DESIGN AND MODELING OF AN AXIAL FLUX PERMANENT MAGNET GENERATOR WITH DOUBLE LAYER TOOTH-CONCENTRATED FRACTIONAL WINDINGS Dan Paunescu, Danela Paunescu, Dan-Crstan Popa and Vasle Iancu Techncal Unversty of Cluj-Napoca 400114, Cluj-Napoca, Romana E-mal: dan.paunescu@mae.utcluj.ro KEYWORDS Axal Flux Permanent Magnet Generator, Current Lnkage, Space Harmoncs, Tooth-Concentrated Wndngs. ABSTRACT Axal Flux Permanent Magnet s beneft from manufacturng advantages and reducton n end wndng length through the use of tooth-concentrated fractonal wndngs but dsplay ncreased space harmonc content, leadng to hgher eddy current losses n the rotor ron and permanent s. The choce of a double tooth-concentrated fractonal wndng for the modelng and desgn of a 24 Slots/20 poles Axal Flux Permanent Magnet Generator s justfed by a comparson between the sngle and double wndng. INTRODUCTION Axal Flux Permanent Magnet Generators (AFPMG) have become an nterestng choce for use as low speed generators because of ther compact desgn, hgh power densty, and possblty to add a hgh number of poles, wthout the need of a mechancal gearbox. By usng tooth-concentrated wndngs the manufacturng of the AFPMG can be smplfed and copper losses can be reduced, due to the short end wndngs (Jussla 2009). The dsadvantage of the tooth-concentrated fractonal wndngs s represented by a hgh current lnkage space harmonc content, because of ther low number of slots per pole and phase (Salmnen 2004; Cstelecan 2010), whch nduce addtonal eddy current losses n the rotor ron and n the permanent s (PM). The theory of the tooth-concentrated wndngs and methods to reduce the eddy current losses n the rotor ron have been studed over the last years. It has been determned that to reduce the coggng torque, to obtan a hgher value of the fundamental wndng factor and to generate a snusodal back-emf, the rght combnaton of number of stator slots Q s and number of rotor poles 2p has to be chosen (Banch et al. 2006; Banch et al. 2007). Another approach les n the use of nonconductve materals, such as fberglass, for the rotor ron and n the segmentaton of the permanent s (Jussla 2009) The nfluence of the number of wndng s n toothconcentrated wndng machnes has also been taken nto consderaton n (El-Rafae and Jahns 2006), and t has been shown that by usng a hgher number of wndng s and usng unequal number of turns for each col, the current lnkage harmoncs can be completely reduced, wth a small nfluence on the wndng factor (Cstelecan 2010). ANALYTICAL DESIGN OF THE AFPMG The topology of the studed AFPMG s a two stator one nternal rotor wth 24 stator slots and 20 rotor poles. The PMs are glued nsde the rotor and defne the rotor thckness. The two stators are connected n seres. Fgure 1: Topology of the Studed AFPMG Fgure 2: Rotor of the Studed AFPMG Proceedngs 25th European Conference on Modellng and Smulaton ECMS Tadeusz Burczynsk, Joanna Kolodzej Aleksander Byrsk, Marco Carvalho (Edtors) ISBN: 978-0-9564944-2-9 / ISBN: 978-0-9564944-3-6 (CD)
The most mportant parameters used for the desgn of the AFPMG are the outer dameter D e and the nner dameter D. The dmensons of external and nternal dameters are very mportant because the length of the stator stack s obtaned from the dfference of the two : l s De D = (1) 2 Another factor that contrbutes to the performance of the machne as well as to ts manufacturablty s the nner-to-outer dameter rato, whch can be defned as: D k d = (2) De In (Parvanen 2005) t s advsed to obtan k d = 1/ 3 to beneft from the hghest possble torque, however ths can lead to manufacturng dffcultes when usng lap wndngs, especally n small machnes. The problem les n the lmted space between the rotor shaft and stator, whch makes t very dffcult to arrange the end wndngs. By usng tooth-concentrated wndngs, the length of the end wndngs can be reduced and more space can be freed up between the stator and the rotor