J. Electrical Systems 9-3 (2013): Regular paper

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1 Z.M.S. El- Barbary J. Elctrical Systms 9-3 (13): JES Corrsponding author: Dpartmnt of Elctrical Enginring, Kafrlshikh Univrsity, Tanta, Egypt, Egypt Dpartmnt of Elctrical Enginring, King Khalid Univrsity, Saudi Arabia Copyright JES 13 on-lin : journal/srgroups.org/js Rgular papr Journal of Elctrical Systms Low-Cost Fault Tolrant Basd Spd Snsorlss Vctor Control of Induction Motor Driv Systm Induction motor is a cast of altrnating currnt motor whr charg ndurs allottd to th rotor clos-at-hand dputation of conductiv charg. Ths motors ar broadly applid in industrial claim du to thy ar arduous along with adhr no contacts. To dvlop highly rliabl and fault tolrant induction motor driv systm a major concrn and xtnsiv rsarch has bn ddicatd. This papr prsntd th prformanc analysis of fault tolrant of thr phas invrtr fd spd snsorlss control of thr phas induction motor driv. To incras th rliability of th driv systm, this papr prsnts fault tolrant of invrtr whn on switch is opn or on lg of six-switch invrtr is lost. Th control of driv systm is basd on indirct rotor fild orintd control thory. Also, th mthodology dpnds on spd snsorlss schm to obtain th spd signal fdback; th spd stimator is basd on modl rfrnc adaptiv systm using stator currnt and rotor flux as stat variabls for stimating th spd. Th fault tolrant algorithm is abl to adaptivly chang-ovr from six switch invrtr to four switch invrtr topologis whn th fault is occurrd; also, it maks a smooth transition of th motor spd, torqu and currnt whn changing ovr from faulty condition to nw halthy status which is Four Switch Thr Phas Invrtr (FSTPI) topology, thus, th Six Switch Thr Phas Invrtr (SSTPI) topology (pr-fault status) almostly rtaind. Th proposd algorithm is simulatd by using th Matlab/Simulink packag. Th obtaind rsults from th simulation modl dmonstrat th prformanc nhancmnt and good validity of th fault-tolrant control for spd snsorlss induction motor driv systm. Kywords: Induction motor driv, Currnt control Voltag sourc invrtr (CCVSI), Fault tolrant, four-switch thr phas invrtr (FSTPI).Insulatd Gat Bipolar Transistor (IGBT) Introduction Thr phas induction motors hav bn th workhors for industrial and manufacturing procsss. Th nrgization of such motors in ths procsss and applications can b achivd through th following ways: (1) dirct on-th-lin starting, () soft-starting, and (3) adjustabl-spd driv (ASD) control. With th dvlopmnt of powr lctronics and digital signal procssor, induction motors ar prdominantly fd from puls width modulation (PWM) invrtr, so, ASDs ar widly adoptd in many industrial applications. In fact, th main rasons for thir adoption in ths applications ar owd to th robust control and high ASDs offrs high prformanc lik soft starting, soft stop, spd rvrsal, braking and many typs of spd control mthods as compard to soft startrs. Nvrthlss, soft startrs ar a low cost mans in comparison to ASDs if th application dos not rquir to spd-torqu control. Th rliability of lctrical drivs is a big aim and has not bn rsolvd bcaus th powr lctronic dvics and control circuit ar fail part of th invrtr. [1-]. Th faults sourcs in th drivs ar, th powr convrtr circuits (about 38 prcnt),control circuits (about 3 prcnt ) and xtrnal auxiliaris(about 9 prcnt) [6]. Thr two typs of powr smiconductor switchs faults of invrtrs. [7-1]. th first typ is transistor short-circuit switch-fault, this fault lads to catastrophic failur of th invrtr if th othr transistor of th sam invrtr lg is turnd-on, this rsulting in a dirct short-circuit of th dc-bus link. To prvnt th short circuit fault, it is ncssary to minimiz possibl lapsd tim aftr th fault occurrd [11]. Th othr typ of faults is opn circuit fault of transistor. Th driv may b oprating with opn circuit fault of any transistor, but with much infrior of prformanc, th lctromchanical torqu is affctd

