Dynamic Demagnetization Computation of Permanent Magnet Motors Using Finite Element Method with Normal Magnetization Curves

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1 Y 中国用户大会优秀论文 Dynamc Dmagnzaon Compaon of Prmann agn oors Usng Fn Elmn ho h ormal agnzaon Crs W.. F an. L. o bsrac m-sppng fn lmn mho (FE) o smla h ransn opraons of prmann magn (P) moors s prsn. I ss only h normal magnzaon crs o arss h ffcs of rrrsbl magnzaon of P marals. n ffc algorhm o mplmn h mhoology h nonlnar raon s prsn. formlaon of on-hson mho sng h r Jacoban marx hch s plcabl o any yp of lmns an any orr of lmns h ansoropy marals s r. marx mho s nroc o xprss spac cors an h FE formlaon can b connnly c. Inx rms Dmagnzaon, lcrc moor, fn lmn mho, magnc fl, nonlnar, prmann magn. P I. IODUCIO EE GE (P) moors ha many osanng aanags nclng smpl mchancal srcr, hgh ffcncy an hgh por nsy hn compar o many nsral rs. P marals ar sally mprar sns an hy can b asly magnz hn opra os hr sgn lms []. m-sppng fn lmn mho (FE), copl h lcrc crcs an mchancal balanc qaon, has many saln mrs sch as flxbly o mol complx gomrs, sanarz programmng chnqs, hgh accracy an allong h nclson of hgh-orr harmoncs. nc hy ar ly s o smla h ynamc opraon of lcrc moors []. In P moors, f h magnzaon cr (- cr) of P marals s nonlnar, h raonal mho s o mo h - cr from h scon qaran o h frs qaran. h corc forc c s an as h xcaon n h fl qaon. or, f h P s magnz, h magnc flx nsy ll no ncras along h orgnal - cr; ll ncras along h rcol cr. om rsarchrs s lnar mols for h P marals [-4]. h rmannc of h lmn n h rgh-han s of h qaon s rs afr h nonlnar raon an rcalclaon of ha m sp s sally rqr. In hs pr a FE o arss h rrrsbl magnzaon procss of P s prsn. Unl many hysrss mols, sch as Prsach mol, no complca aa of h marals, ohr han h normal - crs of h P marals, ar s. In h propos mho, hch s s o sma h possbl magnzaon n P moor as an llsraon, h sas of h oprang pon a ach lmn s rcor an h nonlnar raon s rcly conroll by h r Jacoban marx. oll bac compaon s no rqr an hnc h conrgnc sp s fas. marx mho s nroc o xprss h spac cors an h FE nonlnar formlaon can b asly c []. II. ODEL OF P EIL h mol of P marals s bas on s sngl-al - cr. o aonal aa ar rqr. h har axs s assm o b lnar. h nonlnar - bhaor s scrb along h asy axs. I s assm ha h nal oprang pon of h P s a an r ( r s h rmnan flx nsy). Whn rcs, h oprang pon ll mo along h - cr. Whn ncrass, h oprang pon ll mo along h rcol cr. h rcol cr s n paralll h h angnal ln o h - cr a an r (s Fg. ). Fg.. - cr of prmann magn an s oprang pon.

