A Novel Method for Vector Control of Three-Phase Induction Motor under Open-Phase Fault

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1 6 J. Eng. Tchnol. Sc. Vol. 47, No., 05, 6-45 A Nol thod for Vctor Control of Thr-Pha Inducton otor undr Opn-Pha Fault ohammad Jannat, Syd Ham Agar, Nk Rumz Nk Idr & ohd Junad Abdul Azz UT-PROTON Futur Dr aboratory, Powr Elctronc and Dr Rarch Group, Faculty of Elctrcal Engnrng, Unrt Tknolog alaya, 80Skuda, Johor, alaya Emal: m_jannatyy@yahoo.com Abtract. Th majorty of lctrcal machn uch a nducton motor can b modld by an qualnt two-pha machn modl (d-q modl). A thr-pha nducton motor wth on of th tator pha opnd (faulty thr-pha nducton motor) can b alo modld by an qualnt two-pha machn. If a conntonal ctor control mthod for balancd thr-pha nducton motor ud for th faulty machn, gnfcant ocllaton n pd and torqu wll rult. In th papr, a nol tchnqu for ctor control of faulty thr-pha nducton motor bad on rotor-fld orntd control (RFOC) prntd. Th prformanc of th propod mthod wa aluatd ung ATAB oftwar. Th rult how that t ach gnfcant mpromnt n th ocllaton rducton of th pd and torqu rpon. Kywor: fld-orntd control; opn-pha fault; pd and torqu ocllaton; thr-pha nducton motor; ctor control. 0BIntroducton Nowaday, fld-orntd control (FOC) of nducton motor (I) broadly adoptd to obtan hgh dynamc prformanc n dr ytm. Applyng a conntonal control tratgy uch a FOC to a faulty thr-pha I (thrpha machn undr opn-pha fault) wll rult ngnfcant ocllaton n th pd and torqu output [-4]. It wa hown n [-4] that ung tranformaton matrc, th FOC quaton tructur for a faulty thr-pha I can b tranformd nto a tructur that mlar to that for a balancd I. Howr, th backward trm of th tator oltag quaton wr nglctd n th proc of calculatng th FOC quaton [,]. Th propod mthod n [4] for ctor control of faulty I alo xtrmly dpndnt on th rgulaton of th currnt proportonal-ntgral controllr. Rfrnc [5] rw and compar fault tolrant AC dr on th ba of fatur, cot and lmtaton. It alo ntrtng to not that th thr-pha I modl wth on pha cutoff, n prncpl, mlar to th modl of a ngl-pha I wth two wndng. Rcd Aprl rd, 04, Rd Octobr 7 th, 04, Accptd for publcaton Dcmbr 9 th, 04. Copyrght 05 Publhd by ITB Journal Publhr, ISSN: , DOI: 0.564/j.ng.tchnol.c

2 A Nol thod for FOC of -Pha I undr Opn-Pha Fault 7 In othr wor, a ngl-pha I can b condrd and clafd a an unbalancd two-pha I. It propod n [,6] to u a hytr currnt controllr for rotor fld-orntd control (RFOC) of unbalancd two-pha I. Howr, ung a hytr currnt controllr ha drawback undr lght load condton. In [7], tator fld-orntd control (SFOC) of ngl-pha I wth a pot-ngat qunc currnt controllr propod; th u of th controllr rultd n a complx control ytm. In [8], dcouplng ctor control of ngl-pha I by ntroducng two dcouplng gnal n addton to th dcouplng gnal lk th on ud n thr-pha I dr wa propod. Rfrnc [9] propo an RFOC mthod for ymmtrcal two-pha I a a rplacmnt for ctor control of aymmtrcal two-pha I. Th mthod cannot b ud for ctor control of faulty I du to th unqual nductanc n th faulty I modl. In th majorty of th prouly prntd FOC control chm for two-pha I, th uppoton ( / ) / mployd [5,7,8,0-]. Ung th uppoton rflctd n th pd and torqu rpon of th faulty I a fully dcud n[4]. It wa hown n [4] that a mall magntud of ocllaton at th ynchronou frquncy xtd n th faulty I pd and torqu rpon whn th uppoton / ( q / d ) wa ud. Th man contrbuton of th prnt tudy wa to dlop a nol and xact ctor control mthod bad on RFOC for I, whch can alo b adoptd for I undr opn-pha fault. In th propod mthod, th uppoton of ( / ) /, whch uually condrd n th FOC of two-pha I, not ud. Th prformanc of th propod mthod wa aluatd and chckd ung ATAB oftwar. athmatcal odlng A hown n [], a faulty I quaton tructur, n gnral, th am a a balancd I quaton tructur. Th dffrnc btwn th modl of a balancd and a faulty I ar ummarzd n Tabl. In th papr,, ar th tator d-q ax oltag,, ar th tator d-q ax currnt, λ,λ ar th tator d-q ax flux, dr, qr ar th rotor d-q ax currnt, and λ dr, λ qr ar th rotor d-q ax flux. oror, r and r r ndcat th tator and rotor rtanc,,, r, and ndcat th tator and rotor lf and mutual nductanc. τ, τ l, J and F ar lctromagntc torqu, load torqu, nrta and cou frcton coffcnt rpctly, ω r th rotor pd and T r th rotor tm contant. oror, th uprcrpt and ndcat that th arabl ar n th tatonary and rotatng rfrnc fram rpctly.