2 J. Elctrical Systms 9-3 (13): and pulsating bcaus th motor currnts ar asymmtric du to on phas s currnt is unipolar. Hnc, a driv fault diagnostic systm dtrmins th typ; hnc th fault tolrant taks appropriat corrction action of th fault. Thr ar two ways to tst th driv fault, xprimntally in th actual motor drivs and anothr is fault simulation. [1-1]. This papr prsnts a fault tolrant control of six switch invrtr fd spd snsorlss control of thr phas induction motor driv. Th fault tolrant control dpnds on transition from six to four switch invrtr algorithms. Th transition xcutd by on of th xtra switchs as shown in Figur 1. Th xtra switch rcivs th fault tolrant signal from control systm, and conncts th motor s phas that it lost to th mid- point of a dc capacitor bank. A simulation rsults ar carrid out using. MATLAB/SIMULINK packag. Th proposd systm of fault tolrant of invrtr introducs a good bhavior with spd snslss indirct rotor fild orintd control of induction motor driv. Fig.1 Six-switch invrtr topology with xtra switchs 316 SYSTEM DESCRIPTION Th proposd systm intndd for prformanc analysis of snsorlss indirct rotor fild orintd control of induction motor driv is shown in Figur. This sction prsnts th mathmatical modl of th induction motor driv systm to rvis th rcital of th schm at divrs working sttings. In addition a dtaild analysis of a fault tolrant of invrtr fd spd snslss driv. Indirct Rotor Fild Orintd Control Th fild orintd control (FOC) block rcivs th torqu command T * obtaind from * th spd controllr whil th flux command is maintaind constant. Th fild orintd dr control block prforms th slip calculation and gnrats th currnt command componnts i and i in a rotating rfrnc fram. Ths componnts ar furthr manipulatd by axs qs ds transformations to obtain th abc currnt command componnts i a, i b, and i c. Th axs transformations usd for th prsnt systm ar xprssd as follows;

3 Z.M.S. El-Barbary: Low-Cost Fault Tolrant Basd Spd Snsorlss Vc. Control of IM Driv... s* * i qs coss sin i s qs * s* * ids sins coss ids (1) Whr s rprsnts th sum of th slip and rotor angls. s* s* ias iqs s* 1 s* 3 s* qds abc i bs iqs ids s* 1 s* 3 s* ics iqs ids () Currnt Control Voltag Sourc Invrtr A thr-phas invrtr consists of a six switch (T1 to T6) invrtr as shown in figur 1. Th DC link capacitors fd from thr phas uncontrolld rctifir Th two- lvl currnt control of th six-switch bridg invrtr usd to control th load currnt by forcing it to follow a rfrnc on. This is achivd by th switching action of th invrtr to kp th currnt within th hystrsis band. Th load currnts ar snsd and compard with rspctiv command currnts using two indpndnt hystrsis comparators.th output signal of th comparators ar usd to activat th invrtr powr switchs. This controllr is simpl and provids xcllnt dynamic prformanc. i rf =i max sin(t) (3) i up = i rf + H (4) i lo =i rf - H () Whr, i rf is th rfrnc currnt (may b i ar, i br or i cr ), i up is th uppr band, i lo is th lowr band and H is th hystrsis band. For i ar >.: if i a >i up, thn NA=, this mans that th invrtr output voltag switchs to ngativ in ordr to rduc th lin currnt. In th sam mannr if i a <i lo, thn. NA=1, whr th invrtr output voltag switchs to positiv in ordr to incras th lin currnt. Th sam squnc is followd for phas b and c. Hnc, th control logic for phass ar givn as follow: For i ar >.: if i a >i up, thn NA=, ls if i a <i lo thn NA=1, For i ar <.: if i a <i up, thn NA1=1, ls if i a >i lo thn NA1=, th switchs of ach lg ar controlld complmntary (i.. NA1 = 1 - NA), and th sam logic gnration for phass B and C. Hnc, Th modulatd phass voltags of six switch invrtr ar introducd as a function of switching logic NA, NA1, NB,NB1 and NC,NC1 of powr switchs by th following rlations: Va 1 1NA Vdc V b 1 1 NB 3 V C 1 1 NC (6) 317

