LINE-START PERMANENT MAGNET SYNCHRONOUS MOTORS. ANALYSIS AND DESIGN

Transcription

1 LINE-START PERANENT AGNET SYNHRONOUS OTORS. ANALYSIS AND DESIGN Dan STOIA, ha ERNAT, Kay HAEYER, Drago BAN 3 Translvana Unversty of Brasov, Faculty of Electrcal Engneerng an omputer Scences B-ul Erolor 9, 536 Brasov, Romana, stoaan@ymal.com, m.cernat@untbv.ro RWTH Aachen Unversty, Insttute for Electrcal achnes Schnelstraße 4, 56 Aachen, Germany, ay.hameyer@em.rwth-aachen.e 3 Unversty of Zagreb, Faculty of Electrcal Engneerng an omputng Unsa 3, Zagreb, roata, rago.ban@fer.hr Abstract. The Lne-Start Permanent agnet Synchronous otor (LSPS) attracte a conserable attenton because of the hgher value of the prouct between the power factor an the effcency. The paper proposes an analytcal esgn metho for the permanent magnet, conserng the operatng pont on the B-H characterstc alas the magnetc flux magnetomotve characterstc, a esgn metho for the LSPS conserng the synchronous operaton parameters an the asynchronous operaton (startng) parameters. A esgn example for a motor havng rate power 3.5 W, rate phase voltage V, rate freuency 5 Hz, rate spee 3 rpm wll be presente. Keywors. A machnes, esgn, electrcal machnes, permanent magnet motors, lne-start synchronous motor.. INTRODUTION In the last years, the LSPS has receve more attenton n the acaemc worl an nustres [-38]. Worlwe new legslatons eman hgher effcency motors. The use of LSP can help to acheve the new reurements. It became compettor to cage nucton motor n the general purpose nustral applcatons ue to ts hgh effcency, hgh power factor an ts ablty to self start from the regular fxe freuency supply [5-8]. The structure of LSPS s smlar to ths of the I but wth permanent magnets (Ps) nserte n the rotor [6, 9- ]. The rotor can have many types of confguratons snce the nserte Ps may have fferent shapes, materals, szes an postons [, 4,, 3], whch eeply nfluence the performances of the machne. The lne-start property s obtane thans to the esgn of the rotor wth startng alumnum cage or wth sol ron, or wth a conuctng rng on the surface [5, 4-6]. LSPS s n fact a synchronous machne at whch the exctaton fel s prouces by permanent magnets nstea by a c fel wnng. For startng an transents, the machne has the alumnum cage on the rotor. So, the functonng of the LSPS s characterze by two operaton moes: the synchronous operaton moe at steay state an the asynchronous operaton moe at startng an transents [39]. The synchronzng process has been stue n [-4, 8]. The steay-state characterstcs are measure for fferent values of the output power [8-]. In general, the LSPS has Ps bure below the surrel-cage an these two constructve parts have fferent functons uner fferent states. The Ps operate on algnment torue to rve synchronous spee n steay state an breang torue n startng pero, both epenent of the P operatng pont an the non-loa emf [9, 8, 9, 3, 35]. So, t s necessary to esgn Ps conserng the algnment an breang torue at once. In general, the optmal sze of Ps proves the reure magnetc flux so that the reactve power exchange wth the power supply s mnmal, to get a hghest power factor whch correspons to the mnmum lne current [5]. The rotor cage generates n transent operatng moes (startng an loa changes) an asynchronous torue. The breang torue ntrouce by Ps n startng pero lowers the total torue [, 3, 34]. Because the Ps are bure below the surrel cage, magnetc flux barrers n the rotor bac ron are necessary. So, atonally to the P breang torue, these magnetc flux barrers ntrouce a breang reluctance torue because of rotor salency, whch further lowers the total torue n startng pero. In ths way, the esgn of LSPS s somehow troublesome because of varous lne startng performance egrang effects. For the aforementone reasons, the LSPS esgner has to fn many compromses n the esgn process between an aeuate startng characterstc n the asynchronous operatng regon an the torue capablty an effcency n the synchronous operatng regon. The paper proposes: an analytcal esgn metho for the Ps conserng the operatng pont on the B-H characterstc tang nto account of the ron saturaton effect; followe by an analytcal esgn metho for the LSPS EDPE 9, October -4, 9, Dubrovn, roata

