Novel Axial Flux Brushless Resolver Analysis and Optimization using 3D Finite Element and D-Q Model Method

Transcription

1 Novl Axal Flux Buh Rolv Analy an Optmzaton ung 3D Fnt Elmnt an D-Q Mol Mtho F. Tootoonchan*, K. Aazah* an M. Al* Atact: Rolv a wly u n lctc vn ytm pcally n hgh pcon vomchanm. Both ncapulat an pancak olv uff fom a majo awack: tatc ccntcty (SE). Th awack cau a gnfcant nca n olv output poton o (RPE) whch coul not coct lctoncally. To uc RPE, th pap popo a novl tuctu wth axal flux. Popo topology, gn guln, optmzaton pocu an val ky fatu to mpov th ntvty of axal flux olv (AFR) agant SE a tu. Futhmo, to mnmz RPE an optmz gn attan. Th machn a nvtgat n tal y ung - mol an 3D tm tppng fnt-lmnt analy. Th ult of th two mtho a compa an oth pototyp machn (popo an optmz) a ult. In o to valuat popo topolog, an xpmntal tt tup v. Fnally, th xpmntal ult of th pototyp machn vf th analy ult. Kywo: Rolv, Statc ccntcty, axal flux, Optmzaton, Tm-Stppng 3D- Fnt Elmnt Analy (3D-FEA), - mol Intoucton Hgh pfomanc vomchanm an nvt vn pmannt magnt ynchonou moto (PMSM) pf to u aolut oto poton nfomaton whch a pouc y lctomagntc an optcal []. In convntonal vomchanm optcal nco a th t choc. But, n hgh pcon poc olv a pf cau of th thmal talty, Rtant to nvonmntal polluton, mall z, ay ntallaton an ntgaton wth otatng haft (patculaly n pancak olv) []. Pmay tatonal olv ha uh. But, th avantag of uh uch a no gnaton an n to mantnanc, ha foc thm to gn uh y ung otay tanfom []. Buh olv a gn n two typ [3]: a) woun oto, whch nam convntonal olv (CR), ) ol oto, whch nam vaal luctanc olv (VR). Ianan Jounal of Elctcal & Elctonc Engnng,. Pap ft cv 4 Sp. an n v fom July. * Th Autho a wth th Dpatmnt of Elctcal an Comput Engnng, K. N. Too Unvty of Tchnology, Than, Ian. E-ma: Tootoonchan@ut.ac., Aazah@kntu.ac., Al@kntu.ac.. C R an V R can manufactu capulat (fam) o pancak (fam) [4-6]. All typ of olv th ha ang o ntall on a otatng haft that, ha ang. All typ of ang (allang, oll-ang, mchancal a an tc.) hav ntnc aal acklah whch cau tatc ccntcty (SE) [7]. A t hown n Fg., n th ca of SE, th oto otat aoun t own gomtc ax, whch not th gomtc ax of th tato (th ffnc popotonal to th magntu of O O vcto). Th aon that la to SE may nvolv many ffnt facto. It can cau y [7, 8]: a) Bang wakn, ) Unalanc loa, c) Bnt oto haft, ) Mchancal onanc at ctcal loa an ) manufactu an amly tolanc. Of cou, an nhnt lvl of SE xt vn n nwly manufactu machn u to th ul-up of tolanc ung manufactung an amly pocu. Accong to ISO49 o ABEC tana th a at lat.5 mco mt ntnc acklah n th mot accuat ang whch a u n th mltay an th patal vomchanm. Th man vn th accuat ang hav ntnc SE. Th tana how that th ntnc SE of th ang whch u n lctcal machn up to 35 mco Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp. 43

2 O Fg. Th tatc ccntcty o. mt. If th ccntcty fault occu, t wll a wth th ntnc SE of th ang. Th ccntcty wll tu th flux tuton n th a gap [9]. An, t wll tot th output gna of th olv []. In th conton, th poton o of th olv can nca up to 5 Ac Mnut (mo than ght g) [7]. It mnton n [] that, th lag poton o occu wth th than 6 mco mt ccntcty lvl. Thfo, It can conclu that, convntonal olv wth aal flux tuctu alway uff fom a majo awack whch nam SE [7]. Pvou ach t to how th ffct of SE on th accuacy of ffnt typ olv [7, 9, -3]. In [7] ffnt kn of o whch a ult fom wong ntallaton poc claf. Ao, [7] ha u xpmntal tt to how that, th SE may nca th olv output poton o up to 5 Ac Mnut (mo than 8 g). In [9] th ffct of kw oto an ccntcty o on th accuacy of a uh olv tu ung D fnt lmnt analy. But, th autho of [9] hav xp that th gnfcant ffnc twn mau an calculat ult. Fnally, thy hav jutf that th mol not accuat nough. In [] th ffct of ccntcty o an a gap lngth on th accuacy of th tct angula poton of a VR olv nvtgat ung D FEM. In th ach a laton twn th hamonc of th tct poton wavfom, a gap lngth an ccntcty o tmn ung non-lna gon mtho. 3D FEM u n [] to valuat th nflunc of th on ht pmalty pon an oto ccntcty on th angula poton accuacy of th VR olv. Th pap pnt that μm SE nca poton o upto 9 Acmn. Fnally, [3] ga th nonlnaty chaacttc of ccntcty on th angula poton o of a VR olv. Almot all ltatu hav tu jut th ffct of ccntcty on th olv' poton o an thy hav not uggt any oluton to ca th α O & O O : Roto Symmty Cnt O : Stato Symmty Cnt O : Rotaton Cnt ccntcty o. In o to uc th ffct of SE two novl tuctu a popo n th pap. Th ft on ha an axal flux gomty whch can uc th ccntcty o. Th tuctu optmz to th con on who can mnmz th o. Th pfomanc of oth topolog a calculat ung tm tppng 3D FEM an funcy analy of output gna. Thn, thy a contuct an th tt tup v. Pactcal tt ca out y applyng agnal ccntct an nvtgatng th ntvty of popo tuctu to th vaaton. Th followng pont a ult fom th tuy: a) th SE ha th mnmum ffct on th accuacy of popo tuctu, ) th accptal accoanc twn tm tppng 3D FE ult an xpmntal on, c) ung tm tppng 3D FEM to tuy th no wa vy tm conumng poc (wtch wll olv n an up comng pap). Popo Stuctu Rolv, a an angula poton no, act lk a ynchonou gnato wth two pha. Th fl wnng of th gnato xct wth hgh funcy altnatv cunt (up to khz, E. ) [4]. Ovouly, upplyng th fl wnng wth AC pouc two ampltu moulat (AM) output voltag nta of n an con voltag. Nglctng th col tanc an motonal.m.f. tm, th output voltag can xp y E. (, 3) an a hown n Fg. [, 4]. Th ato of th output voltag gv th oto otaton angl θ m [-, 4]. V x V n t () p V n KVx n θm () p V co KVx co θm (3) P Vn θ θm Actan( ) V (4) co wh K tanfom ato, p pol num an θ an lctcal angl. In th convntonal olv wth aal flux th tatc ccntcty vn n th ang of om mco-mt cau th tong vaaton n th lnkag an lakag nuctanc of oto an tato wnng [9]. Th nuctanc vaaton a th man facto wtch nca th olv tct poton o [9, -]. Ung magntc ccut concpt, th nuctanc of on pha of th olv can wttn a [5]: L( θ) K.P( θ) A P( θ) μ z (5) wh, K: a contant whch pn on th phycal paamt nvolv (.g. th num of tun p pha, 44 Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.

