θ h ε δ x α, β ω τ r τ l θ r, θ s

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1 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. Cu Cooll o ow Fqucy Sgal co a oo Flux Poo Tackg a ow S Duo Bac, Faco Mala, Mb, EEE, P oucho Abac oo lux aal oo ca b ack a ac ach v a low o zo ao qucy a low qucy haoc cu gal c o ao. Th haoc cu co ouc o h oo ubao whch uc volag ocllao h ao wg a h c qucy. By aalyzg h ao wg volag o obl o c h oo lux oo gal o h ao qucy. Th a a ao cu cooll uabl o og oag o ulag haoc cu co a a ho o ackg h oo lux oo h uco ach (M) o a ag ychoou ach (PMSM). Th cooll coa, ao o h aa uaal qucy ba ychoou c a (SF) cu cooll, wo o haoc cu gal cooll lac cv haoc SF. Such x cu cooll o ulaouly wo oa ak: cooll haoc cu co wh zo ay-a o a aao o acula cal coo h ao volag (cal/quc cooo) whch coa h oo lux oo oao. Th hocal aaly, ba o ubao hoy a avagg chqu, gv gal xo whch lk h oo lux oo o M a PMSM o h haoc cu cooll ouu. Two cal ca wh h oaoal a ulag haoc cu co a co o al. aly o h hocal aaly a ably o h ol oo lux oo co a xally v. x T Sol cool, gal co, uco ach v, a ag ychoou ach v. τ τ l θ, θ. NOMENCATUE oo lccal oo coa M loa oqu cooll (ao) a oo lux agl a agl wh c o aoay a Mauc cv Al 0, 00. Acc o ublcao Novb 9, 00. Coygh 009 EEE. Poal u o h aal. Howv, o o u h aal o ay oh uo u b oba o h EEE by g a qu o ub-o@.og. D. Bac wa wh Sch Elcc, Pacy-u-Eu, Fac. H ow wh Gal Elcc, Cool & Pow Elcoc CoE, Gachg b. Much, Gay (ho: 9(0) ; ax: 9(0) ; -al: uo.bac@g.co). F. Mala wh Sch Elcc, Pacy-u-Eu, Fac (-al: aco.ala@ch-lcc.co). P. oucho wh h M PaTch, C Auoaqu Syè, Mahéaqu Syè, Pa 757, Fac (-al:.oucho@-ach.). θ h haoc cooll agl wh c o uaal qucy cool a, ag lux PMSM ao a oo lux oo lux oo cool a δ x ub coo o vaabl x α, β x o vaabl aoay a qucy o c gal alcy ucac PMSM ub o ol a x* x cougao o colx vaabl x -avag coo o vaabl x v, oo colx volag a cu 0 uaal qucy ao volag, - /- quc haoc volag co ao wg ac q quval oo ac ( ( / ) ) q quval ac M o,,- x o vaabl uaal a o / quc haoc cooll a,, ao, oo a agg ucac M quval oal lakag ucac o M, q,q ax ao ucac PMSM avag ao ucac PMSM K, K oooal a gal ga o oo oo ackg loo K, K oooal a gal ga o uaal qucy cu cooll K h ga o haoc gal cooll chacal a, -, /- quc haoc cu co, ao qucy,q x o vaabl cooll a x& vav x/. NTODUCTON Sol vco cool o ac ach (wh o oo oo back) a zo a vy low ao quc a ao challg bcau h oo lux oo ca o b obv h uaal qucy ao cu a volag gal. a o o ovco h lao o h uaal qucy ba ol cool ho co o vaou gal (a qucy ha h uaal) hav b oo o h oo o oo lux oo co [-]. Tycally, lau a wll a h a, uch gal co a cla a haoc co alhough ( gal ca) h quc o o hav o cc lao wh h uaal qucy. cl w ca guh wo ao gou o h haoc co ho: o ba o hgh [-] a oh ba o low qucy haoc gal co [5- ]. Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

