ANALYTICAL COMPUTATION OF MAGNETIZING INDUCTANCES FOR THE SYNCHRONOUS RELUCTANCE MOTOR WITH AXIALLY-LAMINATED ROTOR

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1 Wokshop o ELECTRICAL MACHINES' PARAMETERS Tehal Uvesty o Cluj-Napoa, 6 th o May 00 ANALYTICAL COMPUTATION OF MAGNETIZING INDUCTANCES FOR THE SYNCHRONOUS RELUCTANCE MOTOR WITH AXIALLY-LAMINATED ROTOR Ileaa Toa Eletal Mahes Reseah Laoatoy Romaa Aademy - Tmsoaa Bah. INTRODUCTION The peomaes o the syhoous elutae moto ae essetally depedet o the maget dssymety o the mahe, espetvely o ts oto, as [], [], [3], [4], [5], [6]. The last oe s made om ga-oeted steel lamatos, alteatg wth sulato ad o-maget mateal. The asteg s ealzed wth lampg plates ad sews made om o-maget mateal ass o o-maget staless- steel, to avod the ease o the -as elutae. Both wdth o the lampg plates ad doma ouped o sews depeds o the oto dmesos ad o the ume o pole pas. I Fg. ae show two eamples o oto shapes o the two-pole mahe. The pape pesets a aalytal method o the a gap lu desty ad magetzg dutae estmato. Usg the pogam ased o ths method oe a aalyze ay aally oto shape havg moe tha 3 lamato ad moe tha sulato sheets. I ode to d the appopate oto shape whh a ease the moto peomae, a teatve method o a ukly estmato o the magetzg dutae s vey useul.. SIMPLIFYING HYPOTHESIS. lamatos;. sulato sheet 3. lampg plates 4. o-maget staless steel olt Fg.. Eample o oto shape o a two-pole mahe Oe agees that all the oss setos o the mahe the maget eld s the same; oe eglets the maget eld, whh loses though the ot aea. Oe osdes the m.m.. wth susodal dstuto o the e suae o the stato. The luee o stato slots s take to aout y the Cate ato; the luees o the sulato sheets ad those o the lampg plates o the euvalet a gap legth ae osdeed, as [7]. Oe eglets the pesee o the o-maget staless-steel olts. Oe osdes the o-leaty o the steel lamatos oly o the d-as eld omputato. Oe osdes that the -as eld etwee two adjaet steel lamatos o the oto s a pla-paallel oe. 53