3 Exctaton Voltag Rolv Roto Yok Rolv Stato Yok Rotay Tanfom Roto Co Output Voltag Tm [Sc] Tm [Sc] () Fg. Rolv gna Exctng voltag () Output voltag. th num of tth p tato pol, tc.), P(θ) th pmanc twn on tato an oto tooth a a functon of poton, μ: pmalty of a, A: ffntal co-ctonal aa twn th oto an tato tth an z: lngth of th flux path twn th oto an tato. Accong to E. (5), n popo tuctu th nuctanc mut hav th mnmum ntvty fom th SE. Th u a unfom a gap lngth an a contant ffctv on ufac twn tato an oto. Th unu tuctu who a gap lngth an ffctv on ufac a not chang wth th SE axal flux topology (a hown n Fg. 3). Th pap popo an tu th topology a a novl olv tuctu whch out agant SE. Popo olv wth axal flux tuctu hav tnct avantag ov aal flux on. Som of th avantag a th plana an ajutal a gap, compact contucton, tt vntlaton an coolng. Futhmo, th oto a ntgat aly wth th otatng pat. On th oth han, th typ of olv, cau of th hot axal lngth, can aly aopt nto th contucton of vaou vc an ha avantag n tm of z, appaanc, an functon. Fnally, n ma poucton, accong to Pola thotcal conaton th AF machn n -3 pcnt copp an pcnt on than mla tatonal on [6, 7]. 3 Rolv Mol In th tuy two mtho a popo to mol th AFR. Th ft mol a on - ax thoy an n th lat on tm tppng fnt lmnt analy u to pct th pfomanc of th olv. 3. D-Q Mol Th popo mol a on - ax thoy. Th followng aumpton a con n th analy [4]: a) Stato ha two-lay tut lap wnng. ) Roto ha a wnng wth nuoal upply. c) Th nuctanc of AFR n - ax a unual. Fg. 4 how th mol of olv wnng. Each tato wnng flux cont of lakag flux an man flux, th latt flux lnk th oto [] Dynamc Mol Th voltag uaton n machn vaa can xp a followng: V L V V Rolv Roto Slot Rolv Roto Tooth a Rolv Stato Tooth L n θ a L L L t L L m L m coθ coθ coθ n θ L a a t L n θ L n θ n θ t t a coθ (L L Lm coθ ) t L m Rolv Stato Slot Fg. 3 Popo axal flux olv tuctu. m n θ coθ a L L m L (L L Lm coθ ) L t L m n θ Rotay Tanfom Stato Co n θ coθ a t t a t (6) (7) (8) In th aov uaton th an ucpt not vaa an paamt aocat wth th tato an oto ccut, pctvly. V a, V a th tato voltag, V th xctaton gnal of th olv (V ν co( f tψ), a, a th tato cunt, th oto cunt, th tanc of tato ccut, L, L m a th lakag an magntzng nuctanc of th tato wnng, pctvly,, L a th tanc an lf nuctanc of oto ccut, L th mutual nuctanc twn th oto an tato ccut, th oto angula vlocty an θ lctcal angula placmnt. Th nuctanc of AFR can calculat a [8, 9]: Tootoonchan t al: Novl Axal Flux Buh Rolv Analy an Optmzaton 45

4 V Vf Fg. 4 Axal flux olv wnng mol. 5 Ll N (R R)( λ λo λ λz) (9) P L L L P θ 5 l N (R R)( λ λo λ λz ) m () μπ(r o R )N () 8P g o μπ(r R )N L l () 8P g μπ(r o R )NN L (3) 8P g wh P th pol pa num, th num of lot p pol p pha, Ro an R a out an nn au of co, λ pcfc lot lakag pmanc, λ o pcfc ovhang lakag pmanc, λ pcfc ffntal lakag pmanc, λ z pcfc zg-zag lakag pmanc, g ffctv a-gap lngth twn th ufac of tato an oto, N an N a th num of tato an oto tun, pctvly n ach pha. Th tato vaa a tanf to th oto fnc fam whch lmnat th tm-vayng nuctanc n th voltag uaton. Pak uaton a otan y ttng th p of th tato fam ual to th oto p. Th xpon fo th flux lnkag a: λ L L L L L λ ( ) ( ) m ( L L Lm ) Lm ( L Lm ) L m ( Ll L m ) λ an ψ λ x L thn ψ ( X X ) ψ ψ m X ( Xl Xm ) Xm Xl ψm Xm ( Xl Xm ) Xl ψm ψ m m L m (4) (5) (6) By fng oto vaa to th tato wnng, voltag uaton can wttn a: ψ V ψ t ψ V ψ (7) t ψ V t In o to otan th uvalnt ccut, E. (7) houl plac y E. (6). Thu, th voltagcunt uaton a a followng: p X X Xm V p p V X X Xm (8) V p p Xm X wh: X X X X X X m m,x,x m m X X X X m m (9) an p /t []. Th lctcal uvalnt ccut of th olv a pnt n Fg. 5. Th lctomagntc tou vlop n th olv gvn y: T P ( ψ ψ ) m () An th mchancal uaton of olv n p unt can wttn a: T mch ( pu) T ( pu) T ( pu) m amp H t () wh H nta contant xp n con, T mch loa tou an T amp fctonal tou Stay Stat Mol In tay tat, th lctcal angula vlocty of th oto contant an ual to. In th mo of opaton th oto wnng o not xpnc any chang of flux lnkag []. Thu, wth ual to an th tm at of chang of all flux lnkag nglct, th tay tat von of E. (4, 5) com: V V V V I V I V I x x I I x I m () 46 Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.

