A Comparative Study between Vector Control and Direct Torque Control of Induction Motor Using Optimal Controller

Transcription

1 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 3 A Comparativ Study btwn Vctor Control and Dirct Torqu Control of Induction Motor Uing Optimal Controllr At. Prof. Dr.Abdulrahim Thiab Humod, At. Prof. Dr. Mohammad Najm Abdullah,. Fatma H. Fari Abtract - Thi papr prnt a comparion btwn two famou control tratgi for induction motor: Fild Orintd Control (FOC) and Dirct Torqu Control (DTC). Th two tratgi ar Vctor Control (VC) mthod and provid a olution for high-prformanc iv. Th tratgi ar implmntd uing an induction motor with rating of 3W, 3V and Hz. Th motor paramtr ar timatd uing laboratory tt. From imulation rult th advantag and diadvantag of both mthod ar invtigatd to illutrat th fatur of both mthod. Th prformanc of th two control chm ar valuatd in trm of torqu, currnt rippl and tranint rpon to load toqu variation. Th Spac Vctor Pul Wih Modulation (SVPWM) tchniqu i propod a a voltag ourc invrtr. Alo th Proportional Intgral (PI) controllr tund by Particl Swarm Optimization (PSO) i propod for both tchniqu. A MATAB/SIMUINK program i prpard for imulating th ovrall iv ytm. Kyword - Fild Orintd Control, Dirct Torqu Control, PI PSO Bad Controllr, induction motor.. INTRODUCTION: tudy uing intllignt tchniqu un varying dynamic T condition ar dicud, Pabitra [9] implmntd of h advantag of th Induction Motor (IM) includ calar & vctor control of thr pha induction motor high rliability, rlativly impl, ha ruggd iv, Garcia [] prnt a comparion btwn two tructur, low cot, robutn and high fficinci. control tratgi FOC and DTC for prmannt magnt Th advantag mak th IM advanc in all apct lik ynchronou motor, A. Bnnaar [] prnt th pd chang, pd rvral, tarting and braking. Th prformanc of th norl dirct torqu control (DTC) ovrall ytm prformanc dpnd on th IM dynamic of an induction motor (IM) uing adaptiv unbrgr opration. Du to th wift dvlopmnt in obrvr (AO) with fuzzy logic controllr (FC) for microprocor and powr lctronic, th advancd adaptation mchanim. control mthod hav IM poibl for high prformanc application..modeing AND SIMUATION OF THREE PHASE IM: Variabl frquncy control tchniqu of IM can b Th pr-pha quivalnt circuit diagram of an IM. in dividd into two major typ: calar control, vctor two- axi ynchronouly rotating rfrnc fram ar control, Scalar control or a it i calld V/f control aum illutratd in figur (). From th circuit diagram th a contant rlation btwn voltag and frquncy and following quation can b writtn []. vctor control. Th firt vctor control mthod of induction motor wa Fild Orintd Control (FOC) prntd by K. Ha (Indirct FOC) and F. Blachk (Dirct FOC) in arly of 97 [, ], cond vctor control mthod of induction motor wa Dirct Torqu Control (DTC) wa firt introducd by Takahahi in 9. [ 3 ] Many diffrnt tudi hav bn dvlopd to find out diffrnt olution for induction motor control having th fatur of accuracy, quick torqu rpon and rduction of th complxity of th prntd algorithm and tchniqu, Bndyk [] propo a DTC bad on a High Frquncy AC (HFAC) powr convrtr, Abdulrahim, [] propo a DTC bad on Nuro fuzzy (ANFIS) controllr to improv th prformanc of PI-PSO controllr. ANFIS controllr i traind by uing PI-PSO data to improv th pd and torqu rpon of thr pha IM, Turki, [] prntd a mthod for improving th pd profil of a thr pha induction motor in DTC iv ytm uing a fuzzy logic bad pd controllr, Abdlam [7] prnt a comparativ tudy of fild orintd control and dirct torqu control of induction motor uing an adaptiv flux obrvr, Supriya [] prnt fuzzy logic bad dirct torqu control (DTC) chm of an induction motor (IM) and it comparativ Fig. () dp Stator quation: d Vq = Riq q P qp P I.M Equivalnt Circuit w d...( )

