Parameter Determination of an Induction Machine for Integrated Starter Alternator

Transcription

1 Paamee Deeminaion of an Inducion fo Inegaed ae Alenao C. P. Mudannayake and M. F. Rahman chool of Elecical Engineeing and Telecommunicaion Univeiy of New ouh Wale, ydney, Aualia ABTRACT Thi pape peen paamee idenificaion of an inducion machine fo inegaed ae alenao ( opeaing in vaiable fequency and vaiable exciaion condiion. No-load and and-ill e ae conduced a vaiou fequencie inead of ingle aed fequency in ode o obain he vaiaion of oo eiance, oo leakage inducance and magneizing inducance wih fequency. The vaiaion of magneizing inducance wih he magneizing cuen i alo inveigaed by conducing no-load e a vaiou eminal volage. The paamee obained fom above e ae compaed wih convenional no-load and and-ill paamee a well a paamee obained fom on-line monioing mehod, namely impeed ao volage and impeed ao cuen e. The eul of hee e allow an inenive inveigaion of paamee vaiaion of he inducion machine ( unde vaiable fequency and exciaion condiion.. INTRODUCTION The auomoive elecical yem i demanding high powe geneaion o cae i new and impoved feaue []. The main poblem of high powe geneaion in exiing auomobile elecical yem i idenified a he limiaion of peen Lundell alenao. Alo, he poibiliy of combining ae moo and alenao ino a ingle yem o called inegaed ae alenao ( i encouaging a majo change in cuen alenao machine opology. A a eul, many poenial cheme ae popoed fo uch a inducion machine (, pemanen magne machine and wich elucance machine baed yem. Among hem inducion machine baed yem i one of he mo appealing due o vaiou well known benefi of he inducion machine. Howeve, inducion machine how highly nonlinea behaviou and ignifican paamee vaiaion again changing opeaing condiion uch a ao fequency vaiaion, level of loading and he empeaue [, ]. Thee paamee vaiaion hould caefully ake in o conideaion in deigning an applicaion uch a yem, ince i wide peed ange and highly vaiable loading condiion lead machine o be opeaed ove wide fequency ange and vaiable exciaion condiion ( in field weakening egion. Thi pape peen expeimenal eul of paamee deeminaion of an inducion machine fo ove wide fequency ange and vaiable magneiaion. In ode o idenify he paamee vaiaion, he inducion machine wa ubjeced o no-load and and-ill e a vaiable fequency and vaiable exciaion wih help of PWM invee o upply inducion machine, and a conolled dive moo coupled o he. The eul of above e ogehe wih he DC ao eiance e allow he deeminaion of ao eiance, ao leakage inducance, oo eiance and oo leakage inducance. Among hem, oo eiance and oo leakage inducance ae obained a a funcion of lip fequency, ince hey vay ignificanly wih lip fequency. The magneiing inducance i deemined a a funcion of ao fequency and magneizing cuen. On-line paamee monioing mehod by focing impeed ao cuen and volage [4] ae alo conduced in view of veifying he validiy of obained paamee vaiaion.. INDUCTION MACHINE MODEL.. DYNAMIC MODEL The wo-axi dynamic model ( q - d model of quiel cage inducion machine in aionay efeence fame can be epeened by (-(8 given below [4, 7]. d v q Ri q q d λ ( d v d Ri d d d λ ( 0 d Ri q q d d λ ωλ ( 0 d Ri d d q d λ ωλ (4 λ = Li + L i (5 q q m q d Li d Lmid q Li q Lmiq d Li d Lmid λ = + (6 λ = + (7 λ = + (8 Whee L = Ll + Lm and L = L l + L m v, v i, i q - d axi ao volage and cuen d q d q v, v i, i q - d axi oo volage and cuen d q d q λd, λ q λd, λ q q - d axi ao and oo fluxe R, R ao eiance, oo eiance L m, L l, L l, Magneiing, Roo & ao leakage inducance ω ω ynchonou and oo peed (elec ad/ec e