5 jx l ' I jx ' l a / I V ~ a x m Fg. 6 Stay tat uvalnt ccut of th AFR. V Fg. 5 Dynamc lctcal uvalnt ccut of th AFR n - ax. H th to ato agan nclu to accommoat analy whn th opaton funcy oth than at. In th ynchonouly otatng fnc fam an ung uppca ltt to not th contant tay tat vaa []: ~ Fa F jf (3) wh F ach lctcal vaal (voltag, cunt, flux ~ lnkag), F a phao whch pnt a nuoal uantty, a F an F a al uantt pntng th contant tay tat vaa of th ynchonouly otatng fnc fam. Hnc: V ~ a V jv (4) Suttutng E. () nto E. (4) y: V ~ a ~ X I ( X X ) I X I m (5) Fo ymmtcal olv, X X an. So E. (5) can wttn a: ~ V ~ jx I E ~ E ~ a a wh: X l ( ) XmI X X m a a (6) (7) Conng aov uaton, th tay tat uvalnt ccut of olv hown n Fg D-Q Mol Smulaton Th tat uaton on th otatng - fnc fam a ntouc. MATLAB/Smulnk oftwa u fo mulaton. Input, output an tat vaa a thu Stat Vaa [ ψ, ψ, ψ ] Input Vcto [ V, ΔT ] mch t ] Output Vcto [ Δθ In gnalz thoy of lctcal machn, t mo convnnt to u flux lnkag a th tat vaa [, ]. By th way, th ffntal opato chang to ntgal opato. Ung Euaton (6) an (8), th flux-lnkag uaton coul otan a follow: ( ψ ψ ) ψ t ψ V m X ψ V Xl ( ψ ψ ) m ψ t V ( m ) t X ψ ψ ψ l wh: ψ ψ ψ m ' X m X l X X X l (8) (9) (3) (3) ψ ψm (3) Xm X X An angula poton, tato, an oto cunt can calculat a: θ ( t) δ ( t) θ ( t) θ ( t) t ( ) t θ ( ) θ ( ) (33) ψ ψm (34) x ψ ψ x ψ ψ l m (35) m (36) x Tootoonchan t al: Novl Axal Flux Buh Rolv Analy an Optmzaton 47

6 Bcau of th alty of popo mol to aum ffnt valu fo L an L, t can con th ffct of ccntcty n AFR whch nvtgat n ou out comng pap. Fg. 7 how a lock agam whch u n mulaton. Fg. 8 how th tato an oto of facat AFR fo an aft wnng. Th pototyp ha ngl tato an ngl oto tuctu. Th pcfcaton of th AFR a pnt n Tal an th paamt of t uvalnt ccut a gvn n Tal. Th paamt a otan ung DC-Pu mtho []. In th mtho tato wnng chag wth t nomnal DC cunt. Th cunt gnal hown n Fg. 9 (wth mm a gap lngth). Fg. 9 chag cunt of tato wnng vf coft ψ vf coft ψ V f V V E. (8), (3) an (34) E. (9)-(3) an (34)-(35) ψ ψ T mch E. ()-() an (33) Fg. 7 Block agam of AFR mulaton. θ n θ, coθ Gnaton coθ n θ Tal Th Spcfcaton of Tt Axal Flux Rolv Paamt Valu Unt Funcy 4 Hz Pak to Pak nput voltag V Maxmum poton o Acmn Pol num - Maxmum p 8- pm A gap lngth mm Co out /nn amt 7/5 mm Co lngth, tato/oto / mm Duty cycl S - Num of tun, Stato/Roto /6 - Tal Th Euvalnt Ccut Paamt of Tt AFR Paamt Valu Unt 9 Ω ' f 7 Ω L m H L' lf. -3 H L. -3 H J kg.m () Fg. 8 AFR tato an oto Bfo wnng () Aft wnng. 3. 3D Tm Stppng Fnt Elmnt Analy Th con mtho to valuat th pfomanc of th popo axal flux tuctu 3D tm tppng fnt lmnt analy. To nca th accuacy of th FE mol, th ffct of y cunt an atuaton a con multanouly. Although, th analy vy complx an tm conumng, t vy accuat. So, t a goo choc to vfy th ult of popo topology. Futhmo, to uc computaton tm, oto angula poton valuat fom th ato of th output gna whch fomulat n E. (4). Th maxmum magntc flux nty of.8 T confm that th olv co wa not atuat. A hown n Fg. th B-H cuv of olv co, whch u n FEA, nvtgat xpmntally ung mof Eptn tt [] at 4 khz. 48 Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.

