Switched Reluctance Motors with Concentrated Stator Windings and Salient Poles of Different Shape on Rotor

Transcription

1 Switched eluctance Motor with Concentrated Stator Windin and Salient ole of Different Shape on otor Nicoleta MEDEA, Ioan Adrian VIOEL, Member IEEE SC EneroBit SL, Univeritatea Tehnica Cluj-Napoca Abtract: Two tructure of witched reluctance motor (SM) with concentrated tator windin and with alient pole on rotor of different hape are analyzed. An analytical model i propoed for both tructure and a izin-dein alorithm developed. Two ample motor are deined and their performance calculated analytically and via two dimenion finite element method (D-FEM) are compared. Index Term: witched reluctance motor, alient pole, izin-deinin I. INTODUCTION The witched reluctance motor (SM) wa one of the firt electric motor to be patented, built and employed in a drive ytem by Davidon in The actual SM with true electronically commuted phae upply ynchronized with rotor poition ha been decribed by it eential feature in the 70 lat century. The variou advantae of SM mae it an attractive alternative to DC and AC motor in ome pecific adjutable peed drive [1,, 3]. The conventional SM ha a baic tructure that conit of alient pole on tator and on rotor with the manetic circuit completed by a core bac on both part. The SM torque i produced by the tendency of it rotor to reach a poition where the inductance and the flux produced by the enerized tator windin are maximized. The SM performance depend, lie in the cae of variable reluctance ynchronou motor, on the difference between the phae flux linae in alined and unalined rotor poition. Therefore, different olution to enlare thi difference were propoed, one of them bein a rotor with ement lie for variable reluctance ynchronou motor, [3, 4], another, preented here, with different rotor pole hape. Different variant of tator windin are uitable for a SM with emental or conventional rotor with alient pole. Some apect concernin the SM with emental rotor performance function of the tator windin variant were analyzed [4, 5, 6]. Some of the conventional SM analytical model, baed on air-ap topoloy, are preented in [, 3, 7, 8] and the izindein procedure have been developed too [3, 6, 7]. The analytical model of a SM, independent of it rotor contruction with alient pole or with ement, can be developed baed on finite element method (FEM) analyi reult [9, 10, 11]. In the paper an analytical model, baed on the air-ap variable equivalent permeance concept, i preented in Section II. Such a model, which ue the air-ap eometrical data to define the equivalent permeance coefficient and the FEM reult to calculate a aturation function that varie with the phae current and rotor poition, ha a lare enerality and can be applied to different rotor topoloie. Some practical conideration on the developed izindein procedure baed on the analytical model preented are made in Section III and two ample SM are deined. The ample SM performance are calculated via D-FEM analyi, the comparative reult bein preented and dicued in Section IV. The final concluion are iven in Section V. II. ANALYTICAL MATHEMATICAL MODEL The SM analytical model developed here i baed on the air-ap variable equivalent permeance concept [3, 10, 11], it coefficient, in a implified form, bein calculated function of the rotor tructure in the air-ap. The aturation factor, introduced in the equivalent airap radial lenth, i calculated by uin the reult obtained via D-FEM analyi. Since the tator manetic field axi coincide with the tator phae axi, the air-ap variable equivalent permeance i [3, 10]: 1 1 in *, Q (1) The equivalent air-ap, *, and the variable equivalent air-ap permeance, are: 4 C in () * K C (3) 118

2 (1 f ) (4) (1 f ) f u 1 u u b / (5) 4 1 u t u ln 1 u (6) The Carter factor K C coniderin lot only on rotor i: K C (7) In the above equation, and b p are the rotor pole pitch and pole width, i the actual lenth of the motor air-ap, i the actual rotor anular diplacement and Q i the number of rotor pole. A implified form of the variable aturation function, which depend on the phae current and rotor poition, can be iven by a coinuoidal function a: i A co B, 0 (8) The coefficient A and B are function of phae current and hould be calculated by uin the alined and unalined flux linae veru current characteritic obtained via D-FEM analyi. For dein purpoe, in a firt izin-dein tae, the aturation function can be reduced to a aturation contant, etimated in alined poition, coniderin the core material manetization B=f(H) characteritic. Accordinly, the aturation factor i: 0 Bun 0 (9) B r0 at 1 lc0 1 (10) l where B un, B at are the flux denity unaturated and aturated value, l c0, l are the mean lenth of manetic path in the iron-core and the air-ap repectively, and r0 i the initial relative permeability of the core material. While B at i the correpondin value from B=f(H) characteritic for the iven H, the B un value i obtained from the equation which characterize a traiht line, B 0 r0 H (11) at the ame iven field intenity H value. Since the air-ap flux denity i: i F B 0, (1) The air-ap flux-denity maximum value, obtained in an alined poition, come a: B 1, i F max ( i) B 0 1 * (13) where F i the phae mmf. The air-ap flux denity i then: 1 in B (, i) B max ( i) (14) 1 The inductance for one phae depend on the phae current and on the rotor poition: L 1 in, d S (15) 1 i M i L The phae manetizin inductance in alined poition, the d-axi value, i: M d i B max i N A i p (16) N i the phae turn number, i i the phae current, A p i the tator pole area, and L S i the phae leaae inductance. Calculatin the flux linae derivative, one obtain: d, i di L, i d L, i i dt dt dt d (17) dt Thi lead to: d(, i) 1 in M d i L dt ( ) 1 co M d ( i) i 1 S di dt (18) The electromanetic torque developed by the motor, i: Where: T ' m W T T N B Ap 1 i co max Q (19) (0) The above preented analytical model i imple and ueful in the izin-dein procedure developed for both type of the analyzed SM. Throuh the analytic model preented above the induced emf, phae inductance on d- and q-axi and the electromanetic torque are calculated baed on the SM main dimenion, rated current and phae number of turn. The pea air-ap flux denity value B max i a dein pecification, a are the core material characteritic. 119

