[2009] IEEE. Reprinted, with permission, from Xu, Wei; Zhu, Jianguo; Tan, Longcheng; Guo, Youguang; Wang, Shuhong; Wang, Yi. 2009, 'Optimal Design of

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1 [9] IEEE. Rpintd, with pmission, fom Xu, Wi; Zhu, Jinguo; Tn, Longchng; Guo, Yougung; Wng, Shuhong; Wng, Yi. 9, Dsign of Lin Induction Moto Applid in Tnspottion, Pocdings of Intntionl onfnc on Industil Tchnology, pp This mtil is postd h with pmission of th IEEE. Such pmission of th IEEE dos not in ny wy imply IEEE ndosmnt of ny of th Univsity of Tchnology, Sydnys poducts o svics. Intnl o psonl us of this mtil is pmittd. Howv, pmission to pint/publish this mtil fo dvtising o pomotionl puposs o fo cting nw collctiv woks fo sl o distibution must b obtind fom th IEEE by witing to pubs-pmissions@i.og. By choosing to viw this documnt, you g to ll povisions of th copyight lws potcting it.

2 Dsign of Lin Induction Moto Applid in Tnspottion Wi Xu, Jinguo Zhu, Longchng Tn, Yougung Guo, Shuhong Wng,3, nd Yi Wng (. School of Elcticl, Mchnicl nd Mchtonic Systms, Univsity of Tchnology, Sydny, NSW 7, Austli. Institut of Elcticl Engining, hins Acdmy of Scincs, Bijing 9, hin 3. Fculty of Elcticl Engining, Xin Jiotong Univsity, Xin 749, hin) E-mil: Abstct- Svl optiml dsign schms of singl-sidd lin induction moto (SLIM) doptd in lin mto psntd in this pp. Fistly, th quivlnt cicuit of SLIM fully considing th nd ffcts, hlf-filld slots, bck-ion stution nd skin ffct is poposd, bsd on on-dimnsionl i-gp mgntic qutions. In th cicuit, svl cofficints including longitudinl nd ffct cofficints K (s) nd K x (s), tnsvsl nd dg ffct cofficints (s) nd x (s), nd skin ffct cofficint K f chivd by using th dummy lctic potntil mthod nd complx pow quivlnc btwn pimy nd scondy sids. Futhmo, svl optiml dsign stint qutions of SLIM povidd in od to impov th optionl fficincy nd duc th pimy wight. Ths nonlin qutions solvd by using gntic lgoithm nd mixtu pnlty function mthod. Th optiml schms compd with th oiginl dsign of on compny, wh nlysis on pmts is md in dtil. Ths sults show tht th optiml schms sonbl fo impoving th pfomnc of SLIM. I.INTRODUTION In th cnt ys, th singl-sidd lin induction moto (SLIM) hs bn widly doptd in tnspottion systms, spcilly in intmdit spd ng. Typicl xmpls includ th HSST in Jpn nd th lin mto in nd, wh pow systms both poplld by th SLIMs [-3]. Th SLIM hs th following mits comping with th oty induction moto (RIM): gt bility to xt thust on th scondy without mchnicl contcts, high ccltion o dcltion, lss w of th whls, smll tun cicl dius, nd mo flxibl od lin. Bcus of its cut-opn mgntic cicuit, th lin induction moto (LIM) posssss th inhnt chctistics such s longitudinl nd-ffct, tnsvsl dg-ffct nd noml foc. In ddition, it lso hs hlf-filld slots in th pimy nds. Thfo, n ccut quivlnt cicuit modl of LIM is difficult to b obtind compd to tht of RIM [4]. Mny nlysis tchniqus of SLIM hv bn studid nd dvlopd in th pst ys. Howv, ffctiv