7 Flux Dnty [T] Amp-Tun [A] x 5 () Fg. Mof Eptn ccut () Otan B-H cuv. Tal 3 Th gomtcal mnon of popo AFR. Itm. Valu (unt) Out/Inn amt of tato 7./5 mm Out/Inn amt of oto 7./5 mm Stato an oto co thckn mm Stato/oto num of lot 4/ A gap lngth mm Pow ouc Snuoal, V p 5 V, 4 khz Wnng mtho lay nuoal tuton on lot In th pap, calculatng 4 3D FE mo fo on oto voluton gv on po of olv output gna (whch wat th man tm of th tuy). Although, 3D FEM an accuat mtho, th mot lal ult a xpmntal on. In th tuy, an xpmntal AFR wth pcfcaton t n Tal 3 wa ma an tt (Fg. 8). Tt ult a otan y ung a pcal tup. Th tt tup al to chang th amount of SE an of a gap lngth. In aton, th otay tt ha a pcon otay tycop wa plac on t. So, ffnt otay poton a pouc y th tycop n [, π] aan. Th tuctu v tt tup hown n Fg..... Fg. Dv tt tup of AFR By ung th tup, AFR output gna an mulaton ult (nclung - mol an 3D-FEM) a compa n ach of th angula poton (Th olv output otan fom actangnt of output voltag ato). 4 Rult 4. AFR wthout Eccntcty Pvou ach, uually hav cu jut aout poton o tuton. But, n th pap, not only th poton gnal (Actangnt of th ato of - voltag) ut ao - voltag a pot, too. In pactc, olv output gna a f to th olv to gtal convt (RDC). Th RDC nput tanc vy hgh. Thfo, th cunt n th tato co of AFR, whch apply to th RDC, n th o of mco amp [3]. Accongly, Fg. how th -, FEM an mau voltag of AFR xct wth xta pu ynthz nuoal ouc (Tal 3). Fg. 3 how th compaon of mulat an xpmntal output voltag. Rult how goo agmnt twn tt an mulat (- mol an FEM) voltag. Bcau of th maxmum a gap flux nty than.8 T (calculat y 3D-FEM) AFR wok at lna pat of t B-H cuv. Thfo, t xpct that th ampltu of output mulat an mau gna a mla. Gnally, th olv output gna a convt to poton nfomaton y tackng olv to gtal convt. To o th, tackng RDC u th nvlop of th output gna. Thfo, n th tuy hamonc contnt of an nvlop of an output gnal a takn nto account, too. Fg. 4 how th nomalz hamonc componnt of th con pha output cunt nvlop. Almot all o an vn hamonc xt n th FFT plot. Th mpotanc of FFT plot val whn t compa wth ccntc AFR' FFT plot. Th compaon wll on n nxt cton. In th ach, poton o th ffnc twn th al oto poton (whch otan y man of tt tup) an th tmn oto poton of AFR (ult fom - mol an 3D-FEM). Fgu 5 how th compaon of mulat an mau output poton of AFR an th ffnc. Th fgu Tootoonchan t al: Novl Axal Flux Buh Rolv Analy an Optmzaton 49

8 how th maxmum poton o ffnc twn mau an mulat ult a 6 an 7 Acmn at 45 an 45 g fo - mol an 3D FEM pctvly. But, th maxmum poton o of mulat AFR vu al poton a aout 9, 7 an 5 Acmn (FEM an - mol) at 3, 3, pctvly. Th al poton (θ al ) can calculat y hom t of oto poton ( θ oto ) (agant tato poton), pol num (p) an oto p (f, voluton p con) that : Output Voltag [V] Output Voltag [V] Tm [Sc] x Mau 3D FEM 3D FEM - Mol - Mol Pk Output Voltag [v] Rlatv o [%] () Fg. 3 Compaon of calculat an mau gna Ampltu of AFR con output voltag nvlop () Rlatv o twn calculat an mau gna. π.f θ al θ oto.t p (37) Fnally, Fg. 5 how that th AFR maxmum poton o.5 Acg (aout 9 Acmn). Ampltu Rato [%] - t n 3 4th 5th 6th 7th Funcy [Hz] 3D-FEM D-Q Mol Fg. 4 Hamonc componnt of output cunt nvlop Tm [Sc] x -3 () Poton Eo [Dg] FEM Rult - Mol Mau Eo Dffnc [Dg] Ial Poton [Dg] ( ) (Mau) - (FEM Rult) (Mau) - (- Mol Rult) (c) Fg. Stu AFR output gna wthout ccntcty Rult fom -- mol () Calculat y 3D FEM (c) Mau on ocllocop Ial Poton [Dg] () Fg. 5 AFR poton o 3D-FEM, - mol an mau ata agant al poton () Eo ffnc twn mau an calculat ata. 5 Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.

9 4. AFR wth Eccntcty In popo - mol, - ax nuctanc a ffnt paamtc vaa. Thfo, y ung unual valu fo L an L th ffct of SE can mol. In th mtho th ytm ffntal uaton whch xp t ynamc pfomanc (7- ) houl lna. Th mtho of lnazaton a v nto two catgo: ) analytc ptung mtho, an ) oftwa a mtho. In th fom, th nonlna ffntal uaton a ptu aoun th opatng pont an n th latt, om functon of SIMULIK/MATLAB oftwa a mploy []. In oftwa a mtho, th mulaton lock agam of AFR plott n Smulnk. Thn, th LINMOD functon of Matla u to otan ytm lna mo of onay ffntal uaton (O). Fnally, TRIM functon mploy to fn tay tat paamt fo th Smulnk ytm. Both lnazaton mtho w u. Compaon twn th ult ncat that oth of thm ha an accptal accuacy. Fnally, th mtho of lnazaton u n th ach la to th followng lna tmnvaant ytm of uaton: X AX BU (38) Y CX D U Euaton (38) can wttn a low (ung mall ptuaton aoun opatng pont): Δ X A ΔX B ΔU (39) ΔY CΔX D ΔU wh: Δ t ΔX [ Δψ, Δψ, Δψ,, Δθ ] t (4) ΔU [ ΔV, ΔV, ΔT ] ΔY [ Δθ t ] mch Th numcal coffcnt of E. (38) can calculat y ung avag DC pu pon of tato cunt [4]. Intf paamt confm that L L. To nvtgat th pfomanc of AFR wth tatc ccntcty, th paamt of th ccntc AFR w ntf agan. Th tm, ntf paamt ncat that L unual wth L (L L ). Fnally, placng th paamt n popo - mol AFR output gna w mulat. Fg. 6 how nomalz output voltag of ccntc axal flux olv. Ao, nomalz tm tppng 3D-FEM ult pot n Fg. 6(). Th magntc flux nty of ccntc mol nca.8 tm n compaon wth halthy mol an not ymmty n th co. Fo th aon, th wavfom of SIN an COS a tot n tm of ampltu an pha ffnc a hown n Fg. 6 an 6() an compa n Fg. 6(c). In FE analy u n th tuy, a wnng aum a a ol copp whch t nuc voltag multpl y wnng tun. Output Sgna [pu] Output Sgna [pu] Thfo, th pct wnng tanc wll not accuat nough an th th man aon that pct pha hft y 3D-FEM n Fg. 6() not coct. In - mol, wnng tanc a tmn y DC pu pon [] whch an accuat mtho. Fo accuat compaon, th output poton gna of ymmtc an ccntc AFR a hown n Fg. 7. In th fgu AFR tct poton calculat conng actangnt of output voltag ato. On th a, Fg. 7 how that th μm oto SE cau maxmum.8 an 3. Acg o n AFR tct angula poton y FEM an - mol pctvly. In th fgu although - pct o hap not mla to FEM on ut th amount of maxmum calculat poton o n accptal ang. It m that naccuat pct wnng tanc affct on poton o hap. Whn a 47 Ω tanc a n 3D-FEM mol th - an FEM poton o cuv wll mla. Thfo, f th wnng tanc Sn Pha Dffnc Ampltu Dffnc Con Sn Con Tm [Sc] x Sn Pha Dffnc Tm [Sc] Ampltu Dffnc Con Sn Con [%] [%] Rlatv Eo [%] Rlatv Eo [%] Tm [Sc] () 3D FEM (c) 3D FEM - Mol - Mol () Fg. 6 Output voltag AFR wth μm SE - mol () 3D-FEM (c) Amount of ampltu unalanc () Output gnal pha hft than xctng gnal. Pha Shft [Dg.] Tootoonchan t al: Novl Axal Flux Buh Rolv Analy an Optmzaton 5

