Fault Detection of Broken Rotor Bars Using Stator Current Spectrum for the Direct Torque Control Induction Motor

Transcription

1 Wold Acadmy of Scinc, Engining and Tchnology 4 Fault Dtction of Bon oto Bas Using Stato Cunt Spctum fo th Dict Toqu Contol Induction Moto idha Kchida, Azi Mnac, Adlhamid Bnacha Astact Th numous qualitis of squil cag induction machins nhanc thi us in industy. Howv, vaious faults can occu, such as stato shot-cicuits and oto failus. In this pap, w us a tchniqu asd on th spctal analysis of stato cunt in od to ct th fault in th machin: on oto as. Thus, th num ffct of th as has n highlightd. Th ffct is highlightd y considing th machin contolld y th Dict Toqu Contol (DTC). Th y to fault ction is th dvlopmnt of a simplifid dynamic modl of a squil cag induction moto taing account th on as fault and th stato cunt spctum analysis (FFT). Kywods oto faults, diagnosis, induction moto, DTC, stato cunt spctum. I. ITODUCTIO OTO cag faults a th thid most impotant failu caus in induction motos. Ths failus a motivatd y a comination of intnal and xtnal stsss, acting togth with th natual aging pocss of th moto []. oto cag faults can a sious polm whn induction motos hav to pfom had duty cycls. If thy do not initially caus an induction moto to fail, thy can impai moto pfomanc, lad to moto malfunction, and caus sious mchanical damag to stato windings if lft unctd. Moov, an induction moto with on oto as cannot opat in dangous nvionmnts du to spaing at th fault sit []. Fo ths asons, a sustantial amount of sach has n dvotd to this topic in th past dcads, in od to cat nw condition monitoing tchniqus fo lctical machin divs, with nw mthods ing dvlopd and implmntd in commcial poducts fo this pupos []- [3]. Th sach and dvlopmnt of nw and altnativ diagnostic tchniqus is continuous, howv, sinc condition monitoing and fault diagnosis systms should always suit nw spcific lctic moto div applications [], [3]. This wo is alizd at th LGEB laoatoy (Laoatoy of Elctical Engining of Bisa, Algia) y D Azi Mnac, D Adlhamid Bnacha, at th Dpatmnt of Elctical Engining, Univsity Mohamd Khid, BP 45, 7, Bisa, Algia idha Kchida (-mail: idha.84@gmail.com). Azi.Mnac (-mail mnac_azi@hotmail.com). Adlhamid.Bnacha (-mail: nacha_a@yahoo.f). DTC (Dict Toqu Contol) is chaactizd, as dducd fom th nam, y dictly contolld toqu and flux and indictly contolld stato cunt and voltag. It is an altnativ dynamic contol fo vcto contol. Th ig intst in DTC is causd y som advantags in compaison with th convntional vcto-contolld divs [4]. This contol tchniqu povids maal dynamic pfomanc fo paamtic vaiations poducd y many faults in th machin (oto failus). II. Modl of th Induction Moto [5, 6] Th modl of th induction moto tas into account th following assumptions: ngligil satuation and sin ffct, unifom ai-gap, sinusoidal mmf of stato windings in ai-gap, oto as a insulatd fom th oto, thus no int-a cunt flows though th laminations, lativ pmaility of machin amatus is assumd infinit. Although th mmf of th stato windings supposd is to sinusoidal, oth distiutions of olling up could also considd y simply mploying th supposition thom. It is justifid y th fact that th diffnt componnts of th spac hamonics do not intact. In od to study th phnomna taing plac in th oto, th latt is oftn modld y mshs as shown on figu. i i i i i + i L, oto Fig.. oto cag quivalnt cicuit 3