2 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. Th hgh qucy gal co ba ho [-] a u o c aal vaao o h ach lakag (M) o ychoou (PMSM) ucac o a h oo lux oo. Th ucac vaao ca b cau by agc auao o oo goc alcy a hu h ho ay o b coabl wh all oo g. Th c gal uually h 0.5kHz-kHz ag. Tycally haoc volag co ga by h v v a cul o ov c clo loo cu cool h co qucy hgh (cu cooll bawh lao). A oaoal [,] o ulag (alag) [,] haoc vco volag c a o h v volag c h uaal qucy cu cooll c a. Th lux oo o xac by oulao/hoyg ocg o a cc coo h cu o a h co qucy. h oaoal co o, h oo o gal b h gav quc cu vco a h c qucy []. Wh h ulag gal co, ycally al h cooll ax, h oo o gal b h q ax cu coo a h co qucy []. Th hgh qucy co gal o ca lavly og aubl o whch ay o b accabl o alcao. To avo xlc hgh qucy gal co h a a o a h oo o by co o h cu l cau by h v ul wh oulao [,5]. Th o call low qucy haoc cu co ho [5-] ba o xcao o all oqu a oo ocllao caabl o ucg ocllao h ao back lcoov oc (.) whch ca b c h ao volag o a h co qucy (ycally 5Hz-00Hz ag). oao o h oo lux aal oo ca b v o h ha o h volag cal coo (volag ha obv lav o h c cu ha). Thu o goo oo accuacy c () cool o h cu co oa. Alcao o h cl ha b o o al oo lux oo co PMSM [5] a ol vco cool o M [7-0] a PMSM [-]. Noally a ulag haoc cu vco c o h (lux) ax o h uaal qucy cooll c a a h h co ul al oqu ocllao [7- ]. Wh h au ao volag a o avalabl (o h ca aa vaabl v) h volag c a h ao cu cooll ouu a u o co o h ach volag o. Howv h ca c o h v wch a a volag o houl b co a hy aa a ouc o oo (o) h c volag whch ocally oula by ull zo-cog o h ha cu o by h c cu []. Bac obl alcao o h low qucy haoc co ba ho a o achv c haoc cu vco co a v h volag coo o h cu cooll ouu covyg h oo lux oo o oao. Th aoach o c wok [7-] o o h haoc cu co ug h aa (uaal) cu ychoou c a oooal gal (P) cooll. O avaag o uch aoach ha cao u c haoc cu co wh zo ay a o v h cooll wh hgh bawh. ao, o ola h ao volag coo cayg h oo lux oo oao h a u [7-0], coabl gal ocg o, u o h ao volag quao a kowlg o val ach aa a qu (ulg vy o aac o [0]). Th haoc cu co a oo lux oo ao ho oo h a ha val avaag ov h ho o [7-]. ca ov ulaouly c haoc cu co a o olao o h cal coo h ao volag o lva o h oo lux oo o val whou ug h ach ol. ba o h aa ao cu SF P cooll xa by wo o SF ba haoc gal () cooll. Such cu cooll a quly u acv ow l cool y o lcv a c coao o val ag haoc [6,7] o PWM c cool [8]. ou ca o o h haoc cooll lac a SF oag a h haoc qucy (wh c o h uaal qucy SF) whl h oh o h haoc cooll lac a SF oag a - ( uh x ov a gav quc haoc SF cooll). Wh h haoc cooll c a ± h cu cooll caabl o ocg h ao cu co a boh haoc quc a wh zo aya ackg o. Sulaouly (u o ga o h SF ba gao), h cu gao ouu (clug h aa uaal qucy gal cooll) cly aa h ao c volag o oa cal coo whou ug ay aoal gal ocg a wh o kowlg o h ach aa. Th h oo lux oo oao ca b cly v o h haoc cu cooll ouu. Th a ogaz a ollow. ally Sco h cu cooll ucu. Fuh, aug c haoc cu co, lao bw h haoc gal cooll ouu a oo lux oo o a v yac a by ug h avagg chqu a ubao hoy [9]. Two ca wh M (Sco ) a PMSM ach (Sco ) a aalyz. h boh ca wo chaacc y o haoc cu co, oag a ulag, a co o al. Ba o h v xo Sco a l oo lux oo ackg y a ol lux o cool ba o c xaco o h oo lux oo o o h haoc cu cooll ouu. Fally Sco o xal ul a o vala h hocal aaly. Th xal ul co ha h oo lux oo o Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

3 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. oao ca b cvly xac by ug h oo ho wh h oaoal o ulag haoc co. alo xally oa ha h o gal haoc SF ov quc cooll,q,q ca b xlo o h oo lux oo ackg h M a al oo oo co PMSM. δ q,q,q θ h q - K h 0 v,q v q K, K q 0 v δ q q q uaal SF P cooll -θ h -,q -,q - K h - q v q θ a,b,c -,q -,q q haoc SF gav quc cooll,q a,b,c a b c M Fg.. Sychoou c a uaal qucy cu cool ch aug by ca ychoou c a gal cooll o haoc cu cool. Fo uh aaly h uaal a haoc cu cooll c a a a llua Fg... CUENT CONTO SCHEME Block aga o h cu cool ch how Fg.. coa h aa SF uaal qucy cu P cooll wh ga K a K. Aoally wo o haoc cu cooll wh ga K h a a, lac cv SF oag a h haoc co qucy boh co. Th uaal cu vco c by xal a uch a oqu/ cooll, lux cooll c. Th haoc cu c a ly a a lvl qu o labl lux oo co. Thak o h haoc cooll, h cu cooll caabl o cg oag haoc cu vco h ov () a gav (-) quc wh zo ay a ackg o. Sulaouly h ao volag c a coo o uaal a haoc cal coo (SF gao ouu vco o- ) a K h a cly ov a 0, h Ax. q q - q quc haoc SF - θ h θ h uaal qucy SF - - quc haoc SF Fg.. Fuaal a haoc qucy ao cu cooll c a. Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