mthods on th dsign schm of SLIM hv not bn obtind du to th following sons. Th slction of lctic loding nd mgntic loding by loding distibution is so difficult tht on cnnot clcult th ppnt pow (kva) sily. Th pow fcto nd fficincy ffctd by th nd ffct which is gin ffctd by th dsign tchniqu of SLIM. Th pol pitch cn b vid stuctully nd th slction of fquncy nd td slip is not sy with th dcision on th td vlocity [5]. A nw impovd modl is st out in this pp bsd on th i-gp flux dnsity qution, which fully tks into ccount th nd ffcts, hlf-filld slots, bck-ion stution nd skin ffct. Thn, optiml dsign qutions fo chiving th mximum fficincy nd minimum pimy wight built, which nonlinly constind. It is ncssy to choos suitbl solving mthod to obtin th indpndnt vibls, such s th td slip, numb of pols, pol pitch, stck hight, tio of slot width to slot pitch, scondy luminum (copp?) thicknss, tooth mgntic dnsity, nd scondy ovhng [4-7]. II. PHYSIAL STRUTURE AND MATHEMATIAL ANALYTI MODEL Th stuctu of n SLIM nd its quivlnt cicuit shown sptly in Fig. nd Fig.. In th nlytic cicuit, K f is th skin ffct coction cofficint, K (s) nd K x (s) th longitudinl nd-ffct cofficints, nd (s) nd x (s) th tnsvsl nd-ffct cofficints [8]. Ths coction cofficints xpssd blow. Th skin ffct coction cofficint is K f + B sh ( Kδ ) = A [ B sh ( Kd)] + wh K is th function of slip nd moto stuctu, d is th thicknss of scondy mtl sht, δ is th quivlnt mgntic i gp lngth, nd A nd B cofficints which ffctd by slip nd moto stuctu. δ cn b xpssd s δ = KKg c u wh K c is th t cofficint nd K u is th mgntic stution cofficint. pimy co y z x xit sid hlf filld slots scondy sht bck ion vlocity v nty sid () ()

3 U () Longitudinl sid viw (b) Tnsvsl sid viw Fig.. Simpl constuction digm of LIM I jx jx E x( ) x( ) m b jk I m s K K ( s) ( s) I f / s x do bck Fig.. T-typ quivlnt cicuit of LIM considing th bck ion sistnc A nd B divd s K ρ sh( Kδ ) A = ch K + (3) scond ( δ ) [ ] Sωµ d Sωµ d Kρscond B = [ + ] Kρ Sωµ d scond wh S is th slip, ω is th pimy lcticl ngul vlocity, ρ scond is th sistivity of scondy lcticl sht, nd μ is th pmbility of i. Th longitudinl nd-ffct cofficints K (s) nd K x (s) dnotd by SG K () s = Pτ + ( SG) Kx () s = Pτ + ( SG) + + wh nd th functions of slip S nd goodnss fcto G, P is th numb of quivlnt pol pis, nd τ is th pol pitch. Th tnsvsl nd-ffct cofficints (s) nd x (s) givn by () s () s x SG T + T R[ T ] [R [ ] I m[ ]] s (4) (5) (6) = (7) R [ T] + I m[ T] = (8) I [ T ] m wh T is th function of slip, goodnss fcto nd moto stuctu, nd R nd I m th l pt nd img pt of complx T, spctivly. T is xpssd by λ T = j γ + γ th α α [ ( ) ( )] wh is hlf th pimy lmintion width, α is th tio of c to τ, nd c is hlf th width of th scondy sht ovhng. γ nd λ cn b obtind by λ = + th( α ) th[ K( c )] γ (9) () γ = + jsg () Th fiv pmts in th T-cicuit: pimy sistnc, pimy lkg ctnc x, scondy sistnc, scondy lkg ctnc x nd xciting ctnc x m, divd blow. Th pimy sistnc is = ρ l W / S u v cu () wh ρ u is th