Novel Three Phase Flux Reversal Machine with Full Pitch Winding

Transcription

1 Octber 22-26, 2007 / Exe, Daegu, Krea THD1-1 Nvel Three Phase Flux Reversal Machine with Full Pitch Winding D. S. Mre*, and B. G. Femandes** *Research Schlar, Electrical Engineering Department, Indian Institute f Technlgy Bmbay. **Department f Electrical Engineering, Indian Institute f Technlgy Bmbay, Pwai, Mumbai , INDIA. Phne: , Fax: dsmre@ee.iitb.ac.in bgf@ee.iitb.ac.in Abstract-This paper prpses a cncept f fictitius 'Electrical Gear' in analyzing the flux pattern f Flux Reversal Machine (FRM). Cncept f nvel full pitch winding is presented fr FRM. Finite Element Methd ( FEM ) analysis f cnventinal cncentrated statr ple winding FRM and prpsed full pitch winding FRM are carried ut t validate the cncept. Generatr perfrmance ffull pitch winding FRM is cmpared with cnventinal cncentrated statr ple winding FRM. Full pitch winding arrangement increases the inductance f the machine which results in pr vltage regulatin. Series capacitive cmpensatin is prvided t the machine fr better vltage regulatin. Output pwer f cmpensated full pitch winding FRM is apprximately twice as that f the cnventinal cncentrated statr ple winding FRM. Physical dimensins, electrical and magnetic ladings are kept same in bth the machines. Index Terms-Flux reversal machine, full pitch winding, dubly salient permanent magnet electrical machine, finite-element methd (FEM) analysis. Fig. 1. Laminated statr cre Statr cil Laminated rtr s.-----r cre Permanent Magnet Crss-sectin f cnventinal cncentrated statr ple winding FRM. I. INTRODUCTION SINGLE phase FRM was first intrduced in 1997 by R. P. Dedhar et al [1] fr an autmbile generatr t replace the standard claw ple alternatr. It has numerus advantages such as simple cnstructin, lw inertia, high pwer density and is suitable fr high speed applicatin due t pennanent magnets n the statr ple. This single phase cnfiguratin was fully explred as a generatr and nt as a mtr. Three phase FRM was intrduced by C. Wang et al [2] in The design f the machine was ptimized t (i) increase the peak t peak cil PM flux linkage variatin, (ii) reduce the cgging trque and PM weight, (iii) restrain the self and mutual inductance. The basic machine cnfiguratin has an 8 salient ple rtr and 6 ple statr with cncentrated windings. Permanent Magnets are munted n statr ple. Fig. 1 shws the machine cnfiguratin. FRM fr lw-speed serv drive applicatin was intrduced by In Bldea et al [3] in This lw speed machine has 28 rtr ples and 12 statr ples with tw permanent magnet pairs n each statr ple. This machine was designed fr 128 rpm at 60 Hz. High trque density with less than 3% trque pulsatin with vectr cntrl was achieved. In rder t reduce the cgging trque, rtr teeth pairing methd was prpsed [4]. Attempts were made t reduce the leakage flux by prviding flux barrier n the rtr ples at its edges [5]. Pwer density cmparisn f dubly salient permanent magnet electrical machines were made. FRM has higher pwer density in cmparisn with ther machines in the same class [6]. In this paper, cncept f fictitius 'Electrical Gear' and full pitch winding applicable t FRM is presented. 2-D FEM analysis [7] is carried ut n the cnventinal cncentrated statr ple winding FRM and prpsed full pitch winding FRM. Optimized machine dimensins are btained frm C. Wang et al [2]. The imprtant dimensins f FRM are given in Table I fr ready reference. Sectin II describes the flux pattern linking t the statr winding f the machine and frm there the cncept f fictitius 'Electrical Gear' and full pitch statr winding arrangement is discussed. Sectin III describes the 2-D FEM analysis results btained fr full pitch FRM and cncentrated statr ple winding FRM. The results are cmpared with the results f paper [2]. Sectin IV describes the FEM analysis n lad t find the vltage regulatin f full pitch winding FRM. Effects n machine parameters due t full pitch winding and methd used t imprve the vltage regulatin is als discussed. Sectin V cmpares the pwer density f full pitch winding FRM with PMSM and finally cnclusins are drawn /08/$ EEE 1007