2 Wold Acadmy of Scinc, Engining and Tchnology 4 A. Stato inductanc Th xpssion of mmf a phas "a" is givn y th following: i pπ s a F ( θ ) = cos( θ) m Th induction catd in th ai-gap can wittn as: µ i θ = pπ θ s a B s cos Th main flux is thus wittn as: 4µ s L φ sp = i πp a Th pincipal inductanc of th magntizing stato phas is: L φ 4µ L sp s sp = = ia πp Thfo th total inductanc of a phas is qual to th sum of th magntizing and laag inductancs, thus: () () (3) (4) Ls = Lsp + Lsf (5) Th mutual inductanc twn th stato phass is computd as: L s M s = - (6) M Th givn y: πµ = L (9) M th mutual inductanc twn th adjacnt mshs is ( ) = M (+ ) = M L () ( ) µ i i µ i B π a (+)a Fig.. Fom of magntic induction of oto msh catd y two as, L ( ) ( ) i L, i i ( ) i (+ ) i L, i π i( ), L Fig.3. Elctic diagam quivalnt of a oto msh θ B. oto inductanc Th fom of th magntic induction poducd y a oto msh in th ai-gap is supposd to adial and is psntd in Fig.. Th pincipal inductanc of a oto msh can calculatd fom th magntic induction distiution shown in figu [5, 6]: L π = µ L (7) p th Th total inductanc of th oto msh is qual to th sum of its pincipal inductanc, inductanc of laag of th two as and inductanc of th laag of th two potions of ings of th shot cicuit closing th msh as indicatd in figu 3. L = L + L + L (8) p Th xpssion fo th mutual inductanc stato-oto is can calculatd using th flux and is givn y: wh: π Msn = Ms cos(pθ n + a) () 3 a π p = and 4µ sl a Ms = sin p π Th psntation of stat is appantly a systm of vy high od. Th application of tansfomation th Pa's xtndd of oto systm so as to tansfom th systm in phass in a systm (d,q). W otain a modl of ducd siz of th induction machin. Th systm is put in th following canonical fom: 3

3 Wold Acadmy of Scinc, Engining and Tchnology 4 wh: [ ] [ ] d I L = V - I [ ] [ ][ ] Lsc Ms L sc Ms L 3 = Ms Lc, 3 Ms Lc L s Lscω Msω L scω s Msω =, and c p.l L = L M + +.L cos(a) = +. cos(a) () In od to simulat th dfct of oto on as, a fault sistanc F is addd to th cosponding lmnt of th oto sistanc matix : F = [ ] Consquntly, th squil cag sistanc matix, taing into account th dfct, is dfind y: [ ] [ ] [ ] = + (3) F F Th nw matix of oto sistancs, aft tansfomations, coms: F dd dq = (4) qd qq wh th fou tms of this matix a: = cos( a) + dd ( cos( a) ) ( cos( ) a) + dq = ( cos( a ) ) f sin( ) a qd = ( cos( a ) ) f sin( ) a f qq =. cos( a) + cos f cos( ) ( a ) ( a) chaactizs th position of on a Th quations govning th opation of asynchonous moto with o without oto dfcts com : L M s scω sω scω s sω = dd dq qd qq L M Th mchanical quations must also consid: d with: ω = ω = ( C C J ) dθ Th lctomagntic toqu with th xpssion: (5) 3 C = p..ms ( I ds.iq I qs.id ) (6) 3

4 Wold Acadmy of Scinc, Engining and Tchnology 4 III. DIECT TOQUE COTOL FO THE MACHIE WITH OTO FAULTS DTC is a contol philosophy xploiting th toqu and flux poducing capailitis of ac machins whn fd y a voltag souc invt that dos not qui cunt gulato loops, still attaining simila pfomancs to that otaind y a vcto contol div [7]. Th typical stuctu of a DTC induction moto is psntd in figu.4. A. Bhavio of stato flux In th fnc ( α, β ), th stato flux can otaind y th following quation: d Vs = s.is + φ s (7) By nglcting th voltag dop du to th sistanc of th stato to simplify th study (fo high spds), w find: s s s t φ φ + V (8) Tal I: Slction tal fo dict toqu contol Cflx Cclp - - S V V 7 V 6 V 3 V V 5 S V 3 V V V 4 V 7 V 6 S 3 V 4 V 7 V V 5 V V S4 V 5 V V 3 V 6 V 7 V S 5 V 6 V 7 V 4 V 7 V V 3 S 6 V V V 5 V V 7 V 4 V4() IT: Incas th Toqu, DT: Dcas th Toqu. IF: Incas th Flux, DF: Incas th Flux. IV. Simulation sults Th simulations of th DTC induction moto div w caid out using th Matla / Simulin simulation pacag. Th moto usd in th simulation study is a. W, V, 5 Hz, -pol induction moto, with a oto with 6 as. A. Invsion of th spd and vaiation of th toqu Th tst oustnss of th systm, w applid a changing of th spd fnc fom ad/sc to - ad/sc at t=s with load of toqu 3.5.m at t=.5s and t=.5s (Fig 5). Duing th Invsion of th spd, th toqu psnt xcdd fo stailizing. Th stato cunts psnt undulations at th momnt of th invsion compaal with th pa duing stating. V3() 4 V5() β V() V6() 8 6 V5(DF,AC) V3(DF,DC) V() α V,7 () V(AF,AC) V6(AF,DC) Fig 4: Patition of th complx plan in six angula 5 4 B. Bhavio of th toqu Th lctomagntic toqu is popotional to th vcto poduct twn th stato and oto flux accoding to th following xpssion [8]: C = φ φ = φ φ sin θ (9) s s s C. Dvlopmnt of th commutation statgy Tal, shows th commutation statgy suggstd [9], to contol th stato flux and th lctomagntic toqu of th stato of induction machins. Figu 4 givs th patition of th complx plan in six angula sctos S I =...6. Spd (d/s) Cunt stato ia (A) tim (s) tim (s) B. th fnc tapzoidal wav spd tim (s) Simulations a pfomd to validat th poposd DTC fo fou-quadant spd contol of induction machin. Th squa wav of spd fncs is tstd. Figu 6 show th spons tapzoidal wav spd fncs spctivly. Toqu (.m) Flux ta (w) Flux alpha (w) Fig.5. Invsion of spd and vaiation of th toqu load tst 33