sistivity of copp, l v is hlf th vg lngth of th pimy winding loop, W is th numb of tuns of th pimy winding in sis, nd S cu is th coss sctionl of th pimy winding conducto. Th pimy lkg ctnc X is.58 ( λ λ + λ + λ ) s t d X = fw + q P P (3) wh f is th pimy fquncy, is th width of pimy lmintion, P is th numb of ctul pol pis, λ s is th pimy slot lkg mgntic conductnc, λ t is pimy tth lkg mgntic conductnc, λ is pimy winding nd lkg mgntic conductnc, λ d is pimy hmonic lkg mgntic conductnc. Th scondy sistnc is composd of thos of conducting sht nd bck ion bcus th flux cn pntt though th luminum o copp sht [8], nd thn nt th bck ion. Th dpth of flux dnsity into bck ion, d F, is d = F ρ F ωµ F (4) wh ρ F is bck ion sistivity, μ F is th pmbility of bck ion. Th sistnc of scondy conducting sht sht is

4 = 4mρ sht scond ( WK ) P W dτ (5) wh m is th numb of pimy winding phss, ρ scond is th sistivity of th scondy lctic sht, nd K w is pimy winding cofficint. Th sistnc of scondy bck ion F is = 4mρ F F ( WK ) P W d τ Thfo, th scondy quivlnt sistnc is = + sht F sht F Th scondy lkg ctnc is X K B sh Kd S f ( ) F (6) (7) = (8) Th xciting ction is Vs Xm = 4 mµ ( WK ) P W πδ (9) wh V s is th synchonous vlocity of pimy sid. Th chctistics of SLIM fully considd in th bov cicuit. Whn K (s)=k x (s)= (s)= x (s)=, th cicuit cn b simplifid s th sm s tht of RIM. Thfo, it is vy convnint to nlyz th pfomnc of SLIM in th simil wy s tht of RIM bsd on th cicuit [9]. III. OPTIMAL DESIGN EQUATIONS OF SLIM As n xmpl, this pp dos optiml dsign on n SLIM, which ws poducd by compny nd doptd in lin mto but dos not mt th nticipnt quimnt. Accoding to thi dmnd, futh optimiztion on oiginl dimnsions hs bn md. Th fficincy nd pimy wight gdd s objctiv functions und th givn thust s follows. p min... f ( x) = h = m = + + p in... f( x) Gtth Gyok Gwinding () wh p is th input ctiv pow, p is th output ctiv pow, G tth is th pimy tth wight, G yok is th pimy yok wight, nd G winding is th pimy winding wight. Th following pmts slctd s th constint vibls, including fficincy (h ), pow fcto ( cosϕ ), poduct of pow fcto nd fficincy ( hcosϕ ), flux dnsity in pimy tooth ( B ), pimy lngth (L), pimy t wight (W p ), thust (F ), vticl foc (F n ), pimy phs voltg (U), pimy phs cunt (I), nd pimy conducto cunt dnsity (J) []. Th oth pmts tkn s dsign vibls, such s slip (s), stck hight ( l δ ), slot dpth (h t ), slot width (b s ), pimy hight (h ), pol pitch (τ ), shot pitch fcto ( β ), nd numb of tuns p phs in sis (N s ) []. Th pmts involving subscipt oiginl ons, nd th mining th optiml sults. Th constint conditions givn by g ( x) = ( h h)/ h () g ( x) = (cosϕ cos ϕ) / cosϕ () g ( x) = ( h cosϕ hcos ϕ) / hcosϕ (3) 3 g ( x) = ( B B )/ B (4) 4 t t t g ( x) = ( L L )/ L (5) 5 g ( x) = ( W W )/ W (6) 6 p p p g ( x) = ( F F )/ F (7) 7 g ( x) = ( F F )/ F (8) 8 n n n g ( x) = ( U U )/ U (9) 9 g ( x) = ( I I )/ I (3) g ( x) = ( J J )/ J (3) Th bov qutions ()-(3) nonlin functions influncd