2 2 Nrmal cmpnent f air gap flux density due t three phase currents. When magnets are de-energised E ::c 0.01 " 0 "iii c: Q) -0 x :::J i:i: ::!= L L LO---2-.J50 Distance alng the air gap in mm Fig. 2. II. Fig. 4.. Nrmal cmpnent f armature flux density alng the air gap at full lad with magnets de-energized Flux plt f machine at n lad FLUX PATTERN LINKING TO THE STATOR WINDING AND FULL PITCH STATOR WINDING Gemetry f three phase flux reversal machine (as per Table I ) is shwn in Fig. 2. The flux plt f the machine at n lad is shwn in the same Fig. FRM machine has 6 statr ples and 8 ple variable reluctance rtr. The nrmal cmpnent f flux density at the middle f statr ple alng the periphery f the machine is shwn in Fig. 3. The bservatin f this nrmal cmpnent f flux density plt reveals that the machine has tw ple flux pattern. In ther wrds machine has tw effective ples. Phase flux linkage f FRM is sinusidal and hence induced vltage is als sinusidal [2]. Cnsidering a linear lad the phase current is sinusidal. Nrmal cmpnent f armature reactin alng the air gap at ne instant f time is shwn in Fig. 4. This flux pattern als reveals that machine has tw ples. In general, machine has same number f statr ples Nrmal cmpnent f flux density alng the circle that passes thrugh the middle f statr ple r==::::!::==:=:::!====:::r::::::== - - Nrmal cmpnent f flux density th degree 0.6 and rtr ples. The frequency and speed relatinship fr FRM [3] is given by f = n nr (1) where, n == rtr speed in rpm. == Number f rtr teeth (ples). f == frequency in Hz. FRM machine has tw effective ples, and hence in ne cycle, ux pattern cmpletes ne revlutin. Thus when rtr speed IS n rpm, the flux pattern cmpletes n r x n revlutins per minute. Hence flux pattern rtates n r times the shaft speed. In cnventinal synchrnus machine, flux pattern speed and rtr speed is same. Pictrial representatin f FRM generatr and permanent magnet synchrnus generatr is shwn in Fig. 5. Bth machine representatin is fr same speed and utput frequency. Flux pattern in FRM rtating n r times rtr speed is represented as a fictitius step-up gear and is called as 'Electrical Gear'. Cnventinal synchrnus machine shuld have 2 x n r ples fr same utput frequency. FRM has 6 slts and tw ple flux pattern, hence electrical angle per slt is 60. Cnventinal cncentrated statr ple 'fl r TABLE I DIMENSIONS OF FRM Sr. N J =:::----:-:::----_.L.-_----J1...-._--J..? Distance alng the periphery f the machine at the middle f statr ple in mm Fig. 3. Nrmal cmpnent f flux density Descriptin Air gap in rm Magnet thickness in rm Rtr ple span angle Statr ple span angle Statr ple span in rm Rtr ple span in rm Statr ple height in mm Rtr ple height in rm Outer diameter f rtr in mm Outer diameter f statr in mm Number f turns /phase Stack length f machine in mm Symbl g Value h pm (3r {3s Tps Tpr h ps h pr Di D Nvh l sk 1

3 Octber 22-26, 2007 I EXCO, Daegu, Krea fictitius electrical gear Shaft speed statr nrpm n*n r 2 ple PM Rtr Istatr a) FRM machine Istatr Shaft speed nrpm PM Rtr Istatr b) PM synchrnus Machine f= (n* Or )/60 f= (n*or )/60 Phase flux Linkage ffull pitch winding FRM and cncentrated ple winding FRM 0.05r r r , ,.,.'.'.'.'!J.;;,' :..." : "" 0.01 " " 0" :.!,. C) """, J2 """... ',,>'\" '...'