shaft. Table 1 contans the man parameters of the studed AFPMG that have been obtaned from the analytcal desgn, whch have been further used for the modelng. Table 1: Man Parameters of the Studed AFPMG Number of stator slots Q s 24 Number of pole pars P 10 Number of slots per pole 0.4 and phase Aparent power S n 50 [VA] Rated speed n s 300 [rpm] Lne-to-lne voltage n star 230 [V] connecton U Rated current I n 0.157 [A] Nomnal frequency f 50 [Hz] Argap flux densty B g 1 [T] Wndng turns n seres per 1568 stator wndng N 1 Lenght of argap g 0.001 [m] Stator outer dameter D e 0.11 [m] Stator nner dameter D 0.07 [m] HARMONICS OF TOOTH-CONCENTRATED FRACTIONAL WINDINGS In comparson to ntegral slot wndng machnes, whch operate at the fundamental component of the flux densty, the machnes havng tooth-concentrated fractonal wndngs operate wth some of the flux densty harmoncs ( Jussla 2009). The wndng arrangement of the 24 slots 20 poles AFPMG s the same as n the case of a 12 slots-10 poles base machne equpped wth tooth-concentrated fractonal wndngs, but repeated two tmes. Both of the machnes have the same number of slots per pole and phase q = 0. 4 and operate wth the same harmonc. Thus the problem of determnng the man harmonc of the AFPMG can be reduced to the study of the wndng arrangement for just one half of the generator. The harmoncs of a three phase (m=3) 12 slot-10 poles machne can be determned by use of the followng equaton: The resultng harmoncs are: ν = 1± 2km; k N (3) ν = [ 1, 5, + 7, 11, + 13, 17, + 19...] (4) for the ordnals of the current lnkage. The machne operates at the ffth harmonc ν = 5 whch also has the hghest wndng factor. The fundamental ν = + 1 has a hgh ampltude compared to the fundamental and rotates fve tmes the speed of the ffth harmonc and n the opposte drecton, resultng n hgh losses through eddy currents n the rotor ron. Advantages of double wndngs over sngle wndngs To determne the rght number of wndng s a comparson between the harmonc spectra of both wndng arrangements, presented n Fgure 3, has been carred out. U -U V -V W -W U -U V -V W -W Fgure 3: Wndng Arrangement for the 12 Slot-10 Poles wth Sngle Layer and Double-Layer Tooth-Concentrated Fractonal Wndng
Startng from the defnton of the current lnkage (5) the wndng functon for each phase has been defned. N s Θ = N s (5) number of turns n a slot current passng through the conductor The wndng functons presented n Fgures 4, 5, 6 have been drawn for the sngle and double toothconcentrated fractonal wndng. The number of turns for each slot has been kept N s = 1. As t can be seen, by doublng the number of s, the number of turns n a slot for each phase s halved. To obtan the varaton of the current lnkage, the wndng functons are further multpled wth the values of the phase currents for one chosen moment. In ths case the values taken nto consderaton have been : 1; = 1/ 2; = 1/ 2 (6) u = v w After the multplcaton the resultant of the current lnkage s obtaned by summng up the current lnkages for each phase. Fgure 4: Sngle and Double Layer Wndng Functon of Phase U for 12 Slots and 10 Poles Fgure 7: Resultant Current Lnkage for Sngle and Double Layer Wndng The harmoncs of the resultant current lnkages for one and two s are obtaned through the use of the FFT algorthm mplemented n Matlab and are presented n Fgure 8. Fgure 5: Sngle and Double Layer Wndng Functon of Phase V for 12 Slots and 10 Poles Fgure 8: Current Lnkage Harmonc Content for Sngle and Double Layer Wndng Fgure 6: Sngle and Double Layer Wndng Functon of Phase W for 12 Slots and 10 Poles