by mny vibls, such s stuctul pmts nd lcticl vibls. Thy solvd by both gntic lgoithm (GA) nd mixtu pnlty function mthod. Th GA cn convt th nonlin constint functions into lin sub-poblms so s to find sonbl ng of finl sults vy quickly. Th mixtu pnlty function cn kp th solutions bck to tionl scop by ctifiction whn thy out of th constint xtnt []. Duing th optimiztion pocss, th td vlocity is st s 36 km/h. Schms Itms Stck hight Pimy lngth Pimy dpth IV. OPTIMAL RESULTS Oiginl TABLE I MAIN DIMENSIONS OF SLIM Slot width Tooth width Slot dpth Pol pitch No. of slots

5 Mchnicl clnc No. of slots/pol/phs Shot pitch fcto 8/ 7/9 7/9 7/9 8/9 onducto (mm ) Numb of pols Scondy sht thicknss Scondy sht width Bck-ion thicknss Bs vlocity (Km) Slip fquncy Pimy wight (?) Thust (kn) Efficincy Pow fcto Fig. 4. uvs of fficincy vsus vlocity Th min dsign pmts of SLIM listd in Tbl I. Fou tionl optiml schms gind, which compd with th oiginl on. Th thust cuv is shown in Fig. 3. Th fficincy, pow fcto, nd poduct of pow fcto nd fficincy illusttd in Figs. 4-6, spctivly. Fig. 5. uvs of pow fcto vsus vlocity In Fig. 3, th thust is dcidd by woking quimnt, which cn ovcom th wind nd fiction sistncs, t th sm tim lso poduc dfinit ccltion. Blow th bs vlocity, th thust is kpt lmost constnt though th phs cunt incss. Howv, byond th bs spd, th phs voltg chs its t vlu but th totl ctnc continus to incs, so th phs cunt gdully dcss s wll s th thust. Fig.3. uv of thust vsus vlocity

6 Fig. 6. uvs of poduct of pow fcto nd fficincy vsus vlocity Fom Fig. 4 to Fig. 6, w cn find clly th tnd of fficincy, pow fcto nd poduct of pow fcto nd fficincy. Aft optiml dsign, th fficincy of nw schms hs bn impovd in th whol optionl ng compd with th oiginl schm. Howv, th pow fcto in Fig. 5 ncounts ctin duction in th optiml schms. In od to ttin high fficincy, th slot width, slot dpth nd pol pitch chngd gtly s indictd in Tbl I. Finlly, th tio of totl sistnc to ctnc bcoms smll, which ducs th pow fcto. In Fig. 6, stictions md to th poduct of pow fcto nd fficincy in th nw schms so s to nsu tht th optiml sults not wos thn th oiginl on. In th lin div tnspottion systm, th invt is plcd on th vhicl. Und th sm output pow, th poduct of pow fcto nd fficincy dcids th convt ting pow. Tht is to sy, it will ffct th wight of convt. Hnc, it is significnt to impov th fficincy whil not dcsing th poduct of pow fcto fficincy. In this wy, it cn nsu th mximum nt lod [8, ]. Among th fou nw dsigns, th thid is th bst ccoding to us dmnd. Aftwds, w mk nw moto dsign bsd on th stuctul pmts in Tbl I. Th pfomnc cuvs shown in Fig. 7. Vibls () (3) () (4) ()Thust F(KN)(:) ()Efficincy h(:) (3)Pow fcto cosf(:) (4)Efficincy&Pow fcto hcosf(:) Vlocity v (Km/h) () Fist goup pfomnc cuvs Vibls (3) (4) () (5) (6) () ()Slip fquncy Sf(Hz)(:) ()Input phs voltg U(v)(:) (3)Input phs cunt I(A)(:) (4)Input cpcity Sin(KVA)(:) (5)Input ctiv pow Pin(Kw)(:) (6)Output ctiv pow Pout(Kw)(:) Vlocity v (Km/h) Fig. 7. () Scond