.. ': (I).,', ;'> m & '" ", ' ' Rtr psitin in mech deg. Fig. 7. Phase flux linkage f full pitch winding FRM and cncentrated statr ple winding FRM Fig. 5. Generatr representatin f FRM and PMSM winding has a cil span f 60. Fundamental pitch factr f the statr winding is 0. As electrical angle between the slts is 60, full pitch winding is pssible. The arrangement f full pitch winding is shwn in Fig. 6, which results in unity pitch factr. III. FEM ANALYSIS OF FULL PITCH WINDING FRM AT NO LOAD FRM machine design data is btained frm [2] and given in the Table I fr ready reference. Physical dimensins f the machine and number f turns are kept same in full pitch winding FRM and cnventinal cncentrated statr ple winding FRM. Only the winding arrangement is changed. FEM analysis is carried ut t find the phase flux linkage variatin f bth the machines with rtr psitin. Phase flux linkage variatin f bth the machines withut skewed rtr is shwn in Fig. 7. This variatin is shwn fr ne rtr ple pitch (Le. mechanical 45 ). Fig. 7 clearly shws that full pitch winding FRM statr flux linkage is apprximately twice A Phase slt II B Phase slt [[ill C Phase slt as that f the flux linkage f cnventinal cncentrated statr ple winding FRM. Simulatins are carried ut at different speeds n bth machines t determine the induced vltage n n-lad. Induced vltage at different speed fr bth machines withut skewed rtr is shwn in Fig. 8. The simulated result shws that n lad induced vltage in full pitch winding FRM is apprximately twice as that f the vltage induced in the cnventinal cncentrated statr ple winding FRM. N-lad phase vltage wavefrms f bth cnfiguratins at 8000 rpm are shwn in Fig. 9. Statr phase inductance is calculated using FEM as per prcedure given in [2]. First magnet flux linking the statr winding is btained and then psitive mmft the winding, ttal flux linkage t the winding is btained. The self inductance is btained by subtracting the PM flux linkage frm ttal flux linkage. The same prcedure is used t determine the self inductance when negative statr mmf is applied. The Induced n lad vltaes f FRM fr unskewed rtr 200." --Cncentrated statr ple winding FRM J!} --Full pitch winding FRM g 180. c " Ci).s 140. J: C C) m > 80 J: C. " E '---_...I...-_...I...-_---L..._----I.._----I..&.-_...I..-._--'-----' Speed f machine in rpm Fig. 6. Full pitch winding arrangement Fig. 8. N lad phase vltages f full pitch winding FRM and cnventinal cncentrated statr ple winding FRM 1009

4 Octber 22-26, 2007 I Exe, Daegu, Krea 4 tn '0 > Q) 200, ,..,,,,.,,, " O'l ct'l = > O' ct'l.j::. a Q c: ::l 'U.E Wavefrms f phase vltage in full pitch winding FRM and cncentrated statr ple winding FRM at 8000 rpm 300 r ,----;:::::::!::======:c:====::::::!======:;-, Cncentrated statr ple winding frm --Full pitch winding FRM i -3 I c: 'B c ct'l g -5. 'U (ij -6 ::l 'S X 10-4 Mutual inductance M ab and Mac in full pitch winding FRM r--'--'--""'--'---;::c==::::c::==::!::==::l::==:::i _ Mutual inductance M ac --Mutual Inductance M ab. II. J' f t' I...,. -400' L L ' L J Time in sec :..., ''""!'-'''.: Rtr psitin in mechanical deg Fig. 9. N lad phase vltage wavefrm at 8000 rpm Fig. 11. Variatin f full pitch winding FRM mutual inductance with rtr psitin. average f these tw self inductances represents the actual value f self inductance. The statr phase inductance variatin fr bth machines with rtr psitin is shwn in Fig. 10. Self inductance variatin f full pitch winding FRM is 2.42 mh t 22 mh, whereas this variatin fr cnventinal cncentrated statr ple winding FRM is 0.78 mh t 1.1 mh Full pitch winding arrangement increases the self inductance f winding by 2 t 3 times depending upn the saturatin in the machine. If saturatin is neglected, then self inductance increases by 3 times, whereas variatin f self inductance with rtr psitin is very small in bth cases. Under nrmal perating cnditins sme parts f magnetic circuit gets saturated in the full pitch winding FRM. Mutual inductance variatin is 04 mh t 0.91 mh Under unsaturated cnditin, this variatin is frm mh t 0.93 mh Mutual inductance f full pitch winding FRM is apprximately 0.33 times that f its self inductance. Mutual