Adaptiv Hytri Band Control for Contant Switching Frquncy in Dirct Torqu Control of Induction Machin Driv Mutafa AKTAŞ H. İbrahim OKUMUŞ -mail: makta@ktu.du.tr -mail: okumu@ktu.du.tr Karadniz Tchnical Univrity, Faculty of Enginring, Dpartmnt of Elctrical & Elctronic Enginring, 600 Trabzon, Turky Kyword: Induction Motor, Dirct Torqu Control, Adaptiv Hytri Band, and Contant Switching Frquncy ABSTRACT Hytri band control i on of th implt and mot popular tchniqu ud in dirct torqu control (DTC) of induction machin driv. Howvr th convntional fixd band hytri control ha a variabl witching frquncy which cau riou problm in DTC. In thi papr, th adaptiv hytri band control tratgy i propod, whr th hytri band i controlld in ral tim a variation of applid voltag vctor. Thrby rducing th torqu rippl whilt maintaining a contant torqu witching frquncy. Th propod adaptiv hytri band control tchniqu i vrifid by imulation.. INTRODUCTION Rcnt advanc in powr miconductor and microprocor tchnology hav mad poibl th application of advancd control tchniqu to ac motor driv ytm []. DTC ha bcom a popular tchniqu for th control of induction motor driv a it provid a fat dynamic torqu rpon and robutn to machin paramtr variation without th u of currnt rgulator. Th tchniqu can b implmntd aily uing two hytri controllr (on for flux and anothr for torqu) and a witching tabl to lct th witching voltag vctor. Howvr, convntional DTC uffr from uch ffct a torqu rippl, variabl witching frquncy and flux drooping at low pd. Th ffct rult in incrad ub-harmonic currnt, highr load currnt rippl and variabl witching lo in th invrtr [,]. Thi papr propo a adaptiv hytri band control tratgy, whr th hytri band i controlld in ral tim a variation of applid voltag vctor. Thrby rducing th torqu rippl whilt maintaining a contant torqu witching frquncy. whr Ψ i th tator flux linkag pac vctor and I i th tator pac vctor. In Equation (), both pac vctor ar xprd in th tationary rfrnc fram. By conidring that Ψ = L I + LmI r Ψ r = L r I r + Lm I whr th primd rotor quantiti ar xprd in th tationary rfrnc fram, it follow that I = Ψ / L [ Lm /( Lr L )] Ψr. Thu quation () tak th following from T Lm = P Ψ in γ r Ψ () L L r Th lctromagntic torqu givn by quation () i a inuoidal function of γ, th angl btwn th tator and rotor flux linkag pac vctor. Th magnitud of th tator flux i normally kpt contant and th motor torqu controlld by man of th angl γ. Th rotor tim contant of th tandard induction machin i typically largr than 00 m, thu th rotor flux i tabl and it tabl and it variation i low compard with th tator flux. It i thrfor poibl to achiv th rquird torqu vry ffctivly by rotating th tator flux vctor dirctly in a givn dirction a fat a poibl. q ω 0 +ω Ψ Sctor V 4 V 5 V V 6 V V. GENERAL DESCRIPTION OF DTC In gnral, in a ymmtrical thr-pha induction machin, intantanou lctromagntic torqu i a cro product of th tator and rotor flux linkag pac vctor or tator currnt pac vctor and tator flux linkag pac vctor. γ ω 0 Ψ r Sctor d T = PΨ I () Figur. Optimum voltag vctor in th torqu control and voltag vctor
Figur how tator flux bhaviour compard to rotor flux, aftr a tp variation tator pulation, ω 0 =ω 0 +ω, with ω 0 th initial pulation and ω th tp variation. Controlling th tator flux tator flux and lctromagntic torqu control achivd by uing th appropriat tator voltag can quickly chang th lctromagntic torqu. Chooing uitabl voltag vctor tho incra or dcra γ cau th lctromagntic torqu to incra or to dcra [4]. Tabl. Switching tabl dψ dt ctor ctor ctor ctor 4 ctor 5 ctor 6 V V V 4 V 5 V 6 V 0 V 7 V 0 V 7 V 0 V 7 V 0 - V 6 V V V V 4 V 5 V V 4 V 5 V 6 V V 0 0 V 7 V 0 V 7 V 0 V 7 V 0 - V 5 V 6 V V V V 4 Th cor of th ytm conit of a flux and torqu timator, a pd controllr, a flux controllr, a torqu controllr and an optimum witching tabl. Th timator timat th actual tator flux and torqu uing two maurd motor tator pha currnt, th dc voltag and th tat of th powr witch. Torqu and flux rfrnc ar compard with th actual valu and a twolvl for flux and a thr-lvl for torqu hytri control mthod produc control ignal.. HYSTERESIS BAND CONTROL IN DTC Th hytri band control mthod i a