10 coct n FE mol w can u 3D-FEM nta of - mol whn th ffculty of th DC pu pon maumnt takn nto account. So, th t of th tuy u jut 3D-FEM mof y a tanc. Ao, Fg. 7() how that th poton o ca fom.8 to.5 Acg whn th ccntcty nca fom to 7 μm wth a mm a gap lngth. Futhmo, t almot fx whl th ccntcty mo than 7 μm. Anoth ffct of SE on AFR output gna wa ncat whn output gna nvlop' hamonc componnt a tu. Fg. 8 how an xampl of hamonc contnt n an nvlop of con cunt. Ampltu ffnc of hamonc componnt compa wth tho of a olv wthout ccntcty a hown n Fg. 8(). Hamonc componnt of nvlop how a gnfcant vaaton pnng on th oto ccntcty an th a gap lngth. Fo xampl, Fg. 9 how nomalz ampltu ffnc of hamonc componnt n th mol at th gap lngth of mm an ffnt SE lvl. Th fgu how n tatc ccntcty hot than 8 μm, ampltu ffnc vay n th ang of -.5% to.%, ut thy vay n a naow ang n oth mo. In ccntcty long than 8 μm, th ampltu vaaton of hamonc componnt, xcpt 3, 7th an 9th componnt, how a tnncy to man tal. Th hamonc componnt of 3, 7th an 9th ao vay n a w ang n oth gap lngth mo. In th tuy, th ffct of a gap lngth, pol num an xctaton voltag hamonc on popo AFR poton o nvtgat, too. Ampltu Rato [%] Dffnc of Ampltu Rato [%] Funcy [Hz].. -. t t n n 3 3 4th 5th 6th 4th Funcy [Hz] 7th 5th 6th 7th () Fg. 8 Nomalz hamonc componnt of an nvlop of AFR output con cunt at mm a-gap lngth an μm SE lvl Nomalz ampltu ato () Dffnc of ampltu ato of hamonc componnt of th AFR compa wth tho of a olv wthout ccntcty. Ampltu Dffnc of Hamonc Componnt [%] Statc Eccntcty [μm] Fg. 9 Nomalz ampltu ffnc of hamonc componnt n th mol at th gap lngth of mm. n 3 4th 5th 6th 7th 8th 9th Roto Poton [Dg.] Poton Eo [Dg] Mol 3D-FEM Tm [m] Eccntcty Lvl [μm] () Poton Eo [Dg.] FEM Rult (Gap Lngth mm) - Mol (Gap Lngth mm) Fg. 7 Compaon of - mol an 3D-FEM ult on AFR poton o AFR poton o n mm gap lngth an μm SE () AFR poton o n mm gap lngth an ffnt SE lvl. A hown n Fg., wth mm a gap lngth an nca n SE lvl fom μm to μm cau an ca n poton o fom -.87 to.5 Acg. But, at th oto ccntcty mo than 7 μm, th ufac ha a tnncy to man tal. Ao, Fg. () ga that, conng μm tatc ccntcty, th poton o ca whl th a gap lngth chang fom.4mm to mm. Fg. (c) compa th 3D FEM ult wth mau on at mm gap lngth an µm SE. Nxt, th ffct of pol num n th popo AFR poton o ha n tu. In th tuy th a gap lngth an oto ccntcty a mm an μm pctvly. Fg. pct that th AFR poton o ca whl th pol num nca. Th poton o ucton can attut to th ca n ovhang lakag flux of tato wnng u to ucton of ovhang lngth cau y nca n pol num [4]. Thfo, th poton o ca whl th pol num nca. Fnally, th ffct of xctaton voltag hamonc on th poton o of AFR wth μm gap ccntcty an mm a gap lngth pu n Fg.. 5 Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.

11 3 Poton Eo [Dg] A Gap Lngth mm A Gap Lngth mm Poton Eo [Dg] Hamonc Contnt [%] 6 Poton Eo [Dg] Poton Eo [Dg] Statc Ecc. μm 35 ().5.5 A Gap Lngth [mm] FEM Rult (Ecc μm, Gap Lngth mm) Mau (Ecc μm, Gap Lngth mm) Ial Poton [Dg] (c) Fg. Poton o of AFR vu al poton at mm a gap lngth an ffnt tatc ccntcty () at µm tatc ccntcty an ffnt a gap lngth (c) Compang 3D FEM ult wth mau on at μm tatc ccntcty an mm a gap lngth. Fg. Th ffct of xctaton voltag hamonc on th poton o of AFR wth µm tatc ccntcty an mm a gap lngth. In all of th pcng analy t wa aum that th olv xctaton gnal wa an xta pu ynthz nuoal ouc an contan no atonal hamonc. In gnal, th xctaton gnal contan hamonc an thu th AFR output gna a mplf a: V Snθ Vn Co( nt) n Vc Coθ Vcn Co( nt) n (4) Vn Co( nt) n θ Actg( tgθ ) Vcn Co( nt) n A A pnt n E. (4) an Fg., AFR poton o nca whn, t xctng cunt hamonc contnt (pat A n E. (4)) nca. Fo xampl, whn xctng cunt hamonc contnt nca upto 5%, AFR poton o nca vn upto 4.6 Acg. Poton Eo [Dg] Ecc μm 5 A Gap Lngth mm A Gap Lngth [mm] Fg. AFR poton o vu al poton n % gap ccntcty an ffnt pol num AFR n Compaon wth RFR To tmn th capalt of th popo AFR (wthout any optmzaton) Tal 4 compa two axal an aal flux olv wth th am gn pcfcaton. Th compaon how that, th axal flux tuctu mo out than aal flux on, agant tatc ccntcty. Tal 4 mphaz that th capalt of th AFR lat to t a gap lngth. In gap lngth than.5 mm aal flux olv a pc a axal on. But, n typcal gap lngth ( mm) axal tuctu at lat th tm mo accuat than aal on. Ao, ncang th pol num n o to ca th poton o mo ffctv on AFR than RFR. Tootoonchan t al: Novl Axal Flux Buh Rolv Analy an Optmzaton 53