5 Wold Acadmy of Scinc, Engining and Tchnology 4 Spd (pm) 5-5 w - w f tim (s) 5 Touqu (m) tim (s).5 accoding to th ais of th dfctiv as num. Tal II highlights th influnc of th num of on as on th stato cunt spctum. D. Effct of th load Th ffct of th load on th stato cunt spctum is highlightd y considing a a of two adjacnt as with diffnt slips (s=.9%, s=3.48%, s=6.3% and s=7.77%) and th fnc spd was st to 5 pm (s figu (8)). Stato cunt (A) 5 Flux ta (w) a) - - ) (4. -8.) ( ) tim (s) Flux alpha (w) ia (db) ia (db) Fig.6. Tapzoidal wav spd tst C. Effct of th num of oto on as Th spctal analysis of stato phas cunts highlights th ffct of th dfct th appaanc of though hamonics aound th fundamntal [5, 6]. Thi amplituds incas accoding to th num of dfctiv as at chaactistic fquncis (Eq. ) Fquncy (Hz) c ( ) ( ) ( ) ( ) Fquncy (Hz) d) ( ) ( ) ( ) ( ) dfct f = ±.n.g f, n =,,.. () s (7.9-7.) ( ) ( ) ( ) Sval quantitis w calculatd and analyzd in od to accss th infomation thy containd aout th psnc of th simulatd fault (on and two on oto as). Th moto induction was initially opatd with a load toqu of 3 m and th fnc spd was st to 8 pm () (-6.s).fs (-.s).fs (-4.s).fs (a) (-4.s).fs (-.s).fs Fqunc (Hz) (+.s).fs (+4.s).fs (+6.s).fs Fqunc (Hz) On th figu (7), w notic th appaanc of hamonics on th spctum. Ths hamonic hav amplitud which incass (+.s).fs (+4.s).fs (c) (-6.s).fs (-4.s).fs (-.s).fs (+.s).fs (+4.s).fs (+6.s).fs Fqunc (Hz) Fig 7: Stato cunt spctum fo: (a) On on a () Spacd two on as (c) Adjacnt two on as Fquncy (Hz) W not that th lins du to dfct invisil fo wa slips (figu 8.a) and lss visil with avag slip (figu 8.). So it is difficult to ct th dfct of on as with wa load. On th oth hand, fo nominal loads (figu 8.c, d), th lins a visil. W hav shown y spctal analysis and monitoing th volution of chaactistic fquncis of a dfct psnt in th stato cunt could dduc th stat of th machin. Indd, though its contol of th spd contol of induction machin, w now th spd of mchanical otation, slip stimat and can thfo asily locat th chaactistic fquncis of th lins du to dfault. V. COCLUSIO Fquncy (Hz) Fig.8. Stato cunt spctum with diffnt slips fo adjacnt two on oto as: a) s=.9% ) s=3.48% c) s=6.3% d) s=7.77% This pap psnts within th famwo of th diagnosis asynchonous moto on as simulation asd on th dvlopmnt of a ducd modl. Th stato cunt spctum analysis shows th psnc of a dfct du to th a o th uptu of as thans to appaanc of th diffnt hamonics th givn y quation (). Also, y contolling th spd of induction machin, w now that spd mchanical, slip stimat and can not asily locat th chaactistic fquncis of th lins du to dfct. Futh sach has to don in this fild in od to ma th diagnosis of oto faults mo lial in this typ of div. 34