4 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. Th oo lux oo agl (ackg o) h uaal cooll c a Fg.. q q β oo lux a θ θ θ uaal qucy θ cooll a aoay a α Fg.. Muual oo o h oo lux a uaal qucy cu cooll c a.. OTO FUX POSTON EO SGNA N NDUCTON MACHNES h co h lk bw h oo lux oo o a ouu o h haoc gal cooll a v ca o a M. W wll a o h aa M ol whch u h ao cu, oo lux a oo a h a vaabl. Th ao cu a oo lux vaabl a colx ( * a cougao), ba abov vaabl o ay a/avag vaabl whl all gal ubao aou h ay a o a ga by a x δ. v ( τ ) ( q ) () ( τ ) q () ( τ τ l) () τ ( ) () wh τ h oo coa, ao qucy, quval lakag ucac, q a q a quval oal a quval oo ac cvly, ub o ol a, quval oo a, τ a τ l a lcoagc a loa oqu cvly. ao o h uaal cu coo au ha a all haoc ubao cu δ o zo avag c o h ao by ug h cooll o Fg. : δ (5) Th ubao cu vco ca cb gal ca a llc acoy whch ca b coo o h ov ( ) a gav ( - ) quc oag vco: δ (6) Fo aoxa calculao o h ubao coo h ubao chqu a avagg ho [9] a u. Th y o wll coa a avag coo a oc ubao. Th avag o au o volv a low cal v by h avag h y quao. Accog o [9] h a oc o ca b calcula by l gao o h oc coo h y quao aug ha h y o low (.. bawh 5-0 low ha h co gal qucy ). quval o aoxag h y low a lg bhavou by u gao o h oc. ou ca, cog h ao cu ubao a qucy, h oa ( o) a oo lux ubao oba a gao o cv a quao, wll coa oooal o /. Ec o h o a lux ubao ca b uh co o o oba o accua aoxao o h ach o. cla ha a gao o h a quao () a () h o ubao h a vaabl wll ouc ao ubao whch wll coa oooal /. (co o ). O ca uh ak o accou c o h co o a o o, a oba a aoxa ayoc xao o h oluo (-5) wh c o /. Wh. hgh ough, oally oly val low o a uc o goo aoxao o h ach yac o a h hgh o a aly hg. h M ca wh h ao cu co by (6), h oo yac uc o () a (): * [ ( )] τ l & (7) Fo (7), aug ha lag ough, h ubao yac δ & ca b aa o h avag yac & by yg oc wh zo avag: [ ( δ & )] (8) A gao o (8) w oba: δ (9) houl b oc ha h oo lux ubao a glc (7). Th ac ha l o h oo lux (7) o co u a ha h ocllag o o / h vav o h glc,.. a ubao o o / (9) glc. Sulao ul how ha uch o aoxao o h oo o gv aacoy ul. (8) w hav alo lcly au ha h loa oqu a ac uco o h oo. h ca c o h loa oqu ubao cau by h ubao ca b glc (accog o h avagg chqu [9]). A l hycal xlaao ha h ubao xc by h oo oqu ubao wll b oooal o h ubao (.. / ( (9)). Coquly h gao o h chacal quao, c o h loa Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

5 Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og. Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. oqu ubao ( ak o accou) ca b glc ( coao o h c o h lcoagc oqu ubao) a woul ul h loa oqu la ubao oooal o /. Fo oa loa, wh h loa oqu a yac uco o h, h abov auo val oly h haoc qucy o vcy o h oac quc. Th oo lux ubao cau by h haoc cu co a ubao ca b v o (): q δ δ τ & (0) (0) h o o h ubaoδ clu. A ouco o (6) a (9) o (0) h oo lux ubao yac : q q δ & () gao o () gv: q q δ () O ca ha () a aal xao u o h co o o h lux o aoxao oba (coquc o akg o accou h ubao δ (0)). cluo o h co o h lux o aoxao wa cay g goo achg bw h aalycal a ulao a xal ul. Now o () h ao volag o ca b v. wll b coo o val cal coo ( h ychoou uaal qucy c a): U U v q 0 δ δ δ τ δ () wh 0 h uaal qucy vco,,- a h ov a gav quc vco oag oo co a h co qucy, a U,- a h ov a gav quc vco oag a wc h co qucy. A ouco o h ubao coo δ, δ a δ (6), (9) a () cvly o () a goug h coag, h ao haoc volag vco coo oag a : q q τ () a la a h ao haoc volag vco coo oag a - ca b ou: q q τ (5) Th abov couao coo o h o ayoc xao o h oluo (-5) wh c o /. ou ca h xao o a o (/ ). uh aaly o ou acula o laoh bw h oo lux oo o a volag gal gv () a (5) o wo ycal haoc cu co o: oaoal a ulag. A. oaoal Haoc Cu co h cal ca u o (l ay) ov quc oaoal cu haoc vco c: 0 δ (6) A oucg (6) o (5) w oba: τ q (7) al a o h gav quc haoc volag - covy oao o h oo lux oo o: ) co( ) ( ) ( τ Aug ha h oo lux o ally alg wh h uaal qucy cooll c a a ha h lux oo o ( ) all ( 0, () a co() ), h calg K, ga A a o B ca b h oo o gal (cau by h co o h lux o ()): B A K K A τ B (8) Magu o h calg K cly a o h co cu agu a vly a o h loa a a co qucy. To oba aacoy gal/o ao, hgh co cu a/o low co quc a cally wh h loa a hgh. O oh h co cu agu l by h ach lo whl low co quc