12 Howv, although th axal flux tuctu pfomanc tt than th aal tuctu ut, whn th ccntcty occu, th poton o of AFR nca upto 3.6. In th tuy, th popo axal flux tuctu optmz to mnmz th AFR ntvty agant tatc ccntcty. Tal 4 Fnt lmnt analy of Axal Flux Rolv (AFR) n compaon wth Raal Flux Rolv (RFR). Itm. Valu (unt) RFR AFR Out/Inn amt of tato 7./5. mm 7./5. mm Out/Inn amt of oto 5./. mm 7./5. mm Stato an oto co thckn mm mm Stato/oto num of lot 4/ 4/ A gap lngth mm mm Pow ouc nuoal, V p 5 V, 4 khz nuoal, V p 5 V, 4 khz Wnng mtho lay nuoal tuton on lot lay nuoal tuton on lot Pol Num Hamonc o whch ha not any tnncy to man contant (Fg. 9) Max. Poton Eo n μm Statc Eccntcty an mm gap lngth Max. Poton Eo n μm Statc Eccntcty an.4 mm gap lngth Max. Poton Eo n μm Statc Eccntcty, mm gap lngth an 6 po 3, 4 3, 7, Optmzaton of AFR Stuctu Th accuacy of th oto poton pot y an R/D convt lmt y th ualty of th olv gna poc y th RDC. Accong to ISO49 o ABEC tana an Fg., on of th mot gnfcant ouc of poton o whch mut mnmz though olv gn th o ncu u to th ntnc SE. Although, n axal flux tuctu whn SE occu th a gap lngth o not chang ut th common ffctv on ufac twn oto an tato wll chang (Fg. 3). Th tth hap o common ffctv on ufac twn oto an tato can calculat y olvng th nv lctomagntc fl polm []. Gnally pakng, th poc of olvng uch an nv lctomagntc fl polm wll, ftly, to aum on gomty hap an th coponng tmul tuton n th fl aa, thn to calculat th fl y ung th fnt-lmnt mtho (FEM), thn to optmz th gomty y mployng ctan optmzaton mtho []. 5. Roto Shapng y Solvng th Inv Polm Tooth chmatc of th tato an oto of th tu AFR a hown n Fg. 3. Fgu 3() how, whn tatc ccntcty occu n popo AFR th common ffctv on ufac twn oto an tato wll chang. Thfo, th pmanc, nuctanc an output voltag wll chang pctvly. In th 3D FE analy u to tmn th optmal tooth paamt, t wa foun that no nft wa gan y allowng th tooth lop to tnct. Fo that aon, th tooth lop w t ual to ach oth n all th analy conuct. Colaton twn tm of th AFR, uch a th poton o, th yok lngth, th oto ccntcty an o on, a valuat y man of th multpl gon analy [5]. Th colaton twn th o ffnc an th oto ccntcty not foun n th lna gon analy. Thfo, th non-lna gon analy appl to valuat two npnnt vaa (ccntcty an th yok lngth) whch lat to th poton o. Non-lna analy how that th poton o colat wth th cu of th oto ccntcty an th ua of yok lngth. So, th polm nhntly a multmnonal optmzaton on, an nonlnaty xt. Thfo, tatonal optmzaton mtho uch a ga mtho a not utal fo th polm. On way to u th tal an o mtho, that, to manually v th hap aft ach tal. Ctanly, th wll conum long calculatng tm wth only appoxmat ult ach. Anoth way to aopt gloal optmzaton mtho lk th Gntc Algothm (GA). A typcal GA t n th ca an th ojctv functon fn a low [6]: V Sn ( ε, yot ) ξ ( ε, y ) actan ot θ (4) al VCo ( ε, yot ) wh ξ o functon whch houl mnmz, θ al th al poton of oto, V Sn an V Co a AFR output voltag whch a lat to ccntcty (ε) an oto yok lngth (y ot ). Th al poton (θ al ) can calculat y hom t of oto poton ( θ ) (agant oto tato poton), pol num (p) an oto p (f, voluton p con) that : π.f θal θ oto.t p (43) Accong to E. (4, 43), th followng valu of gntc opato w u n th algothm. ) Intal populaton: N 3 ) Poalty of poucton: p.5 3) Poalty of mutaton: pm.5 4) Poalty of coov: pc.5 Aft a ctan num of uccon, om ult w otan. On tooth of calculat oto hap hown n Fg. 3(c). Th fgu how n optmz oto hap (Fg. 3(c)) oto yok lngth uc. 54 Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.