2 Wokshop o ELECTRICAL MACHINES' PARAMETERS Tehal Uvesty o Cluj-Napoa, 6 th o May THE CALCULATION OF THE D-AXIS AIR GAP FLUX DENSITY Cosdeg the mahe data kow geometal dmesos, B-H uve o the eomaget mateal ad the stato m.m.. dstuto o the e stato suae, oe a ota the d-as lu desty dstuto the a gap, B d. Fg. pesets the appomate eld le, ode to ompute the m.m.. the ase o a two-pole mahe. The legth o the appomate eld le s alulated as uto o the geometal data ad o the ume o pole pa. Fo ay eld le, the m.m.. o the maget ut seto a gap, stato yoke, stato tooth ad eomaget oto aea depeds o the value o the lu desty the a gap pot M, ossed y the eld le osdeed. The oodate dees the posto o the pot M elatg to the d-as. Oe dvde the moto a gap to setos whee the lu desty s osdeed the same, havg the value oespodg to the pot the mddle o the seto. The ume o pots whee the lu desty s omputed depeds o the deee aepted etwee B d values o two adjaet setos. Fo lamato wdth less tha mm oe a osde a sgle pot staght to eah lamato. Fo the osdeed pot oe gves as tal value the B d that oespods to the ase µ e. θ B d d µ 0 Wth ths value oe omputes the mageto-motve oe o eah seto o the maget ut. The omputed esultat m.m.. osdeg µ e te, eame geate tha θ tally osdeed ad the a ew value s gve o the a gap lu desty. The teatve poess otues utl the deee etwee the omputed value o the m.m.. ad the tal admtted value s smalle tha the ed eo. I the st a gap aea staght to the oto pat omposed o lamato ad sulato sheets, oe osdes a sgle pot staght to eah lamato o lu desty alulus, eause the lamato wdth s usually less tha mm. As esult, o ths a gap aea oe omputes the lu desty o a ume o pots eual to the lamato ume,. I the seod a gap aea staght to the lampg plates, the lu desty otas a low value eause o the hgh value o the a gap wdth, due to the lampg plates, so t s ot aeted y the o-leaty o the eomaget mateal. Theeoe, oe omputes the lu desty o pots, eg less tha. Fgue 3 pesets the d-as lu desty dstuto alog the hal pole pth etwee d ad as o the oto o two ases: osdeg the o-leaty o the eomaget ut ad osdeg µ e. The moto has the ollowg data: P 0.55kW, p, I A, 59 oto sulato sheets, 0.mm wdth o the sulato sheets ad 0.5mm wdth o the oto lamato. The ampltude o the udametal o the d-as lu desty the a gap s otaed om the ollowg euato: 4 k k B d B s s Bk s s k B d [ T ] Fg.. The appomate eld le o a two-pole mahe B d [ T ] µ [ m ] Fg. 3. The d-as lu desty dstuto alog a hal pole pth etwee d ad -as o the oto 4. THE CALCULATION OF THE Q-AXIS AIR GAP FLUX DENSITY The -as a gap lu desty s omputed osdeg the maget ut law ad the maget lu law. The vaale dees the posto o the lamato elatg to the d-as o the oto. The Fg. 4 pesets the oto lamatos ad. The sulato sheet wdth s,. 54

3 Wokshop o ELECTRICAL MACHINES' PARAMETERS Tehal Uvesty o Cluj-Napoa, 6 th o May 00 d S,, Fg. 4. Eplaatoy o the -as eld omputato The -as a gap lu desty B staght to the lamato s: θ V B µ 0 3 The -as lu whh oss ay lamato,,,- has two tems: the -as lu Φ, peetatg om lamato tough the sulato sheet, ad the -as lu whh peetates om the a gap though the aea lmted y the oodates ad. θ V Φ Φ µ 0 l d 4 Oly o, the euato o the -as lu whh peetate the lamato has a sgle tem: Φ / θ V µ 0 l d 5 Fo eah sulato sheet plaed etwee the lamatos ad oe a wte the maget ut law:, V V Φ 6 S, µ 0 Wtg euatos as 4 ad 6 o all the lamatos,, oe otas a system havg euatos ad ukow uattes: values o the -as lu Φ ad values o the maget sala potetal V. Solvg ths system oe otas the -as lu ad the maget sala potetal o eah lamato depedg o the geometal data, the ampltude o the stato mageto-motve oe ad the pemealty o the a gap. Wth ths values oe a estmate the a gap lu desty staght to eah lamato, that s the -as a gap lu desty B dstuto alog the pole pth. The ampltude o the udametal o the -as lu desty the a gap s: B µ 0 3 θ 7 whee: 55

4 Wokshop o ELECTRICAL MACHINES' PARAMETERS Tehal Uvesty o Cluj-Napoa, 6 th o May θ V C os os 4 s s 8 k l os 9 C k V l 4 3 θ 0 tg tg The tems, ad 3 deped o the geometal data ad emphasze the lampg plates luee. Fgue 5 pesets the -as lu desty dstuto alog the hal pole pth etwee d ad as o the oto o the same moto. 5. THE CALCULATION OF INDUCTANCES The maget lu ad the d-as magetzg dutae oespodg to Β d ae omputed ad 3: Φ k k k k d B B l s s s s 8 θ d md Nk m L Φ 3 The -as magetzg dutae oespodg to Β s: [ m ] B [ T ] Fg. 5. The -as lu desty dstuto alog a hal pole pth etwee d ad -as o the oto