3 8 ohammad Jannat, t al. Tabl Comparon btwn modl of balancd and faulty nducton motor. Balancd Inducton otor Faulty Inducton otor q-ax mutual nductanc: q-ax mutual nductanc: m m q-ax lf nductanc: q-ax lf nductanc: l + m l + m A faulty I tator quaton can b tranformd nto an unbalancd d-q tator quaton ung th normalzd tranformaton matrx a drd n [], whch gn by (): fault T In RFOC, th machn quaton ar tranformd to th rotatng rfrnc fram. Th tranformaton prformd ung th wll-known rotatonal tranformaton matrx gn by () [4] (n (), th angl btwn th tatonary rfrnc fram and th rotatng rfrnc fram): co n T n co () By applyng () to th quaton of th faulty thr-pha I, th tator and rotor oltag quaton n th rotatng rfrnc fram can b obtand a forward and backward componnt [4]. Th backward trm ar producd bcau of dffrnt nductanc n th faulty I quaton. It pobl to control a faulty I by ung th forward and backward componnt paratly; howr, th wll rult n a ry complx control ytm. W old th problm by ntroducng two rotatonal tranformaton. It wll b hown that by ung th rotatonal tranformaton, th RFOC quaton tructur of th faulty I bcom mlar to that of th balancd I. Equaton of th Propod Vctor Control for Faulty I Th man da of ung th tranformaton obtand from th mplfd tady-tat qualnt crcut of a ngl-pha I a hown n Fgur. All of th paramtr n Fgur ar dfnd n [5] and (). ()

4 A Nol thod for FOC of -Pha I undr Opn-Pha Fault 9 Z F Zd Zd, ZB Z + Z + Z Z + Z + Z lm b d lm f d ( ) Zlm + Z f + Zd ZF Zd ZF Zlm + Zb + Zd ZBZd Z, V I Z Z Z Z F B F B b () Fgur Equalnt crcut of a ngl-pha I. Fgur () and () ndcat that t pobl to chang th qualnt crcut of th ngl-pha I nto two balancd crcut that rprnt th forward and backward crcut [5]. It alo pobl to rprnt th qualnt balancd crcut (Fgur ()). Th quaton of th forward and backward oltag and currnt can b rprntd by th followng quaton [5]: Va Va V V j, V V j, I I jai, I I jai a + + a ( ) ( ) f m b m f m a b m a Eq. (4) th tranformaton matrx for th tranformaton of th arabl from unbalancd mod to balancd mod (.g. th tady-tat qualnt crcut of a ngl-pha I to Fgur ()). Bad on (4), th tranformaton matrc for th tranformaton of th arabl from an unbalancd t to a balancd t ar obtand a follow []. ν ν [ T ] ν ν co n n ν ν co co n T n co It xpctd that by applyng th rotatonal tranformaton (E. (5) and (6)) to th quaton of th faulty I, th unbalancd quaton of th faulty motor (4) (5) (6)