4 J. Elctrical Systms 9-3 (13): rf PI * dr T * Indirct Fild Orintd Controllr i ds i qs dq to dqs to abc Transformations i a i ar i b i br i c i cr PWM Invrtr DC V s V a V b V c I s IM 318 Control sl r Spd Estimator abc to dqs to dq Transformations Fig. Block Diagram of th Proposd Spd Snsorlss Control Systm Induction Motor Modl Squirrl-cag induction motor is rprsntd in its d-q dynamic modl. This modl rprsntd in synchronous rfrnc fram is xprssd as follows; RspL L p V qs L r L r I qs V L ds m Ids L Rs pl p (7) Lr Lr qr RL r m RrpL ( r) dr RL r m ( r)l m R rpl Th lctromchanical quation is also givn by; dr T TL J Br (8) dt Whr, th lctromagntic torqu is xprssd as: 3 p T. ( Iqsdr I ds qr ) (9) Lr Equation (3) dnots that th torqu can initially proportional to th quadratur componnt of th stator currnt ( I qs * ) if th q -axis componnt of th flux bcoms zro (d -axis is alignd with th rotor flux axis), and th d -axis componnt ( *) is kpt constant. This is dr th philosophy of th vctor control tchniqu. In accordanc, Eq.(9) is linarizd as : T = K I t dr qs (1) This quation is similar to that of th sparatly xcitd dc motor. Th angular slip * frquncy command ( sl ) is calculatd as follow: L Iqs * * = m. (11) sl * * r dr Also from Eq. (4) * 1 * * I = (1+ r p) (1) ds dr Angular frquncy is obtaind as follows, V ds V qs i ds i qs

5 Z.M.S. El-Barbary: Low-Cost Fault Tolrant Basd Spd Snsorlss Vc. Control of IM Driv... r sl (13).dt (14) Th torqu producing currnt componnt is calculatd from: * * 1 ) K ps [1+ css] I = r r qs k t * css dr Whr r is th motor spd obtaind as in th following sction. MRAS Basd Spd Estimation Modl Rfrnc Adaptiv Systms (MRAS) tchniqus ar applid in ordr to stimat rotor spd. This tchniqu is basd on th comparison btwn th outputs of two stimators. Th stimator that dos not involv th quantity to b stimatd (th rotor spd r ) is considrd as th induction motor voltag modl. This modl is considrd to b th rfrnc modl (RM).And th othr modl is th currnt modl, drivd from th rotor quation, this modl is considrd to b th adjustabl modl (AM). Th rror btwn th stimatd quantitis by th two modls is usd to driv a suitabl adaptation mchanism which gnrats th stimatd rotor spd; r to b usd in th currnt modl was dvlopd [16]. In this papr, th obsrvr dpnds on th MRAS and spd obsrvr basd on stator currnt and rotor flux is shown in Figur 3. Th stator currnt is rprsntd as: Th stator currnt is rprsntd as: 1 ids dr rtr qr Tp r dr L m (16) 1 iqs qr rtr dr Tp r qr L m Using th abov Equations, th stator currnt is stimatd as 1 ids dr rtr qr Tp r dr L m (17) 1 iqs qr rtr dr Tp r qr L m Th diffrnc in th stator currnt is obtaind as Tr ids ids qr r r (18) Tr iqs iqs dr r r Equation (18) may b rwrittn as: T r (ids i ds ) qr qr r r (19) T r (iqs i qs ) dr dr r r Sinc th stator currnt rror is rprsntd as a function of stimatd spd, an adaptiv flux obsrvr can b constructd from th machin modl quation. Th modl outputs ar th stimatd valus of th stator currnt vctor îs and th rotor flux linkag vctor ˆr. From Eqn. (19), (1) 319

6 J. Elctrical Systms 9-3 (13): T r (ids i ds ) qr (iqs i qs ) dr ( qr dr ) r r () Hnc, th rror of th rotor spd is obtaind as follows: r r [(ids i ds ) qr (iqs i qs ) dr ]/K T (1) r whr K ( qr dr ) Th right hand trm sms as th trm of spd calculation from adaptiv obsrvr, so th spd can b calculatd from th following quation. 1 r [( Kp ( ids ids ) qr ( iqs iqs ) dr ) K ( KI ( ids ids ) qr ( iqs iqs ) dr )] () 3 DC Currnt Fault dtction Mthod Fig.3 MRAS spd stimation schm This mthod of th invrtr fault dtction dpnds on which transistor is opn. opnd switch dos not pass any currnt, th phas currnt can only b positiv or ngativ and bhav charactristically, Also, Th dc currnt componnt appars, whras ths componnt of dc currnts disappar in halthy condition. Th dc currnt fault dtction mthod stats as follow, using th Park's Vctor transformation in () axis, quations (3) and (4) xplaind th currnts yilds to trajctoris as displayd in figur 4. I I a (3) Ib I I c 3 (4) Th dirct componnt is usd as diagnostic variabl and calculatd as follow; 1 N v = I v ( k ) N 1 () Th rsulting spac vctor can b dscribd by magnitud and angl as follow; = v (6) arg (µ)= arctan (7) v [, ] In halthy condition (no fault) th avrag valu of currnt is zro and th currnt spac vctor runs in a circl. To rsist nois and transints; if th magnitud xcds a crtain