2 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 33 V d = R id d Rotor quation: V V = R = R ri ri d d d w q...() ( w wr )...(3) ( w wr )...() Whr: th uprcript notation "" rfrrd to th ynchronouly rotating rfrnc fram quantiti. It' obviouly that in quirrl cag I.M Vq =, thn th prviou quation can b rwrittn: qm dm = m = m q d m r m r...()...() Whr: m =...() ( ) m From th prviou quation th dynamic modl of an induction motor i imulatd a hown in figur (). r d q = V q R i q wd...() d d = V d R id w...() q d = Rri ( w wr )...(7) d = Rri ( w wr )...() Th dvlopmnt torqu by intraction of air gap flux and rotor currnt can b found a: T = (3/) (P/) m I r...(9) Fig. () IM Simulation By rolving th variabl into d-q componnt: 3. VECTOR CONTRO OF INDUCTION MOTOR : T = (3/) (P/) ( diq qid )...() Vctor control bad on rlation valid in dynamic Th dynamic torqu quation of th rotor: tat, not only magnitud and frquncy but alo intantanou poition of voltag, currnt and flux linkag pac vctor ar controlld. Th mot popular vctor dwr T = T ( ) J...() control mthod ar th Fild orintd control (FOC) and P dirct torqu control ( DTC ). Whr: ωr = i th rotor pd; P: no. of pol; J = rotor inrtia; T = load torqu.th tator currnt can b found by: i d i q = = d q Th air gap flux dm qm...()...(3) 3. Fild-Orintd Control Vctor or Fild-Orintd Control (FOC), allow a quirrl-cag induction motor to b ivn with high dynamic prformanc. It tranform th dynamic tructur of th A.C motor into that of paratly xcitd D.C motor [], [ ]. For D.C motor, th fild flux i proportional to th fild currnt, if th fild aumd to b contant and indpndnt of armatur currnt, th armatur currnt provid dirct control torqu, o that: T I f I a... (7) With th induction motor tranformd to d-q plan, it look lik a paratly xcitd D.C motor. Th (FOC) tchniqu dcoupl th two componnt of tator currnt;

3 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 3 on providing th air-gap flux, and th othr producing th torqu. Th currnt componnt provid indpndnt control of flux and torqu and th charactritic i linar [], [], []. Th componnt ar tranfrrd back to th tator fram bfor fding back to th rotor. Th two componnt ar d-axi i d analogu to fild currnt I f, and q-axi i q i analogu to armatur currnt I a of th paratly xcitd D.C motor [], [], []. Thi tratgy can b implmntd by align th rotor flux vctor along th d-axi of th tationary fram a hown by th phaor diagram in figur (3). Th fundamntal of vctor control implmntation can b xplaind in figur (), whr th motor modl i prntd in a ynchronouly rotating rfrnc fram, th voltag-fd SPWM invrtr produc thr-pha voltag ( v a, v b, v c ) according to th rfrnc command voltag ( v a, v b, v c ) th flux componnt of tator currnt (i d ) and th torqu componnt of th tator currnt (i q ) i ud a a control ignal to th ytm, which ar invrly tranformd to thr-pha rfrnc currnt ( i a, i b, i c ), and thn tranfrrd to thr-pha voltag (v a, v b, v c ) through (PI) controllr [], []. Th vctor control FOC can b implmntd by ithr dirct or indirct mthod, th mthod ar diffrnt ntially by how th unit vctor (coθ and inθ ) i timatd for th controllr. 3.. Flux Vctor Etimation: Thr ar two commonly mthod of flux timation; voltag modl, and currnt modl. Th firt on ha trong prformanc in high pd rgion but not in low pd. Whra, th cond mthod ha an accptd prformanc in both low and high pd []. Th currnt modl dpnd on th main rotor quation in th two ax tationary fram d-q, uprcript "" rfrrd to tationary fram quantiti: d R ri wr =...() d R ri wr =...(9) Adding trm (mrr/r) i d and (mrr/r) i q and implifying, gt: = [ m Tr = [ m Tr i i ω r ω r ] () Tr ] () Tr Whr: Tr = r i th rotor tim contant. Rr Equation ( & ) giv rotor flux a a function of tator currnt and pd. Thrfor, knowing th ignal, th rotor flux and corrponding unit vctor (coθ and inθ ) can b timatd by man of DSP microprocor to implmnt th following quation [], [ ]: r = = r inθ = r coθ () Fig. (3) Corrct Rotor Flux Orintation Or: inθ = r coθ = r Flux timation by th currnt modl rquir a pd nco, but th advantag i that th iv opration can b xtndd down to low and zro pd. It' important to mntion, that th input ignal to th timator ( i q and i d ) mut b filtrd by a low pa filtr tag. Th imulation of th currnt modl timator can b hown in figur (). Fig. () Fild Orintd Vctor Control

