Proeedngs of he 7h WSES nernonl Conferene on Smulon odellng nd Opmzon Beng Chn Sepemer 5-7 007 434 Effes of he eomer of he Roor Slos on he ehnl Vron of Three-phse nduon oors P.PO-L-OR *Ψ S.PEYOUN ** T.ULWORWNCPON * nd S.SUJTJORN * * Shool of Elerl Engneerng nsue of Engneerng Surnree Unvers of Tehnolog Nhon Rhsm 30000 TLND ** RT dem r Eduon nd Trnng Commnd Bngo 00 TLND Ψ orrespondng uhor: pde@su..h sr: - Ths pper presens he developmen of mheml models nd smulons of mgne feld nd mehnl vron n hree-phse squrrel-ge nduon moor. s m s o ompre he vron mgnude when he moor possesses dfferen geomerl roor-slo shpes. The ross seonl res of wo pl sem-losed slo shpes (rengulr nd round shpes) re ep equll onsn ordng o he EEE sndrd. Under n ssumpon of snusodl moor eon he smulon wors emplo he fne elemen mehod (E) nd he Newon-Rphson mehod o solve me vrng nonlner equons. The numerl soluons oned nde he eleromgne fore dsruon over he moor ross seonl re. Suh fores use mehnl vron n he moor. To evlue hs vron he dsplemen of sor nner permeers ws oserved refull. s resul he round roor slo gves 4.8% less vron hn he rengulr roor slo does. e-words: - ehnl Vron Eleromgne ore Compuer Smulon ne Elemen ehod nduon oors Roor Slos nroduon ehnl vron n nduon moors hs long hsor. n prevous wors he sud of n nduon moor onsdered resuln moor vron. The wors durng 990-993 [] onsdered vron used roor eenr nd suppl hrmon produed n nverer soure. The wor [3] suded he effes of roor slo sewness on moor vron. rom 997 ll presen he numer of sor nd roor slos hs een refull desgned o redue moor vron [45]. The sud of he shpes of roor slos h nfluene he moor vron hs no een onsdered efore. Ths s n mporn ssue ddressed hs pper. B our pproh omprson sudes of roor slo shpes ffeng moor vron ordng o wo EEE sndrd shpes hve een omplshed [6]. Ths pper llusres numerl pproh o mgne feld modellng of squrrel-ge nduon moor fed snusodl soure. The wodmensonl nonlner me-seppng fne elemen mehod (E) s used for eleromgne feld ppromon n he moor operng wh full-lod sed-se revoluon. The ompued eleromgne fores re used s he eernl fores ppled o he moor o use vron. The pprohes of vron nlss re E. The effes of he roor slo shpes on vron re lso nvesged. odellng for Compuonl Eleromgne nd ehn n mgne feld lulon he mgne veor poenl rres undle of nformon onssng of flu dens B nd ndued mgne fores. or onvenene some ssumpons re mde s follows: he mgne feld presens n he ross-seonl () plne; he mgne merls of he ores re nonlnerl sorop. ene Eq. () desres he emporl nd spl vrons of [7]. ν ν s σ J 0 0 () where ν s he reluv of he merl σ s he onduv of he roor ondung med s s he moor slp nd J 0 s he ppled urren dens. Our wors [89] hve ulzed he fne elemen mehod for solvng he equon (). We doped he lern weghed resdul mehod o derve he elemen equon on he ss of he well s equons. Resulng from equon () wh he
lern weghed resdul mehod ppled [0] we rrve he followng epresson [ ]{ } [ ]{ } { } ɺ () where [ ] sσ e [ ] e Sm ν 4 { } 3 J 0 e where e s he re of he rngulr elemen whh s e The equon () desres he mgne veor poenl s spe-me funon. To smule he moor movemen we need o dsreze equon (). We use he wrd dfferene mehod for he dsrezon euse of s good onvergen proper. ene he me dervves of he mgne veor poenl n e epressed { } { } { } ɺ (3) The dsree form of equon () me s [ ]{ } [ ]{ } { } ɺ (4) nserng equon (3) no equon (4) one ould on [ ] [ ] { } [ ]{ } { } (5) To solve equon (5) requres n effen erve mehod of solvng nonlner me-seppng equons. We ppl he N-R mehod o solve he equons. ddonll our pproh emplos he BC mehod s s nernl sruure o solve lnerzed equons. Regrdng o he pproh he mr form of he N-R equon governng he elemen n e found s equon (6) where he lefmos mr s Jon (6) n whh nd represen he frs seond nd hrd row equons emedded n equon (5) respevel. gure shows he proposed sem-losed roor slo shpes whh hve equl ross-seonl res. The ross-seons of he moors re dsrezed no mnue rngulr elemens. gure shows some prs of he dsrezed ross-seons. The enre ross-seon of moor for eh slo shpe onns 54 elemens nd 688 nodes. g.. Dmensons (n mm) of roor slo shpes: ) rengulr roor slo ) round roor slo Proeedngs of he 7h WSES nernonl Conferene on Smulon odellng nd Opmzon Beng Chn Sepemer 5-7 007 435