2 .. TEADY TATE EQUIVALENT CIRCUIT V I R Ll Em I m L m Ll I E Figue : eady ae pe phae equivalen cicui fo inducion machine The eady ae equivalen cicui of an inducion machine i hown in figue. The coe lo i no included o hi model a a lumped paamee by auming ha he cuen hough uual coe lo eiance i much malle compaed o he magneizing cuen I m. The coe lo i eaed epaaely, and obained a a funcion of magneiing cuen and he ao fequencyω. R e The equivalen impedance Z eq of he eady ae equivalen cicui can be obained a below []. R jωelm( + jωell Zeq = R + jω ell + (9 R + jωe( Ll + Lm Whee, V = IZeq The acive powe conumed by one phae of he moo can be expeed a in (0 R P = I R + I + P coelo (0 ω = ωe ( Whee,, ω - lip and lip fequency. V, I -ao phae volage and cuen veco., coelo P P -ingle powe inpu and ingle phae coe lo epecively.. METHOD OF DETERMINATION The paamee of he inducion machine wee deemined mainly by conducing no-load and and-ill e unde vaiable fequency and vaiable exciaion. Impeed cuen and volage e uing fo on-line monioing wee alo caied ou on he ame inducion machine. The decipion fo hee e ae aed below... VARIABLE FREQUENCY BLOCK ROTOR TET -Phae Recifie Invee PWM f ef Powe analyze PZ 4000 Inducion Blocked oo V ef Figue : Oveview of vaiable fequency and-ill e. The and-ill e can be ued o deemine he oo eiance and he leakage inducance of an inducion machine. In convenional and ill e, he oo i locked mechanically and applied volage a aed fequency o he machine eminal. Then he volage i inceaed unil machine daw he aed cuen and meaued line volage and hee phae powe of he machine. The oo eiance and leakage inducance can be calculaed fom hee meauemen. Howeve, he oo eiance and oo leakage inducance vaie ignificanly wih lip fequency, mainly a a eul of kin effec. The convenional andill e i uually conduced a aed ao fequency and hence cuen induced in he oo ha ame fequency, becaue he oo i and ill. The ypical opeaing lip fequency of an inducion machine i fa le han aed ao fequency (ypical maximum of oo lip fequency duing he opeaion i abou 0%; hence he opeaional oo eiance and leakage inducance i ignificanly diffeen fom he value obained fom convenional e. Theefoe, he oo eiance and leakage inducance ae funcion of lip fequency and can be expeed a R = R( ω and Ll = Ll ( ω. In view of inveigaing vaiaion oo eiance and leakage inducance wih lip fequency, vaiable fequency and-ill e wa conduced. The oveview of vaiable fequency and ill e i hown in figue. A can be een in figue, vaiable volage and vaiable fequencie ae geneaed by adjuing he magniude and fequency of inuoidal efeence o PWM geneao, which poduce wiching ignal o he IGBT invee. The volage i inceaed unil he inducion machine daw aed cuen and meaue he line volage and hee phae powe of he machine a vaiou fequencie uing YOKOGAWA PZ 4000 Powe Analyze. The lip fequency (o fequency of induced oo cuen i equal o he fequency of ao ( ω = ωe a and-ill, ince he lip i equal o one (i.e. =. Alo, i can be aumed ha magneiing impedance i vey lage compaed o oo impedance (i.e. R + jωll <<< jωlm. Theefoe, he (9 can be implified o, Zeq = ( R + R + jω ( Ll + Ll ( The coe lo can be negleced duing and-ill e ince vey low volage i applied o he machine compaed o he aed volage. Theefoe, oal acive powe i diipaed a coppe lo, and hence ingle phae acive powe can be expeed a below. P = I ( R + R ( The vaiaion of oo eiance and oo leakage inducance wih lip fequency can be obained by pefoming ( and ( a vaiou fequencie, when he ao eiance and ao leakage inducance ae known. The R can be deemined uing DC eiance e. The ao leakage inducance i calculaed by auming ha ao leakage inducance i equal o he oo leakage inducance a aed fequency, and oo leakage inducance emain conan fo all ohe fequencie.