inductance variatin with rtr psitin is shwn in Fig. 11. IV. FEM ANALYSIS OF FULL PITCH WINDING FRM AT STEADY STATE ON LOAD FEM simulatin is carried at different lad cnditin t determine the vltage regulatin f machine at 2000 rpm fr bth types f winding cnfiguratin. Terminal vltage variatin with lad current is shwn in Fig. 12. It is seen that regulatin f full pitch winding FRM is pr as cmpared t cncentrated statr ple winding FRM. Regulatin f full pitch FRM can be imprved by using series capacitive cmpensatin [9]. The arrangement fr capacitive cmpensatin is shwn in the Fig. 14. The value f capacitr is given by [8]. where, w== Induced EMF frequency in rad/sec. L s == synchrnus inductance f the machine in Henry. (2) Self inductance variatin with rtr psitin Terminal vltage variatin with resistive lad 50...;;;;;;;;;;;..,..----:=:::::;::==::::c::====:::::!::====::::!::====::;-, !3 35 '0 > 30. Q) O'l 2 > T ;--_ 20. E Rtr angle in mech.deg O' L L L.---' I I Out put lad current in Amps Fig. 10. Variatin f Self inductance f full pitch winding FRM and cncentrated statr ple winding FRM with rtr psitin Fig. 12. Terminal vltage variatin with resistive lad 1010

5 Octber 22-26, 2007 I Exe, Daegu, Krea 5 Lad characteristics ffull pitch winding FRMI 60 r :---:::::::!:==::::::!====!:::==:::!=:==::!:::;l _ Un-cmpensated full pitch winding FRM...Cmpensated full pitch winding FRM C) S g 30.,. ị 2 E 0.15 :a 0.1' 0.05" O i ' ii: Distance alng airgap in mm L--..L l4 L L I :':12=------:1:':"4----;16 Lad current in Amps E :c 'm c: -0. ::::J ii: -1 OL'---5.L L :-150: :----:-;250 Distance alng air gap in mm Fig. 13. FRM Tenninal vltage variatin with resistive lad fr full pitch winding Fig. 15. Flux distributin in FRM and PMSM fr same utput vltage and frequency at cmmn shaft speed. C = capacitance fr series cmpensatin in Farad. Synchrnus inductance Ls is btained frm regulatin results f uncmpensated full pitch FRM shwn in Fig. 13. The value f L s is 3.76 mh Series cmpensatin capacitr f 94.7J-LF is chsen fr a speed f 2000 rpm. FEM simulatin f cmpensated full pitch FRM is carried ut at different lads t access the regulatin f the machine. Terminal vltage variatin at different lads is btained. Terminal vltage variatin fr cmpensated and uncmpensated full pitch FRM is shwn in Fig. 13. Cmpensated FRM gives better regulatin which is less than 15%. Obseving the external (lad) characteristics frm Fig. 12 and Fig. 13, it can be cncluded that cmpensated full pitch winding FRM has apprximately duble utput pwer as cmpared t cnventinal cncentrated statr ple winding FRM fr same electrical and magnetic lading. V. POWER DENSITY OF FULL PITCH FRM The flux linkage in full pitch winding FRM is shwn in the Fig. 7. Frm this Fig. it can be bserved that maximum phase flux linkage is Wh. The relatinship between maximum flux linkage 'l/ji (max) and maximum flux density Bml(max) is given by [11]. Bml(max) x is x T X 2 X Nph (3) 'l/ji(max) = -...:...; r C se ;e--- FRM statr winding Fig. 14. Three phase star cnnected resistive lad Circuit diagram fr series cmpensatin where, is = stack length f the machine in meter. T = ple pitch distance in meter. Nph = number f turns per phase. T = m fr equivalent PMSM. (Euivalent PMSM has 16 ples.) T = m fr full pitch FRM.(Full pitch FRM has effective 2 ples.) Using the abve equatin Bml(max) in FPFRM is Wb/m 2, whereas Bml(max) in PMSM is Wb/m 2. Flux density distributin is assumed t be sinusidal as flux linkage is sinusidal. Calculated flux density distributin alng the air gap fr bth machines is shwn in the Fig. 15. Flux density distributin pattern f FRM rtates at n x n r rpm, whereas flux density distributin pattern f PMSM rtates at n rpm fr a cmmn shaft speed f n rpm. Bth flux pattern generates same utput vltage and frequency. Hence equivalent cnventinal PMSM shuld have a flux density f Wb/m 2 fr the same utput pwer as full pitch winding FRM. Maximum pssible air gap flux A phase slt B phase slt C phase slt Fig. 16. Full pitch winding arrangement fr lw speed FRM with 12 statr ples and 16 rtr ples 1011

