and tato flux magnitud [13, 76]. In pit of it implicity, DTC allow good toqu contol in both tady and tanint tat. It main chaactitic i th good pfomanc, obtaining ult a good a th claical vcto contol. Fig 5. Show th Block diagam of th IM div ytm bad on DTC chm [3, 75, 76]. DTC mthod till quid futh ach in od to impov th moto pfomanc, a wll a achiv a btt bhavio gading nvionmnt compatibility (Elcto Magntic Intfnc and Engy), that i did nowaday fo all indutial application. 4.2 CLASSICAL DIRECT TORQUE CONTROL Claic DTC mak u of hyti compaato with toqu and tato flux magnitud o a input to dcid which tato voltag vcto i applid to moto tminal. Th complx plan i dividd in ix cto, and a witching tabl i dignd to obtain th quid vcto bad on th hyti compaato output [3, 4]. Du to fat tim contant of tato dynamic it i vy difficult to kp machin toqu btwn th hyti band. Thi can do ith by incaing th ampling fquncy a in, thu incaing witching fquncy, commutation lo and computation quimnt, o uing multilvl convt. Th u of hyti compaato in claic DTC implmntation giv i to vaiabl witching fquncy (VSF), which dpnd on oto pd, load, ampl fquncy, tc. VSF may xcit onant dynamic in th load and hnc contitut a iou dawback of DTC. Gnally th a two mthod to duc th toqu and flux ippl fo th DTC div. On i multi lvl invt; th oth i pac vcto modulation (SVM) [77, 78]. In th fit mthod, th cot and th complxity will b incad, in th cond mthod, th toqu ippl and flux ippl can b ducd, howv th witch fquncy till chang. In th nxt ction a fuzzy appoach i givn to duc toqu ippl [8]. Thi goal i achivd by th fuzzy contoll which minat th did amplitud of toqu hyti band. 4.3 TORQUE EXPRESSIONS WITH STATOR AND ROTOR FLUXES Th toqu xpion fo induction machin can b xpd in vcto fom a, 3 P I (39) 2 2 Wh j and I i ji. In thi quation, I i to b placd by oto q d flux. In th complx fom, and can b xpd a function of cunt a, m L I L I (40) q d Availabl 41

11 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX L I LmI (41) Fom quation 39, 40 and 41: 3 P Lm ' 2 2 L L (42) That i, th magnitud toqu i 3 P Lm ' 2 2 L L in (43) Wh γ i th angl btwn th flux, indicating th vcto,, and fo poitiv dvlopd toqu. If th oto flux main contant and tato flux i changd incmntally by tato voltag V a hown and th coponding chang of γ angl i, th incmntal toqu xpion i givn a 3 P Lm T in ' (44) 2 2 L L 4.4 CONTROL STRATEGY OF DTC Block diagam of th IM div ytm bad on DTC chm i hown in Fig 6. Th pd contol loop and th flux pogam a a function of pd a hown a uual and will not b * dicud. Th command tato flux and toqu T magnitud a compad with th pctiv * ˆ timatd valu and th o a pocd though hyti-band contoll, a hown [2]. Th flux loop contoll ha two lvl of digital output accoding to th following lation: H fo E HB (45) Wh H 1 1 fo E HB (46) 2 HB = total hyti-band wih contoll. Th cicula tajctoy of th command * ˆ flux vcto with th hyti band otat in an anti-clockwi diction a hown in Fig 7. Th actual tato flux i containd within th hyti band and it tack th command flux in a zigzag path. Th toqu contol loop ha th lvl of digital output, which hav th following lation [2]: H 1 fo E HB (47) H H 1 fo E HB (48) 0 fo HB E HB (49) I Availabl 42

12 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX Fig 6: In pincipl th DTC mthod lct on of th ix nonzo and two zo voltag Fig 7: Invt voltag vcto and coponding tato flux vaiation in tim Δt. Figu 8: Dict toqu and flux contol block diagam. Availabl 43