6 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. uc achvabl oo oo ackg bawh. So, o a gv loa a, a a o u b a wh lcg a aoa lvl o h co cu a qucy. Tycal co qucy 5Hz-50Hz a co cu agu bw /-/ o h oo oal agzg cu. Fo (8) w alo ca ha h ga A o h avag oo. To uc h c cay o u h co qucy coably hgh ha h oo ag whch h oo lux ackg o b loy ( >> ). Th (uabl) o B (8) ha lavly low luc k ucly hgh ha τ -. Aoally c - ca b coa a ga x (g o τ aac o) a -owa a h oal oo o gal (a c o h calg K ov, Sco ). Mao avaag o h oaoal co ha ul ual ocllao v h cooll alg wh h oo lux ax (0): δ co( ) (9) B. Pulag Haoc Cu co h oa cal ca a ulag cu co u.. boh quc o h oaoal haoc cu co vco a al: δ co( ) (0) Now h oo lux oo o gal ca b xac by cobg h haoc gal cooll ouu o h boh quc: q ( τ ) () al a o h cob haoc volag la o h oo lux oo o a ollow: ( ) ( ) q () Th volag xo gv by () la o ha gv by (8). Howv ca b ha h h oo avag ac h o. Ec o h o ca b glc all coa o o a/o aoxaly coa (g o q aac o) cly h gal () a -owa a.. NTA OTO MAGNET FUX POSTON DETECTON N PEMANENT MAGNET SYNCHONOUS MACHNES h co w wll vga how al oo o h oo ca b c PMSM by ug h cu cooll how Fg.. Fo ha, lao bw h lux oo o a haoc cu cooll ouu hav o b v. Mol o a al ol PMSM wll b u o h vao. gal ca whou ug oo o h cooll c a ay o b alg wh h lux/oo a. Thu h ol wll b w h cooll c a oag a h ao qucy wh h a alg o bw h lux a cooll a (Fg. ). v ( ) ( ) () () q (5) q (6) τ ( ) (7) ( τ τ l) (8) Th h oo ag lux. Th ucac a a h avag a h alcy ucac cvly whch valu o h ach ychoou ucac a q. A h M ca ally au ha h ao cu vco ub by a abay llc haoc gal co. Th avag ao cu au o b zo (ug al oo oo): δ δ (9) Th c ubao cu ca ollowg avag a ocllag yac (o (7) a (8), a (9) ouc ()): ( ) & (0) δ & () A gao o (), h ocllao a: δ () Th ao volag o ca b v (9) a () a ouc (). Aga h haoc cu co ul ull cal coo (a quc a quc) h ao volag o: Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

7 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. v δ δ ( δ δ ) ( δ)( δ ) () 0 U U O acula o h oo lux oo co a wo ao volag vco coo a oag a h co qucy ±. Cobg (), (9) a () a xacg coag ± yl: () ( ) (5) ( ) Fo () a (5) w ca coclu ha h volag coo a uco o h oo lux agula oo o. Thu hy ca b u o ackg o h oo oo. Fuh, laly a h M ca, o ca co wo ycal y o h haoc co: oaoal a alag cu vco co. A. oaoal Haoc Cu co Wh h oaoal haoc cu vco al, h ubao cu vco : δ,.., 0 (6) Th gav quc haoc cu vco gula o zo whl h gav quc haoc volag vco (7) ouc by h ubao. ( ) (7) al a ( ax coo) o h gav quc haoc volag vco covy h oo lux oo o oao: ( ) ( ) (8) ( ) Wh h y o co h wll b o avag coo h oo oqu cau by h haoc xcao ( τ 0 ) v c o h ucac alcy. Howv ual /oqu ocllao wll v h cool y cly alg wh h oo c a (9): δ co( ) ( ) co (9) B. Pulag Haoc Cu co h ca wo haoc cu vco a al, wh a agu oag a h haoc quc ±. quval o alyg a ulag haoc cu h cooll ax: δ co( ) (0) Aga boh quc o h ao volag a h co qucy () a cob o v h oo oo. Th ax coo o h cob volag a o h oo lux oo o: q () ( ) 6 ( ) () Wh h y o xcao a avag oqu coo ca b ouc h ucac alcy (0): τ () Thu o oo ov ca b ca h loa co oqu glgbl. A oa avaag o h alag gal co ha h o a oqu ocllao wh h oo lux a cooll c a a alg (ubao cu al h lux co). Tho o accal alcao h y o haoc co coul b o accabl. C. Mag Flux Polay Dco Fo h aaly o ca ha h ag lux oo o gal a uco o oubl oo lux oo agula o (). Th ac a ha PMSM ach obl o c (by ug oo ackg ba o gal) oly oo o h oo ag lux ax bu o oao (o lux olay, o call 0π abguy). Thu a aoal qu o h oo lux olay). h PMSM ach ha a alcy ( 0), obl o c h lux olay by ug a xo o h oo cu cooll. By ug wo o aoal haoc cooll, lac SF a oag a ±, obl o xac h co haoc volag coo (U a U - ) whch ca b v o (): U 5 U () (5) Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

