VECOR CONROL OF INDUCION MOORS USING UPWM VOLAGE Abtract SOURCE INVERER G. Emaly (M.Sc.), A. Khoabakhhan (Ph.D), K. Jamh (Ph.D) Faclty of Engneerng, Ifahan Unverty, Ifahan, Iran he objectve of th paper to e the metho of the vector control n the recton of the rotor flx nrectly for ncton motor. he pace vector of the tator crrent ve nto two component: magnetzng crrent an torqe-procng crrent. By ng the nform ple wh molate nverter, torqe platon wll be rece an a robt control wth qck ynamc repone for ncton motor acheve. he compter mlaton relt how that the performance of the vector control of the ncton motor exactly the ame a the performance of the eparately excte DC motor. 1. INRODUCION In recent year the control of hgh-performance ncton motor rve for general ntry applcaton an procton atomaton ha receve weprea reearch nteret. Many cheme have been propoe for the control of ncton motor rve, among whch the felorente control [1, 2], or vector control, ha been accepte a one of the mot effectve metho. he vector control trategy formlate n ch a way that the tator crrent phaor, n the two-ax ynchronoly rotatng reference frame, ha two component: magnetzng crrent component an torqe-procng crrent component. he generate motor torqe the proct of the two. By keepng the magnetzng crrent component at a contant rate vale, the motor torqe lnearly proportonal to the torqe-procng component, whch qte mlar to the control of a eparately excte DC motor. Becae the vector control formlate n the two-ax coornate frame, the metho reqre on-lne coornate tranformaton that convert three-phae lne crrent nto two-ax repreentaton an vce-vera [3]. he npt an otpt comman of a vectorcontrolle ncton motor rve are torqe/flx an three-phae reference voltage, repectvely. he torqe comman generate from the peeloop controller, wherea the flx comman electe accorng to the operaton reqrement n ether contant torqe or contant horepower regon. In orer to execte the vector control trategy, motor lne crrent are controlle n ch a way a to follow the reference voltage comman [2]. Althogh a voltage-controlle nverter ng hytere controller eay to realze an can be e to atfy the crrent control reqrement, t ha the followng avantage: 1) he wtchng freqency epen on the natre of the loa. 2) he crrent rpple hgh. 3) Performance at hgher pee natfactory [4]. hee avantage can be overcome by ng a contant wtchng freqency ple wh molate (PWM) nverter to control the tator crrent by a voltage orce nverter. he nverter to be e here the nform ple wh molaton (UPWM) []. Wth th backgron the vector control of ncton motor realze a hown n the block agram of Fgre 2 gven n Secton 2 [2]. he mlaton relt how that the performance of the vector ncton motor rve exactly the ame a the performance of the eparately excte DC motor. h paper organze a follow: Secton 2 ecrbe the mathematcal moel an vector control whle Secton 3 gve the mlaton relt. 2. Mathematcal moel an vector control he mathematcal moel of a three-phae, Y- connecte, qrrel-cage ncton motor an loa ecrbe by eqaton n the ynchronoly rotatng reference frame (x-y) a [2]
x = y R + p L L Lm x L R + p L Lm y p ( ) + ( ) Lm r Lm Rr p Lr r Lr ( ) ( ) rx r Lm r Lr Rr + p L r ry where p=/, an r J D e = + L where an x, y x, y rx, ry R, R r L ( ) m x ry r y rx (1) (2) 3 (3) = P e 2 = x- an y- ax tator voltage = x- an y- ax tator crrent = x- an y- ax rotor crrent = tator retance an rotor retance referre to the tator L, L m, L r = tator nctance, mtal nctance, an rotor nctance referre to the tator e, L = electromagnetc torqe an mechancal loa or trbance torqe J, D = moment of nerta an vco coeffcent of the motor P = nmber of pole of motor, r = ynchronoly anglar pee an rotor anglar pee Eqaton (1)-(3) repreent x-tate frt-orer nonlnear fferental eqaton. he mathematcal formlaton of the vector control trategy can be mmarze a follow. he tator an rotor voltage eqaton are tranlate to the rotor flx reference frame an among fferent metho gven n the lteratre the pace phaor metho e [2]. A hown n [2] the followng eqaton can be obtane. x x = + x R y y + = y R 2 Lm L L Lr L R L = R + x y ( ) ( ) (4) () = (6) = (7) where (8) L, = tranent nctance an tranent tme contant of tator repectvely = tme contant of tator = magnetng rotor crrent he pace phaor of the tator crrent on the rotor flx reference frame hown n Fgre 1. Fgre 1. Repreentaton of