7 Z.M.S. El-Barbary: Low-Cost Fault Tolrant Basd Spd Snsorlss Vc. Control of IM Driv... thrshold fault is dtctd. And th opnd switch is dtrmind using tabl (I). Th mthod dvlopd by Abramik [17] also uss th dirct componnt, of th phas currnts, which is calculatd by avraging ovr on priod ().To obtain a diagnostic variabl that is indpndnt of th actual load, th first ordr harmonic cofficints of th phas currnts ar computd by mans of a DFT (8), (9) Dividing th dirct componnt by th calculatd DFT cofficint provids th diagnostic variabl v,this is don for all thr phass (). = v v a b (9) 1,v 1,v i k a 1,v = I v(k )cos( ) N KiN 1 N i k b 1,v = I v(k )sin( ) N KiN1 N 1: i d 1,i ={ : i 1:.4 i d,i ={ :.4 v a,b,c i (34) Th dcision on whthr thr is a fault and which transistor is faulty is basd on tabl (1) with (3) and (33), as statd in [13]. (3) (31) (3) (33) Fig. (4) Trajctory of phas currnts in Park's Vctor 31

8 J. Elctrical Systms 9-3 (13): Tabl 1: LOCALIZATION OF FAULT WTHN ORMALIZDECD CURRENT Transistor d 1,a d 1,b d 1,c d,a d,b d,c T1 1 1 T T3 1 1 T T T Four-Switch Invrtr Topology Whn th fault occur th fault dtction systm forc Th modulatd phas voltags to oprat as four switch invrtr by opning th othr switch in th faulty lg as shown in figur (), and th phas voltags ar bcom: V a = E dc (4NA + NB -1) 3 (3) V b = E dc (-NA+ 4NB -1) 3 (36) E V = dc c (-NA-NB+) 3 (37) During fault as a function of switching logic NA, NA1 and NB, NB1,whrars phas C is faulty.in matrix form, Va 4 1NA Edc Vb 4 1 NB 3 V c 1 (38) Also, it will b assumd that a stiff voltag is availabl across th two dc-link capacitors [18]. RESULTS AND DISCUSSION 3 Fig. Four-switch invrtr topology Th proposd control systm shown in Fig. (1) is dsignd for a simulation invstigation. Simulation is carrid out using th gnral purpos simulation packag Matlab/Simulink [19], Simulation rsults ar prsntd to show th ffctivnss of th proposd schm at diffrnt oprating conditions. Ths rsults ar classifid into two cas studis; th first rprsnts systm rspons with fault condition whil th scond rprsnts th systm rspons with fault tolrant. In th First cas study, th systm starts and runs normally in