13 It can conclu that, th latt ca (optmz oto hap) wll al to mnmz th Vaaton of th common ffctv on ufac twn oto an tato. Bcau, n mof tuctu th on ufac of tato gg than that of oto (Fg. 3(c)). So, f th tatc ccntcty occu (Fg. 3()), t xpct that, th vaaton of th pmanc, nuctanc an output voltag th mnmz o vn lmnat. Optmz oto wa ma an ha n hown n Fg. 4. Th man gn paamt of th optmz AFR a hown n Tal 5. Statc Eccntcty Stato Tth Whn Statc Eccntcty Occu Popo Stato Popo Roto Optmz Roto () Fg. 4 Optmz AFR 3D-FEM chmatc () Manufactu. AFR wth Statc Eccntcty () Statc Eccntcty Optmz AFR wth Statc Eccntcty (a ) Roto Tth Stato Tth Whn Statc Eccntcty Occu Roto Tth AFR wthout Statc Eccntcty a Optmz AFR wthout Statc Eccntcty (a) () (c) Fg. 3 Tooth gomty wth an wthout tatc ccntcty (a,) Popo tuctu (c,) Optmz topology. Tal 5 Gomtcal mnon of optmz AFR. Itm. Valu (unt) Out/Inn Damt of Stato 7./5. mm Out/Inn Damt of Roto 68./56. mm Stato/Roto Co thckn /6 mm num of tato/oto lot 4/ A gap lngth mm 5. Th Effct of Eccntcty on Optmz AFR In o to valuat optmz oto of AFR t wa ma an plac wth ntal oto. Fg. 5 how th ttng ult of th AFR wth optmz oto nclung th ocllocop gaph, nomalz output gna, an angula poton n ccntc optmz AFR compa wth tho of an AFR wthout tatc ccntcty. Fo accuat compaon, th output poton gna of ymmtc an ccntc optmz AFR a hown n Fg. 5(c). In th fgu AFR tct poton calculat conng actangnt of output gna ato. On th a, Fg. 5(c) ga that th oto ccntcty of μm cau maxmum.8 Acg o n tct angula poton. In compaon wth ntal (non-optmz) AFR th poton o ca 7.4%. Although, th poton o uc utantally agant SE ut.8 Acg poton o a gnfcant o n compaon wth ntal AFR wthout ccntcty wth maxmum. Acg poton o. It m that th ovhang lakag flux may ult th o. Bcau, whn oto plac y man of a mchancal foc th ovhang lakag flux affct on of tato mo than oth. Thfo, th 3D FE analy pat wth cunt ht nt of wnng. In th ca, a hown n Fg. 6 th poton o of optmz AFR ca to.6 Acg. Although, placng cunt ht nta of oto wnng not pactcal. But, t uggt that to uc th ffct of th ovhang lakag flux, t tt to nca aal lngth of oto co. Whn, aal lngth of oto co nca a % of out amt of optmz oto th maxmum poton o of optmz AFR ca to.8 Acg (Fg. 7). Tootoonchan t al: Novl Axal Flux Buh Rolv Analy an Optmzaton 55

14 3.5 Poton Eo [Dg].5.5 Output Sgna [pu] Roto Poton [Dg] Sn Con Ampltu Dffnc Tm [Sc] x () Concntc AFR AFR wth Statc Eccntcty Tm [Sc] x (c) Fg. 5 Ttng ult of AFR wth optmz oto. Ocllocop gaph mau (Ch: Exctng Voltag; Ch, 3: Output gna). () Nomalz output gna of ccntc AFR vu tm wth 4 Hz xctaton. (c) Compaon of angula poton n ccntc an ymmtc optmz AFR. Roto Poton [Dg] 5-5 Concntc AFR AFR wth Statc Eccntcty Tm [Sc] x Fg. 6 Compaon of angula poton n ccntc an ymmtc optmz AFR wth cunt ht plac wth oto wnng Tm [Sc] x Poton Eo [Dg] Poton Eo [Dg] 3D FEM Mau Fg. 7 Compaon of optmz AFR poton o wth cunt ht (n 3D-FE analy) an nca aal lngth of oto co (n pactcal tt) Statc Ecc. μm 6 Fg. 8 Ttng ult of AFR wth optmz oto. 6 Incang th Accuacy of Popo Stuctu A cu aov, ovhang lakag flux wa th man facto n whch, AFR ntvty agant SE wa affct. So, th followng mtho a popo to mpov th ntvty of th AFR. Dtal analy an xpmnt wll pnt n an upcomng pap. Howv, y ung tm tppng 3D FE analy wth ual tooth lop, th yok wth whch mnmz th maxmum AFR o a hown n Fg. fo th a gap lngth g.5,.,.5 an mm. Th nfomaton n Fg. 6-8 llutat val ky fatu to mpov th ntvty of th AFR agant SE. Thy a: Mnmzng th AFR ntvty agant SE popotonal to aal lngth of oto co;.. long aal lngth of oto co la to mall SE ntvty, () Incang pol um ca ovhang lngth of co, ovhang lakag flux an thn SE ntvty (c) th optmum yok wth fo a patcula a gap lngth a not ual. Thfo, tatonal optmzaton mtho uch a ga mtho a not utal fo th polm, () AFR poton o cau y SE nvly popotonal to a gap lngth, thfo th lag th a gap lngth th mall th AFR o (cau y SE), an () Th optmum yok wth vay latvly lttl wth a gap lngth vaaton. 7 Concluon In th wok th gn an optmzaton of a novl axal flux olv (AFR) tuctu whch can out agant tatc ccntcty (SE) ha n con. Bac olv opaton wa vw an tatc ccntcty ntf a a ctcal olv (o olv mount haft) ang chaacttc whch tmn olv nhnt poton o. Ung - mol, tm tppng 3D-FEM an pactcal tt how that wth am gn paamt (uch a a gap lngth, tato an oto lot num, ) an SE lvl, AFR a.79 tm auat than convntonal aal flux olv. Howv, whn SE occu, AFR' Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.