2 conserng the asynchronous an synchronous behavour, for operatng the motor at steay state near the unty power factor.. THE OPERATING POINT OF THE P WITHOUT ARATURE REATION Neglectng of agnetc Saturaton Fg. presents the stue LSPS. The stator s the same as that of an usual nucton motor. The lne-start property s obtane thans to the rotor esgn, whch contans an alumnum cage for asynchronous lne startng, two Ps mae of NFeB an two non-magnetc materal flux barrer on the uarature axs to mnmze the nter-pole P leaage flux. "!" Fc B" S" & S" H c " "! S " & rec & rec!" S" l p wth the flux concentraton factor: an the permeance coeffcent (b) (c) S / S ". (3) p l / " (4) 3 Fg.. The euvalent crcut of the LSP machne wthout armature reacton. In Fg. 3 N s the operatng pont of the P n the fluxmmf coornates, whch s at the ntersecton of the lnear emagnetzng characterstc of the rare-earth P (L rec ) an the loa lne (L l ). Fg.. ross secton of the rotor of a LSPS: - permanent magnet; -cage; 3-non-magnetc flux barrer. For etermnng the operatng pont of the P use n LSP motors, the machne s operate as a no loa generator. Fg. shows the smplfe euvalent crcut of the LSP machne at no loa functonng (wthout armature fel). In general case, the resultant permeance! t of the external magnetc crcut conssts of two components: the useful permeance whch s the permeance of the ar-gap an the leaage permeance:!!" %!# #!" t () The useful permeance!" correspons to the useful flux n the actve porton of the magnetc crcut. The leaage permeance!# s the referre leaage permeance of a sngle P or of the P wth armature (n rotor an stator slots, the non-magnetc materal an the ar spaces between the magnet an the lamnatons steels). The permeances are: rem! Fc Brem S H c l & & rec S l (a) Fg. 3. Determnng of the operatng pont of the P:! rem - remanent flux; F c coercve mmf; (L rec ) - the recol lne, (L l ) the loa lne wthout armature fel; (L " ) the ar-gap loa lne; N the operatng pont wthout armature fel. In Fg. 3, the euatons of (L rec ), (L l ) an (L " ) lnes are [4, 4]: ( Lrec ) : rem %! ( Ll ) : (! t F; ( L" ) : (! " F; F; respectvely. onseuently, the coornates of the operatng pont N are: (5) EDPE 9, October -4, 9, Dubrovn, roata

3 ,! t ) N rem ;! %! N t : + (6) ) rem FN ( )*! t %! an the expresson of the ar gap flux s:!" " rem (7)! %!" #! t # - (8) "!" The ar gap permeance can be expresse as / p. p l! " " The arter coeffcent = s r can be calculate for the stator slots an for the rotor slots separately [3]: 6 s FE & (9) 5 t 3 s s (a) 4 ts ( 6 s " < : bs bs arc tg ( ln = : " " :; 5 b 3 % 4 " 4 s (b) The coeffcent of the leaage flux can be calculate by [9]: # 4 l < = " 9 % ln : % 7 () = & rec /. p :; ( ( / ). p 78 In ths way, by neglectng the magnetc saturaton of ron, the ar gap flux at no-loa operaton can be expresse as " rem! # %!" rem rec # % µ p () From the above euaton, the expresson of the unsaturate flux ensty on the ar-gap results: B" Brem (3) rec # % µ p The bac EF can be expresse as rem U 4,44 f ww (4) rec # % µ p The permeance coeffcent p represents the slope of the ar-gap lne n the secon uarant of the B-H plane. Ths s a measure of the capablty of the magnet to wthstan emagnetzaton; a value of the permeance coeffcent between 5 an guarantees a successful esgn. A low value mnmzes the magnet cost. For the szng proceure of NFeB P motors, the ar-gap flux ensty can be ntally estmate as B " # (.7-.9) B rem. It s note that an ncrease value of the ar-gap flux ensty can reures wer tooth n orer to avo saturaton. In most electrc machne applcatons, for to get mnmum resultng machne volume, the stator tooth wth t s must be half of the stator slot ptch s (.e. stator slot an tooth wths are eual): t s. s / (5) The next tas s to etermne the pole ptch coverage coeffcent % an the raal length l of the P for obtanng ths structure. The raal length of the magnetc crcut can be expresse as: l " P (6) > % /? S " / / / S (7) S /. p l Fe (8) The ar-gap length " s usually etermne by mechancal constrants an s a gven ata. The tooth wth t s s gven by ts = D B" Fe Zs Bsat (9) where B sat results from the B-H characterstc of the magnetc materal. After nsertng B " from E. (3), t s gven by E. (9) s a nonlnear functon of %. Ther values can be foun teratvely; an ntal value for % s chosen an the values of ar-gap flux ensty an tooth wth are calculate. onton (5) s chece an the value of % s ajuste. Tang nto account of agnetc Saturaton The expresson () of the ar-gap flux ensty was euce conserng a lnear magnetc crcut. For motors usng hgh-energy Ps t s necessary to conser the nonlnear magnetc characterstcs of the steel. On the other han, the bggest savantages of the NFeB magnet are the epenence of ts remanent flux ensty wth temperature. The temperature coeffcent of B rem have negatve values (n range of.7%-,3%), thus the accuracy of esgn can be nfluence. The usual proceure s to a up the mmf rops aroun the magnetc crcut, tang nto account the nonlnear B-H curve of the steel an eual ther sum to the apparent opencrcut mmf of the P, whch s efne as F () ca l Hca For a NFeB P at room temperature, H ca =H c. In Fg. 4, the emagnetzaton curves an ther varaton wth the temperature s presente for Ps mae of NFeB. The effect of temperature varatons on the P causes the ar-gap flux ensty an the nuce bac emf to vary. By proceeng wth the nvual mmf rops, an startng wth the ar-gap, the ar-gap magnetc flux ensty s ntally assume to be eual to the value calculate n E. (). Then: 3 EDPE 9, October -4, 9, Dubrovn, roata