3 .. VARIABLE FREQUENCY NO-LOAD TET.. PREED TATOR VOLTAGE TET -Phae Recifie Invee Powe analyze PZ 4000 Inducion peed conolled dive yem D Invee + Conolle -Phae Recifie Invee a b c Inducion PWM V ef f ef π p ω yn Figue : Oveview of vaiable fequency-vaiable volage no-load e. In convenional no load e, he inducion machine i diven a ynchonou peed coeponding o aed fequency by mean of a dive moo (uually a DC moo o ha he oaional loe ae ovecome by he dive (i.e. he lip of he inducion machine i zeo. Then aed volage a aed fequency i applied o he inducion machine eminal and meaue he line volage, line cuen and he hee-phae powe of he machine. The coe lo and he magneiing inducance can be calculaed fom hee meauemen povided ha ao eiance and he leakage inducance ae known. Howeve, he magneiing inducance obained fom convenional e i accuae only a aed fequency and aed magneizaion. Bu magneiing inducance vaie ignificanly wih magneiing cuen and ao fequency (i.e. Lm = Lm( Im, ωe. In ode o inveigae he vaiaion of magneiing inducance wih ao fequency and magneiing cuen, he no-load e i caied ou unde vaiable fequency and vaiable volage condiion. The oveview of he no-load e eup i hown in figue. A can be een in figue, vaiable volage and vaiable fequencie ae geneaed by adjuing he magniude and fequency of inuoidal efeence o PWM geneao which poduce wiching ignal o he IGBT invee. The peed efeence of conolled dive moo i deived fom he efeence fequency a indicaed in figue. The line cuen and he hee phae powe wee meaued a vaiou fequencie and line volage uing YOKOGAWA PZ 4000 Powe Analyze. The lip of he inducion moo i zeo unde no load condiion (i.e. = 0, ince he inducion machine oae a ynchonou peed. Theefoe, he (9 can be implified o, Z = R + jω ( L + L (4 eq e l m The coe lo i alo a funcion of magneiing cuen and ao fequency (i.e. P coelo = P coelo ( ωe, Im can be expeed a below P coelo = ( P I R (5 The vaiaion of magneiing inducance and coe lo of he inducion machine can be obained by pefoming (4 and (5 fo vaiou magneiing cuen and ao fequencie. wiching ignal a b c a b Figue 4: Block diagam fo impeed ao volage e and wiching ignal The impeed ao volage e i mainly ued o deemine he ao anien inducance L. Thi mehod can be adoped in auomaing he paamee idenificaion, ince i i no neceay o lock he oo o dive by ome ohe moo [4]. In hi e, ho volage pule ae applied o he ao eminal of he inducion machine uing a hee-phae invee a hown in figue 4. The wiching ignal a, b and c hown in figue 4, geneae line volage v ab and v ac a hown in figue 5a. Thi volage plue caue cuen o flow a indicaed in figue 5b. v, v (a i ab d (b = i ac V d ( i d 4 c V d ( i d + Figue 5: Volage and cuen duing impeed volage e uch volage pule and cuen can be epeened in aionay efeence fame by conideing ae phao definiion a decibed (6, (7 below. ( ( ( vd + jvq = va + avb + a vc ( (6 ( ( ( id + jiq = ia + aib + a ic ( (7 j e π Whee, a = and va (, vb (, vc (, ia (, ib (, ic ( ae volage and cuen of phae abc.,, The phae volage duing he pule can be expeed a va( = Vd, vb( = Vd and vc( = Vd (8 ubiuing (8 o (6, vd = Vd (9 The phae cuen fo e can be expeed a

4 ia( = i, ib( = i and ic( = i (0 ubiuing (0 o (7, i = i ( d Combining (, (6 and (8, and eaanging d Lm d v = d Ri + d L id d d + L d λ ( The inducion machine emain andill duing he e (i.e. ω = 0. Combining (4 and (8, d T d d Lmid d λ + λ = ( Combining ( and ( ef d Lm v = d ( R + R i + d L id d d L T λ (4 ef Lm L Lm Whee, R = R, T = and L = L( L R LL If he duaion of he volage pule ae choen o be much hoe han he oo ime conan T, he volage pule ime i no enough o build up flux in he oo and he oo flux can heefoe aume o be zeo (i.e. λ d = 0. If he ao cuen i d = 0, hen (4 can be educed o (5 below. d vd = L id (5 d The ao anien inducance L can be deemined fom he d-axi ao volage and he gadien of id when i d = 0 a decibed in (5. The gadien a i d = 0 i appoximaely equal o aveage lope of he i duing ime peiod (, and hence he ao d 4 anien inducance L can be expeed a below. vd ( 4 = ( id ( id 4 + L.4. PREED TATOR