tator crrent an rotor flx a a pace vector, SD-SQ tatonary coornate ytem, x-y fel coornate that rotate wth anglar pee A een n Eqaton (4) an () the tator crrent x (the component of procng the exctaton flx) an y (the component of procng the torqe) are epenent on each other becae x an y are both epenent on y an x. However, thee component mt be controlle eparately to obtan the vector control trategy on the rotor flx reference frame [2]. Snce there no elay tme on an eal rve an t nverter alo oe not have any ea tme, there wol not be any elay on the proce. By conerng the flx rotor a a contant vale ( =ct.) the tator crrent component can be controlle nepenently by ng Eqaton (4) an (). Let coner the eparate voltage component a follow; = (9) x y L L x y ( L L ) = + (1) By ang thee voltage to the otpt voltage of the crct n whch the crrent are controlle (, ) an, therefore, the crrent x an y can x y be controlle eparately. Coneqently, the x-ax tator voltage wll be eqal to x + x an the x- ax otpt voltage of the crrent controlle crct calclate a follow; x x = R + (11) x L
Fgre 2. Vector control mplementaton on the recton of the rotor flx nrectly ng voltage orce nverter Smlarly, the y-ax tator voltage wll be eqal to y + y an the y-ax otpt voltage of the crrent controlle crct calclate a follow; y y = R + (12) y L Ung the above eqaton an by amplng of the three-phae tator crrent ( a, b, c ) an rotor pee the vector control of the ncton motor realze an hown n the block agram of Fgre 2. h ha two nner crrent control loop, one for x control an one for y control. he two oter loop namely, the pee control loop an the flx control loop generate reference vale for y an x control repectvely. All controller e here are PI one [2]. he cro coplng term n the tator eqaton elmnate wth the help of voltage ecoplng crct (ee Eqaton (9) an (1). he reference voltage for the nverter obtane wth the help of tator eqaton. 3. Smlaton relt he nverter to be e here can be ether noal ple wh molaton (SPWM) or nform ple wh molaton (UPWM). A hown n [] nce the UPWM nverter ha got he mlaton relt are hown n Fgre 3 (a-f) an 4 (a-f) for tartng, then recng the pee of the ncton motor an the performance of the ncton motor n the revere recton repectvely. Fgre 3f, 4f how that the performance of the vector control of the ncton motor rve exactly the ame a the performance of the eparately excte DC motor. Fgre 3c an 4c alo how the ablty of the vector control technqe n controllng the ncton motor n all for qarant of the torqe-pee coornate. By ng the nform ple wh molaton, torqe can be rece (ee Fgre 3e an 4e), an a robt control wth qck ynamc repone for ncton motor rve can be acheve (ee Fgre 3c an 4c). Fgre 3b an 4b alo how that the magnetzng crrent are contant rng mlaton program an th correpon wth Fgre 3a an 4a n whch the x-ax tator crrent are contant. mch le harmonc than the SPWM one, the former e a the voltage orce nverter.
Ix (A) 1 2 4 6 8 1 12 14 (a) I (A) 1 2 4 6 8 1 12 14 (b) Wr 1 2 4 6 8 1 12 14 (c) Iy (A) 2 2 4 6 8 1 12 14 () 6 6 e (Nm) 4 2 2 4 6 8 1 12 14 (e) e (Nm) 4 2 1 2 3 4 Iy (A) (f) Fgre 3: Startng an recng the pee of the ncton motor Ix (A) 1 1 2 2 (a) I (A) 1 1 2 2 (b) Wr 1-1 2 2-1 - Iy (A) 4 2 1 2 2-2 -4 (c) () Fgre 4: Performance of ncton motor n the revere recton
e (Nm) 2-2 1 2 2 - (e) e (Nm) 6 4 2-4 -2-2 2 4-4 -6 Iy (A) (f) Fgre 4: Performance of ncton motor n the revere recton 4. Conclon h paper ha preente a vector control ytem for ncton motor rve. he vector control methoology gven by [2] ha been mlate by the avantage of ng UPWM n whch the le harmonc have been acheve. he mlaton relt howe that the performance of the ncton motor wa exactly the ame a the eparately excte DC motor havng alo a qck ynamc repone an low torqe platon.. Reference [1] F. Blachke, he prncple of fel orentaton a apple to the new tranvector cloe -loop control ytem for rotatng-fel machne Semen Rev, vol. 39, no. 3, pp. 217-22, may 1972. [2] P. Va, he control of AC machne Oxfor Unv., 199. [3] P.C. Krae, Electrc machne, prentce Hall, 198. [4] M.P. Kazmerkowk, A novel vector control cheme for trantor PWM nverter-fe ncton motor rve, IEEE ran. On nt. Vol. 38, No. 1, Feb 1991, pp. 41-47. [] J. Soltan, G. Emaly, Dynamc performance of the elf controlle ynchrono motor rve ytem pple by SPWM an UPWM voltage orce nverter, ICEE, ehran, May 1996, pp. 311-318