4 " " B l" µ F () Fg. 4. The emagnetzaton curves by fferent temperatures. Assumng that the stator yoe flux s eual to the ar-gap flux crossng over half of the pole area: S" " Bsy B" (a) Ssy hy l Fe H y H y ( B ) (b) " The functonal notaton represents a lnear nterpolaton along the B-H curve of the steel. For ths purpose, the B-H characterstc of the steel s lnearze pecewse an approxmate by two lne segments (Fg. 5). untl F s wthn.% of F ca. An upate value B " nonln s obtane. The flux ensty nto the stator an rotor teeth, stator yoe of the machne are compute an wll be use to etermne the core losses. The bac emf of the machne can be calculate for each spee by usng rem U 4,44 f ww (8) rec # % µ sat p F" % Fst % Frt sat (9) F" 3. THE OPERATING POINT OF THE P WITH ARATURE REATION Neglectng of agnetc Saturaton Fg. 6 shows the euvalent crcut of the LSP machne wth armature reacton. Fg. 5. Pesewse lnearze B-H characterstc of the P. The effect of temperature varatons on the P causes the ar-gap flux ensty an the nuce bac emf to vary. The magnetc flux an the magnetc flux ensty are: N # " (3) B" S" # BN # B" (4) S The euaton of the emagnetzaton characterstc s: B N & & rech N % Brem (5) s use to fn H NO, an: F l H (6) N N Now, all the mmf rops are to a together: F F % Fsy % Fst % Frt % Fry % F " (7) The prncple of teraton s apple. If F>F ca, B " s ecrease an the calculaton s repeate. If F<F ca, B " s ncrease an the calculaton s repeate. These contnuous Fg. 6. The euvalent crcut of the LSP machne wth armature reacton. In Fg. 7 pont N s the operatng pont of the P n the flux-mmf coornates, whch s at the ntersecton of the lnear emagnetzng lnear characterstc of the rare-earth P an the loa lne. In contons of the armature fel acton, usually ths fel emagnetzes the P, so that the new operatng pont N s obtane by translaton of the N pont wth the -axs armature reacton mmf referre to the rotor F a. In flux-mmf coornates, the euatons of (L l ) an (L " ) lne are [4, 4]: respectvely. ( Lrec ) : ( Ll ) : ( L" ) : rem %! F (! t (!" > F % Fa? > F % F? a (3) onseuently, the coornates of the operatng pont N n Fg. are > (! F?! t rem t a N ;! t %! rem %! Fa FN (.! t %! The useful ar-gap flux wth armature reacton s: (3) 4 EDPE 9, October -4, 9, Dubrovn, roata

5 > (! F?!" rem a "! %!" # (3) B " B rem # % & rec a! F ( S" sat Thus, the bac emf can be expresse as U e p a p (38) rem (! F 4,44 f ww. (39) rec # % & sat 4. THE STEADY STATE BEHAVIOUR Fg. 7. Determnng of the operatng pont of the P:!rem- remanent flux; F c coercve mmf; (L rec ) recol lne; (L l ), (L l ) loa lne; (L " ), (L " ) ar-gap loa lne; N operatng pont wthout armature fel; N operatng pont wth armature fel. In ths way, by neglectng the magnetc saturaton of ron, the ar gap flux the at loa operaton can be expresse as rem (! Fa "! # %!" rem (! Fa rec # % & p (33) From the above euaton, the expresson of the unsaturate flux ensty on the ar-gap results:! F B a rem ( S" B" rec # % & p (34) Thus, the emf by tang nto account the armature reacton s efne as Ue The volume of the P s rem (! Fa,44 f ww rec # % & p 4. (35) V /. l l (36) Tang nto account of agnetc Saturaton By tang nto account the magnetc saturaton of ron, the ar gap flux the at loa operaton can be expresse as: " rem # (! F! %! " a p Fe # rem % & (! rec F a sat p (37) From the above euaton, the expresson of the saturate flux ensty on the ar-gap results: The voltage euaton of LSP motor s [, 4, 9, ] U % > I I? % > I I? U % R I % j (4a) U U % R I % # j % j I a a (4b) orresponngly, t results the vector agram presente n Fg. 8. Fg. 8. The vector agram of the LSP motor. > R % j?% I > R j? U U % j # I % I a % a (4a) U U U R I e ( ( j # e U % j a I I % I I > I % I? I % I ; a (4b) a r (4) I I ; I I cos@ The nput voltage projectons on the -axs an -axs are: 5 EDPE 9, October -4, 9, Dubrovn, roata

6 U % sn A I R I (43a) U % cos A U ( I I (43b) The components of the current are U ( cos A ( R sn A) ( U I (44a) % R U ( R cosa % sn A) ( U R I (44b) % R are obtane by solvng Es. (4) As t can be seen n E. (), the vector of the nput current I can be ecompose n two other components, namely the actve component I a an the reactve component I r. But P 3 U a r em I I % I I % I (45) Usng Es. (44) on obtan: I B U D ( % R D cosa ( Rsn A ( U % ( R cosa % sn A ( U ) R) % / (46) an by neglectng the armature resstance an the leaage reactance, the components Ia an Ir of the nput current are < U 5 9 : U 3 ( ( a I a cos A7 sn A (47a) : 3 ; a a 4 a 7 8 < U U 5 9 ( : ( U 3 ( ( a I r cos A7 cos A (47b) : 3 ; a a a 4 a 7 8 Any change n the nput voltage at T l = or T l =const results n a change n the armature current an power factor. The V curve at no-loa operaton The loc of the armature current wth