9 Z.M.S. El-Barbary: Low-Cost Fault Tolrant Basd Spd Snsorlss Vc. Control of IM Driv... six-switch invrtr algorithm with a load torqu of (3N.m) and spd rfrnc of 1 rad/sc. At t=.7s, th fault is occurrd and th lg A is faulty. Systm continus to run by FOC six- switch invrtr. Th stator currnts, dc componnts of thos currnts, lctromagntic torqu ar masurd. Also, th motor spd is masurd and stimatd. In th scond cas study, th fault tolrant systm has bn applid for both on switch opning and two switchs opning faults. If on switch is opnd th control systm disconnct th othr switch in th sam lg also, by snding a fault tolrant signal command to an xtra switch, th switch connct th rlatd motor trminal to that to th mid-point of dc link capacitors, finally, th FOC systm oprats with four switch invrtr algorithm. Figurs 6 and 7, prsnt th motor rspons in th prvious cass. Figur 6 shows that thr is obvious componnt suprimposd on th motor currnts rlatd to phass a and b. Figur 7 shows that a dc componnt hav bn vanishd du to fault tolrant control action. Figurs 8 shows th stator currnt in - axis systm undr fault condition, whr, figur 9 shows th sam currnt componnts undr fault tolrant condition, its notd that th distortion in th currnt wav form whn th systm transition from fault to fault tolrant conditions is liminatd. Figurs 1 show th masurd and stimatd spd signals and lctromagntic torqu rspctivly in fault cas its notd that th stimatd spd of motor and lctromagntic torqu signals is mor affctd than th masurd spd bcaus it dpnd on th motor currnt. Whras, figur 11 shows th sam rsults whn th fault tolrant control systm is applid, its notd also th lctromagntic torqu in th rgion aftr fault tolrant (four switch invrtr ) is mor rippl than bfor fault (six switch invrtr). CONCLUSIONS A fault tolrant control systm basd on spd snsorlss IRFOC tchniqu of induction motor driv systm is proposd. Th fault tolrant algorithm and driv systm is vrifid by simulation using a 1.kW/38V/Hz induction motor. Th fault tolrant systm has bn applid for ithr on switch opnd or loss of on lg faults. If on switch is opnd th fault tolrant control systm disconnct th othr switch in th sam lg and connct th rlatd motor trminal to that lg to th mid-point of dc link capacitors. It givs a good changs-ovr from faulty condition to a nw halthy condition dpnding on mntiond algorithms of thr phas invrtr whn th fault occurs. Th control systm includs two cass; on for six-switch (pr-fault condition) and th othr is four switch invrtr, (postfault condition); Th rsults shows that a dc componnts in th motor phas hav bn vanishd du to fault tolrant control action.also, it shows that th stimatd spd signal of th is mor affctd than th masurd on bcaus it dpnd on th motor currnt. Its notd also th lctromagntic torqu in th rgion aftr fault tolrant (four switch invrtr ) is mor rippl than bfor fault (six switch invrtr).th obtaind rsults shows th ffctivnss of th proposd fault tolrant systm with spd snsorlss induction motor driv, Also givs good bhaviors aftr fault tolrant closd to th halthy condition (prfault) with six switch invrtr. 33

10 J. Elctrical Systms 9-3 (13): Ia (A) Ia - DC (A) - - Ib (A ) Ib - DC (A) - - Ic (A ) Ic - Dc (A) - - Fig.6 Phas currnts and DC currnt componnts of th systm undr fault condition 34

11 Z.M.S. El-Barbary: Low-Cost Fault Tolrant Basd Spd Snsorlss Vc. Control of IM Driv... Alfa- Currnt (A) Bta- Currnt (A) Ia (A ) Ia -D C (A ) Ib (A ) Ib-D C (A ) Ic -D C (A ) - - Fig.8 ( and ) currnts undr fault condition Ic (A ) Fig.7 Phas currnts and DC currnt componnts of th systm undr fault tolrant control systm 3

12 J. Elctrical Systms 9-3 (13): Alfa Currnt (A) - Bta Currnt (A) - Fig.9 ( and ) currnts undr fault tolrant control systm 11 Wr (rad/sc) (a) 11 Ws (rad/sc) (b) T (N.m) 1-1 (c) Fig.1 (a) Masurd spd (b) Estimatd spd (c) Dvlopd torqu undr fault condition 36