2 Y 中国用户大会优秀论文 Fg.. Whn h oprang pon mos blo h axs. Whn h oprang pon mos blo h axs ( < ), h orgnal - cr s xn so ha h smlaon can conn (Fg. ). or a arnng ll b gn o h sr bcas h - cr n h scon qaran, as spcf by mos commrcal manfacrrs, s no nogh o xprss h proprs of P flly. hro sch saon s no allo n praccal plcaons an srs ha o rs hr sgns. III. IPLEEIO I IE-EPPIG FE. asc FE Formlaon In orr o c h FE formlaon, n hs pr, a spac cor s xprss n a marx. For xampl, h magnc flx nsy s xprss n marx form as: x ˆ ˆ y x () y h basc fl qaon n h rgons of ar, ron cors, sol concors an Ps s: σ l hr, s h magnc cor ponal, s h rlcy of maral an σ s s concy, l s h ph of h mol n h z-rcon, V b s h olag of h concor. y plyng h Galrn mho an sng h sh fncon as h ghng fncon, ( ) ( ) σ V b ˆ J () c σ σ V ˆ b l J ( ) () c hr s a cor. In o-mnsonal (-D) FE, spposng h solon oman s on h x-y plan, an only ha h componns n h z rcon, ˆ (4) ˆ () h scalar arabls an ar h componns n h z rcon, rspcly. 6 ( x, y) [ 4 6] y [ ] (6) 4 6 x 4 6 (7) y y y y y y x x x x x x 6 In h abo o qaons, [ ] (8) 4 6 s h s als on ach no as an xampl. r scon orr 6-no lmn s s. For h xy solr: y (9) x y z y x z x In h Galrn mho, h ghng fncon s: W [ ] () 4 6 an ( ) ( ) ( ) ( ) y y x () y x x hr s a cor n h z rcon.. onlnar Iraon Formlaon P s characrz for s o snc rcons, h asy axs an h har axs, an h magnc ansoropy nonlnar raon formlaon ns o b r. o h FE problm, h algbrac qaon oban afr scrzaon s [6] [ ]{ } { P} () Is nonlnar ra formla of h on-hson mho s n n n n [ J ] { } { P} { } n () Dfnng f { } (4) h Jacoban marx s ( f P) f J () From h fl qaon n h P rgon, on has f ( ) ( )( ) W (6) (Gass pon) hr W s h ghng al a h h Gass pon. h magnc cor on no s no as. oror, ( ) f W (7) (Gass pon) o prform lmn assmbly on P marals, h coornas ar roa o h - coornas an on has

3 Y 中国用户大会优秀论文 ( ) ( ) ( ) (8) hrfor, f ) ( ( ) ( ) pon) (Gass W ( ) ( ) ( ) ( ) pon) (Gass W (9) hr () For lnar marals or h saon of frozn,, so hr s no frs rm n (). In h follong h calclaon of () s scrb. ccorng o, on obans an. ccorng o, on has an. () () () (4) r h follong rlaonshp s s: () C. Crc Eqaon Coplng Usng Loop ho h lcrc crc qaons of h nngs n h magnc fl oman ar copl h FE qaons. h orall qaons ar [6]: ( ) a σ (fl qaon) (6) (branch qaon) (7) a (aonal qaon) (8) hr; s h polary ( or ) o rprsn, rspcly, h forar pahs or rrn pahs of h nngs; s h oal cross-sconal ara of h rgon occp by h nng n h solon oman; s h oal concor nmbr of hs nng; a s h nmbr of paralll branchs n h nng; s h.c. rssanc of h nng; an ar h branch crrn an olag of h nng, rspcly; p s h symmry mlr hch s fn as h rao of h orgnal fll cross-sconal ara o h solon ara. h aonal crrn a ar nroc n rgons of sol concors o nsr h las coffcn marx of h fl - crc copl qaons s symmrcal [6]. Usng h Galrn mho o scrz h fl qaon an crc qaons n h magnc fl rgons, h sysm qaons can b rn n marx forma as: a a (9) Usng h bacar Elr s mho o scrz h m arabl an mly o h aonal qaon an h branch qaon, on obans h rcrrnc formlas: a () h branch qaon of h xrnal crcs s: { } { } { } () hr s h marx of h rssanc an s h colmn marx assoca h sorcs. lyng -/ o h o ss of (), on has: { } () ng h xrnal crc qaons () no () gs: a () Usng h loop mho, h rlaonshp bn h branch crrn b an h loop crrn l s: { } { } l b (4) hr s h loop-o-branch ncnc marx. h Krchhoff s olag la can b xprss as, { } b () bsng hs rlaonshps no h sysm qaons, on obans h fnal global qaons:

4 Y 中国用户大会优秀论文 l a (6) hr h coffcn marx s symmrcal. D. h Implmnaon of onlnar Problm h ra s pnn on h hsory of h oprang pon n ach lmn. h aa ar sor lmn by lmn for all nonlnar P marals. h rcon of magnzaon rmans as hos assgn bfor. Each fn lmn of h P marals ss s on rcol cr n h rspc ransn smlaon. hrfor h ors cas of magnzaon for h nr ransn smlaon s rcor. Whn rsarng h smlaon, h msh an gomry ms b ncal h hos of h pros sgn an arg sgn. In ach obc h h sam maral, h rcor aa ar c an q. In ach lmn, h rcor aa ar: mn : h mnmm al of ( s h rcon of magnzaon) n h smlaon hsory. ceq : h crrn qaln c (hch s pnn on h oprang pon). mn_mp : h mporary al of mn. I s n n nonlnar raon. ceq_mp : h mporary al of ceq. I s n n nonlnar raon. as s a flag s o rmmbr h locaon of h oprang pon: : oprang pon on nonlnr cr as (7) : oprang pon on rcol cr h procrs n m sppng FE ar: () Inalz h aa: mn r, ceq q r, mn_mp r, ceq_mp q r, as. () h bgnnng of h nonlnar raon: mn_mp mn, ceq_mp ceq ; s as. () Drng h nonlnar raon, rmn h sas accorng o h calcla : (a) f < mn, as, h oprang pon s on h nonlnar cr; c s s; pa: mn_mp, ceq_mp q ; (b) f mn, as, h oprang pon s on h rcol prmably ln; h rcol ln h q an ceq s s. fr h compaon of ach m sp, f as, pa: mn mn_mp, ceq ceq_mp. has srfac mon cramc magn. h ransn procss s smla hn on phas s snly shor-crc hn m s. s. Fg. shos a ypcal flx plo. Fg. 4 shos h saor phas crrn. h shor-crc crrn s abo. ms of h ra crrn. h armar racon rng h shor crc magnzs h P. Fg. shos h chang of h arag ceq n h P. for h shor crc, s al s abo /m; afr h shor crc, s al s rc o abo 6 /m. I can b obsr ha rrrsbl magnzaon ll hpn for hs sgn. Fg. 6 shos ha h srbon of c of P s sll nform afr h shor crc crrn rachs say-sa. Fg.. h flx plo of h P moor. Fg. 4. h saor crrn hn on phas s snly shor-crc. ceq (/m) Fg.. Changs of arag ceq n h P hn on phas s snly shor-crc. IV. PPLICIO O P OO h propos mho s pl o analyz h prformanc of a P moor. h rang of h moor s 9 W a 4 V; has pol pars, 4 saor slos, an opras a 6 rpm; h roor

5 Y 中国用户大会优秀论文 Fg. 6. h srbon of c cor of P afr shor crc (.8 s). V. COCLUIO y sng a marx o xprss a spac cor, h nonlnar formlaon of FE can b connnly c. I s plcabl o any yp an any orr of fn lmns, an also o ansoropy marals sch as Ps s n hs pr. m-sppng fl-crc copl FE o arss h rrrsbl magnzaon procss of P s lop. Only normal - crs of h P marals ar s. n ffc algorhm o mplmn h mhoology h nonlnar raon s prsn. h sas of h oprang pon a ach lmn s rcor an h nonlnar raon s rcly conroll by h r Jacoban marx. VI. EFEECE [] J.-.. z, J.. osro,. G. Espnosa an L. omral, Dcon of magnzaon fals n prmann-magn synchronos moors nr nonsaonary conons, IEEE rans. agn., ol. 4, no. 7, pp , Jly 9. [] W.. F,. L. o,. L. L an. C. Wong, mlslc copl fn-lmn mho h nn slc lngh son for h smlaon sy of lcrc machns, IEEE rans. agn., ol. 9, no., pp , ay. [] K-Chan Km, Kangsoo Km, Jn Km an J L, Dmagnzaon analyss of prmann magns accorng o roor yps of nror prmann magn synchronos moor, IEEE rans. agn., ol. 4, no. 6, pp , Jn 9. [4]. oho, E. Dlala an. ro, Comparson of magnzaon mols for fn-lmn analyss of prmann-magn synchronos machns, IEEE rans. agn., ol. 4, no., pp , o. 7. [] W.. F an. L. o, arx analyss of -D y-crrn magnc fls, IEEE rans. agn., ol. 4, no. 9, pp. 4-, pmbr 9. [6] W.. F, P. Zho, D. Ln,. anon an Z. J. Cns, olng of sol concors n o-mnsonal ransn fn-lmn analyss an s plcaon o lcrc machns, IEEE rans. agn., ol. 4, no., pp , arch 4.