ncreaseng the armature voltage are the orey s V curve of the P motor (Fg. 9). V curve where the current s smallest, where the LSPS uses nether fel weaenng nor fel strengthenng s expresse as: U lm U % ( m I) m (48) >? / % a a a a (49) In ths moe of operaton, the nput current s slghtly leang. The electromagnetc torue The phasor agram can also be use to fn the nput power,.e: P 3U I cose 3U ( I cosa ( I sn A) (5) n From Es. (4) an E. () t results P n 3[ U I % RI % I I ( ( )] (5) Because the stator cote less has been neglecte, the electromagnetc power s the motor nput power mnus the stator wnng losses: F P w 3 R I 3 R ( I % I ) (5) P em Pn ( FPw 3 [ U I ( I I ( ( )] (53) The electromagnetc torue evelope by a salent-pole synchronous motor, by neglectng the armature resstance s: Pem Tem = ns < 9 (54) 3 U U 5 : U A % 3 sn ( sn A7 = n : 3 s ; whch can be expresse also as: 3U I 3 Tem cos@ % > (? I G G (55) From Es. (9) an () t can be seen that the electromagnetc torue s n rect proporton to the bac emf. The emf s n rect proporton to the magnetc remanence of the P. So, ue to the temperature effect on the magnetc materal, the emf can have fferent values. By ecreasng of the remanence of P, the value of the breang torue wll ecrease too. In E. (9), the angular synchronous spee G (56) s = n s s eual to the mechancal angular spee of the rotor. In a P salent-pole synchronous motor, the electromagnetc torue has two components (Fg. 4): T em Tsyn % Trel (57) 3 U U T syn sn A = ns (58) Fg. 9. V curve of the LSPS at no-loa operaton. For operatng the machne at unty power factor, the arma ture voltage U lm corresponng to the operatng pont of the 3 U 5 3 T ( rel sn A (59) = n 3 s 4 From Es. (5)-(6) t can be seen that the synchronous 6 EDPE 9, October -4, 9, Dubrovn, roata

7 torue T syn s a functon of both nput voltage an no-loa emf, whle, the reluctance torue T rel epens only of the nput voltage U. The effect of the temperature growng on the maxmum value of the electromagnetc torue.e. pull-out torue s obtane n orer to smplfy the euaton. Let A 3 p U U 5 3 ( ; = n 3 s 4 So, the electromagnetc torue s (6a, b) Tem A U sn A ( A sn A (6) an the pull-out torue can be expresse as: T p. o. A D 5 33U 4 3 % U % U U 3 % 3 % 3 ( U D (6) Fg. presents the pull-out torue as a temperature growng functon. Fg.. The pull-out torue as a temperature growng functon. Analyss of the Steay State of the Desgne LSPS The esgn nput ata are shown n Tab.. The specfcatons of the chosen permanent magnet are shown n Tab. Tab.. The nput ata of the esgne LSPS. Rate actve power [W] Rate phase voltage, rms value [V] Rate freuency [Hz] Synchronous spee [rpm] P N 3.5 U N f N 5 n s 3 Ferromagnetc materal use n stator an rotor bac rons s chosen base on ther losses at worng pont an saturaton level. From the B-H characterstc, the saturate magnetc flux ensty B sat =.8 T (at 5 Hz) results. The stacng factor of the magnetc crcut s % stac =.94. Tab. 3 shows the numercal values of the parameters of the esgne LSPS, relevant for the steay state operatng moe. Tab.. The permanent magnet specfcatons Permanent magnet type Remanent flux ensty [T] oercve magnetc fel ntensty [A/m] agnetc energy ensty [J/m 3 ] >? max Recol relatve permttvty Temperature coeffcent of remanent flux ensty [ - ] Q3G3SH B rem.6 H c 88 BH 39 & rec.5 / B -.% Tab. 3. The parameters of the esgne LSPS, relevant for the steay state operatng moe. The voltage corresponng to the mnmum of the current on the orey s V curve, rms value, rms value [V] Rate current, rms value [A] U lm 35 I N Stator resstance [&] R.675 Stator leaage reactance [&] #.78 agnetzng reactance [&] 5 -axs synchronous reactance [&] axs synchronous reactance [&] m 5.6 Salency rato H. Wth these parameters, by applyng Es. (), (3) on obtan the orey s V curve at no-loa operaton. From the V curve of the esgne motor at no-loa an at power unt factor, the value of U lm can be obtane. The compute values of the steay state man parameters are: T em max =3.74 Nm, T em n = Nm, I max =7.8 A; n = ; lm =98 ; cos (=.99. Fg. shows the torue-angle characterstc of the esgne motor. Fg.. The synchronous torue an the reluctance torue of the esgne LSPS. 7 EDPE 9, October -4, 9, Dubrovn, roata