13 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX Th fdback flux and toqu a calculatd fom th machin tminal voltag and cunt. Th ignal computation block alo calculat th cto numb S(k) in which th flux vcto li. Th a ix cto (ach /3 angl wid), a in Fig 7(a). Th voltag vcto tabl block in Fig 8 civ th input ignal H, and S(k)and gnat th appopiat contol voltag vcto H, (witching tat) fo th invt by lookup tabl, which i hown in tabl 1 (th vcto ign i dltd) [2, 3]. Th invt voltag vcto and a typical a hown in Fig 7(b). Nglcting th tato itanc of th machin, w can wit. d V ( ) (50) O. t (51) V Which man that can b changd incmntally by applying tato voltag V fo tim incmnt Δt. Th flux incmnt vcto coponding to ach of ix invt voltag vcto i hown in Fig 7. Th flux in machin i initially tablihd to at zo fquncy (dc) along th tajctoy OA hown in Figu 7. With th atd flux, th command toqu i applid and th vcto tat otating [2, 3]. Tabl1: Switching tabl of invt voltag vcto. H Ψ H S(1) S(2) S(3) S(4) S(5) S(6) 1 V2 V3 V4 V5 V6 V1 * 1 0 V0 V7 V0 V7 V0 V7-1 V6 V1 V2 V3 V4 V5 1 V3 V4 V5 V6 V1 V2-1 0 V7 V0 V7 V0 V7 V0-1 V5 V6 V1 V2 V3 V4 Tabl2: Flux and Toqu vaiation du to applid voltag vcto in. Voltag vcto V1 V2 V3 V4 V5 V6 V0 o V7 Ψ 0 T Tabl 1 appli th lctd voltag vcto, which ntially affct both th toqu and flux imultanouly [2, 3]. Th flux tajctoy gmnt AB, BC, CD and DE by th pctiv voltag vcto V3, V4, V3, andv4 a hown in Figu 7(a). Th total and incmntal toqu du to a xplaind in Fig 7(b). Not that th tato flux vcto chang quickly by, but th chang i Availabl 44

14 vy luggih du to lag tim contant T. Sinc J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX i mo filtd, it mov unifomly at fquncy ω, wha movmnt i jky. Th avag pd of both, howv, main th am in th tady-tat condition. Tabl2 ummaiz th flux and toqu chang (magnitud and diction) fo applying th voltag vcto fo th location of hown in Fig 7(b) [2, 3]. Th flux can b incad by th V1, V2, andv6 vcto, wha it can b dcad by th V3, V4, andv5 vcto [2]. Similaly, toqu i incad by th V2, V3, andv4 Vcto, but dcad by th V1, V5, andv6 vcto. Th zo vcto (V 0 o V 7 ) hot-cicuit th machin tminal and kp th flux and toqu unaltd. Du to finit itanc (R ) dop, th toqu and flux will lightly dca duing th hot-cicuit condition. Conid fo xampl, an opation in cto S(2) a hown in Fig 7(a), wh at point B, th flux i too high and th toqu i too low; that i, H 1 and H 1. Fom tabl 1, voltag V 4 i applid to th invt, which will gnat th tajctoy BC. At point C, H 1 and H 1 and thi will gnat th V 3 vcto fom th tabl. Th div can aily opat in th fou quadant, and pd loop and fild-wakning contol can b addd, if did [80]. Th toqu pon of th div i claimd to b compaabl with that of a vcto-contolld div [2]. 5. FUZZY APPLICATION Soft computing tchniqu can apply fo nonlina ytm [80-83]. A fuzzy contoll i intoducd to allow th pfomanc of DTC chm in tm of flux and toqu ippl to b impovd [84-87]. Th pd gulato a convntional PI contoll (CPIC), which qui pci math modl of th ytm and appopiat valu of PI contant to achiv high pfomanc div. Thfo, unxpctd chang in load condition o nvionmntal facto would poduc ovhoot, ocillation of th moto pd, ocillation of th toqu, long ttling tim and cau ioation of div pfomanc [84-87]. Th lctd voltag vcto i applid fo th nti witching piod, and thu allow lctomagntic toqu and tato flux to vay fo th whol witching piod. Thi cau high toqu and flux ippl. To ovcom th poblm in DTC, two fuzzy contoll a widly analyzd in litatu [2, 3]. Tho a: 1. Fuzzy PI Contoll (FPIC) to achiv pciion pd contol. 2. Fuzzy Logic Duty Ratio Contol (FLDRC) to minimiz toqu & flux ippl. Whn Fuzzy Logic i ud fo th on-lin tuning of th PI contoll, it civ cald valu of th pd o and chang of pd o. It output i updating in th PI contoll gain bad on a t of ul to maintain xcllnt contol pfomanc vn in th pnc of paamt vaiation and div non-linaity [87]. Block diagam of th mthod with clo-loop toqu and flux contol in tato flux coodinat ytm i pntd in Fig 9. Th output of th PI flux and toqu contoll can b intptd a th fnc tato voltag componnt V x, V y a th tato flux ointd coodinat (x y). Dign of Fuzzy Logic Contoll i dpnd on Slction of input vaiabl, Slction of output vaiabl, Numb of fuzzy contoll, Slction of Mmbhip function and Slction of dfuzzification. H, w had takn two fuzzy contoll fo toqu and flux, tiangula mmbhip and cntoid dfuzzification. FPIC do dynamically adjut th gain k P and k I to nu th tability of ytm ov wid toqu-pd ang, Swift pd pon, L ovhoot and, Extmly mall tady tat o. FLDRC do Minimiz toqu & flux ippl ffctivly, incad fficincy, Low acoutic noi, Opat at a low witching fquncy compad to th xiting mthod, and Rduc computation budn. Availabl 45