4 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 3 H ψ H T S() S() S(3) S() S() S() V V 3 V V V V V V 7 V V 7 V V 7 - V V V V 3 V V V 3 V V V V V V 7 V V 7 V V 7 V - V V V V V 3 V Fig. () Currnt Modl Flux Etimation 3. Dirct Torqu Control (DTC) Dirct Torqu Control dcrib th way in which th control of torqu and pd ar dirctly bad on th lctromagntic tat of th motor, imilar to a DC motor, but contrary to th way in which traditional PWM iv u input frquncy and voltag. Dirct torqu control i th firt tchnology to control th ral motor controlld variabl a torqu and flux [3]. Th baic principl in convntional DTC for IM i to dirctly lct tator voltag vctor by man of a hytri tator flux and torqu control a in Fig.( ). Gnrally, in a ymmtrical thr pha induction motor, th intantanou lctromagntic torqu i proportional to th cro product of th tator flux linkag pac vctor and th rotor flux linkag pac vctor []. T = 3p ψ ψ in δ)... (3) r Whr ψ, i th tator flux linkag pac vctor, ψ r i th rotor flux linkag pac vctor rfrrd to tator and ( δ ) i th angl btwn th tator and rotor flux linkag pac vctor. Th timator quation for tator flux (ψ ), tator flux poition(θ )and torqu ar: ψ = ψ q ψ d.... () θ = tan ( ψ q ).... () ψ d T = 3p (ψ i d q ψ q i d )... (). PARTICE SWARM OPTIMIZATION (PSO) Fig. () DTC block diagram From thi figur tator flux * and torqu T* ar compard with th corrponding timatd valu. Both tator flux and torqu rror ar procd by man of hytri band comparator. In particular, tator flux i controlld by a two lvl hytri comparator, whra th torqu i controlld by a thr lvl comparator. On th bai of th hytri comparator and tator flux ctor a propr VSI voltag vctor i lctd by man of th witching tabl givn in Tabl. Tabl ( ) Switching Tabl of invrtr Th PSO algorithm i on of th optimization tchniqu dvlopd by Ebrhart and Knndy in 99. Thi mthod ha bn found to b robut in olving problm faturing non-linarity and non-diffrntiability, which i ivd from th ocial-pychological []. It wa inpird by th ocial bhavior of bird flocking and fih chooling, and ha bn found to b robut in olving continuou nonlinar optimization problm. PSO bcom a focu th day du to it implicity and a to implmnt []. In PSO, ach ingl olution i a bird in th arch pac; thi i rfrrd to a a particl. Th warm i modld a particl in a multidimnional pac, which hav poition and vlociti. Th particl hav two ntial capabiliti: thir mmory of thir own bt poition and knowldg of th global bt poition. Mmbr of a warm communicat good poition to ach othr and adjut thir own poition and vlocity bad on good poition []. Th particl ar updatd according to th following quation ( 7 & ). v(k ) i,j = w. v(k) i,j c r gbt x(k) i,j. (7) c r (pbt j x(k) i,j ) x(k ) i,j = x(k) i,j v(k) i,j. ()