8 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. O acula h U ( haoc ov quc) coo ha uco o h oo o oly. Thu h lux oao ca b uabguouly olv by aalyzg g o h gal (U ). U U h PMSM ach alcy zo ( 0), agc auao c u b u o h ag lux olay co o olv h 0π abguy. Th auao ca a ayy bw h ov a gav hal o o h c volag ( haoc). So u ou ha h ha oao o h co haoc ca b aga u o oluo o h 0π abguy. Th auao c ca b al by boog h haoc co agu a h o h oo oo ackg ha o ha h oo lux olay ca b lably olv. D. Ec o Goc a Sauao uc Salcy oa o ha ha h oo lux oo o gal gv by (8) a () x all PMSM ach, v h ucac alcy zo ( 0). Acually h ucac alcy h a ubac aco whch ac agu o h o gal (uco o h haoc co qucy a oo, ( ) (8) a ()). Th a ha coa wh vaou hgh qucy co ho ha h ucac alcy o h oo oo co. obvou ha, h co qucy ucly ca, h xc by h oo ocllao wll bco glgbl a h oo lux oo o wll bco avalabl oly va h ucac alcy ( lav c ca a h co qucy ca). oh wo h c o h alcy, a acula a co gal quc, a og c bw h wo hoa ca aa. Th h h low o hgh qucy co ba ol co ho a labl. Thu h co gal qucy houl b ucly low o hgh ha o ha o o h wo hoa claly oa. woh og h ha h c o agc auao h alcy c ( 0) ca b ohw cylcal PMSM a M ach. h ca a cv aal aooy ca u o ca agc lucac h aua lux ah. A h auao lvl o h boh ax cu, a cocoulg alcy wll aa h ucac ax (o o oao o h aa ol o aua cylcal AC ach []). Th auao uc alcy ucac a uco o c bw h ucac by h c gal wh al alog h auao ax (yac ucac) a culaly o (ac ucac) a wo agl bw h co a alcy ax. cla ha h auao-uc alcy ca ac h accuacy o h oo lux oo ao ba o h oo ho a la way a h goc alcy. Pacula obl ao o h luc ha oo o h auao alcy ax ay o h loa a/o lux lvl a ay o b x o h oo lux (oo) oo a all. Howv ca b o (8) a () ha, wh choog h gal co qucy, obl o choo ucly low o ha h aac g o h ucac alcy bco lavly all coa o h xc by h chacal ocllao.. OTO FUX TACKNG h aaly ha b how ha h oo lux oo o gal ca b v cly o h - cu haoc cooll ouu o (g o y o co). A oalzao w hav: (6) No wh No o y o h co a ca b uc o quao (7), (), (8) o (). A oo lux oo ackg loo v by ug h o gal ca b ca by ug, o xal, a ha lock loo aoach (P) a how Fg (ulag haoc cu vco co au). Th cool c a oo ca b alg o h oo by gulag h oo o o zo by ug a P cooll: K K (7) No -/ Fg.. oo lux oo ackg va a P. K, K θ Ba o h lux oo ackg loo, a ol l o vco cool ch alcabl a low ca b couc a how Fg. 5. Th lux oo ackg loo aa h ao qucy a cooll c a oo o ha h cooll ax k alg wh h oo lux. Th ao qucy gal ( o h uaal qucy cool SF) u alo o ao o h oo a clog h loo. Dyac o o h oo lux oo o co ba o h low qucy co lavly low coa o ha o h uaal qucy [9,0] o hgh qucy co ba [] ol cool chqu. Thu h ch o Fg. 5 coul b accal aly o loa ha o o qu hgh yac (o all loa qu hgh yac). Th low qucy haoc co ba lux Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

9 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. oo o ackg ca b alo g wh a covoal uaal qucy ba lux ao o ov h ovall y yac o a obu [9-0] o o xa ag o h aa ol cool [0]. O obly, o xal, o loy o aaao o h ao ac. Bu h oc ou o co o h a. Flux c S P cooll K, K T K T q Cu cool (Fg.) Fg. v,q v q a,b,c v l calculao K l (uco ach) l K, K θ θ q,q a,b,c a b c M Fg. 5. oo lux o vco cool wh h oo lux oo ackg ba o h low qucy haoc cu co.. EXPEMENTA ESUTS Sval xal hav b o o chck valy o h hocal aaly a llua oou o accal lao o h lux oo o co ho. Th oo a cooll aa u h x ca b ou h Ax. A. oo Flux Poo Eo Sgal alao wh M a oaoal Haoc co h x a kw, 5, 7.9A, 5, 50Hz M wa u (oo aa ou Ax ). Th a wa o vala h xo o h oo o (8) (oaoal haoc co). Fo h h M ach wa ul h cu cool o wh oal cu a coa ao qucy by ug a cocal kw 00 vaabl v wh o cool owa. Th v a ha b coa by hawa whl c o h v wch volag o wa aoxaly coa owa by ug h wch volag o ol. Th haoc co qucy wa a 5Hz whl h haoc cu agu wa a 50% o h oal agg cu (.9A). Th cu co lvl o h u l o h ycal ag bw 5%-50% o (bw 0%-5% o h oal cu, g o ach) o o axz h oo o gal o o ao. Fo h auho accal xc, h hgh qucy co ho u o ackg o auao uc alcy (5%-0%), h co cu lvl ha o b a coaabl ag, bw 5%-5% o h oal oo cu. Howv h low qucy co wll ouc low lo ha h hgh qucy co. Thu blv ha h co cu lvl cho h xal o accal. o loa coo, h ach l zo a h oo lux alg wh h cu co (cooll ax, 0). Wh h loa oqu al o h oo, h oo l a hc h oo lux oo o h cooll ax ( 0). h way obl o - qualavly xally vy h lk bw h volag a oo lux oo o (8) ly by chagg h loa oqu. Th ul o Fg. 6 how ha h a aly coa o h - volag o h loa o ao qucy (lgh vaao a cau by h lux lvl chag). Th au o hgh ha ha c by (8) h aa ach aa Tabl a u h calculao. Th abu o a uco o h agg ucac by h c gal u o auao (yac ucac). ca b alo ha h loa oqu ogglg a coog lux oo o a cabl o h - gal. A low ao qucy (Hz, Fg. 6 (a) a (b)) h ga la o boh oo co. A hgh ao quc (0Hz, Fg. 6 (c) a ()), h ga - gcaly ac by h g o h ao qucy. Th goo qualav ag wh h hoy (c o h ga (8)). Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