15 J. M. R. Malla t. al. / Intnational Jounal of Nw chnologi in Scinc and Engining Vol. 1, Iu. 1, Jan. 2014, ISSN XXXX-XXXX By uing th two fuzzy contoll w achiv good pd and toqu pon. Aft output of th fuzzy contoll (aft dfuzzification) w gnat Vx and Vy, again convtd thi X-Y coodinat componnt to α-β componnt. By uing thi valu gnat 6 pul with th hlp of Spac Vcto Modulation.). ω* Vdc ω PI T* Contoll T Ψ* Fuzzy Fuzzy Vx Vy x-y to α-β Vα Vβ SVM θ Invt Induction Moto Ψ ABC to αβ Flux, Toqu and θ timato Vdc Iα Iβ Fig: 9. Two fuzzy bad DTC-SVM modl CONCLUSIONS Th pap ha pntd a DTC div with fuzzy contoll. Thi contoll minat th did amplitud of toqu hyti band. Th main advantag i th impovmnt of toqu and flux ippl chaactitic at any pd gion; thi povid an oppotunity fo moto opation und minimum witching lo and noi. Th two-fuzzy bad DTC-SVM-IMD ytm, thby damatically ducing th toqu ippl. A fuzzy contoll m to b a aonabl choic to valuat th amplitud of toqu hyti band accoding to th toqu ippl lvl. Fuzzy-PI Contoll to achiv pciion pd contol and Fuzzy Logic Duty Ratio Contol i ud to minimiz toqu & flux ippl. Whn Fuzzy Logic i ud fo th on-lin tuning of th PI contoll, it civ cald valu of th pd o and chang of pd o. REFERENCES [1] I.P. Kopylov, Mathmatical Modl of Elctic Machin, Tanlatd fom th Ruian by P.S. Ivanov, Rvid fom th Ruian dition, [2] Bo B.K, Modn Pow Elctonic and AC Div, 4 th Edition, [3].Jyothi Mangavni Chitta and Sinivaa Rao Matuu, Snol Pmannt Magnt Synchonou Moto (PMSM) Fo Toqu Rippl Rduction, Intnational Jounal of Emging Tnd in Elctical and Elctonic (IJETEE ISSN: ),, Vol. 8, Iu. 1, pp. 1-7, Oct-2013, [4].G. Subba Rddy, Vcto Contoll bad Spd Contol of Induction Moto Div with 3-Lvl SVPWM bad Invt, Intnational Jounal of Emging Tnd in Elctical and Elctonic (IJETEE ISSN: ), Vol. 1, Iu. 4, pp. 1-11, Mach-2013, [5].M. Anjali.U.Jawadka, D.G.M.Dhol, SRPaaka, S.S.Jadhao and M.A.Bg, Application of ANN fo Induction Moto Fault Claification Uing Hilbt Tanfom, Intnational Jounal of Emging Tnd in Elctical and Elctonic (IJETEE ISSN: ), Vol. 1, Iu. 1, pp. 7-12, Mach-2013, [6].Niaj Kuma Shukla and D. S K Sinha, Fuzzy and PI Contoll Bad Pfomanc Evaluation of Spaatly Excitd DC Moto, Intnational Jounal of Emging Tnd in Elctical and Elctonic (IJETEE ISSN: ), Vol. 2, Iu. 1, pp , Apil-2013, ω Availabl 46

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