5 Wokshop o ELECTRICAL MACHINES' PARAMETERS Tehal Uvesty o Cluj-Napoa, 6 th o May 00 4µ 0l L m m Nk 3 Computg L md ad L m o deet values o the phase uet I oe ota the vaato L md I ad L m I. The pape deals ot wth the omputato o the leakage dutae. Based o ths method oe had developed a pogam o the estmato o the a gap lu desty ad the magetzg dutae osdeg kow the moto data geometal dmesos, wdg data, B-H uve o the eomaget mateal ad the stato phase uet. Oe has used the pogam to aalyze a two-pole mahe wth aally lamated oto. All the sulato sheets have the same wdth, z ; the lamato wdth s e. The ug tme o ths pogam s sgatly shote ompaso to the te elemet method EXPERIMENTAL RESULTS The valdato o the dutae s ealzed usg the d.. deay test [8],[9]. The tested moto has the ated powe 0.55kW, the supply euey 50Hz, the phase voltage 0V, the ume o poles ad the stato phase esstae 3.8 Ω. Fg. 6 pesets the depedee o d-as magetzg dutae, L md, o the uet I d. L md [ H ] alulated values measued values Id [ A ] Fg. 6. Vaato o the dutae L md, o the uet I d I Fg. 7 s show the vaato o the -as magetzg dutae L m, o the phase uet. L m [ H ] alulated values measued values I [ A ] Fg. 7. Vaato o the dutae L m o the uet I Oe ds a satsatoy oespodee etwee the omputed ad measued values. 57

6 Wokshop o ELECTRICAL MACHINES' PARAMETERS Tehal Uvesty o Cluj-Napoa, 6 th o May CONCLUSIONS The pape pesets the theoetal detemato usg a aalytal method o the a gap lu desty espetvely o magetzg dutae o the syhoous elutae moto wth aally lamated oto. Epemetal esults o a 0.55kW tested moto valdate the poposed method. The ug tme o the used pogam s sgatly shote ompaso to the te elemet method. Theeoe oe a aalyze a lage omato o the oto data wdth ad ume o the sulato sheet ad o the lamato ode to ota the eued moto peomaes. 8. APPENDIX d et - oute stato damete; - supply euey; k - wdg ato; l - legth o the stak; m - ume o phases; - ume o oto lamatos; - ume o pots osdeed o the omputato o B d staght to the lampg plates; N - ume o tus pe phase; - oto adus; - geometal a gap legth; - wdth o the lampg plate; - euvalet a gap legth oespodg to the eomaget aea ;, - wdth o sulato sheet plaed etwee the lamatos ad ; µ 0 - vauum pemealty; θ - ampltude o m.m..; -pole pth 9. REFERENCES [] Boldea, S. A. Nasa, "Emegg elet mahes wth aally lamated asotop otos: a evew", EMPS, vol. 9,. 6, 99, pp [] D. A. Stato, T. J. E. Mlle, S. E. Wood, "Mamsg the Saley Rato o the Syhoous Relutae Moto", IEE Poeedgs-B, Vol. 40, No. 4, July 993, pp [3] Boldea, Z. X. Fu, S. A. Nasa, "Peomae Evaluato o Aally-Lamated Asotop ALA Roto Relutae Motos", IEEE Tasato o Idusty Applatos, Vol. 30, No. 4, July/August 994, pp [4] Fatta, A. Vagatt, "Aally lamated elutae moto: a aalytal appoah to the maget ehavo", Poeedgs o the ICEM, ICEM-988, Asaldo, Psa. [5] Boldea, Relutae syhoous mahes ad dves, Claedo Pess, Ood, 996. [6] V. Haovova, M. Lko, J. Mhok, P. Raajdus, L. Jaousek, Peomaes o elutae syhoous moto wth aally lamated oto, Poeedg o EPE-PEMC 000, Kose, pp [7] I. Toa, A aalytal model o the syhoous elutae mahe wth aally lamated oto Ph. D. thess, Uvestatea "Polteha" Tmsoaa, 999. [8] Boldea, Elet mahe paametes - detato, estmato ad valdato, Ed. Aademe Romae, Buuest, 99 [9] P. Vas, Paamete estmato, odto motog ad dagoss o eletal mahes, Claedo Pess, Ood,