To verfy the results obtaned through the analytcal method, two radal flux machne models of the AFPMG have been mplemented and smulated n Cedrat Flux 2D. To determne the current lnkage generated by the three phased wndngs, the PM materal has been replaced wth ar. The motor has been used at the synchronous speed namely 300 rpm. 1 st harmonc. Another factor that nfluences the harmonc content are the slot openngs. The 2D FEA method takes nto consderaton the slot openngs, whereas the analytcal method does not. Ths can consderably hnder the correct determnaton of the harmonc content of the current lnkage. As can be seen from the two harmonc spectra the 2D FEA method determnes correctly the harmoncs of the tooth concentrated wndng compared to the analytcal method whch dentfes also other harmoncs. Table 2: Comparson between the man harmoncs for the analytcal and 2D FEA method Fgure 9: 2D Fnte Element Analyss (FEA) Current Lnkage obtaned at the Argap Crcumference for Sngle Layer and Double Layer Wndng The varaton of the current lnkage for the smulated machnes has been drawn n Fgure 9. When compared to the analytcal method, the smulatons takes also the slot openngs nto account, whch have an mpact on graphcal representaton of the current lnkage. Harmonc % of the fundamental MATLAB Sngle wndng Double wndng % of the fundamental 2D FEA Sngle wndng Double wndng 1 124 36.2 118 31.5 5 100 100 100 100 7 55.8 50.1 79.1 80.1 11 11.7 5.96 27.3 8.2 13 11.4 9.9 5.1 2.2 17 30 30.5 15 14.1 19 14.8 7.2 14.7 15.4 MODELING OF THE AFPMG USING TOOTH- CONCENTRATED FRACTIONAL WINDINGS Axal Flux s come n a varety of topologes sharng one common feature namely the flux s flowng n the axal drecton nstead of the radal one. The drecton n whch the flux s flowng has an mpact on the FEA of the AFPMG, because the model of the machne should be made n 3D. However the research has shown that the FEA of Axal Flux s can be smplfed to a 2D model, namely the machne s modeled as a lnar (Geras 2004; Parvanen 2005) or as a radal flux machne (Jussla 2009). The plane at whch the analyss s carred out s ether at the arthmetc (Geras 2004; Jussla 2009) or at the geometrc mean (Valtonen 2007). Fgure 10: Current Lnkage Harmonc Content for the 2D FEA for Sngle Layer and Double Layer Wndng The harmoncs of the three phase current lnkage have been determned by means of the FFT algorthm mplemented n Matlab and are dsplayed n Fgure 10. When comparng the results from the analytcal and 2D FEA Method n table 2, we can observe that there s a bg dfference between them for both sngle and double wndngs. The relatve ampltude of the other harmoncs to the workng harmonc s dfferent for each of those methods, the most accurate results beng for the 3D Axal Flux Model 2D Lnar Model AFPMG 2D Radal Flux Model Quas-3D Modellng Fgure 11: AFPMG Modelng Optons
In (Jussla 2009 ) t s mentonend that f the arthmetc or geometrc mean s used, the wdth-topole-ptch rato should be constant at dfferent rad and the stator should not be skewed. The 2D FEA of an Axal Flux s accurate enough for power, voltage and coggng torque calculaton, but for determnng the ron losses, 3D FEA should be employed. Another method to determne the ron losses wthout usng the 3D FEA has been presented n (Parvanen 2005) and t s called the quas-3d method. The prncple of ths method les n cuttng the stator stack n many planes of nterest and determne the parameters for each plane. The average dameter D avg of a specfc computaton plane startng from the outer dameter s expressed as follows: D avg ls, = De j (7) N Where N represents the number of computaton planes and j = 2 1. All the other parameters are determned for each ndvdual computaton plane, summed up and dvded by the number of computaton planes N, to get an accurate pcture regardng the ron losses, nduced voltage, flux densty or other parameters of nterest. Modelng of the Studed AFPMG The topology of the AFPMG presented n ths artcle has been modeled as a radal flux Permanent Magnet Synchronous (PMSM) by means of 2D FEA at the arthmetc and geometrc mean. For the modelng of the AFPMG only the use the double tooth-concentrated fractonal wndng has been consdered. The arthmetc mean, whch s usually used as a desgn plane (Geras 2004; Jussla 2009), can