8 5. THE STARTING BEHAVIOUR The euatons of LSP motor can be euce from the general euatons of the Blonel ynamc moel. So, n - axs the followng set of euatons s val [9,, 39]: u R % p I ; u R % p I; D RD / s % p ID ; DRD / s % p ID. The lnage fluxes n the above euatons are efne by: I I I I D D ( I > L % L? D D > La % L#? % La D L ( I La % > La % LD? L % > L % L? a L a % L a # a D % L From the above euatons on obtan 5 p La I ( I 3 L ( 4 RD / s % p L 5 I 3 L ( 4 R wth the operator p j s J. s D p L D a a D / s % p L D % L D a L p L D p (63) (64) (65) The operatonal mpeances Z p an Z p of the LSP motor, relate to the power source are efne as [5] Zp ; (66) R % JsLp The nput euvalent mpeance s []: Z n R % j Zp R % JsLp > R / s % j? D D# j m % RD / s % j D# % j m # (67) In general, nto the euaton of the torue there are three components: the non vbratory torue (effectve torue), whch oes not change wth tme, the frst vbratory torue, whch changes wth tme an slp freuency f s =s f an the secon vbratory torue, whch changes wth tme an the ouble slp freuency. Durng asynchronous operaton, the rotatng fel passes on the magnet poles wth the spee. 6 fs n > ( s? (68) p The breang torue The synchronous part of the LSP machne sees the supplyng networ as a termnal short-crcut because of low values of the operatonal reactance at low freuency s) s. In these contons, the breang torue wll be assocate wth the stator copper losses because of the current nuce by the Ps [4]: > ( s? ( ( s) % R I U (69) ( ( s) % R The actve power generate by the short-crcut current s By ntroucng the notatons 3 R I P (7) H (7) / K (7) R / the power expresse by E. (7) prouces the breang torue: 3p ( ( s) U K ( ( s) % K T br ( (73) Js B( ( s) / H % K The slp value for obtanng the maxmum breang torue: 3 3 s ( K > H (? % > H (? % H. (74) From E. (73) t can be seen that the P brang torue s n rect proporton to the suare of emf, whch can be expresse as n E. (8). The cage torue The expresson for the cage torue can be wrtten as [3]: T c 3p U J s m < a RD : R % # ; b R RD m ; c s R D a % b s % c s > %? > # m % D# m % # D#? % R > %?. # m 9 m 7; 8 % (75) (76a, b) R D RD RD; D# D# D#. (77) The electrc spee at whch the asynchronous torue s maxm s gven by [3]: J c s Js Js a / c (78) In startng process, the surrel cage s one ey pont. The esgn of the surrel cage manly contans the menson esgn an the number selecton of rotor slots. In a LSPS, the surrel cage s only functonal when the rotor s startng up. Therefore, the esgn of the surrel cage manly focuse on a goo startng ablty. Whle the cage resstance s relatvely hgh, the motor wll prouce hgh startng torues even uner low startng current. Whle the cage resstance s relatvely low, the synchronzng capablty s better but the startng current s hgher. Pyrform slots wth flat bottom are n general use on the rotor core for the purpose of reucng the leaage coeffcent. Due to the sn effect, at the begnnng of startng, the rotor resstance wll ncrease an the leaage euvalent resstance wll ecrease. In these contons, the startng performances wll be greatly mprove. Durng the startng process, the average torue have two components,.e. the brang torue an the cage torue: 8 EDPE 9, October -4, 9, Dubrovn, roata

9 T av Tbr % Tc (79) The slope of the ampe oscllatons near to the en of the startng process, s entfe as [3]: > T ( T T? p D c br ( Js s (8) In startng process, the varety of armature current can be approxmately ve nto four stages. Stage one: acceleratng process. The rotor accelerates from stanstll. Due to the low spee, the slp s close to, the armature current s hgh an the electromagnetc torue s also hgh, thus the rotor runs wth hgh acceleraton. Stage two: approachng synchronzng process. The spee rses contnuously, an the slp s close to zero, but acceleraton becomes lower an the armature current ecreases sgnfcantly. Stage three: pullng nto synchronzaton pero. The motor goes nto the ampe oscllaton proceure. Stage four: synchronous operaton pero. The waveforms of the armature current ten towars stablzaton after several oscllatons. For the purpose of obtanng a hgher value of the prouct between the power factor an the effcency uner loa operaton, the man value of nput voltage must be lower than ts rate value (35 V versus V). For the esgn purpose, the cage resstance s relatvely hgh an the motor wll prouce hgh-startng torue even uner low startng current. However, ncreasng the rotor resstance has a benefcal effect on the early start. On the other han, the hgher rotor resstance means that the slope of the asynchronous torue near the synchronous spee s very low. Due to the presence of the magnet brang torue, whch s proportonal to the suare of the no-loa voltage, the effectve slope or the ampng constant D has a value that s much epenent on the no-loa voltage. An ncrease of the no-loa voltage can lea to a reuce crtcal loa torue. An optmum can be foun for the noloa voltage to maxmze the crtcal loa torue. Note that the ecreasng of the volume of the Ps gves a better synchronzaton capablty of motor wth hgh power factor. On the other han, the value of the bac emf of the P affects the value of the reactance m : ncreasng the amount of magnets ncreases the no-loa voltage an ecreases the magnetzng reactance. Therefore, by ncreasng the volume of magnet on obtan a better synchronzaton capablty but a lower crtcal loa torue. Analyss of the Startng Process of the Desgne LSP achne Tab. 4 