3 III. SIZING-DESIGNING OCEDUE Nowaday, the dein procedure for any electric machine, SM included, hould conit of four compulory tae: i) Sizin-deinin tae to obtain eneral dimenion initial value ii) FEM analyi of the electromanetic tructure iii) Heatin-coolin calculation iv) Entire drive ytem imulation on computer reviouly to tart the SM deinin proce one hould anwer to an important quetion concernin the phae number. The minimum phae number of a ymmetrical SM i three and there i no upper limit. By tain a larer number of phae the torque ripple can be reduced. Since the exterior diameter i limited in mot cae, the deiner mut mae an adequate compromie and adopt the minimum of three phae, but increae the number of tator pole to obtain a horter flux path, and to aure the adequate lot area. For example, in thi paper, a three phae conventional ample SM wa conidered with 1 pole on tator and 8 on the rotor. A maller number of rotor pole mean a reduced frequency at the ame peed and conequently a reduced amount of iron-core loe. A concentrated tator windin wa adopted, each pole with it coil, four pole in quadrature for one phae. Such a tructure aure hort end windin and a lower leaae flux. Aaint the conventional SM rotor topoloy, or a emental rotor dicued in [4, 5, 6] here a pecific hape of the rotor pole i propoed in order to tronly reduce the flux linae in unalined poition without a too important reduction of the alined poition phae flux linae. The SM izin-deinin procedure tart by calculatin the averae air-ap diameter, which i a function of [, 3, 7]: i) Dein pecification a rated output power, rated rotor peed and rated efficiency ii) Initially conidered value for the tator electrical loadin A and pea air-ap flux denity B max. iii) Adopted SM topoloy which mean mainly the tator and rotor number of pole, rotor contruction and tator phae windin iv) The value of the apect ratio coefficient which repreent the ratio between the tac lenth and the air-ap averae diameter v) The initially taen value for ome izin contant and Carter factor The value of the tator electrical loadin, of the pea air-ap phae denity and of the izin contant are taen coniderin the exitin data, the motor topoloy and power and the iron core material. The apect ratio coefficient value tronly depend on the drive requirement and hould be taen a to aure, beide the deired SM eometry, the bet ratio of the output torque to core loe. Once the averae air-ap diameter calculated and choen the air-ap lenth, which depend on SM power, the main dimenion, a tac lenth, pole pitche and pole width can be calculated. Coniderin the impoed rated current and choen tator electrical loadin a firt value of the pole or phae, number of turn i calculated. Thi value hould be checed via the induced emf calculation too. Now the tator lot area reult and the tator tructure includin the exterior motor diameter, i completely defined. Initially the tator pole width can be equal to the tator lot openin and to the rotor pole width; thee dimenion would be ettled after the FEM analyi. The phae induced emf, the phae inductance and the electromanetic torque are calculated by uin the equation obtained via propoed model, preented in the previou ection. TABLE I. Sample SM main dimenion. ectanular pole Trapezoidal pole Mean air-ap diameter, mm Stac axial lenth, mm Air-ap flux denity pea value, T Air-ap lenth, mm Slot fill factor Stator tooth width, mm Stator lot width, mm otor tooth width, mm otor lot width, mm otor core bac depth, mm Stator core bac depth, mm The dimenion of the two ample SM obtained via the izin-deinin procedure, preented above and employin the actual analytical model, are iven in Table 1. Fi. 1. SM with rectanular rotor pole 10

4 The tructure of the ample motor are preented in Fi 1 and. In order to compute manetic field, D finite element method wa ued. The two confiuration preented in Fi. 1 and in Fi. were ued for computin the manetic flux line. The reult obtained from the imulation proram employed are preented in the followin. The firt confiuration analyzed uin FEM i the SM with rectanular pole. Manetic flux line were conidered for three poition of the rotor: alined poition, hown in Fi. 3, unalined poition, Fi. 4 and maximum torque poition, Fi. 5. Fi.. SM with trapezoidal rotor pole In Fi. 1 the tructure of the ample SM with rectanular conventional rotor pole i iven, the main domain for D-FEM calculation bein: C1 motor haft CO1 rotor tructure CO4 tator tructure C tator core 1 to 4 windin The ample SM tructure, with trapezoidal rotor pole, i hown in Fi.. The main domain for D- FEM calculation are: C1 motor haft C tator core C4 rotor core C3 rotor pole CO rotor tructure CO1 tator tructure Fi. 3 SM with rectanular pole alined poition IV. CALCULATED ESULTS The two SM confiuration, with the main dimenion iven in Table 1, performance were calculated baed on the uual izin equation, [3, 7] for intance, and the developed analytical model. The main reult obtained are preented in Table II. TABLE II. Analytical reult ectanular pole Trapezoidal pole eitance per phae () Windin loe (W) Core lo (W) Electromanetic torque (Nm) Delivered power (W) Efficiency Equivalent power factor Fi. 4 SM with rectanular pole unalined poition 11

