Modelling and Design of a Low Speed Flux Reversal Machine

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1 Modlling and Dsign of a Low Spd Flux Rvsal Machin R. Saou, M.E. Zaïm and K. Alitouch. Abstact This pap is dvotd to th lctomagntic dsign and th optimization of a 10 kw, 50 dict div Flux Rvsal Machin, xcitd by dfb magnts locatd on th inn sufac of th stato plots. Th optimization of th machin dimnsions, focusd on th maximization of th mass to toqu atio, is caid out by a gntic algoithm combind with th finit lmnt mthod. Th lctomagntic chaactistics of th optimizd machin, including flux, back lctomotiv focs EMF, static toqu, tc., obtaind by finit lmnts a thn analyzd. Th sults show that th machin psnts good pfomancs and can constitut an altnativ to th dict divs at low spds. stuctus impoving th pfomancs can b obtaind [5-9]. Ths stuctus a calld Doubly Salint Pmannt Magnt machins (DSPM) and Flux Rvsal Machins (FRM). Thy a widly studid. Howv, thy a gnally with lag tth and inappopiat fo low spd applications. Th low spd flux vsal machin, studid in this wok and illustatd in Fig.1, can b gadd as a nw mmb of th FRM family adaptd to dict divs applications at low spd. It is a th-phas machin psnting a doubly salint stuctu and uss concntatd windings. Its fild xcitation is povidd by non-otating annt magnt locatd in th stato without any magnt o winding in th dntd oto. Ky wods Flux vsal, finit lmnt, gntic algoithms, low spd, annt magnts. I. ITRODUCTIO owadays, th us of lctic machins, oftn of synchonous typs, fo dict div applications to opat with high toqu and low spd is bcoming mo and mo fqunt. Th taditional stuctus of ngy convsion qui a ga duc. This is vy inconvnint bcaus it adds wight, gnats nois, incass losss and quis gula maintnanc. Th limination of th gabox quis slow machins paticulaly adaptd to dict divs calld also dict attack machins. Duing th last fw yas, w assist to a gowing intst fo th study and th dsign of this typ of machins. Thy a indd incasingly usd as moto fo populsion of ships, cas, lvatos and, as gnato, fo wind tubin. Ths stuctus a oftn of synchonous typs (with fild winding o magnts) with lag numb of pols and high toqu. Th machin can b adial, axial o with tansvs flux. Oth spcial configuations of dict attack machins a also givn in th litatu [1-6] such as th vaiabl luctanc machins, xcitd o not. Vaious studis show that by intoducing annt magnts in switchd luctanc machins (SRM), nw Manuscipt civd Jun 30, R. Saou and K. Alitouch a with th Laboatoi d Géni Elctiqu d Béjaia. Univsité d Béjaia Algéi. (-mail: saou06000@yahoo.f ; k_alitouch@yahoo.f ) M.E. Zaïm is with Th IREEA- Institut d Rchch n Elctotchniqu t Elctoniqu d ants Atlantiqu, Boulvad d L Univsité, BP 406, Saint-azai Cdx, Fanc. (-mail: Elhadi.Zaim@univ-nants.f ) Fig. 1 Low Spd Flux Rvsal Machin 1-winding phas A, 2- stato yok, 3-magnt, 4-oto yok Th aim of this wok is th lctomagntic dsign and th optimization of a 10 kw, 50 dict attack FRM xcitd by dfb magnts. Th optimization of th machin dimnsions is caid out by a gntic algoithm combind with th finit lmnt mthod. Th objctiv is to maximiz th mass to toqu atio which psnts an ssntial cition fo machins with high toqu fo low spd divs. Th optimization applis on th local dimnsions (tth, magnts) as wll as th global paamts such as th oto and th stato yok, oto adius, coil hight and th angula slot opning. Th lctomagntic chaactistics of th optimizd machin such as phas flux linkag, back EMFs, static toqu tc., a thn dtmind and analyzd. Th sults show that th machin psnts good pfomancs and can constitut an altnativ to th dict divs at low spds.