shows the numercal values of the parameters of the esgne LSP machne, relevant for the startng operaton. From the V curve at no-loa operaton, the armature voltage U lm corresponng to the operatng pont of the V curve where the current s smallest, where the LSPS uses nether fel weaenng nor fel strengthenng s euce from Fg. 9 an the no-loa emf s calculate by E. (8). l Tab. 4. The parameters of the esgne LSP machne, relevant for the startng operatng moe No-loa emf (wthout armature reacton), rms value [V] Stator resstance [&] age (amper) resstance [&] U 3 R R R.675 D D D R R R.675 Stator leaage reactance [&] # # #.78 age leaage reactance [&] D# D# D#.37 agnetzng reactance [&] m 5 Salency rato H. Number of stator slots Z s 3 Number of rotor slots Z r Lamnaton stac length [mm] l Fe 9 P length [mm] l 6 ean P ameter [mm] D 9 Ar-gap length [mm] ".8 Pole ptch coverage coeffcent of the P /.85 The conton of a goo startng capablty wth a hgh value of the prouct between the power factor an the effcency at loa operaton s []: U L (8).93Ulm Durng the acceleraton tme nterval of the startng process, the slp s hgh (from to.6), the freuency of the rotor current s also hgh, the average cage torue s postve an contrbutes to rotor acceleraton, whle the average P torue s negatve an acts as a brae. For the chosen archtecture of the LSPS, the salency s very low (*=.) an conseuently the reluctance component of the brang torue s very low too. The armature current I, the nuce current I, the nput mpeance an the components of the torue have the values ncate n Tab. 5 an Tab. 6. Tab. 5. Values of functonng parameters for s B.6, s I [A] I [A] T c [Nm] T b [Nm] Z p [&] O When the slp value becomes less than s =.6, the pull-n effect of the synchronzaton occurs, acceleraton becomes lower an corresponngly the armature current ecreases raply (Tab. 5). When the slp value becomes less than s =.3, the motor goes nto the ampe oscllatons (Tab. 6). When the slp s less than s =.5 the value of the nput mpeance becomes very hgh Z p = &, an the rotor s accelerate up to the synchronous spee, manly by the P torue. 9 EDPE 9, October -4, 9, Dubrovn, roata

10 Tab. 6. Values of functonng parameters for s B.3,.5 S I [A] I [A] T c [Nm] T b [Nm] Z p [&] When the slp s less than s =.3 the value of the nput, mpeance becomes very hgh Z p = &, an the rotor s accelerate up to the synchronous spee, manly by the P torue. N the compromse between the value of startng torue, whch epens manly on the surrel-cage esgn an materal, an the startng current; N the compromse between the value of brang torues (ue to the presence of Ps n the asynchronous operatng regon) whch epens manly on the placement, mensons an the value of energy prouct of Ps, whch has the prncpal effect on the motor s synchronzaton capablty; N the compromse between an aeuate startng characterstc n the asynchronous operatng regon an the torue capablty an the prouct power factor effcency n the synchronous operatng regon. 7. REFERENES Fg.. age torue (), brang torue () an average torue (3) of the esgne LSPS. At s = -. the value of the P torue s T P = 5 Nm. The cage torue becomes oscllatng wth a zero mean value. After the synchronzaton, the cage torue an the brang torue approach small values but not zero The nuce current s I = A, the P torue s T P =.5 Nm, an the cage torue s T r =.3 Nm because the - an -axes reactances are about the same value. 6. ONLUSION In ths paper a grapho-analytcal metho for the sze up proceure of Ps use n LSPS s propose. Usng ths theoretcal approach the amount of magnet for the reure ynamc an steay state performances of ths motor can be calculate. The esgne operatng pont of the P offers the avantage of a large magnetc energy ensty, near of ts maxmum. Then an analytcal esgn metho for the LSPS conserng the synchronous operaton parameters s propose. Usng ths theoretcal approach, the steay state characterstcs an the synchronous (algnment) torue were been calculate. In the esgn process, the LSP esgner has to fn the compromse between an aeuate startng characterstc n the asynchronous operatng regon an the torue capablty an power factor effcency prouct n the motor s synchronous operatng regon. Then an analytcal esgn metho for the LSPS conserng the asynchronous startng parameters (voltage, emf an euvalent resstance of the rotor cage) s propose. The LSP esgner has to fn many compromses n the esgn process: [].A. a Slva, J. aroso, an R. arlson, Analyss of a Three-Phase LSP by Numercal etho, IEEE Trans. agnetcs, Vol. 45, No. 3, arch 9, pp [] F. Lbert, J. Soular, an J. Engstrom, Desgn of a 4- pole lne start permanent magnet synchronous motor, Proc. IE, Brugge, Belgum, Aug.. [3] J. Soular an H.P. Nee, Stuy of the synchronzaton of lne-start permanent magnet synchronous motors, Proc. of IEEE In. Appl. onf., Roma, 8- Oct., vol., pp [4] K. Kurhara an A. Rahman, Hgh-effcency lnestart nteror permanent-magnet synchronous motors, IEEE Trans. In. Appl., vol. 4, no. 3, ay/jun. 4, pp [5] E. Peralta-Sanchez an A.. Smth, Lne-start permanent-magnet machnes usng a canne rotor, Proc. IED 7, 3-5 ay 7, vol., pp [6] J. Salo, T. Hela, J. Pyrhonen, New low-spee hgh-torue permanent magnet synchronous machne wth bure magnets, Proc. IE, 8-3 August,, Espoo, Fnlan, vol., pp [7] A. Abbas, H.A. Yousef, O.A. Sebahy, FE Parameters Senstvty Analyss of an Inustral LS Interor P Synchronous otor, IEEE Power an Energy Socety General eetng onverson an Delvery of Electrcal Energy n the st entury, - 4 July 8 pp.