5 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 3 Whr, vi,j : vlocity of particl i and dimnion j. xi,j : poition of particl i and dimnion j. c, c : known a acclration contant. w : inrtia wight factor. r, r : random numbr btwn and. pbt : bt poition of a pcific particl. gbt : bt particl poition of th group.. Prformanc critria of PSO-PI controllr In mot intllignt optimization algorithm, thr ar commonly prformanc critria uch a: Intgratd Abolut Error (IAE), th Intgratd of Squar Error (ISE), and Intgratd of Tim Squar Error (ITSE). That can b valuatd analytically in frquncy domain. Th prformanc critria ar including th ovrhoot, ri tim, ttling tim and tady-tat rror. In addition, it ha bn indicatd th optimization, and robut of th iv ytm.th prformanc critrion formula ar a follow[]: Intgral Squar Error (ISE) = (t)... ( 9 ) Intgral Abolut Error (IAE) = (t).. ( 3 ) Intgral Tim Squar Error (ITSE) = t. (t)... ( 3) In thi papr th (ITSE) tim domain critrion i ud a a "fitn function" for valuating th PI controllr prformanc. A t of good controllr paramtr K p and K i can yild a good tp rpon that will rult in prformanc critria minimization.. SIMUATION AND RESUTS Each of th two control chm ar imulatd uing MATAB/Simulink. Th input to th imulation modl ar th applid voltag and rotor pd. Thn th modl calculat th tator currnt, tator flux, rotor currnt, rotor flux, and torqu.th valu of th lctrical dign paramtr for 3-pha quirrl cag IM ud in th imulation ar hown in th appndix A and th look up tabl that ud for optimum witching tat i hown in tabl ( ). Figur (7) and ( ) how th MATAB/ Simuink circuit of FOC and DTC. Swarm iz (Numbr of bird) Numbr of itration 3 Cognitiv cofficint (CR R). Social cofficint (CRR). Inrtia wight (w).3