2 II. PRESETATIO OF THE STUDIED MACHIE AD MODELLIG Th flux vsal machin (FRM) is a doubly salint stuctu with annt magnts glud onto th intnal sufacs of th plots. Th otation of th dntd oto vss th polaity of th magntic flux, du to th magnts, gnatd in th stato phass windings. dp pais of oth-south magnts a glud on th sufac of ach of ps plots of th stato facing th ai-gap. Th magnts a altnatly magntizd in opposit dictions. Th oto tth pitch is idntical to th stato pol pitch which cosponds to two succssiv oth-south magnts. Th stato numb of plots ( ps ), th total numb of magnts pais of th stato ( s ), th numb of th oto tth ( ) as wll as th numb of magnts pais p plot ( dp ) a latd by th following lations [4-6, 9]. flux du to th cunt, facd th oto slots; total flux in this cas would b minimal (Fig. 3). 1 K ps q s ps dp (1) Fig. 2 Conjunction position K is intg numb gat than 1. q is th numb of phass. Th oto spd is givn by: 2 f (2) Fo an opation with spd na 50 cosponding to a typical fquncy of 50 Hz, th numb of oto tth must b clos to 60. Ou choic fll on a th-phas stuctu fo =64 tth, s=48 pais of altnat magnts at a at of 4 plots p phas and of 4 pais of altnat magnts p plot (Fig.1). Th stato and oto of th FRM a fomd of a stack of fomagntic sht. Th plots ba th stato windings of th th phass and th oto is passiv without winding. A concntatd coil suounds ach stato plot and th winding of ach of th th phass is constitutd of fou concntatd coils connctd in sis so that thi magntic fluxs a additiv whn thy a fd by an lctic cunt. Th magnts cat a multipola magntomotiv foc which is modulatd by th anc vaiation of th slottd oto. Th motion of th oto vss th polaity of th stato phas flux linkag. Subjct to th stato xcitation fild, th magnts ointd in th diction of flux tnd to b placd so as to fac th oto tth. Th paticula positions of conjunction and opposition of th flux vsal machin a dtmind accoding to th diction of th amatu action flux linkag, th lativ position of th oto tth and th diction of magntization of th annt magnts which fac thm. So, whn th magnts magntizd in th diction of th flux, du to th stato cunt, a facing th oto tth, total flux is maximal. This cosponds to th position of conjunction (Fig. 2). This would cospond to th position of opposition if th magnts, whos diction of magntization coincids with th Fig. 3 Position of opposition Th instantanous applid voltag to a phas of th machin is linkd by Faaday's law to th total magntic flux Ψ as: d v Ri (3) dt i and R psnt spctivly th cunt, th sistanc p phas. Th winding flux linkag Ψ is composd of Ψ flux du to th annt magnts and of Ψ W flux du to th phas cunt as shown in Fig. 4. Th luctanc of th magntic cicuit sn by ach phas is ovall constant fo all th positions θ of th oto, flux Ψ W is, of this fact, pactically constant fo a fixd phas cunt and can b xpssd in lina mod by: L i w (4) Wh th phas inductanc L is pactically indpndnt of θ, Total flux Ψ is thn: Li (5)