Proeedngs of he 7h WSES nernonl Conferene on Smulon odellng nd Opmzon Beng Chn Sepemer 5-7 007 436 gp. Surfe plos n fgure 4 dslose he spe-me dsruons of he rdl fores s our ompuonl resuls ordng o he roor slo shpes. The rengulr roor slo gves slghl hgher rdl fores whh use moor vron hn he round pe does. g.. Dsrezed ross-seon of n nduon moor: ) rengulr roor slo ) round roor slo The fne elemen pproh s lso ulzed o lule he moor s vron. The moon n e desred equon (7) n whh [] [C] nd [] re he mss dmpng nd sffness mres respevel. {} represens he eernl fore veor. or our ompuonl vron he sor ore nd he moor frme re onsdered. s ssumed h he fore ng on he ener of eh sor ooh ould e rnsmed hrough o he moor frme []. g. 3. lu lne dsruon: ) rengulr roor slo ) round roor slo [ ]{ dɺ} [ C]{ dɺ } [ ]{ d} { } ɺ (7) The fore ppled o he moor s he ompued mgne fore he ener of eh sor ooh. n ddon he moors re onsdered o hve hnple ross seons []. 3 Resuls nd Dsusson The mhne onsdered hs sud s hreephse four-pole Y-onneed 5-hp squrrel ge nduon moor wh doule ler wndng of 7/9 ph ol. The moor possesses 36 sor slos nd 44 un-sewed roor slos. The snusodl soure provdes 380-V 50-z full lod (slp s 0.03). The ompuon of flu lnes nd eleromgne fores ws ondued usng n E solver developed n C he uhors. Numerl resuls of he mgne veor poenl for eh se re llusred s shown n fgure 3. gure 3 llusres he flu lne dsruons hrough he moor rossseons orrespondng o he roor slo shpes. s n e seen he rengulr roor slo produes more lnge flu flowng no he slo hn h of he round roor slo. The url of he mgne veor poenl s mgne flu dens B (B ). well s sress equons were used o deermne he dsruon of he mgne fores ross he r g. 4. Spe-me dsruon of rdl fores: ) rengulr roor slo ) round roor slo Our E solver developed n C hs een used o solve he moon equon o on he vron soluons. The E solver provdes soluons
Proeedngs of he 7h WSES nernonl Conferene on Smulon odellng nd Opmzon Beng Chn Sepemer 5-7 007 437 dslosng he dsorons of he sor nner permeer s shown n fgures 5 nd 6 for he rengulr nd he round roor slos respevel. The sold lnes n hese fgures represen he permeer n norml suon. The dshed lnes show he nsnneous dsplemen or dsoron mgnfed 0 9 mes. The verge dsplemens n one revoluon re 6.963 0-8 nd 5.8989 0-8 mm orrespondng o he rengulr slo nd he round slo respevel. n he mehnl vron pon of vew he round shpe gves 4.8% less vron hn he rengulr one does due o he shllowness of he rle slo. Therefore here re less mgne flu lnes flowng no he slo n hs se o use less vron ompred wh he deeper slo of he rengulr pe. 4 Conlusons Ths pper presens he mheml desrpon nd he grphl nerpreon for mehnl vron of nduon moors resulng from ndued eleromgne fores. When he EEE sndrd roor slo shpes of equl slo res.e. ) rengulr shpe nd ) round shpe re hllenged oservng he mehnl vron round he sor nner permeer he round se gves less vron of 4.8% hn he rengulr se does. We n onlude h when he mehnl vron s en no oun n he roor slo desgn he round shpe s preferle o gve less vron hn he rengulr one les he resuls from our omprehensve sudes. owever for ompleon of moor s roor desgn oher fors suh s orque-speed urves hrmon urren drwn from suppl e. re lso vl nd should lso e onsdered durng he desgn phse. g. 5. Dsoron of he sor nner permeer orrespondng o he rengulr roor slo g. 6. Dsoron of he sor nner permeer orrespondng o he round roor slo Referenes: [] R.J.. Belmns D. Verd W. esen R.D. ndl Elero-mehnl nlss of he udle nose of n nverer-fed squrrel-ge nduon moor EEE Trnsons on ndusr pplons Vol.7 No.3 99 pp. 539-544. [] W.R. nle Nose n nduon moors-uses nd remens EEE Trnsons on ndusr pplons Vol.7 No.6 99 pp. 04-3. [3] D.. Dorrell Clulon of unlned mgne pull n smll ge nduon moors wh sewed roors nd dnm roor eenr EEE Trnsons on Energ Converson Vol. No.3 996 pp. 483-488. [4] T. osh. Tm. o S. Shuw Effes of slo omnon on ous nose from nduon moors EEE Trnsons on gnes Vol.33 No. 997 pp. 0-04. [5] B.T. m B.. won S.C.Pr Reduon of eleromgne fore hrmons n snhronous ron moor dpng he roor slo numer EEE Trnsons on gnes Vol.35 No.5 999 pp. 374-3744. [6]. Bolde S.. Nser The nduon mhne hndoo lord US 00. [7].E. Ngw R.E. nhon E.D. rhm Deeon of roen rs n he ge roor on n nduon mhne EEE Trnsons on ndusr pplons Vol.8 No. 99 pp. 65-7. [8] P. Po-l-or S. Peoung T. ulworwnhpong S. Suorn odellng
Proeedngs of he 7h WSES nernonl Conferene on Smulon odellng nd Opmzon Beng Chn Sepemer 5-7 007 438 nd smulon for mgne flu dsruon n nduon moors Pro. he 4 h STED nernonl Conferene on odellng denfon nd Conrol (C 005) usr 005 pp. 339-344. [9] P. Po-l-or T. ulworwnhpong S. Suorn S. Peoung Dsruons of lu nd Eleromgne ore n nduon oors: ne Elemen pproh WSES Trnsons on Ssems Vol. 5 No. 3 006 pp. 67-64. [0] T.W. Preson.B.J. Reee P.S. Sngh nduon moor nlss me-seppng ehnques EEE Trnsons on gnes Vol.4 No. 988 pp. 47-474. []. shsh. mmoo S. Nod. om Smll nduon moor nose lulon EEE Trnsons on Energ Converson Vol.8 No.3 003 pp. 357-36. [] J.S. Ro Dnms of ples Nros Pulsher New Delh 999.