6 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 37 of flux controllr, ( kp = 3.3, ki =.73 ) for PI of torqu controllr )] and for DTC ( kp=., ki=.3 ). Figur ( 9,,,, ) how th pd rpon for abov valu of pd for no load at ( -. ) c,. N.m. at (.. ) c and N.m. at (. ) c. Th pd rpon for FOC how pak to pak rippl valu (.,.3,.,. ) r.p.m and th prcntag valu for rippl (.3%,.%,.%,.% ) rpctivly for abov pd whil DTC how pak to pak rippl valu (.,.3,.,.) r.p.m. and th prcntag valu of rippl (.%,.%,.%, % ).Thi rult how that th pd rpon for DTC ha rippl mor than FOC. Th ovrhoot in th pd rpon for FOC ar (%,.3%, 3%, 3%) and unhoot at applid load i (%) rpctivly for abov pd whil DTC ar (.3%,.%, 3%, %) and unhoot i ( 3% ). Figur ( 3,,, ) how th torqu rpon for abov pd valu for no load at ( -. ) c,. N.m. at (.. ) c and N.m. at (. ) c. Th tarting torqu for FOC qual ( 7.3, 7.,.3,. ) Fig. 7. FOC with PI-PSO Matlab/Simulink circuit N.m rpctivly for abov pd whil DTC qual ( 7,.,.,. ) N.m. Th torqu rpon for FOC ha pak to pak rippl valu (.,.,.9,.) N.m. rpctivly for abov pd whil DTC ha pak to pak rippl valu (.,.,.9,.7) N.m. Th torqu rpon for DTC ha Fig.. DTC with PI-PSO Matlab/Simulink circuit rippl mor than FOC. Figur ( 7,, ) how th pd and torqu rpon Th PSO tuning mthod in thi work dpnd on ITSE for FOC and DTC at diffrnt pd for ramp input with prformanc indx. Th paramtr of PSO algorithm that lop (. c ), thi figur how that th tarting torqu achiv bttr olution ar litd in tabl ( ). valu for FOC l than DTC. Comparion critrion FOC DTC. Concluion Dynamic rpon Quickr Slowr Thi papr prnt a comparion btwn two torqu Torqu rippl ow High control mthod for induction motor iv. Th dcription of two control chm and thir principl of Paramtr nitivity Dcoupling dpnd on For a norl opration hav bn prntd. DTC wa dvlopd a an d, q,m,r timator: R altrnativ to FOC that had bn in u for a numbr of yar, it can b hown that th FOC algorithm provid Rquirmnt of rotor Y NO poition fatr rpon than DTC. FOC ha lowr rippl than DTC in th pd and torqu rpon pcially at low Coordinat Y NO pd. Th torqu rippl in DTC ha no ignificant ffct tranformation on th pd rpon. Th comparion btwn two mthod of control hown in tabl (3). Complxity and procing rquirmnt Highr owr Control tuning PI gain Hytri band and PI Gnral Good Good Tabl ( ) PSO paramtr Th rpon of th pd and torqu for FOC and DTC with PI- controllr tund by PSO tchniqu at diffrnt load and pd condition. Whr th lctd pd ar ( 3,,, ) r.p.m., for load torqu ar (,., ) N.m.. Th obtaind gain of PI-PSO tchniqu for FOC ar [ ( kp =.77, ki =.73 ) for PI TABE 3 comparativ btwn FOC and DTC of IM REFERENCES [] Bimal K. Bo, "Mon Powr Elctronic and AC Driv", Prntic Hall,. [] Quay. Hamdi, "Dign of Indirct Fild-Orintd PWM Invrtr for Thr-Pha Induction Motor", Ph.D. Thi, Al-Rahd collag of nginring, Univrity of Tchnology, 7. [3] I.Takahahi and Y.Ohmori, High-prformanc dirct torqu control of an induction motor, IEEE Tranaction on Indutrial Application, vol.: 7-, 99. [] M. Bndyk, P. C. K. uk, P. Jinupun," Dirct Torqu Control of Induction Motor Driv Uing High Frquncy Pul Dnity Modulation for