3 Fig. 4 Phas flux linkag vsus oto position Th lctomagntic toqu T fo on phas on opation can b wittn as: 1 2 dl d T i i (6) 2 d d Toqu T is considd as th sum of two componnts T and T so as: T T T (7) Ψ Ψ Ψ w T : hybid toqu du to th intaction btwn th magnt flux and flux du to phas cunts. T : luctanc toqu. As th inductanc L is pactically indpndnt of th oto position, its divativ is null and consquntly th luctanc toqu T can b considd null. Hybid toqu T is thus th dominant componnt of th total toqu and it can b poducd by applying ith a positiv cunt to th phas winding (at th tim of th gowth of th flux of th magnts) o a ngativ cunt (whn th flux is dcasing). d T T i (8) d Although th toqu poducd in this configuation is a hybid toqu, indpndnt of th ovall luctanc of th magntic cicuit, it also occus howv by th ffct of th vaiation of luctanc. It is th local luctanc of th lmnt of th magntic cicuit associatd with th pai of magnts considd which vais. Th total luctanc of th plot mains constant. Th FRM can b supplid by a bidictional convt (cunts positiv and ngativ), but w consid, in this wok, only th cas wh ach phas is fd by a DC div unidictional by imposing a ctangula cunt shap accoding to th oto position. In 2D, fo th studid machin, th systm to b solvd is xpssd as follows: 1 AZ 1 AZ ( J z J ) x x y y (9) Az 0 on th machin contou Wh A z and J z a th z componnts of magntic potntial vcto A and th cunt dnsity J, spctivly; J is th quivalnt sufac cunt dnsity of th magnt and μ th magntic ability of ion. Th Maxwll stss tnso is wll adaptd to calculat th lctomagntic toqu of th machin, studid by th finit lmnt mthod. In two-dimnsional, th lctomagntic toqu T is obtaind fom th intgal along a closd contou Г suounding th oto and locatd in th ai-gap: T L H t Bnd (10) B n and H t cospond spctivly to th adial of th flux dnsity and th tangntial fild componnts and L th lngth of th machin (in axial diction Z) umical os can howv b intoducd paticulaly in computing H t. Akkio [10] poposs th calculation of th avag valu of th toqu opatd in th spac which constituts th ai-gap. T ( s 1 ) s T d (11) Wh s and a th out and th inn adii of th ai gap. And by considing th sction of th ai-gap S ag, th toqu can b obtaind as follows L T H t BndS (12) s S ag III. THE DESIG PROCEDURE AD OPTIMIZATIO Th aim is th lctomagntic dsign and th optimization of a 10 kw low spd flux vsal machin thanks to a gntic algoithm coupld with th finit lmnt mthod. A. Machin dimnsions and dsign appoach Fo th dimnsioning of th machin (Fig.1), w st th following constaints and quimnts. - Pow : 10 kw - Toqu : 2000 m - Maximum xtnal diamt of th machin : 600 mm - Cunt dnsity: 5 A/mm 2. - Copp fill facto: Ai-gap: 0.5 mm. Th stl lamination usd is of typ: FV ha, [9, 10] Th annt magnt is an d-f-b, with a lina dmagntizing chaactistic, chaactizd by: B =1,29T, =1.049

Vaious magnts and oto tth shaps can b chosn in od to impov paticulaly th machin pfomanc in tm of toqu poduction. Th shap of annt magnts is slctd to b ctangula.

4 Vaious magnts and oto tth shaps can b chosn in od to impov paticulaly th machin pfomanc in tm of toqu poduction. Th shap of annt magnts is slctd to b ctangula. Thi dsign and thi addition to th stato plots a thfo asy to cay out. Th oto tth shap taind a tapzoidal. Th tapzoidal shap bing asy to aliz, constituts a gnal cas of oth shaps of tth [4, 6]. Th magnts as wll as th oto tth a dfind thanks to th following paamts (Fig.5) - Magnt hight h m - Roto tth dpth h - Roto tth cyclic atio 1 and 2. - Tth pitch angl τ =2π/. hm h τα 2 Fig. 5 Tapzoidal oto tth shap and magnt dimnsions Th global stuctu (Fig.6) is ntily dtmind fom th following 10 paamts: - Th width of th oto and stato yoks E and E s. - Coil hight h b. - Angula plot opning. - Th A point position ( R a, a ) With R a bing th distanc btwn A point and th machin cnt O - Tapzoidal tth paamts h, 1 t 2. - Magnt hight h m. τ τ/2 τα1 Fig.6 Global dsigns paamts B. Dsign pocss by gntic algoithm coupld with th finit lmnt mthod Th gntic algoithms dvlopd fo th pupos of optimization, a volutionay sach algoithms and allow th sach fo a global xtmum. Thy a wll adaptd fo th dsign of lctical machins and lctomagntic dvics [11-13]. Stating fom an initial population catd andomly, a nw population of individuals is gnatd, at ach itation, using th opatos: cossov, mutation and slction. Th two fist a opatos of xploation of spac, whil th pupos of th slction is to pomot th fittst and volv th population towads th optimum of th poblm so that th objctiv function is minimizd (o maximizd). Th sach continus until th stopping cition is satisfid. Th stopping cition may b th numb of gnations. Th final vsion of th gntic algoithm dvlopd fo ou wok is as follows: 1. Dfin of th objctiv function. 2. Random initialization of a population of machins 3. Evaluations of th objctiv function of ach machin. 4. Slction of th bst machins 5. Apply th gntic opatos: cossov and mutation to gnat a nw population. 6. Evaluat th nw population. 7. Stop cition is not satisfid go to Stp End Th sach gion of th 10 gomtic paamts of th FRM is stictd in od to impov th sach fo th optimum. Th high and low limits of ach of th vaiabls to b optimizd a summaizd in Tabl 1. 05mm (E, E s ) 50mm 5mm hb 100mm 1 (, a ) 15 (angls mécaniqus) Rc/3 (R, R A ) 0.9 Rc 0.2 mm (hm, h) d (pas dntai n mm) R-h-E > Rc/3 0.2 ( 1, 2 ) 0.5 Tab.1 Paamts constaints Th mass to toqu atio is th optimization cition chosn fo th dsign of ou machin. Maximizing th mass to toqu atio would man minimizing th objctiv function f dfind as follows: 1 T f (13) M M psnts th activ mass of th machin (copp, ion and magnts). T is th maximum toqu valu. Fo this studid machin, T cosponds to th position of th oto θ=90 lctic [6]. Th opposition position cosponds to θ = 0 whil th conjunction position is at θ=180 lctical. This toqu is calculatd by th finit lmnt mthod.