10 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. Fg. 6. Ouu o h haoc cooll wh oaoal gal co a vaou ao quc a loa oqu. Fg. 7. Ouu o h cob haoc cooll ouu wh ulag gal co a vaou ao quc a loa oqu. B. oo Flux Poo Eo alao wh M a Pulag Haoc co Sval au wh h ulag gal co hav b a. Th oly c coa o h vou x ha h haoc co al oly h cooll ax. Th lux oo o cau by h loa oqu chag lc h gal a llua Fg. 7. O ca ha h gal ( Fg. 7 how ---) coa a o whch agu a g a a. Th ga o a o h. gal o h, h loa oqu ogglg alway ca a wg h gal. Th ul a ull ag wh h hocal ul gv by (). Th l vbl h -- gal Fg. 7 u o h c o hgh o haoc ha a o ccally c by aoal cooll oag cv SF a. Alhough c o h l o h cool oac coably aua by h ach a uco, a ao lg aco o accally achvabl loo a oqu co cool bawh. C. Sol co Cool o M Th cooll o Fg. 5 wa u o oa vco cool o h M a a zo. Th xal loo wa acva a c wa a.5 Hz. Th ulag haoc co o 50% o h oo oal agg cu (.9Aak) a 5Hz wa al h ca. Th cool ho a o h low ag bw 0%-0%. Th ho coul b al a hgh bu h ao lg o aag o auao h cool o h ao cu a volag. Fgu 8 how h uao wh h loa oqu wa ca gav co ocg h oo o oa h gao. h x h oqu cool coul b aa v wh h ao qucy ach zo. Howv, laly a [8-9], ou ha oly lavly low o oa cool yac achvabl (lagly o h co qucy Ω) by ug h low qucy co chqu. Th ho ca b aly u o alcao ha o o qu a ackg ( cycl ackg a oqu ubac co) wh a bawh o ha Hz. ou h cool loo bawh wa o Hz (Tabl ). Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

11 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. Fg 8. Coco o h oo lux oo o a zo qucy a loa oqu ca. Fg 9. Covgc o h oo ackg PMSM. Flux olay co ba o obvao o g o h co haoc h ao volag c (o coco by π). Fg 0. Covgc o h oo ackg PMSM. Flux olay co ba o obvao o g o h co haoc h ao volag c (coco by π). D. al oo Poo Dco PMSM wh Pulag Haoc co Fally h al oo oo co ha b v o a PMSM wh low alcy (Ax, Tabl, 90% q ) ug h ch o Fg. a co o ha o h co haoc o h lux olay abguy oluo. h h ulag ax haoc cu co wa al wh agu 5% o h oo oal cu a qucy π 0Hz. A qualavly llua Fg. 9 h oo oo ackg (ba o gulag h oal coo volag o zo, Sco ) covg wh 500. Th oo lux olay olv by obvao o h g o h co haoc h ao volag o (.. hal o ayyco co o h lux qu low volag ha co h oo co. Fgu 0 llua qualavly a uao wh h cooll oo agl coc by π a h ackg ha ha b col. Th l Fg. 9 a 0 h haoc volag wavo u o h c o h haoc ha o ccally c by aoal cooll oag SF a a /-. h, h al oo oo co ho abl ooh a o h PMSM whou ucooll oo ov. Alhough a ull acal chaaczao o h oo o ha o b col, a og val oz o, a a o h a oo accuacy ha b a by coag wh h oo oba by ug h oo oo o (olv). Th ca ha h oo o o h co qucy a cu agu. Fo xal, wh h co cu o 0% a qucy a 50Hz, h al oo ao o wa wh ±5g. Wh h co cu 50% o h oal a qucy a 0Hz h o wa wh ±0g. Whl vaou hgh qucy gal co ba ho ca ov uo ackg yac, o oa au o h ho a ha o o qu ay oo alcy, o o ouc coabl aubl o a o u o alcao wh a log hl oo cabl a/o v ouu (u) l.. CONCUSONS Th a oo a ho o xaco o h oo lux oo o by ug a ao cu cool ch ycally ou lcv acv ow l cool y. Th cu cooll ga wo ak: ao cu haoc co cool a cal cooo o h ao volag o. h oo ho x o gh (wh h haoc co) SF ba gal cu cooll a u, ca o vy cal coo o. h way h uaal a haoc cu co a o wh zo aya o whl cv cal coo o h ao volag o a aly avalabl a h SF gao ouu whou ay aoal gal ocg. By ug h ubao chqu h lk bw h haoc gal cooll ouu a oo lux oo o hav b ablh h M o PMSM ach a wh wo chaacc y o h haoc co (oaoal a ulag). Th oo aoach ha b vala val x. ally by alyg h low qucy haoc cu co o a M xally co ha xaco o h oo lux oo o o h haoc cooll ouu abl accog o h hocal ul. Fuh wa xally oa ha h lux oo o ca b u o h oo lux o ol cool a vy low ao quc o o al oo oo co PMSM. uu wok val oc a o b uh u: yac o a ably aaly o h ol cool, oal cu cooll ga lco, c h Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