15 poton o nca too an n to ca futh. Although, uch a pcon uffcnt fo mot moto commutaton applcaton, ut AFR tuctu optmz fo pc applcaton wth gntc algothm (GA) y olvng th nv lctomagntc fl polm ung a tm tppng 3D FEM appoach. Optmzaton poc tmn th oto yok paamt whch mnmz th AFR ntvty agant SE. In aton, t can conclu that th poton o of optmz oto manly com fom th ovhang lakag flux. To uc th ffct of th flux, t uggt that th aal lngth of oto wnng houl nca aout %. Fnally, val mpovmnt mtho a popo, nclung ncang th num of tato po, cang oto yok lngth (changng to th optmal on), ncang th a gap lngth, an aoptng a nuoal tut wnng pattn. Futh ult wll pnt n an upcomng pap. Rfnc [] Sun L., "Analy an Impovmnt on th Stuctu of Vaal Rluctanc Rolv", IEEE Tan. Magn., Vol. 44, No. 8, pp. - 8, Aug. 8. [] Khau D. A., Tootoonchan F. an Na- Gha Z., Paamt Intfcaton of a Buh Rolv Ung Chag Rpon of Stato Cunt, Ianan Jounal of Elctcal & Elctonc Engnng, pp. 4-5, Jan. 7. [3] Sun L. an Lu Y., "Roto-Poton Snng Sytm Ba on On Typ of Vaal- Rluctanc Rolv", 3 n Annual IEEE Inutal Elctonc (IECON6) Conf. Poc., pp. 6-65, Pa, Fanc, 6. [4] Gnal Katalog of Tamagawa Company, "Sngyn (Supo Flat Aolut Angl Sno)", 579n3.pf, cv at 389//5. [5] Gnal Katalog of Tamagawa Company, "Smatyn-8", cv at //5. [6] Tchncal not fom Enco Tchnology LTD, "Smatyn FA-Solv", cv at //. [7] Tchncal not fom Enco Tchnology LTD, "Intucton Book fo Rolv (Smatyn an Sgnayn)", cv at 389//5. [8] L X., Wu Q., an Nan S., Pfomanc Analy of a Th-Pha Inucton Machn wth Incln Statc Eccntcty, IEEE Tanacton on Inuty Applcaton, Vol. 43, No., pp , Mach/Apl 7. [9] Maak K., Ktazawa K., Mmua H., N M., Tuchmch K., Wakwaka H. an Yamaa H., Magntc Fl Analy of A Rolv wth A Skw an Eccntc Roto, Ev Tan. Sno an Actuato, pp. 97-3,. [] Buk D. M. an Jack A. G., "Magntc Flux Dtuton n th En Rgon of Hgh Pcon Sla Rolv an Syncho", 5 th Intnatonal Elctcal Machn an Dv Conf. Poc., pp , Lonon, UK, 99. [] Na M., Yamamotoa Y., Ktazawa K., Kkuch Y., Kamyac A. an Wakwakac H., "Angula Eo Analy of An 8X-VR Rolv wth An Eccntc Roto", Jounal of Magntm an Magntc Mata, Vol. 4-45, No., pp. 5, Apl. [] Cv M., Juf M., Wy W. an Fav E., "Vaal Rluctanc Rolv Moaton an Angula Poton Eo Dtcton", 9th Annual Sympoum on Incmntal Moton Contol Sytm an Dvc (IMCSD) Poc., pp , Bkly, Canaa, July. [3] Km K., Hwang S., Sung K. an Km Y., "A tuy on th fault agno analy of vaal luctanc olv fo lctc vhcl", 9 th IEEE Sno Conf. Poc., pp. 9-95, Kona HI, USA, -4 Nov.. [4] Khau D. A., Tootoonchan F. an Na- Gha Z., Dynamc Pfomanc Pcton of Buh Rolv, Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 4, No. 3, pp. 94-3, July 8. [5] Hanlman D. C., Thoau R. E. an Smth D. J., "Vaal-Rluctanc Rolv Dgn Guln", IECON, IEEE Inutal Elctonc (IECON'89) Conf. Poc., pp. 3-8, Nw Yok, USA, 989. [6] Vaga J. S., Magntc an Dmnonal Popt of Axal Inucton Moto, IEEE Tanacton on Engy Convon, Vol. EC-, No., pp , Jun [7] Kuzla S. an Wglnk B., Magntolctc n Inucton Moto wth Dk Roto, IEEE Tan. on Magn., Vol. 4, No., pp , Jan [8] Chan C. C., Axal-Fl Elctcal Machn Dgn an Applcaton, IEEE Tan. on Engy Convon, Vol. EC-, No., pp. 94-3, Jun [9] Zhang C., Tng K. J. an Nguyn T. D., Analy an Compaon of Axal Flux PM Synchonou Moto an Inucton Moto, 9th IEEE Intnatonal Pow & Engy Conf. (IPEC ), pp , Suntc, Sngapo, 7-9 Oct., Vol.. [] Kau P. C., Analy of Elctcal Machny, McGaw-Hll n lctcal ngnng, Pow & ngy, 986. [] Ong C. M., Dynamc Smulaton of Elctc Machny Ung Matla/Smulnk, Pntc Hall PTR. Upp Sal Rv, Nw Jy, 998. Tootoonchan t al: Novl Axal Flux Buh Rolv Analy an Optmzaton 57

16 [] Zhao Z., Lu F., Chng Z., Yan W., Lu L., Zhang J. an Fan Y., "Maumnt an Calculaton of Co- Ba B-H Cuv an Magntzng Cunt n DC-Ba Tanfom", IEEE Tan. on Appl Supconuctvty, Vol., No. 3, pp. 3-34, Jun.. [3] Analog Dvc Company, RDC Dataht, pnt at cv at Nov.. [4] Pyh onn J., Joknn T., Haovcov a V. an Nml a H., "Dgn of Rotatng Elctcal Machn", John Wly an Son Lt., ISBN: (H/B), 8. [5] N M., Yamanoto Y., Kohayah K. an Mauyama T., "Tou Fom Dgn of La Scannng Actuato Ba on Stattcal Mtho", IEEE Tan. on Magn., Vol. 33, No. 5, Spt [6] Sun L., Zhang G., an Png L. Y., "Applcaton of gntc algothm to gn moto pol hap", J. Han Int. Tchnol., No., pp. 7-74,. Fa Tootoonchan ha cv h B.Sc. an M.Sc. g n Elctcal Engnng fom th Ian Unvty of Scnc an Tchnology, Than, Ian n & 7 pctvly. H ha tat h PhD pogam nc 8 at K.N. Unvty of Tchnology, Than, Ian. H ha on ov 8 nutal pojct nclung on natonal pojct, hl 5 patnt an puh mo than 5 jounal an 3 confnc pap aout lctcal machn an no ov th ya. H ach ntt gn of mall lctomagntc machn an no. Kam Aazah cv th B.S. g n Communcaton Engnng fom K.N. Too Unvty of Tchnology, Than, Ian, n 994, an th M.S. an Ph.D. g n Elctcal Engnng fom Am Ka Unvty of Tchnology, Than, Ian, n 997 an, pctvly. H jon fom to 3, a a vtng chola at Txa A&M Unvty, Collg Staton. In July 3, h jon th Dpatmnt of Elctcal Engnng, K.N.Too Unvty of Tchnology, Than, Ian. H man ach ntt an xpnc nclu fault agno of lctc machny, analy an gn of lctcal machn, an no vaal-p v, multpha vaap v fo tacton an popuon applcaton. H ha autho ov 9 puh tchncal pap n th f. H actvly nvolv n pntng hot cou an conultng n h aa of xpt to vaou nut. Mohamma Al cv M.Sc. g fom th Unvty of Taz n 976 an h Ph.D. g fom th Unvty of Wa (Caff) n th U.K. n 99. H ach fl analy an gn of lctcal machn an magntc mata. H now Aocat Pofo at th lctcal patmnt of K.N.Too Unvty, Than, Ian. 58 Ianan Jounal of Elctcal & Elctonc Engnng, Vol. 8, No. 3, Sp.