be calculated as follows: R arth Re + R = (8) 2 The defnton of the geometrc mean s gven by (9): R geom = R R (9) Where Re s the outer and R s the nner of the Axal Flux. The steps by whch the geometry of an AFPMG has been converted nto a 2D model of a radal flux machne, at the arthmetc or geometrc mean can be observed n the Fgure 12. e The obtaned dmensons for the two radal flux machnes are shown n Table 3. As can be seen from the table the most mportant changes le n the dmensons of the teeth and n the nner and outer stator and rad. The other dmensons lke the length of the stator stack, the heght of the tooth, the openng of the slot and the wdth and heght are kept the same. Determne the arthmetc or geometrc mean of the AFPMG Determne the nner stator of the radal flux machne from the crcumference Determne the outer stator of the radal flux machne Fgure 12: Steps to model the Axal Flux as a Radal Flux Modeled Dmenson Inner stator Outer stator Inner Outer Length of the stator stack Tooth wdth Tooth heght Slot openng Magnet wdth Magnet heght Table 4: Dmensons of the AFPMG AFPMG Radal Flux (Arthmetc Mean Radus) Radal Flux (Geometrc Mean Radus) 35 [mm] 43.92 [mm] 42 [mm] 55 [mm] 66.42 [mm] 64.5 [mm] 35 [mm] 40.42 [mm] 38.5 [mm] 70 [mm] 42.92 [mm] 41 [mm] 20 [mm] 20 [mm] 20 [mm] 4 9 6.5 [mm] 6 [mm] [mm] 8 [mm] 8 [mm] 8 [mm] 5 [mm] 5 [mm] 5 [mm] 10 [mm] 10 [mm] 10 [mm] 2.5 [mm] Determne the tooth and slot wdth for the respectve Determne the nner stator crcumference of the radal flux machne by summng up the wdths of the teeth and those of the slots Buld the whole geometry of the radal flux machne by also usng the dmensons from the AFPMG desgn 2.5 [mm] 2.5 [mm]
The nduced phase voltages whch has been obtaned for the arthmetc and geometrc mean rad can be observed n Fgure 13. Fgure 13: Induced Voltages for the Arthmetc and Geometrc Mean Radus The values of the nduced phase voltages are half of the values obtaned through the analytcal desgn because just one stator and only half of the rotor have been smulated. Because the stators are connected n seres the actual value of the nduced voltage s double of that obtaned n the smulatons. The ampltude of the nduced phase voltage for the model that uses the geometrc mean s smaller than n the case of the model that uses the arthmetc mean. By use of the geometrc mean to model the AFPMG as a radal flux machne the wdth of the stator tooth as well as of the nner and outer stator rad are reduced, as can be seen from Table 4. Table 5: Reducton n Induced Voltages n Functon of the Reducton n Dmensons Modeled Dmenson Inner stator Outer stator Inner Outer Tooth wdth Induced voltage Radal Flux (Arthmetc Mean ) Radal Flux (geometrc mean ) Reducton 43.92 [mm] 42 [mm] -4.4% 66.42 [mm] 64.5 [mm] -2.9% 40.42 [mm] 38.5 [mm] -4.8% 42.92 [mm] 41 [mm] -4.5% 6.5 [mm] 6 [mm] -7.7% 67.15 [V] 63.4 [V] -5.6% Fgure 14: Argap Flux Densty for the Arthmetc and Geometrc Mean Rad taken for 12 slots/10 poles The two smulated radal flux machnes dsplay the same ampltude and form of the argap flux densty but the two curves can not be supermposed. Ths comes from the fact that the crcumference of the argap at whch the flux densty was determned s shorter n the case of the machne modeled at the geometrc. CONCLUSIONS Axal Flux Permanent Magnet Generators usng toothconcentrated beneft from constructon advantages but dsplay ncreased current lnkage space harmonc content whch can be determned by means of analytcal or 2D FEA methods. A comparson between the use of sngle and double tooth-concentrated fractonal wndngs has been made wth the concluson that the use of double wndng for the AFPMG leads to the reducton of the current lnkage harmonc content. Another comparson between two modelng methods of the AFPMG wth the help 2D FEA has been presented and the results show only a small varaton n the nduced voltage and n the argap flux densty. Further research