6 Octber 22-26, 2007 / Exe, Daegu, Krea 6 density in PMSM is 0.9 Wb/m 2 [10]. Hence full pitch FRM (equivalent PMSM) has 13.17% higher pwer density than cnventinal PMSM in lw speed, lw pwer range. VI. FRM CONFIGURATIONS AND FULL PITCH WINDING FRM machine cnfiguratins fr lw speed are presented by In and et.al. [3]. The cnfiguratins are lw speed FRM with ple PMs n statr. lw speed FRM with inset-pms n statr. These cnfiguratins have 12 statr ples (slts) and flux pattern f 4 ples. Full pitch winding arrangement is als pssible fr bth cnfiguratins. Full pitch winding arrangement fr lw speed FRM machine with 16 rtr ples and 12 statr ples with 2 PM ple pieces per statr ple is shwn in Fig. 16. End turn length will be less in higher ple machine which decreases the end turn leakage inductance and cpper lss. Hence full pitch winding cncept is applicable t all FRM cnfiguratins. [5] Tae Heung Kim and Ju Lee "A study f the design fr the flux reversal machine," IEEE Trans. n Magnetics., vl. 40, N.4, pp , July 2004 [6] Jianzhng zhang, Ming Cheng, Wei Hua and Xiayng Zhu, "New apprach t pwer equatin fr cmparisn f dubly salient electrical machines," in in Prc.IEEE Industry Applicatins Annu. meeting., pp , [7] "Flux 2-D FEM Sftware, CEDRAT, France". [8] C. Wang, I. Bldea, S. A. Nasar "Characterizatin f three-phase flux reversal machine as an autmtive generatr.," IEEE Trans. n Energy Cnversin., vl. 16, N.1, pp , March, [9] Nbuyuki Nae "Vltage cmpensatin f permanent Magnet generatr with capacitrs". Prc. f IEEE electrical Machines and Drives., pp. wb wb2.14.3, [10] Miller TJ.E. "Brushless Permanent Magnet and Reluctance Mtr Drives. Clarendn Press. Oxfrd [11] Gieras J. F. and M. Wing " Permanent Magnet Mtr Technlgy. Design and Applicatins. Marcel Dekker Inc VII. CONCLUSION Full pitch winding cncept fr FRM is intrduced. Output pwer f cmpensated full pitch winding FRM is apprximately twice as that f cnventinal cncentrated statr ple winding FRM. Full pitch winding FRM is fully analyzed and simulated with flux-2d FEM sftware [7]. Full pitch winding arrangement increases the self inductance f machine by 2 t 3 times depending upn saturatin in the machine which results in pr vltage regulatin. Series capacitive cmpensatin is prvided t imprve the regulatin f full pitch winding FRM. Fictitius 'Electrical Gear' cncept is intrduced which makes it pssible t cmpare the pwer density f full pitch winding FRM with PMSM. It is fund that pwer density f cmpensated full pitch winding FRM is 13.75% higher than cnventinal PMSM. Full pitch winding FRM is a cmpetitive candidate fr lw speed, lw pwer generatr and mtr applicatins. VIII. ACKNOWLEDGMENT D. S. Mre is faculty member in Electrical Engineering Department f Walchand Cllege f Engineering Sangli, , (India). The financial assistance prvided by Walchand Cllege f Engineering Sangli fr registratin and travel is highly acknwledged. REFERENCES [1] R. P. Dedhar, Savante Andersn, In Bldea and T. J. E. Miller, "The flux reversal machine: A new dubly salient permanent magnet machine," IEEE Trans. Industry Applicatins., vl. 33, N.4, pp , July/August [2] C. Wang, S. A. Nasar, l. Bldea "Three phase flux reversal machine (FRM)," lee Trans. Electrical pwer applicatin., vl. 146, N.2, pp , March [3] In Bldea, Jichum Zhang, S. A. Nasar, "Theretical characterizatin f flux reversal machine in lw speed serv drives-the ple PM cnfiguratin." IEEE Trans. Industry Applicatins., vl. 38, N.6, pp , Nvember/December [4] Tae Heung Kim, Sung Hng Wn, Ki Bng and Ju Lee, "Reductin in cgging trque in flux reversal machine by rtr teeth pairing." IEEE Trans. n Magnetics. vl. 41, N. 10, pp , ctber