5 40 ohammad Jannat, t al. can b tranformd nto quaton that ha a tructur mlar to tho of th balancd motor ( Tabl ). Th dffrnc btwn th RFOC quaton of conntonal ctor control for th balancd I and th RFOC quaton of th propod modfd ctor control for th faulty I ung th tranformaton matrc ar ummarzd n Tabl (n RFOC: λ dr λ r and λ qr 0). It concludd from Tabl that th only dffrnc btwn th RFOC quaton for th balancd I and tho for th faulty I that n faulty mod / m, l +/ m obtand and w ha th backward trm a dfnd n Tabl ( rf-b, d-b, rf-b and d-b ), whra n balancd mod, w ha / m, l +/ m and thr ar no backward trm. Bad on Tabl, Fgur propod for fault-tolrant thr-pha I ctor control. Tabl Comparon btwn two ctor control mtho. Balancd I Faulty I q-ax mutual nductanc: m q-ax mutual nductanc: m Stator lf nductanc: m l + Stator lf nductanc accordng to (7): m l + to tranformaton for th tator oltag: + c b a 0 to tranformaton for th tator oltag: b a to tranformaton for th tator currnt: + c b a 0 to tranformaton for th tator currnt: b a Inr of balancd rotatonal tranformaton for th tator oltag: co n n co Inr of unbalancd rotatonal tranformaton for th tator oltag: co n n co

6 A Nol thod for FOC of -Pha I undr Opn-Pha Fault 4 Balancd I Balancd rotatonal tranformaton for th tator currnt: co n n co Stator d-ax oltag: ˆ d r ˆ + ω dt d λr + ( ) r dt whr: ˆ r Stator q-ax oltag: d r + ˆ + ωˆ dt + ω λr r Faulty I Unbalancd rotatonal tranformaton for th tator currnt: co n n co Stator d-ax oltag: d r + ω dt d λr d b rf b + ( ) + + dt r r, d b whr: ω ( ) rf b d r r + ( ) ( ) dt co n co n co n Stator q-ax oltag: d r + + ω dt d b rf b + ω λr + + r whr: d b ω ( ) d rf b r r + ( ) ( ) dt 4 Smulaton Rult and Comparon To how th ffctn of th propod dr ytm, a mulaton of th ytm wa conductd ung ATAB oftwar. Th mulatd motor wa fd by a pul wdth modulaton (PW) thr-lg oltag ourc nrtr (VSI). Th Rung-Kutta algorthm wa ud for olng th faulty thr-pha I dynamc quaton. Th mulatd thr-pha I data wr a follow: oltag:5v, f50hz, numbr of pol4, powr475w, r 0.6Ω, r r 9.5Ω, lr l 0.084H, m 0.85H, J0.008kg.m. Th rfrnc pd n th mulaton wa t to 400rpm and th load torqu wa ard a follow: from

7 4 ohammad Jannat, t al. Fgur Block dagram of th propod ctor control for fault-tolrant I.

A Nol thod for FOC of -Pha I undr Opn-Pha Fault 4 t0 to t0.4, T l 0N.m,

Fgur dmontrat that th conntonal ctor controllr cannot control th faulty I proprly.

pd ocllaton aftr applyng load and at tady tat ~ rpm at a rotor pd of 400rpm, whra whn ung th modfd controllr, th pd

Th rult how that th modfd RFO controllr dcrad th torqu ocllaton gnfcantly wth an mpromnt n th motor pd rpon.

8 A Nol thod for FOC of -Pha I undr Opn-Pha Fault 4 t0 to t0.4, T l 0N.m, from t0.4 to t, T l N.m and from t to t7, T l.5n.m. Th RFOC ung th conntonal and th propod modfd controllr bad on Fgur wr mulatd wth th fault ntroducd at t. Fgur dmontrat that th conntonal ctor controllr cannot control th faulty I proprly. Epcally w a condrabl ocllaton n th lctromagntc torqu and motor pd (a can b n from Fgur, whn ung th conntonal controllr, th pd ocllaton aftr applyng load and at tady tat ~ rpm at a rotor pd of 400rpm, whra whn ung th modfd controllr, th pd ocllaton wa rducd notably to ~0.8rpm). Th rult how that th modfd RFO controllr dcrad th torqu ocllaton gnfcantly wth an mpromnt n th motor pd rpon. (a) (a) (b) (b) (c) (c) (d) Fgur Smulaton rult of th conntonal (lft) and modfd (rght) controllr: (a) rotor a-ax currnt, (b) tator a-ax currnt, (c) pd, (d) torqu. (d) 5 Concluon In th papr, a nol approach of ctor control for faulty thr-pha or unbalancd two-pha I, bad on RFOC propod. Th tchnqu mploy two nw tranformaton matrc that tranform th RFOC quaton of an unbalancd two-pha I nto quaton that ha th am tructur a tho of a balancd thr-pha I. Th chm not only can b ud for th ctor control of unbalancd I but alo approprat for ngl-pha I.