n mprovng the analytcal method to determne the current lnkage harmoncs and n valdatng the 2D FEA wth the results from 3D FEA s necessary. REFERENCES Banch N., Bolognan S., Da Pre M., Grezzan G. Desgn Consderaton for Fraconal Slot Wndng Confguratons of Synchronous s, IEEE Transactons on Industry Applcatons, Vol. 42 No.4 2006 p.997-1006 Banch N., Da Pre M., Albert L., Fornasero E. Theory and Desgn of Fractonal-Slot PM machnes, Tutoral Course Notes, CLEUP, Unversty of Padova, Sept. 2007 Cstelecan M.V., Ferrera F.J.T.E, Popescu M. 2010 Three Phase Tooth-Concentrated Multple-Layer Fractonal Wndngs wth Low Space Harmonc Content. In
Proceedngs of the 2010 Energy Converson Congress and Exposton (Atlanta, GA, Sept. 12-16), IEEE, Pscataway, NJ, 1399-1405, ISBN 978-1-4244-5286-6 El-Rafae, A.M., Jahns T.M. Impact of Wndng Layer Number and Magnet Type on Synchronous Surface PM s Desgned for Wde Constant Power Speed Range Operaton IEEE Transactons on Energy Converson, Vol. 23, No.1 p. 53-60 Geras J., Wang R-J., Kaamper M.J. 2004 Axal Flux Permanent Magnet Brushless s, Kluwer Academc Publshers, Dordrecht, ISBN 1-4020-2661-7 Jussla H. 2009 Concentrated Wndng Multphase Permanent Magnet Desgn and Electroc Propertes Case Axal Flux PhD. Thess, Acta Unverstats Lappeenrantaenss 374, Lappeenranta Unversty of Technology, ISBN 978-952-214-883-4 Kurronen P. 2003 Torque Vbraton Model of Axal-Flux Surface-Mounted Permanent Magnet Synchronous PhD. Thess, Acta Unverstats Lappeenrantaenss 154, Lappeenranta Unversty of Technology, ISBN 951-764-773-5 Parvanen, A. 2005 Desgn of Axal-Flux Permanent Magnet Low-Speed s and Performance Comparson between Radal-Flux and Axal-Flux s, PhD. Thess, Acta Unverstats Lappeenrantaenss 208, Lappeenranta Unversty of Technology ISBN 952-214- 030-9 Salmnen P. 2004 Fractonal Slot Permanent Magnet Synchronous Motors for Low Speed Applcatonns PhD. Thess, Acta Unverstats Lappeenrantaenss 198, Lappeenranta Unversty of Technology, ISBN 951-764- 983-5 Valtonen M. 2007. Performance Characterstcs of an Axal- Flux Sold-Rotor-Core Inducton Motor PhD. Thess, Acta Unverstats Lappeenrantaenss 285, Lappeenranta Unversty of Technology, ISBN 978-952-214-474-4 DAN-CRISTIAN POPA was born n Satu-Mare, Romana, on the 7th of August 1978. He graduated Mha Emnescu hghschool from Satu-Mare (1997) and then obtaned the dploma n electrcal engneerng at Techncal Unversty of Cluj-Napoca (2002). He defended hs PhD thess n 2008 n the doman of lnear transverse flux reluctance motor. Hs e-mal address s: : Dan.Crstan.Popa@mae.utcluj.ro VASILE IANCU was born n Petrest (Alba), Romana, on the 5th of March 1945. He graduated the Sebes hgh-school (1963) and then obtaned the dploma n electrcal engneerng at Techncal Unversty of Cluj-Napoca, (1968). In 1977 he obtaned the doctor s degree from Techncal Unversty of Tmsoara. Hs major feld of nterest are: electrcal machnes and drves, electrcal tracton. Dr. Vasle Iancu s the author and co-author of more than 110 publcatons (books and scentfc papers). He s PhD supervsor n domans lke varable reluctance and axal flux machnes. Between 1996 and 2004 he was the vce-rector of Techncal Unversty of Cluj- Napoca. Hs emal address s Vasle.Iancu@mae.utcluj.ro AUTHOR BIOGRAPHIES DAN PAUNESCU was born n Clujnapoca, Romana and went to the Techncal Unversty of Cluj-Napoca, where he studed electrcal engneerng and obtaned hs degree n 2008. He started to work on hs PhD. at the same unversty n 2008 on the topc of Axal Flux Permanent Magnet Generators for use n wnd turbnes. Hs e-mal address s : dan.paunescu@mae.utcluj.ro DANIELA PAUNESCU was born n Craova, Romana and went to the Techncal Unversty of Cluj-Napoca, where she studed manufacturng engneerng and obtaned her degree n 1980. She works now as an Assocate Professor at the Department of Manufacturng Engneerng of the Techncal Unversty of Cluj-Napoca. Her e-mal address s : danela.paunescu@tcm.utcluj.ro