-6. [8] T. Dng, N. Taorabet, F.. Sargos, an. Wang, Desgn an Analyss of Dfferent Lne-Start P Synchronous otors for Ol-Pump Applcatons, IEEE Trans. agnetcs, Vol. 45, No. 3, arch 9, pp [9] V.B. Honsnger, Permanent agnet achnes: Asynchronous Operaton, IEEE Trans. Power Apparatus an Systems, Vol. PAS-99, No. 4 July/Aug 98, pp [] J.F. Geras,. Wng, Permanent magnet motor technology, arcel Deer Inc. New Yor,. []. Rahman, A. Osheba, T. Rawan, Synchronzaton process of lne-start permanent magnet synchronous motor, Electrc achnes an Power Systems, vol. 5, 997, pp [] Q.F. Lu an Y.Y. Ye, Desgn an Analyss of Large EDPE 9, October -4, 9, Dubrovn, roata

11 apacty Lne-Start Permanent-agnet otor, IEEE Trans. agnetcs, Vol. 44, No., Nov. 8, pp [3] W.H. Km, K.. Km, S.J. Km, et al., A Stuy on the Optmal Rotor Desgn of LSP onserng the Startng Torue an Effcency, IEEE Trans. agnetcs, Vol. 45, No. 3, arch 9, pp [4] A.. Knght an.i. clay, The esgn of hgheffcency lne start motors, IEEE Trans. In. Appl., vol. 36, no. 6, Nov./Dec., pp ,. [5] D. Roger, H.. La, R.J. Hll-ottngham, P.. oles an F. Robnson, A new hgh effcency lne start motor wth hgh startng torue, Proc. Int. onf. PED 6, 4-6 Aprl 6, pp [6] L. Wel, Z. aochen,. Shuang,. Junc, Stuy of Sol Rotor Lne-Start PS Operatng Performance, Proc. IES 8, 7- Oct. 8, pp [7] D. Stoa,. Antonoae, D. Ilea,. ernat, Desgn of Lne Start P otors wth Hgh Power Factor, Proc. POWERENG 7, Setubal, Portugal, -4 Aprl 7, publshe on D-Rom, IEEE atalog Number 7E654, ISBN: , paper 86. [8] G. Yang, J. a, J.. Shen, an Y. Wang, Optmal Desgn an Expermental Verfcaton of a Lne-Start Permanent agnet Synchronous otor, Proc. IES 8, 7- Oct. 8, pp.: [9] L. Zhang, L. Yngl, L. aofang, Z. Jan, Pull out Torue omputaton for Lne Start Permanent agnet otor, Proc. IES 8, 7- Oct. 8, pp [] I. Tsubo, I. Hrotsua, T. Taegam, an. Naamura, Basc oncept of an Analytcal alculaton etho an Some Test Results for Determnaton of onstant of Lne Start Permanent agnet otor, Proc. IES 8, 7- Oct. 8, pp [] H.-P. Nee, L. Lefevre, P. Theln, an J. Soular, Determnaton of an Reactances of Permanent-agnet Synchronous otors Wthout easurements of the Rotor Poston, IEEE Trans. In. Appl., Vol. 36, No. 5, September/October, pp [] T. arcc, G. Stumberger, B. Stumberge,. Hazselmovc, an P. Vrtc, Determnng Parameters of a Lne-Start Interor Permanent agnet Synchronous otor oel by the Dfferental Evoluton, IEEE Trans. agnetcs, Vol. 44, No., Nov. 8, pp [3] A. Levran, E. Lev, Desgn of Polyphase otors wth P exctaton, IEEE Trans. agnetcs, Vol., No. 3, ay 984, pp [4]. omanescu, A. Keyham, an n Da, Desgn an analyss of 4-V permanent-magnet generator for automotve applcatons, IEEE Trans. Energy onverson, Vol. 8, Issue, arch 3, pp. 7. [5] D.. Hanselman, Brushless Permanent-agnet otor Desgn. New Yor: cgraw-hll, 994. [6] J.R. Henershot an T.J. E. ller, Desgn of Brushless Permanent-agnet otor. Oxfor, U.K., agna Physcs/larenon, 994. [7] T.J.E. ller, Brushless Permanent agnet an Reluctance otor Drves, larenon Press, Oxfor, 989. [8] D. Stoa,. ernat, Eucatonal Bench of Lne-Start Permanent agnet Synchronous otors, Part II: The The synchronous operaton, Proc. of the 4 th Internernatonal onf. on Interscplnarty n Eucaton IIE 9, Vlnus, - ay 9. [9] D. Stoa,. ernat, Eucatonal Bench of Lne-Start Permanent agnet Synchronous otors, Part III: The The asynchronous operaton, Proc. of the 4 th Internatonal onf. on Interscplnarty n Eucaton IIE 9, Vlnus, - ay 9. [3] L. Lefevre, J. Soular, Fnte element tme-transent start of a lne-start permanent magnet synchronous motor, Proc. IE,. [3] D. Stoa,. ernat, Eucatonal Bench of Lne-Start Permanent agnet Synchronous otors, Part I: The Operatng Pont of the Permanent agnet, Proc. of the 4 r Intern. onf. on Interscplnarty n Eucaton IIE 9, Vlnus, - ay 9 [3] H. Nam, S.B. Par, G.H. Kang, J.P. Hong, J.B. Eom, an T.U. Jung, Desgn to Improve Startng Performance of Lne-Start Synchronous Reluctance otor for Househol Applances, Proc. IEEE IAS Annual eetng 4, pp [33]. Popescu, T.J.E. ller,. cglp, D.. Ionel, S.J. Dellnger, A Unfe Approach to the Synchronous Performance Analyss of Sngle an Poly- Phase Lne-Fe Interor Permanent agnet otors, Proc. IEEE