12 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. v o-la (a-, wchg vc volag o) a c o h cu acquo a oo aa o. A. Ax X. APPENDXES Fo h clo loo ably o h cu P cooll wh aoal haoc cooll uc o co h l (o xal M) ol: v q w (A) Wh w a ubao au alo coa h. w ak: (A) wh haoc co qucy a a - a coa agu. Th cu cooll yl h ollowg ao volag: w v q K 0 ( τ ) ( τ )) q ( ( τ ) ( τ )) K ( ) ( τ (A) τ 0 K h ( τ τ ) τ 0 Th clo loo y ha aoal colx vaabl, h gal a a vaabl. Thy wll b o by x, x a x. Th clo loo yac h: ( ) K K x Kh x Kh x x x ( ) x ( ) ( ) (A) Th clo loo y abl a a a h cooll ga K, K a K h a cly ov a 0. Th ul o covgc o zo o h la vaa y: K q K Kh z z z ( z z) z z z z z z z z (A5) wh (z, z, z, z ) a o (, x, x, x ). Th oulao a z K z Kh z z a yauov uco: K q z (A6) vaac aall cl how ha z covg o zo. B. Ax h Ax w l all lva oo a cooll aa u h Sco. Tabl. Paa o M. P kw 5 7.9A 50Hz N 5 (a) 0.0 kg.9a 0H 0.6H.55 q 0.9 Tabl. Paa o PMSM. 9.9A T 5N 00Hz kg (ak) 0. Wb.5H q.75 Tabl. Cooll aa u h. K 0 (*) π K 0 (*) 5Hz K h (*) K ( ) ξ 0 π 0 K ( ) 0 50Hz π K ξ.5hz K ξ ξ (*) Th cooll ga a o ach aa: ucac ( o a q o M a PMSM cvly) a oo a. X. EFEENCES [] P.. a,. D. oz, Taucl Fl Oao Coc Eloyg Sauao-uc Salc uco Mach, EEE Taaco o uy Alcao, ol., No. 6, Nov./Dc. 996, Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. [] [] [] [5] [6] [7] [8] [9] [0] [] [] [] [] [5] [6] [7] [8] [9] [0] M. k,. Kl,.

Sawaua, Sol Dv o Suac-Mou Pa-Mag Moo by Hgh-Fqucy Sgal co Ba o Magc Salcy, EEE Taaco o uy Alcao, ol. 9, No., uly/aug. 00,. 0-09. M. k,. Kl,.

ooh Shok K, Sug K Sul, Nw Sa-Sll Poo Dco Sagy o PMSM Dv whou oaoal Tauc, Coc Pocg o h Nh Aual Al Pow Elcoc Coc a Exoo, APEC '9., ol., -7 Fb. 99,.6 69. E.K.K. Sg, A-C. w, T.A. o, Nw Obv-Ba DFO Sch o S Sol Fl-O Dv o ow-zos Oao, EEE Taaco o Pow Elcoc, ol.