5 Th gntic algoithm is coupld with th finit lmnt mthod. FEMM [14] is th softwa usd. It is a whol of pogams fo th solution, in low fquncy, by th finit lmnt mthod, th two-dimnsional magntostatic and lctostatic poblms in a plan o axisymmtic domain. IV. RESULTS OF OPTIMIZATIO Th algoithm is un with an initial population of 50 machins. Th cossov and mutation opatos a fixd spctivly to b 0.8 and Th sach is stoppd aft 50 itations. Th duation of on optimization is 2 days using a 3 GHz pocsso. A) Evolution of th optimizd paamts accoding to th gnations Fig.7 psnts th volution of th avag valu as wll as th bst valu of th objctiv function of ach gnation of machins. Th lctomagntic toqu obtaind ov gnations is shown in Fig.8. Aft th 30 fist gnations, th impovmnt of th objctiv function and th lctomagntic toqu is insignificant. Th optimal mass to toqu atio cospondnt is of m/kg. Objctiv function 0,2 0,18 0,16 0,14 0,12 0,1 0,08 bst avag Gomtical paamts E [mm] E [mm] Hb [mm] β[ ] R a[mm] Β a[ ] R [mm] α 1 α 2 h [mm] hm[mm] f 1 (m/kg) Slctd machin 25,6 28,95 47,2 5,6 248,75 5,74 223, ,6 3, Tab.2 Optimizd machin data 1) Magntic flux linkag and lctomotiv foc Fig.9 illustats, fo on phas, th magntic flux chaactistic ψ (θ, I) accoding to th cunt and oto position. Ths chaactistics dtmind by th finit lmnt mthod, a obtaind fo cunts vaying fom 0 to 120 A. Fig.7 0, gnations Objctiv function valus ov gnations Toqu(m) gnations Fig.8 Toqu ov gnations B) Gomtical paamts and lctomagntic chaactistics of th optimizd Th dimnsions of th optimizd machin a psntd in Tabl 2. Fig.9 Phas flux linkag ψ (i, θ) vsus cunt fo diffnt oto position At no load, th back EMF inducd by th magnts in th phas winding is givn by: d d 2 n dt d 60 (14) Ψ, and n psnt spctivly, th magntic flux du to th annt magnts, th oto angl and th oto spd in Fig.10 shows th layout of th inducd lctomotiv focs in th th phass of th FRM at th atd spd of 50. On can obsv that thi wavfom is almost sinusoidal. This wavfom is typical to flux vsal machins. [6-8]

Fig.10 EMF(V) 200 150 phas1 100 phas2 50 phas3 0-50 0 60 120 180 240 300 360-100 -150-200 Elctical Angl( ) Back EMFs wavfoms fo th optimizd machin 2) Elctomagntic toqu Fig.