13 Z.M.S. El-Barbary: Low-Cost Fault Tolrant Basd Spd Snsorlss Vc. Control of IM Driv... 1 Wr (rad/sc) Ws (rad/sc) 1 9 (a) (b) 6 T (N.m) 4 REFERENCES Fig.11 (a) Masurd spd (b) Estimatd Spd (c) Dvlopd Torqu undr fault tolrant control [1] P.Thogrsna, F.Blaabjrgb Adjustabl Spd Drivs in th Nxt Dcad: Futur Stps in Industry and Acadmia,Elctric Powr Componnts and Systms,pags (13-31)- Volum 3, Issu 1, 4 [] Mahmoud M. Gaballah Dsign and Implmntation of Spac Vctor PWM Invrtr Basd on a Low Cost Microcontrollr. Arab journal of Sinc Enginring. 1 [3] Channgowda, P.; John, V.: Filtr optimization for grid intractiv voltag sourc invrtr. IEEE Trans. Ind. Elctron. 17, (1) [4] Khalaf Salloum Gaid Fault Tolrant Control of Induction Motor Modrn Applid Scinc Vol., No. 4; August 11 [] M. E. H. Bnbouzid, "Bibliography on induction motors faults dtction and diagnosis," IEEE Trans. Enrgy Convrsion, vol. 14, pp , Dc [6] D. Kastha and B. K. Bos, "Invstigation of fault mods of voltag fd invrtr systm for induction motor driv," IEEE Trans. Ind. Application., vol. 3, pp , July [7] B. A. Wlchko, T. A. Lipo, T. M. Jahns, and S. E. Schulz, Fault tolrant thr-phas ac motor driv topologis: A comparison of faturs, cost, and limitations, IEEE Transactions on Powr Elctronics, Vol. 19, No. 4, pp , Jul. 4. [8] R. Spé and A. K. Wallac, Rmdial stratgis for brushlss dc driv failurs, IEEE Transactions on Industry Applications, Vol. 6, No., pp. 9-66, Mar./Apr [9] A. M. S. Mnds, X. M. Lopz-Frnandz, and A. J. M. Cardoso, Thrmal bhavior of a thrphas induction motor fd by a fault-tolrant voltag sourc invrtr, IEEE Transactions on Industry Applications, Vol. 43, No. 3, pp , May/Jun. 7. [1] B. A. Wlchko, J. Wai, T. M. Jahns, and T. A. Lipo, Magnt-flux-nulling control of intrior PM machin drivs for improvd stady-stat rspons to short-circuit faults, IEEE Transactions on Industry Applications, Vol. 4, No. 1, pp , Jan./Fb. 6. [11] M. E. H. Bnbouzid t ai., "A loss-minimization DTC schm for EV induction motors," in Proc. IEEE VPPC, Chicago, IL, Sp., pp [1] C. Grada, M. Sumnr, J. Arllano-Padilla Sch. Invstigation of induction machin phas opn circuit faults using a simplifid quivalnt circuit modl, Elctrical. & Elctron. Eng., Univ. of Nottingham, Nottingham 1/8; 37

14 J. Elctrical Systms 9-3 (13): [13] C. C. Chan, "Th stat of th art of lctric and hybrid vhicls,"proc. IEEE, vol. 9, no., pp.47-7, Fb.. [14] Brian A. Wlchko, Thomas A. Lipo, Thomas M. Jahns, and Stvn E. Schulz, "Fault tolrant thr-phas AC motor driv topologis: A comparison of faturs, cost, and limitations," IEEE Trans. Powr Elctronics., Vol. 19, NO. 4, July 4. [1] M. E. H. Bnbouzid, D. Diallo, and M. Zraoulia, "Advancd fault tolrant control of inductionmotor drivs for EV /HEV traction applications: from convntional to modrn and intllignt control tchniqus," IEEE Trans. Vhicular Tchnology., Vol. 6, NO., March 7. [16] Chul-Woo Park, Woo-Hyn Kwon Simpl and robust spd snsorlss vctor control of induction motor using stator currnt basd MRAC Elctric Powr Systms Rsarch 71, pp. 7 66, 4. [17] S. Abramik, W. Slszynski, J. Nicrnanski, H. Piqut. A Diagnostic Mrhod fir &-Lin Foul1 Dtction and Localizarion in VSI-Fd AC Drivr, EPE 3, 1th Europcan Confcrcncc on Powcr Elctronicsand Applicatians.Toulousc, Franc. CD-ROM papcr [18] M. Monfard, H. Rastgar, H. M. Kojabadi, "Ovrviw of modulation tchniqus for th fourswitch convrtr topology," PECon 8, 1-3 Dc 8, Johor Baharu, Malaysia. [19] Matlab/Simulink Toolbox Usr s Guid, Th Mathworks Inc., Natick, MA, USA, May APPENDICES A.1. Motor Data and Paramtrs: Machin paramtrs of th applid induction machin Ratd powr 1.1 kw Ratd load torqu 7. N.m. No. of pols 4 Stator rsistanc ohm Rotor rsistanc ohm Rotor lakag inductanc.1 H Stator lakag inductanc.1 H Mutual inductanc.4114 H Supply frquncy Hz Motor spd 1 r.p.m. Supply voltag 38 volts Inrtia. kg.m A.. List of Principl Symbols; L L s L m Lr Tr L r Rr 1- LL s r V qs,v ds q -d axis stator voltag I qs, I ds q -d axis stator currnt qs, ds q -d axis stator flux linkag R s, R r stator and rotor rsistancs J, B momnt of inrtia and viscous friction cofficints L s, L r, L m stator, rotor and mutual inductancs T, T L lctromagntic and load torqu 38