13 Th acl ha b acc o ublcao a uu u o h oual, bu ha o b ully. Co ay chag o o al ublcao. [] [] [] [5] [6] [7] [8] [9] [0] [] [] [] [] [5] [6] [7] [8] [9] [0] M. k,. Kl,. Holz, Sol Poo Cool o Pa Mag Sychoou Mach whou ao a Zo S, Pocg o EEE 8h Aual coc o ual Elcoc Socy, ECON 0, ol., Nov. 00, H. ag, S.-K. Sul,.-. Ha, K., M. Sawaua, Sol Dv o Suac-Mou Pa-Mag Moo by Hgh-Fqucy Sgal co Ba o Magc Salcy, EEE Taaco o uy Alcao, ol. 9, No., uly/aug. 00, M. k,. Kl,. Holz, Sol S a Poo Cool o Sychoou Mach ug Alag Ca co, Pocg o EEE aoal Elccal Mach a Dv Coc, EMDC 0, ol., u 00,. -7. ooh Shok K, Sug K Sul, Nw Sa-Sll Poo Dco Sagy o PMSM Dv whou oaoal Tauc, Coc Pocg o h Nh Aual Al Pow Elcoc Coc a Exoo, APEC '9., ol., -7 Fb. 99, E.K.K. Sg, A-C. w, T.A. o, Nw Obv-Ba DFO Sch o S Sol Fl-O Dv o ow-zos Oao, EEE Taaco o Pow Elcoc, ol., No. 5, S. 998, M. a,. uo, oo Flux Agl Tackg Cooll o Sol uco Moo Dv, EEE uy Alcao Coc, 7h AS Aual Mg, ol., Oc. 00, M. a,. uo, S-Sol uco Mach Cool o Zo S a Fqucy, EEE Taaco o ual Elcoc, ol. 5, No. 5, Oc. 00, M. Hkka, -M. a,. uo, Flux Obv Ehac wh ow-fqucy Sgal co Allowg Sol ZoFqucy Oao o uco Moo, EEE Taaco o uy Alcao, ol., No., a./fb. 005, M. a,. uo, Obv Ug ow-fqucy co o Sol uco Moo Cool Paa Svy Aaly, EEE Taaco o ual Elcoc, ol. 5, No., Fb. 006,. 6-. T. Kzy, -M a,. uo, Sol Cool o Suac Mag Sychoou Moo a ow S Ug ow-fqucy Sgal co, Th 9h Aual Coc o h EEE ual Elcoc Socy ECON 0, Nov. 00,. 9-. M. Ekola, H. Tuua, Sol Cool o Sal Pol PMSM Ug a ow Fqucy Sgal co, Euoa Coc o Pow Elcoc a Alcao, S. 005,. -0. S. Wu, Y., X. Mao, Coao o Sgal co Mho o Sol cool o PMSM a y ow S, EEE Pow Elcoc Scal Coc, PESC 007, u S. Ogaawaa, H. Akag, A Aoach o al-t Poo Eao a Zo a ow S o a PM Moo Ba o Salcy, EEE Taaco o uy Alcao, ol., No., a./fb 998, M. A. oglbg, S. Gubc, T.G. Habl, T.M. Wolbak, Ug PWM-uc Ta Excao a Avac Sgal Pocg o Zo-S Sol Cool o AC Mach, EEE Taaco o ual Elcoc, ol. 57, No., auay 00, S.., S.K. Sul, A Haoc c Fa Ba Cu Cooll o Acv Fl, Fh Aual EEE Al Pow Elcoc Coc a Exoo, 000. APEC 000, ol., 60 Fb. 000, D. Bac,.S. a, P.K. Muk, Haoc Flg o HghPow -Pul c oa wh a Slcv Hyb Fl Sy, EEE Taaco o ual Elcoc, ol. 8, No. 6, Dc. 00, Xao Pg, K.A. Coz, G.K. ayagaoohy, Mull c Fa-Ba Cool o Th-Pha PWM Boo c u Ubalac a Do u Coo, EEE Taaco o Pow Elcoc, ol., No. uly 008, Haa K. Khall, Nola Sy, Pc Hall, Th Eo, 00, Cha 0., Pag 0-. C. Slva, G.M. Ah, M. Su, Hyb oo Poo Obv o W S ag Sol PM Moo Dv clug Zo S, EEE Taaco o ual Elcoc, ol. 5, No., Al 006, [] P. a, co Cool o AC Mach, Oxo Uvy P, USA, 990. Duo Bac cv h Dl. g. g lccal gg o h Uvy o Nov Sa, Sba, h M.E. g lccal gg o h Uvy o Blga, Sba, 99, a h Ph.D. g lccal gg o h Uvy o Tchology, Syy, Auala, h o PD Elcoc, Sch-Elcc &D c Na, Nw Zala, a a Elccal Eg/So Eg wokg o g a vlo o aa vaabl v. 006 h o Sch-Elcc &D c Pacy-u-Eu, Fac wh h wa wokg a a So Cool Eg /Sch Gou Ex o vlo o oo cool y. Sc Novb 00 h ha o Gal Elcc, Cool & Pow Elcoc C o Excllc Much, Gay, a a So Pow Covo Eg. H ach a cool a g o ow lcoc cov a lcc v, acv lg a ow qualy. Faco Mala (M 05) cv h loa o g o h Ecol Suéu 'Elccé (G u Yv) 995 a h PhD g auoaca a al ahac 00 o h C Auoaqu Syè a M PaTch. 000, h o Moo Cool a Sch Tohba v (ST). Sc 00, h ha o h Pacy Tchology C o Moo&Dv a o Sch Elcc. H chag o acao a vlo o h aa v o. H l o a cao a ola cool o ow lcoc, lccal ach, a alcao o v. P oucho wa bo 960 SaE, Fac. Gaua o Ecol Polychqu 98, h oba h PhD Chcal Egg a M PaTch , h oba h ``hablao à g chch'' Mahac a Uvy PaSu Oay. Fo 99 o 005, h wa aoca oo a Ecol Polychqu Al Mahac. Fo 998 o 00, h wa h ha o h C Auoaqu Syè o M PaTch. H ow oo a M PaTch. H l o clu ola cool a y hoy wh alcao. H cobuo clu al la a xo o oal y, ola obv a y, oc cool, oo lag a ackg o chacal y, back ablzao a ao o lccal v, al cobuo g a quau y. Coygh (c) 00 EEE. Poal u. Fo ay oh uo, Po u b oba o h EEE by alg ub-o@.og.

The far field calculation: Approximate and exact solutions. Persa Kyritsi November 10th, 2005 B2-109

The far field calculation: Approximate and exact solutions. Persa Kyritsi November 10th, 2005 B2-109 Th fa fl calculao: Appoa a ac oluo Pa K Novb 0h 005 B-09 Oul Novb 0h 005 Pa K Iouco Appoa oluo flco fo h gou ac oluo Cocluo Pla wav fo Ic fl: pla wav k ( ) jk H ( ) λ λ ( ) Polaao fo η 0 0 Hooal polaao