impl and common form of clod-loop control. Th block diagram for th two-lvl and thr-lvl hytri band control mthod ar hown figur blow. Hytri band control i widly ud bcau of it abilitiy to b imply implmntd. Bid th fat rpon th inhrnt pak currnt limiting capability and xcllnt dynamic prformanc that i offr, it do not rquir an accurat knowldg of th load paramtr. In addition, hytri band control i ntially an analog tchniqu. Dpit th advantag givn by th digital controllr, in trm of intrfacing, maintnanc, flxibility, and intgration, thir accuracy and rpon pd ar oftn inufficint for currnt control in highly dmanding application, uch a activ filtr and high prciion driv. In a DTC chm, Ψ * (t) Ψ (t) d -/ / Ψ Ψ(t) Figur. Block diagram of two-lvl Hytri Band Control - t * (t) t (t) -/ / d t t (t) Figur. Block diagram of thr-lvl Hytri Band Control th objctiv i to rduc both th tator flux and torqu rror to zro uing hytri comparator lct th optimum voltag vctor. Hytri comparator li at th hart of DTC chm and ar rponibl not only for dtrmining th optimum voltag vctor to b witchd, but alo for dtrmining how long that vctor or action rmain lctd. Hytri i ud to prvnt th powr dvic from witching unncarily at ach nw updat or witching dciion. In thi tudy, a two lvl hytri comparator, a hown Figur, ud in DTC to compar th actual valu of tator flux to th intrnal rfrnc valu producd by tator flux rfrnc controllr. In th imilar mannr, a thr lvl hytri comparator, a hown in Figur, i ud to compar th actual valu of th torqu to th intrnal rfrnc valu producd by th pd torqu rfrnc controllr [4]. Th output of th comparator ar updat vry ampling tim and thy indicat whthr th flux or torqu ha to b varid. 4. ADAPTİVE HYSTERESİS BAND STRATEGY In a DTC chm, for fixd torqu band amplitud T, th invrtr witching frquncy i rlatd to th amplitud of th flux hytri band Ψ. A mall flux hytri bandwidth rult in a highr witching frquncy, th tator flux vctor locu approach a circl and th pha currnt wavform i narly inuoidal. Th oprating condition rult in low harmonic coppr lo in th machin whil witching lo in th invrtr ar high. Altrnativly, a larg hytri bandwidth for tator flux dcra th witching frquncy and th tator flux vctor locu bcom a hxagon. In thi ca th witching lo dcra in th invrtr whil th harmonic coppr lo incra in th machin [5]. Adaptiv hytri band ha bn wll invtigatd a a two lvl tratgy. Th adaptiv hytri band tratgy can b xtndd to thr lvl hytri band. It i dmontratd that adapting th width of th hytri band for th thr lvl tratgy a a function of pul numbr FR and dpth M. Th block diagram of thr lvl hytri band to b analyd i illutratd Figur 4. Output t (t) track th rfrnc function t * (t) to within a band who limit i +Σ. It i important to not th Σ quantity i rquird only to crat th thr voltag lvl in th output of th hytri lmnt. In imulation -
rult Σ i dcra down a vry mall valu and for th imulation rult prntd in thi papr it wa t to b /00. Σ t * (t) t (t) d / -/ - t (t) Σ Figur 4 Block diagram of thr lvl adaptiv hytri band control Adaptiv hytri band i hrntly an analogu proc bcau witching i producd at th intrction of th rror btwn t * (t) and t (t) and th adaptiv hytri band limit. Th quation dcribing th intrction point ar nonlinar and trancndntal and t ( t ) + t p = () t t t (t) V lop=p tˆ t (t ) t (t) t (t ) lop=0 0 t t t Figur 5. Production of on pul for thr lvl adaptiv hytri band control thrfor mut b olvd off-lin. Th following analyi illutrat th pul-poition that occur in thr-lvl adaptiv hytri band control. Th production of on pul for th thr-lvl adaptiv hytri band control mthod i illutratd in Figur 5 to xplain th analyi in blow. By inpction of Figur 5 th lop of th ignal t (t) whn th output i +V/ can b dcribd a. It i ncary to aum a fixd lop for th rfrnc function to dcrib th adaptiv hytri band proc a a continuou function of tim. Thi aumption ha not bn found to produc ignificant rror in th witching angl uing th analogu imulation [5]. By auming a fixd gradint of t (t) ovr ach witching priod th on or t -t tim can b approximatd a t on = (4) p t (t) Th lop of output ignal tˆ during th tim t <t<t i zro bcau th output voltag i zro in thi tim