6 Wold Acadmy of Scinc, Engining and Tchnology 4 TABLE II SIMULATIO FEQUECIES AD MAGITUDES OF THE STATO CUET SPECTUM: a) On on as ) Spacd two on as c) Adjacnt two on as s=7.84 % s=7.95 % s=8 % f cal=(-6s)f s f cal=(-4s)f s f cal=(-s)f s f cal=(+s)f s f cal=(+4s)f s f cal=(+6s)f s calculatd f(hz) dducd f (Hz) Magnitud (db) calculatd f(hz) dducd f (Hz) Magnitud (db) calculatd f(hz) dducd f (Hz) Magnitud (db) APPEDIX Fo th simulatd induction moto Pn Output pow. W Vs Stato voltag V fs Stato fquncy 5 Hz p Pol num s Stato sistanc 7.58 Ω oto sistanc 6.3 Ω oto a sistanc.5 mω sistanc of nd ing sgmnt.5 mω L oto a inductanc. µh L inductanc of nd ing. µh L sf Laag inductanc of stato 6.5 mh M s Mutual inductanc 46.4 mh s um of tuns p stato phas 6 um of oto as 6 L Lngth of th oto 65 mm Ai-gap man diamt.5 mm J Intia momnt EFEECES.54 g m [] Dif, M.; Cadoso, A. J. M.; "Th Instantanous activ Pow Appoach fo oto Cag Faults Diagnosis in Induction Moto Divs", Poc IEEE Pow Elctonics Spcialists Conf. - PESC, hods, Gc, Vol., pp , Jun, 8. [] M. Eltaach, A. Chahata and I. Zin, A compaison of xtnal and intnal mthods of signal spctal analysis fo on oto as ction in induction motos, IEEE Tans. on Ind. Elc., vol. 5, n, pp. 7-, F. 4. [3] M. E. H. Bnouzid, Biliogaphy on induction moto faults ction and diagnosis, IEEE Tans. on Engy Conv., vol. 4 n 4, pp , Dc.999. [4] W.S.H. Wong and D. Holliday. "Minimisation of flux doop in dict toqu contolld induction moto divs", IEEE, 7 ov 4, pp , pocdings onlin no [5] Mnac, A. Bnacha, M.S. ait Said, S. Did, "Stato Cunt Analysis of Incipint Fault into Induction Machin oto Bas", Jounal of Elctical Engining, oumani, Vol 4, -4, pp 5-. [6] Mnac, S. Moau, A. Bnacha, M.S. ait Said " Effct of th position and th num of on as on Asynchonous Moto Stato Cunt Spctum", EPE-Pow Elctonics and Motion Contol, Potooz, Slovnia, 6. [7] S. Bnaggoun, S. Blacm,. Adssmd, "Snsolss Dict Toqu Contol of PMSM Div with EKF Estimation of Spd, oto Position and Load Toqu Osv", Asian Jounal of Infomation Tchnology 6 (): 36-4, 7. [8] Canudas, " Modélisation Contôl Vctoil t DTC ", Edition HAMES Scinc Euop, Ltd. [9] Taahashi, T. oguchi, "A w Quic spons and High Efficincy Contol Statgy of an Induction Machin", IEEE. Tans. Indus. Applid, : idha Kchida was on in El-oud, Algia, in 984. H civs th B.Sc. dg in lctical ngining fom th Univsity of Bisa, Algia, in 7, and woing to gt an th M.Sc. lctical ntwos fom th Scinc and Tchnology Institut of El-oud Cnt Univsitai, Algia. His sach intsts includ contol of lctical divs, in paticula, th dict toqu contol in asynchonous motos and diagnosis, (idha.84@gmail.com). Mnac Azi was on in Batna, Algia, in 968. H civs th B.Sc. dg in lctical ngining fom th Univsity of Batna, Algia, in 99, and th M.Sc. dg in lctical contol fom th Elctical Engining Institut of Bisa Univsity, Algia, in 996. H civs th Ph.D. dg in lctical contol fom th Univsity of Batna and LAII Laoatoy of Automatic and Industial data pocssing, Univsity of Poitis, Fanc, in 7 and th hailitation dg in 9 fom Univsity of Bisa Algia. Cuntly, h is a Taching Assistant with th Elctical Engining Institut at th Univsity of Bisa and mm of LGEB Laoatoy of Elctical Engining of Bisa, Algia. His majo filds of intst in sach a diagnosis, idntification and contol of lctical machins. (mnac_azi@hotmail.com). Bnacha A/Hamid was on in 96 in Ais, Algia. H had achivd a M.sc. in 98 and a B.Sc. in 983 fom th Univsity of Batna, Algia, and a Mast of Scinc in 985 and a Ph.D. in lctonics fom th Univsity of Clmont-Fand, Fanc. Sinc 99, h tachs at th Univsity of Bisa, Algia. H is mm of th sach Laoatoy of lctotchnic of Bisa and th had of th sach goup: Simulation of sliding mod contol of an asynchonous machin. His oth sach intsts a: Elctic machins (dsign, modlling, idntification, contol), pow lctonics, lctomagntism (antnnas, f popagation), lctonics (tlvision). (nach_a@yahoo.f) 35