6 Fig.10 EMF(V) phas1 100 phas2 50 phas Elctical Angl( ) Back EMFs wavfoms fo th optimizd machin 2) Elctomagntic toqu Fig.11 illustats th static toqu chaactistics of th FRM accoding to th cunt and th oto position. Ths chaactistics, also dtmind by finit lmnts, a obtaind fo cunts vaying fom 0 to 120A with stps of 10A. Fig.11 Static toqu p phas vsus oto position fo diffnt phas cunts vaying fom 0 to 120A 3) Cogging toqu Fig.12 shows cogging toqu vsus oto positions of th optimizd FRM. Cooging toqu(m) Elctical Angl( ) Fig.12 Cogging toqu of th optimizd machin This cogging toqu is du to th intaction btwn th annt magnts glud on th sufac of plots and th oto tth which fac thm. It is dtmind by th FEM by imposing a null cunt in th th phass of th machin. Thus, th cogging toqu obtaind psnt fo th optimizd FRM a lativly wak pak (3% of th maximum toqu) and xhibits a piodicity of 120 lctical angl. V. COCLUSIO A nw topology of flux vsal machin FRM was psntd, modlld and dsignd fo low spd lctic divs. This oiginal stuctu is doubly salint. Th optimization, focussd on th maximization of th mass to toqu atio of th machin, which psnts an ssntial fatu in low spd applications, is caid out by a gntic algoithm combind with th finit lmnt mthod. Th sults obtaind show that th optimizd machin psnt good pfomancs and can b an altnativ in th dict-divs and low spd applications REFERECES [1] M.R. Dubois, Rviw of Elctomchanical Convsion in Wind Tubin, Rpot EPP00.R03, Apil 2000, Faculty ITS Goup Elctical Pow Pocssing. [2] Lampola, P., Dictly divn, low-spd annt-magnt gnatos fo wind pow applications, Elctical Engining Sis, o. 101, Hlsinki, Acta Polytchnica Scandinavica, [3] B. Multon, J. Bonal, Ls ntaînmnts élctomécaniqus dicts : divsité, containts t solutions, Colloqu SEE, CEMD 99, Cachan, 4 févi 1999, pp [4] Moau, L., Machmoum, M., and Zaïm, M. E., Dsign of low spd slottd switchd luctanc machin fo wind ngy application, Elct. Pow Compon. Syst., Vol. 34, o. 10, pp , Oct2006. [5] R.Saou, K. Alitouch, M.E.Zaïm, On th Pfomanc Impovmnt of a Low Spd Switchd Rluctanc Machin with Pmannt Magnt Excitation, ICEM 2006, Chania, Ct Island, Gc, Spt 2-5, 06. [6] R. Saou, Modélisation t optimisation d machins lnts à aimants annts: Machin à doubl saillanc t à invsion d flux, Thès d Doctoat d état, Ecol ational Polytchniqu d Alg, nov 08. [7] I.Bolda, C.X.Wang and S.asa, Dsign of a th phas flux vsal machin, Elctic Machins Pow Systms, vol 27, 1999, pp [8] T.H.Kim and J.L, A Study of th Dsign fo th Flux Rvsal Machin, IEEE Tans. On Magntics, vol. 40,.4, July 2004, pp [9] Saou, R., Zaïm, M. E., and Alitouch, K., Optimal Dsigns and Compaison of th Doubly Salint Pmannt Magnt Machin and Flux-vsal Machin in Low-spd Applications, Elct. Pow Compon. Syst., Vol. 36, o. 09, pp , Spt 08. [10] A.Akkio, Analysis of induction motos basd on th numical solution of th magntic fild and cicuit quations, Hlsinki, Acta Polytchnica Scandinavica, Elctical Engining Sis, o.59, [11].Bianchi and S.Bolognani, Dsign optimisation of lctic motos by gntic algoithms, IEE Pocdings - Elctic Pow Applications - Volum 145, 5, Sptmb 1998,pp [12] G.F.Ul, O.A.Mohammd and C.S.Koh, Dsign Optimization of Elctical Machins using gntic algoithms, IEEE Tans. On Magntics, vol. 31,.3, May 1995, pp [13] Alitouch, K.; Saou, R.; Zaim, M.E, Analytical optimization of inst annt magnts machin basd on a gntic algoithm, Intnational Agan Confnc on Elctical Machins and Pow Elctonics, ACEMP 07. Elctomotion 07 Bodum, Tuky, Spt. 07, pp [14] D.C.Mk, Finit Elmnt Mthod Magntics, Vsion 4.0.1,

EFFICIENCY ANALYSIS OF INDIRECT VECTOR CONTROLLED THREE PHASE INDUCTION MOTOR DRIVE

EFFICIENCY ANALYSIS OF INDIRECT VECTOR CONTROLLED THREE PHASE INDUCTION MOTOR DRIVE ISSN (Pint) : 3 3765 ISSN (Onlin): 78 8875 Intnational Jounal of Advancd Rsach in Elctical, Elctonics and Instumntation Engining (An ISO 397: 7 Ctifid Oganization) Vol., Issu 8, August 13 EFFICIENCY ANALYSIS