CURRENT TET (6 The ao eiance and he efeed value of oo eiance can be deemined by applying diffeen level of DC ao cuen o he moo and analying he eulan volage anien [4]. The oveview of hi e i hown in figue 6. The ao cuen efeence uiable fo hi pupoe and he eulan ao volage wavefom ae hown in figue 7. -Phae Recifie Cuen Conolle Refeence Cuen * i a Invee PWM PI a b i a Inducion Figue 6: Block diagam fo impeed cuen e i (a (b d v d = i = L v ( i d ( v d ( i d ( v d ( i d + 4 ( v d + Figue 7: (a Cuen and (b volage vaiaion duing impeed ao cuen e The volage and cuen in hi e can be epeened a dq-componen, in aionay efeence fame by ubiuing following phae volage (7 o (6. va( = vl, vb( = vl and vc ( = 0 (7 vd = vl (8 Whee, vl i he volage beween phae a and b. ubiuing phae cuen ( ia( = i, ib( = i and ic ( = 0 o (7, id = i (9 The ao cuen i conolled o be DC duing peiod (, ( and ( 4. Theefoe, duing hee peiod d i d = 0, and combining ( and (4, he d- d axi ao volage v d can be epeened by d T vd + vd = Rid (0 d A decibed by (0 and he figue 7b, he v d decaying exponenially duing ime peiod(,( and( 4. The decaying ime conan i equal o oo ime conan. Alo, in he end of peiod and ao volage each eady ae. Then he (0 can be e-wien a v = Ri ( d d Theefoe, ao eiance can be calculaed a below ( vd ( vd R = ( ( id ( id The iniial value of volage v d a beginning of peiod ( 4 (i.e. = + can be obained fom (4, ( ( ef ( Lm v ( d R R id λ d = + ( + + LT + The oo flux a end of peiod (i.e. = can be obained fom (. ( λd Lm ( id = (4 Howeve, he oo flux can no be changed uddenly 4

5 Theefoe, ( λd ( λd = (5 + Combining (, (4 and (5, he efeed value of oo eiance can be obained a below. R ( vd R ( id ( id ( id ef + + = 4. TET REULT + (6 The above dicued e mehod ae caied ou exenively on a 5.5kW/V, 6-pole, and 50Hz inducion machine inegaed ae alenao in ode o obain he paamee vaiaion, and compae wih he convenional e paamee value. The inducion machine i upplied by hee phae IGBT invee. The DC volage o he invee i obained uing a diode bidge, and mainained o be 4V by mean of a vaiable hee-phae AC volage upply. The algoihm need o pefom hee e ae implemened in dpace 04 developmen boad hoed on a andad PC. 4.. NO-LOAD AND BLOCK ROTOR TET REULT The paamee obained fom convenional no-load and block oo e a aed fequency ae hown below in able. Table : Convenional e eul ao Reiance ( R 6.5 mω ao Leakage Inducance ( L l 0.70 µ H Roo Reiance ( R. mω Refeed Roo Reiance ( R.97 mω Roo Leakage Inducance ( L l 0.70 µ H Roo Time Conan ( T Magneiing Inducance ( L m 5.86 µ H The vaiable fequency and-ill e i conduced ove fequency ange 4-50Hz and obained he oo eiance. Figue 8 how he vaiaion of oo eiance wih lip fequency ogehe wih vaiaion of efeed value of oo eiance. Figue 9 how he vaiaion of oo leakage inducance wih lip fequency. A can be een in hee figue, he oo paamee ignificanly vay wih lip fequency, and convenional and-ill e a aed fequency doe no povide accuae paamee. ef Figue 9: Roo leakage inducance vaiaion wih lip fequency The vaiable fequency no-load e i conduced ove fequency ange 5-70Hz a diffeen magneiaion cuen (i.e. diffeen volage applied o he ao. The vaiaion of magneiing inducance and coe lo ae calculaed a decibed ealie. Figue 0 how he vaiaion of magneiing inducance wih he magneiing cuen a vaiou ao fequencie. The magneiing inducance vaie ignificanly wih magneiing cuen and alo depend on ao fequency, epecially when magneiing cuen i low. Figue how he vaiaion of coe lo wih magneiing cuen a vaiou ao fequencie. Figue0: Magneiing inducance vaiaion wih magneiing cuen a vaiou fequencie Figue : ao coe lo vaiaion wih magneiing cuen a vaiou ao fequencie Figue 8: Vaiaion of oo eiance and efeed value of oo eiance wih lip fequency 4.. PREED TATER VOLTAGE TET REULT The impeed ao volage e i conduced in ode o obain ao anien leakage inducance. Figue how he ao volage and he cuen duing he e. The ao anien inducance of he inducion machine i calculaed fom peiod T0, a decibed in ecion.. The calculaed value of ao anien inducance i given in able.