goup pfomnc cuvs dsign pfomnc cuvs In th moto dsign schm, th two gions: constnt cunt nd constnt pow. Blow th bs spd of 36 km/h, th pimy phs cunt is kpt constnt (57 A), nd th slip fquncy is lso constnt (6 Hz). Du to pow condition voltg limit, th constnt voltg option (with phs voltg of 36 V) is pplid bov bs spd []. Th phs cunt dcss vy quickly whn th sistnc incss. In od to mt th opting quimnt, it is ncssy to incs th slip fquncy linly fo voiding quick duction of thust. Th mximum slip fquncy is.5 Hz t 5 km/h. V. ONLUSIONS In this pp, mximum fficincy optiml dsign of SLIM fo subwy is pfomd. By th optiml schms, svl positiv conclusions cn b dwn blow. Fistly, whn th numb of pols is lg nd th pol nd slip smll, th fficincy will b impovd. Scondly, th fficincy is contdictoy to pow fcto. It is ncssy to limit th poduct of pow fcto nd fficincy so s not to incs th invt wight und th sm output pow. Th sults indict tht th quivlnt cicuit nd optiml mthods tionl. VI. AKNOWLEDGEMENT Th uthos gtful to A/Pof. Yumi Du in th Institut of Elcticl Engining, hins Acdmy of Scincs, nd Pof. Zhngming Zho in th Fculty of Elcticl Engining, Tsinghu Univsity, Bijing, hin, fo thi hlpful suggstions on th optiml schms. REFERENES [] Wi Xu, Yohu Li nd Gungshng Sun, Singl-sidd lin induction moto quivlnt cicuit modl, Th Sixth Intntionl Symposium on Lin Divs fo Industil Applictions(LIDIA), Lill, Fnc, Spt.7.

7 [] Wi Xu, Gungshn Sun nd Yohu Li, Rsch on tctiv chctistics of th singl lin induction moto, IEEE onfnc on Industy Tchnology (IIT), Mumbi, Indi, Dc.6, pp [3] Km Idi, Liuchn hng nd Hping Di, Eo-bsd globl optimiztion ppoch fo lctic moto dsign, IEEE Tnsctions on Mgntics, Vol.34, No.5, pp , Sptmb 998. [4] Wi Xu, Gungshn Sun nd Yohu Li, A nw nlys mthod fo pfomnc of lin induction moto, Th Fouth Pow onvsion onfnc (P), Nogoy, Jpn, Ap. 7, pp [5] Tsuyoshi Higuchi nd Skuto Nonk, On th dsign of high fficincy lin induction motos fo lin mto, Elcticl Engining in Jpn,Vol.37, No., pp , August. [6] Sng-Bck Yoon, Jin Hu nd Dong-Sok Hyun, A mthod of optiml dsign of singl-sidd lin induction moto fo tnsit, IEEE Tnsctions on Mgntics, Vol. 33, No. 5, pp , Sptmb 997. [7] Wi Xu, Yohu Li nd Jinqi Rn, Pfomnc study fo lin induction moto conncting winding function mthod with contol schm, IEEE Intntionl onfnc on Industil Tchnology (IIT), hngdu, hin, Ap. 8, pp [8] Xiling Long, Thoy nd mgntic dsign mthod of lin induction moto (in hins), hin: Scinc Publishing ompny, 6, pp. 4-. [9] Wi Xu, Gungshng Sun nd Yohu Li, Rsch on pfomnc chctistics of lin induction moto, IEEE onfnc on Industil Elctonics nd Applictions (IIEA), Hbin, hin, My 7, pp [] Skuto Nonk nd Tsuyoshi Higuchi, Dsign of singl-sidd lin induction motos fo ubn tnsit, IEEE Tnsctions on Vhicul Tchnology, Vol. 37, No. 3, pp , August 988. [] Wi Xu, Yohu Li, Gungshng Sun, nd Jinqi Rn, Pfomnc study on high pow lin induction moto in tnspottion, Intntionl onfnc on Elcticl Mchins nd Systms (IEMS), Soul, Ko, Oct.7, pp.5-7.