7 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 3 Rducd Torqu Rippl and Switching o", IEEE, Powr [] Fadhil A. Haan and ina J. Rahad," Particl Swarm Optimization for Elctronic Spcialit Confrnc (PESC), 7- Jun, 7. pp. -9 Adapting Fuzzy ogic Controllr of SPWM Invrtr Fd 3-Pha IM", [] Dr. Abdulrahim T. Humod, Wiam I. Jabbar, " Dirct Torqu Control of an Eng. & Tch. Journal, Vol. 9, No.,. Induction Motor Bad on Nurofuzzy " Eng. & Tch. Journal, Vol. [] Y. Yan - W.A. Klop and M. Molnaar - P. Nijdam, " Tuning a PID 3,Part (A), No. 7, 3. Eng. &Tch. Journal, Vol. controllr: Particl Swarm Optimization vru Gntic Algorithm", [] Turki Y. Abdalla, Haroution Antranik Hairik and Adl M. Dakhil," Fbruary. Minimization of Torqu Rippl in DTC of Induction Motor Uing Fuzzy Mod Duty Cycl Controllr", Iraq J. Elctrical and Elctronic Enginring, Vol. 7 No.,. [7] Abdlam Chikhi,a), Mohamd Djarallah,b), Khald Chikhi,c)," A APPENDIX: Comparativ Study of Fild-Orintd Control and Dirct-Torqu - Induction motor data Control of Induction Motor Uing An Adaptiv Flux Obrvr", Ratd powr 3 W Srbian Journal Of Elctrical Enginring Vol. 7, No., May. Ratd voltag 3 V [] Supriya Mor and Anant Kulkarni," Dirct Torqu Control of Induction Motor Uing Fuzzy ogic Controllr " IOSR Journal of Elctrical and Ratd frquncy Hz Elctronic Enginring (IOSR-JEEE) -ISSN: 7-7,p-ISSN: 3- Ratd pd 3 rpm 333, Volum, Iu Vr. I PP 3-, Sp Oct.. Numbr of pol [9] Pabitra Kumar Bhra, Manoj Kumar Bhra, Amit Kumar Sahoo3, " Stator ritanc R =.3 Ω Comparativ Analyi of calar & vctor control of Induction motor Stator inductanc =.3 H through Modling &Simulation ", Intrnational Journal Of Innovativ Rarch In Elctrical, Elctronic, Intrumntation And Control Rotor ritanc Rr =.7 Ω Enginring Vol., Iu, April. Rotor inductanc r =. H [] X. T. Garcia, B. Zigmund, A. Trlizzi3,R. Pavlanin,. Salvator3, Mutual inductanc m =.7 H " Comparion Btwn Foc And Dtc Stratgi For Prmannt Magnt Momnt of inrtia.73 Kg.m /c Synchronou Motor " Advanc in Elctrical and Elctronic Enginring. [] A. Bnnaar*, A. Abbou, M. Akhrraz, M. Barara, " Fuzzy ogic Bad Adaptation Mchanim For adaptiv unbrgr Obrvr Snorl Dirct Torqu Control Of Induction Motor " Journal of Enginring Scinc and Tchnology Vol., No.,. [] S.K. Pillai, "A Firt Cour on Elctrical Driv", cond dition, 99. [3] S Allirani, V Jagannathan, High Prformanc Dirct Torqu Control of Induction Motor Driv Uing Spac Vctor Modulation IJCSI, Vol. 7, Iu, Novmbr. [] Ali Huin Numan, "Spd and Poition Snorl Vctor Control of Hybrid Stppr Motor Uing Extndd Kalman Filtr'', Dpartmnt of Elctromchanical Enginring, Univrity of Tchnology, Baghdad, Iraq, Ph.D. Thi, May, 9. FOC DTC Spd ( r.p.m ) Spd ( r.p.m ) dird Spd ( r.p.m ) dird Fig. 9. Spd rpon for N=3 r.p.m.

8 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April Fig.. Spd rpon for N = r.p.m dird dird dird Rfranc Actual Fig.. Spd rpon for N= r.p.m. dird dird Rfranc Actual Fig.. Spd rpon for N = r.p.m. FOC DTC oad Torqu 7 oad Torqu Torqu ( N.m.) Torqu ( N.m ) Fig. 3. Torqu rpon at N = 3 r.p.m.

9 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 37 oad Torqu 7 oad Torqu Torqu ( N.m ) - Torqu ( N.m ) Fig.. Torqu rpon at N = r.p.m oad Torqu 7 oad Torqu Torqu ( N.m. ) 3 Torqu ( N.m. ) 3 - Torqu ( N.m ) Fig.. Torqu rpon at N = r.p.m oad Torqu oad Torqu Fig.. Torqu rpon at N = r.p.m. FOC DTC 3 3 dird 3 3 Dird

10 Intrnational Journal of Scintific & Enginring Rarch, Volum 7, Iu, April- 37 Fig. 7. Spd rpon at diffrnt valu 7 oad Torqu oad Torqu Torqu ( N.m ) 3 Torqu ( N.m ) Fig.. Torqu rpon at diffrnt pd