6 5. CONCLUION Exenive inveigaion on paamee vaiaion of an inducion machine baed inegaed ae alenao ove wide ange of ao fequency and vaying exciaion i caied ou. The paamee of he inducion machine ae obained by deploying vaiable fequency vaiable volage no-load e, and vaiable fequency and-ill e. The paamee vaiaion ae compaed wih conan paamee obained by convenional e. Figue : ao volage and cuen duing impeed volage e Table : Impeed volage e eul ao Tanien Inducance ( L 9.8 µ H 4.. PREED TATER CURRENT TET REULT Figue how he cuen applied o ao and he eulan ao volage unde impeed cuen e. The oo ime conan i obained by exponenial cuve fiing fo decaying ao volage duing peiod T. The efeed value of oo eiance obained uing iniial value of he ao volage in la decaying peiod (T a dicued in ecion.4. The eul ae hown in able. The efeed oo eiance value hown in able i vey cloe o he exapolaed 0Hz value of vaiable fequency and-ill e hown in figue 8. Thi veifie he validiy of oo eiance vaiaion obained fom he and ill e. Table : Impeed cuen e eul ao Reiance ( R 6.6 mω Refeed Roo Reiance ( R.84 mω Roo Time Conan ( T ef Figue : ao cuen and volage duing impeed cuen e The oo eiance of he inducion machine inceae wih he lip fequency, and oo eiance a ypical opeaional lip fequencie ae ignificanly le han he value a 50Hz. The efeed value of oo eiance obained fom he impeed cuen e cloely ageed o he 0Hz value fom vaiable fequency and-ill e. The magneizing inducance how ignifican vaiaion wih he magneizing cuen and fequency. The influence of ao fequency on magneizing inducance gealy appea when magneizing cuen i low. Thi inenive inveigaion of paamee vaiaion i gealy ueful in impoving machine deign a well a deigning of opimal conolle fo inducion machine applicaion. 6. ACKNOWLEDGEMENT The auho would like o acknowledge Enegy Technology diviion of Commonwealh cienific & induial Reeach Oganiaion (CIRO fo he financial aiance fo he pojec. REFERENCE [] J.G. Kaakian, H.C. Wolf, J.M. Mille and C.J. Huon, Auomoive elecical yem cica 005, IEEE pecum, vol,, iue 8, Augu, 996, p [] C. Ganham D. J. McKinnon, Rapid Paamee Deeminaion fo Inducion Moo Analyi and Conol, IEEE Tanacion on Induy Applicaion, vol.9, No. 4, pp04-00, 00. [] H. T. Yazdi and C. Ganham, On Line Roo Paamee Deeminaion of Thee-Phae Inducion Moo, in poceeding of IEEE Inenaional confeence on powe eleconic and dive yem vol. pp89-84, 995. [4] P. Va, Paamee Eimaion, Condiion Monioing, and Diagnoi of Elecical. Oxfod: Claendon Pe., 99. [5] J. K. eok,. I. Moon and. K. ul, Inducion Paamee Idenificaion uing PWM Invee a andill, IEEE Tanacion on Enegy Conveion, vol., No., pp7-, 996. [6] A. Gail, Idenificaion of Inducion Moo Equivalen Cicui Paamee Uing ingle-phae Te, IEEE Tanacion on Enegy Conveion, vol.4, No., pp5-56, 997. [7] D. W. Novony and T. A. Lipo, Veco Conol and Dynamic of AC Dive. Oxfod: Claendon Pe., 996.