IAS Annual eetng 7, 3-7 Sept. 7, pp [34] Z. Bngy, Z. We, Z. Fuyu, F. Guhong, Desgn an Startng Process Analyss of ultpolar Lne-Start PS, Proc. IES 7, Seoul, 8- Oct., 7, pp [35] B. Zhang, W. Zhang, F. Zhuang, G. Feng, Desgn an Startng Process Analyss of ultpolar Lne-Start PS, Proceeng of Internatonal onference on Electrcal achnes an Systems 7, Oct. 8-, Seoul, Korea, pp [36] T. ller, Synchronzaton of lne-start permanentmagnet A motor, IEEE Trans. Power Apparatus an Systems, vol. PAS-3, July 984, pp [37] T. ller, Transent performance of permanent magnet A machnes, IEEE IAS Annual eetng 98, Phlaelpha, pp [38] B.L Ahn, W.H. Km, B.S. Km, et al., A Stuy on the Optmal Barrer Desgn for Hgh Effcency of LSP, Proc. IES 8, 7- Oct. 8, pp [39] A. Ncolae, Electrcal achnes. Scrsul Românesc, raova, 975. [4] G.E. hatzaras, Noal Analyss Optmzaton Base on the Use of Vrtual urrent Sources: A Powerful New Peagogcal etho, IEEE Trans. Eucaton, vol. 5, no., February 9, pp [4] D.h. Karamousantas, G.E. hatzaras, G.N. Korres, P.J. Katsas, Obtanng State Euatons for Planar Nonegenerate Lnear Electrc rcuts usng esh Analyss wth Vrtual Voltage Sources," IJEEE (Internatonal Journal of Electrcal Engneerng EDPE 9, October -4, 9, Dubrovn, roata

12 Eucaton), anchester Unversty, Vol. 45, No. 3, July 8, pp APPENDI: NOENLATURE B - magnetc flux ensty; B - pont on the lnearze characterstc B = f (H); b - slot openng; B N - magnetc flux ensty corresponng to the operaton pont N ; B rem - remanent magnetc flux ensty; B sat - saturate magnetc flux ensty; B sy - yoe magnetc flux ensty B " nonln - unsaturate magnetc flux ensty; B " - magnetc flux ensty corresponng to useful argap flux! " ; p - permeance coeffcent;! - flux concentraton factor; D - mean P ameter; f - freuency; F - magnetomotve force (mmf); F a - rotor referre armature reacton mmf; F c - coercve mmf; F ca - apparent coercve mmf; F N - mmf corresponng to the P operaton pont N; F rt - rotor tooth mmf; F ry - rotor yoe mmf F st - stator tooth mmf; F sy - stator yoe mmf; F " - ar-gap mmf; H - magnetc fel ntensty; H c - coercve magnetc fel ntensty; H ca - apparent coercve magnetc fel ntensty; h y - yoe heght; H y - yoe magnetc fel ntensty; - armature current, nstantaneous value; I - armature current, rms value; a - armature reacton factor; - arter s coeffcent; f - form factor of the exctaton fel; f - form factor of the armature reacton fel; Fe - lamnaton stac coeffcent; sat - saturaton coeffcent; w - stator wnng factor; # - coeffcent of the P leaage flux; L - synchronous nuctance; L a - self nuctance; l Fe - lamnaton stac length; L m - magnetzng nuctance; l - P length n magnetzaton recton; l y - yoe length; L + - leaage nuctance; n s - synchronous spee; p - operator p=/t; p j s Js ; p - pole par number; P em - rate electromagnetc power; P n - nternal power; R - stator wnng resstance; R D - stator referre amper resstance; R D - amper resstance; s - slp; S - - P cross secton area; S sy - yoe cross secton area; S " _ yoe cross secton area; t - tooth wth; T - torue; T av - average torue; T c - cage torue; T em - electromagnetc torue; T l - loa torue; T br - breang torue; T p.o. - pull-out torue; T rel - reluctance torue; T syn - synchronsaton torue; u - armature voltage, nstantaneous value; U - stator voltage, rms value; U e - emf wth armature reacton, rms value; U - no-loa emf (wthout arm. reacton), rms value; U lm -voltage corresponng to the mnmum of the current, rms value; V - P volume; w - number of stator wnngs; - synchronous reactance; a - armature reacton reactance; m - magnetzng reactance;! - leaage reactance; Z r - number of rotor slots; Z s - number of stator slots; % - pole ptch coverage coeffcent of P; " - ar-gap length;,p w - stator wnng losses; - nternal angle of the synchronous motor; - angle between U an U e vectors; - - permeance - - P permeance; - t - permanence of the external magnetc crcut; - " - useful permeance (argap+teeth+yoe); P leaage permeance;. - permeablty of vacuum;. rec - recol relatve permeablty; p - pole ptch length; s -tooth ptch length; ( - loa angle, between U an I vectors;! - magnetc flux;! - P magnetc flux;! N, F N - coornates of the operaton pont N of the P n flux-mmf coornates;! N, F N - coornates of the operaton pont N of the P n flux-mmf coornates;! rem - remanent magnetc flux;! " - useful ar-gap flux wth armature reacton;! " - useful ar-gap flux wthout armature reacton; / - flux lne by the stator wnng; - power angle, angle between U an I vectors; / a -armature reacton flux lne by the stator wnng; / D - flux lne by the amper wnng; / u -mutual fluxb etween the P an the stator wnng; & - geometrcal synchronous angular spee: ) c - cage angular freuency; & s - angular synchronous spee; ) s - synchronous angular freuency; * - salency rato. EDPE 9, October -4, 9, Dubrovn, roata