5 Fi. 5 SM with rectanular pole maximum torque poition Next, the SM confiuration with trapezoidal rotor pole wa tudied via FEM analyi. Manetic flux line for the three poition, alined poition, Fi. 6, unalined poition, Fi. 7 and maximum torque poition, Fi. 8, are preented too. Fi. 7 SM with trapezoidal pole unalined poition Fi. 8 SM with trapezoidal pole maximum torque poition Fi. 6 SM with trapezoidal pole alined poition Torque for different rotor poition wa computed by uin D FEM. The reult are ummarized in Table III, where repreent the rotor anular diplacement. Torque [Nm] otor poition Fi. 9 Comparion for torque value SM with rectanular pole SM with trapezoidal pole TABLE III. Torque a a function of rotor poition Torque (ectanular Torque (Trapezoidal pole) [Nm] pole) [Nm]

6 In Fi. 9 a comparion between the torque value obtained from FEM analyi for the ample SM i preented. A one can ee the difference between the pea torque value calculated via D-FEM and repectively analytic baed on the developed model are mall for the both ample SM conidered. It prove the validity of the analytic model and how that it i accurate enouh. In the izin-dein proce the ample SM with trapezoidal rotor pole ha larer air-ap to avoid the rotor pole tip aturation. For the ame reaon the airap flux denity pea value wa taen only 1.5T, even if the iron core material would allow larer value. V. CONCLUSIONS A pecial trapezoidal topoloy of rotor pole for SM i propoed in order to dratically reduce the unalined flux linae. A comparion between two imilar ample SM with rectanular, repectively with trapezoidal rotor pole i made evincin the fact that the variant with trapezoidal rotor pole ha better performance even if it ha a 0% larer air-ap to avoid the aturation of the rotor pole tip. The two ample SM are deined baed on a izin dein procedure completed with an adequate analytic mathematic model which ha a lare enerality. The calculation were done alo by uin D-FEM analyi, and the reult tand by to utain the accuracy of the analytic model. A an overall concluion it hould be mentioned that thi pecific trapezoidal topoloy of the rotor pole offer the poibility to improve the SM performance. In a further wor the influence of the trapezoidal pole tip width will be preented and a uboptimal tructure will be propoed. Acnowledment The wor wa upported in part by SC EneroBit SL. eference [1] T.J.E. Miller, Switched reluctance motor and their control. Clarendon re, Oxford, 1993 []. Krihnan, Switched reluctance motor drive. CC re, 001 [3] G. Hennenberer, I. A. Viorel, Variable reluctance electrical machine. Shaer Verla, Aachen, Germany, 001 [4] B. C. Mecrow, J.W. Finch, E. A. El-Kharahi and A. G. Jac, Switched reluctance motor with emental rotor. IEE roc. Electr. ower Appl., vol. 149, no. 4, pp , 00 [5] B. C. Mecrow, E. A. El-Kharahi, J.W. Finch and A. G. Jac, Semental rotor witched reluctance motor with inle tooth windin. IEE roc. Electr. ower Appl., vol. 150, no. 5, pp , 003 [6] B. C. Mecrow, J.W. Finch, E. A. El-Kharahi and A. G. Jac, The dein of witched reluctance motor with emental rotor. In roc. Int. Conf. on Electrical Machine, Brue, Belium, Auut 00 [7] V. A. adun, Dein conideration for the witched reluctance motor. IEEE Tran on Indutry Application, vol. 31, no. 5, pp , 1995 [8] V.A. adun, Analytically computin the flux lined by witched reluctance motor phae when the tator and rotor pole overlap. IEEE Tran on Manetic, vol. 36, pp , 000 [9] H.-. Chi,.-L. Lin, J.-F. Chen, Simplified fluxlinae model for witched reluctance motor. IEE roc. Electr. ower Appl., vol. 15, no. 3, pp , 005 [10] J. H. Chan, D. H. Kan, I. A. Viorel, L. Strete, Tranvere flux reluctance linear motor analytical model baed on finite element method analyi reult. IEEE Tran on Manetic, vol. 43, no. 4, pp , 007 [11] C. J. Hwan, D. H. Kan, I. A. Viorel, I. Tomecu, L. Strete, Saturated double alient reluctance motor analytical model. In roc of Int. Conf. on Electrical Machine, Chanaia, Greece, September