priod. Thrfor from inpction of Figur 5, th lop of th rfrnc function can b xprd a t ( t ) t ( t ) t = (5) t t t t and thrfor th corrponding off tim may b xprd a t off = t t = (6) t By combining quation (4) and (6) th total intantanou tim priod T i i dcribd a Ti = ton + toff = + (7) p t t Th corrponding intantanou angular frquncy, i dtrmind by quation (8) ω i, π ωi = (8) Ti Th carrir frquncy, ω c, which dtrmin th pul numbr i th avrag valu of th intantanou frquncy, ω i, ovr on fundamntal priod and i xprd a A ω π ωc = Aωp (9) p Th analyi prntd ha dmontratd that th pul numbr, FR, i a function of rfrnc function amplitud, A, lop, p, of th output ignal, tˆ, and th width of th hytri band,. Thrfor, it i ncary to adapt th width of th hytri band o that it ha a contant width along a fundamntal priod according to Equation (0). Thi nabl only th pul numbr, FR, and dpth, M, to b th pcifid paramtr in th modulation proc [5]. Thrfor, th width of th adaptiv hytri band can b xprd a 4Mp Mπ = ω 4 c (0)
whr ω c = FRω, and th dpth, M, i dfind a Aω M = () p 5. SIMULATION RESULTS A imulation tudy for th propod adaptiv hytri band control tchniqu wa carrid out uing th matlab oftwar packag. Th motor paramtr ud in th imulation ar givn in th appndix. In th imulation th propod DTC driv i opratd in th pd control mod with a load of 0 nm and tator flux and rotor pd rfrnc of 0.8wb and 00 rad/ rpctivly. Whn fig. 7(b) ar fig. 8(b) ar compard it i obrvd that fig. 8(b) i circular whil fig. 7(b) look lik a hxagon. It hould b notd that th ffct of th propod chm can b n vry aily at low pd from th imulation rult. Contant invrtr witching frquncy i obtaind by uing adaptiv hytri bandwidth. Furthrmor, invrtr witching frquncy with adaptiv hytri band i obtaind and thi i illutratd in figur 6. in addition, witching frquncy i mall at low pd. In ordr to incra th witching frquncy th torqu adaptiv hytri band width i dcrad. Thu tator flux locu bcom circular. In concluion, th obtaind imulation rult fig. 7(a) and 8(a), fig. 7(b) and 8(b), fig. 7(c) and 8(c), fig. 7(d) and 8(d) ar hown for comparion. a) Elctromagntic torqu, T (or t ) b) Stator flux vctor locu (Ψ d -Ψ q ) 6. CONCLUSIONS In thi papr a adaptiv hytri band control tratgy, whr th band i controlld a variation of applid voltag vctor in ordr to kp th witching frquncy contant at any oprating condition i propod. Th propod control tchniqu i vrifid by imulation. With propod tchniqu, th witching frquncy of th invrtr i narly hld contant. 6000 c) Switching frquncy, f c witching frquncy 5000 4000 000 000 000 adaptiv hytri band contant hytrii band (tb=%0) 0 0 0 40 60 80 00 0 angular pd Figur 6. Effct to witching frquncy of adaptiv hytri band control. d) Stator flux vctor Ψ d Figur 7. Fixd hytri band (t band =%0) 4
a) Elctromagntic torqu T (or t ) b) Stator flux vctor locu (Ψ d -Ψ q ) REFERENCES. Bo Bimal K., An Adaptiv Hytri-Band Currnt Control Tchniqu of a Voltag-Fd PWM Invrtr for Machin Driv Sytm, IEEE TRANS. IND. ELECTRON., vol 7, pp. 40-408, Oct. 990. Caadi D, Grandi G, Srra G, Effct of Flux and Torqu Hytri Band Amplitud in Dirct Torqu Control of Induction Machin, IECON 94, Bologna, Italy, 5-9 Sptmbr 994, pp.99-04.. J.K.Kang, D.W. Chung, S.K. Sul, Dirct Torqu Control of Induction Machin With Variabl Amplitud Control of Flux and Torqu Hytri Band, IEEE/ IEMD Intn. Conf. (999) 640-64. 4. Okumuş H. İ., Improvd Dirct Torqu Control of Induction Machin Driv Phd Thi, UNİVERSİTY OF BRİSTOL, UK, July 00 5. Bow S.R, Grwal S, Thr-lvl hytri band modulation tratgy for ingl-pha PWM invrtr, IEEE Proc.-Elctr. Powr Appl., Vol. 46, No 6, Novmbr 999 6. I. Takahahi, T. Noguchi, A Nw Quick-Rpon and High-Efficincy Control Stratgy of an Induction Motor, IEEE Tran. Indutry App. IA- (986) 80-87. 7. P. Va, Snorl vctor and dirct torqu control, Oxford Univrity Pr, Nw York, 998. 8. J.K. Kang, S.K. Sul, Nw Dirct Torqu of Induction Motor for Minimum Torqu Rippl and Contant Switching Frquncy, IEEE Tran. Indutry App., 5 (999) 076-08. Appndix Motor Paramtr Ud For th Simulation R = Ω, R r = 5.6 Ω, L = L r =0. H, M = 0.09 H c) Switching frquncy f c d) Stator flux vctor Ψ d Figur 8. Adaptiv hytri band 5