9 44 ohammad Jannat, t al. Unlk othr RFOC mplmntd for ngl-pha or unbalancd I, th tchnqu propod n th papr do not mploy th uppoton ( / ) /. Th rult ndcat that th propod tchnqu can condrably rduc pd and torqu ocllaton. Rfrnc [] Jannat,., onad, A., Idr, N.R.N., Azz,.J.A. & Faudz, A.A.., Vctor Control of Faulty Thr-Pha Inducton otor wth an Adapt Sldng od Control, Prz Elktrotch, 89(), pp. 6-0, 0. [] Jannat,. & Fallah, E., odlng and Vctor Control of Unbalancd Inducton otor (Faulty Thr Pha or Sngl Pha Inducton otor), In Powr Elctronc & Dr Sytm & Tchnolog Confrnc (PEDSTC), 00 t, pp. 08-, 00. [] Jannat,., Idr, N.R.N. & Salam, Z., A Nw thod for odlng and Vctor Control of Unbalancd Inducton otor, In Enrgy Conron Congr and Expoton (ECCE), 0 IEEE, pp. 65-6, 0. [4] Jannat,., Idr, N.R.N. & Azz,.J.A., A Nw thod for RFOC of Inducton otor Undr Opn-Pha Fault, In Indutral Elctronc Socty, IECON 0-9th Annual Confrnc of th IEEE, pp , 0. [5] Wlchko, B.A., po, T.A., Jahn, T.. & Schulz, S.E., Fault Tolrant Thr-Pha AC otor Dr Topolog: A Comparon of Fatur, Cot, and mtaton, IEEE Tranacton on Powr Elctronc, 9(4), pp. 08-6, 004. [6] Corra,.B., Jacobna, C.B., ma, A..N. & da Sla, E.R.C., Rotor- Flux-Orntd Control of a Sngl-Pha Inducton otor Dr, IEEE Tranacton on Indutral Elctronc, 47(4), pp. 8-84, 000. [7] Corra,.B., Jacobna, C.B., da Sla, E.R.C. & ma, A..N., Vctor Control Stratg for Sngl-Pha Inducton otor Dr Sytm, IEEE Tranacton on Indutral Elctronc, 5(5), pp , 004. [8] Vaz-Zadh, S. & Haroon, S.R., Dcouplng Vctor Control of Sngl Pha Inducton otor Dr, In Powr Elctronc Spcalt Confrnc, 005, PESC'05, IEEE 6th, pp. 7-78, 005. [9] Jang, D.H., Problm Incurrd n a Vctor-Controlld Sngl-Pha Inducton otor, and a Propoal for a Vctor-Controlld Two-Pha Inducton otor a a Rplacmnt, IEEE Tranacton on Powr Elctronc, 8(), pp , 0. [0] Jml,., Bn Azza, H. & Goa,., Ral-Tm Implmntaton of IRFOC for Sngl-Pha Inducton otor Dr Ung Dpac DS 04 Control Board, Smulaton odllng Practc and Thory Journal, 7(6), pp , 009.

10 A Nol thod for FOC of -Pha I undr Opn-Pha Fault 45 [] Jml,., Bn Azza, H. & Bouak,., Snorl Indrct Stator Fld Orntaton Spd Control for Sngl-Pha Inducton otor Dr, IEEE Tranacton on Powr Elctronc, 4(6), pp , 009. [] Vra, R.P. & Grundlng, H.A., Snorl Spd Control wth a RAS Spd Etmator for Sngl-Pha Inducton otor Dr, In Powr Elctronc and Applcaton, 009, EPE'09, th Europan Confrnc on, pp. -0, 009. [] Azza, H.B., Jml,., Bouak,. & Goa,., Hgh Prformanc Snorl Spd Vctor Control of SPI Dr wth On-n Stator Rtanc Etmaton, Smulaton odllng Practc and Thory, 9(), pp. 7-8, 0. [4] Va, P., Vctor Control of AC achn, Oxford cnc publcaton, Oxford, 990. [5] Ftzgrald, A.E., Kngly, C. & Uman S.D., Elctrc achnry, cgraw-hll, Nw York, 00.

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