MODELING OF GENERATOR PERFORMANCE OF BLDC MACHINE USING MATHEMATICA SOFTWARE
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1 Pe Nukowe Itytutu Mzy, Npędów Poów Eektyzyh N Potehk Wołwkej N Stud Mteły N 8 8 Fp UTT*, Mhł MICHNA* odeg of eet he peet get, BDC MODEING OF GENERATOR PERFORMANCE OF BDC MACHINE USING MATHEMATICA SOFTWARE I th te thee dffeet ut ode of BDC oto e oped: gge eeget ode, ty efeee fe ode d utpe efeee fe ode. Suto of geeto pefoe we yzed. A thee ode wee deveoped Mthet 5. oftwe.. INTRODUCTION Ye fte ye tehoog pte of udg BDC he of gte powe d otto peed og the ppto e eg. Th otuto ow the poputy to hgh eetoget toque to oto et to d powe to weght to. BDC he e o vey to oto. Vey pott deveopet of ew ode of th he. Oe whh ow ft eut eevg d o the othe hd w e egetg t poe of ety. Mode whh ow e te dgot of he.. MODEING OF BRUSHESS DC MACHINE.. PHISICA MODE Th ppe peet odeg of ufe outed peet get BDC he (fg. ) peeted [] d [5]. Bk EMF geeted tto wdg y PM extto fed tpezod. Stto ftted wth -phe yet wdg, whh egg of tto o e deed ( ), edg of tto o e * Potehk Gdńk, Wydzł Eektotehk Autotyk, ted Eegoeektok Mzy Eektyzyh, 8-95 Gdńk u.nutowz /, h@ey.pg.gd.p
2 58 deed ( ). Beue of PM ue of ode ve e e th tdd woud fed he. A peeted ode e egetg the effet of get tuto, ey, hytee, oggg toque. Fg.. BDC ode tto (,, ) d oto (d, q) xe, whee: F, F tto d oto geto otve foe (MMF), ω eet otto peed, ω eh otto peed, T e eetoget toque, T od toque, J oto et, B eh dupg due to fto, oto poto.. AGRANGE ENERGETIC MODE (MODE-) gge eeget ode deveoped how [4], d ed o vey pe ut wth tto o e edued to e epeeted y get eeet whee: ef d M utu dute d y dptve eeet, whee: R tto wdg ete. The od epeeted y get eeet whee: ef dute d y dptve eeet, whee: R od ete. R epeetg oeto of geeto eut pot to od uppy eut pot. gge futo geezed ve (,,,, ω ): ( ) ( ) () g J t t t M M M ω π π ()
3 584 d the Regh dpto futo geezed ve (,,, ω ): P R () R R ( t) ( ) R ( ) R ( t) R ( t) ( ) ( ) R Dω R The opete gge eeget ode e deved fo: d g g PR v v dt q d g g PR v v dt q d g g PR v dt q d g g PR T dt ω ω () ().. ARBITRARY REFERENCE FRAME MODE (MODE-) The ty efeee fe ode ed o R. H. Pk tfoto peeted [], wth upto tht k EMF (BEMF) uod. Votge equto oto efeee-fe (ty efeee fe) ve: whee: v d qd qd ω dq (4) d t qd qd d the eh equto: q ( t) d ( t) ( t) qd P P Te T Jω Bω P Te ( dq qd ) (5) ()
4 MUTIPE REFERENCE FRAME MODE (MODE-) A t eoted te [] th ode to oe pevou eto exept upto tht BEMF uod. It eey to epeet PM extto fux ouped wth tto o Foue ee [] eue of o uod hte of tto BEMF. Aug tht BEMF hf wve yet thee e oy odd eeet. Th ow u to te tto fux kge equto: ( ) ( ) ) ( (7) Votge equto utpe efeee fe ode e exty the e ty efeee fe. Oy dffeee depto of utu tto d oto fux: ( ) d d d q q q (8) d the eetoget toque defed : ( ) o d q e P T (9). SIMUATION.. STEP CHANGE OF GENERATOR OAD CHARACTERISTICS Fgue how dy htet of BDC geeto dug tep hge of od t.5 []. Dffeee e ee geeted uet etwee ode d (whh e ) d ode. Cuet geeted th uto of MODE- uod d pot fo othe two ode to tpezod. Tht eut fo the ft tht MODE- d MODE- hve defed extto fux Foue ee d the devtve of th ee tpezod.
5 58 Fg.. Dy geeto htet dug od ete tep hge.. SYMMETRICA -PHASE FAUT CHARACTERISTICS Fgue how dy htet of geeto dug yet e-to-e fut. Th fut epeeted y pd hge te t.5 [] of od ete to zeo. I htet of phe uet t e ee tht the ot uuu outo of MODE- whee the fuee of hghe ho oe gft the MODE-. Tht ugget tht MODE- d MODE- e ette th e. Nothg futhe fo the tuth, whe t e tht eh htet outo of MODE- d MODE- e pty ke. Moeove peod opoet of hot ut uet e oeved. Fg.. Dy geeto htet dug yet -phe fut 4. CONCUSIONS Peeted ode we deveoped Mthet 5. oftwe [7]. Th oftwe to othe thet ppto uh MthCAD o Mt. It h vey exteded gph ege wth hepfu peetg eut of uto. It poe to dte whh of thoe thee ode the et. It deped o outoe we expet fo ut ode of eet he. Whe we wt deted htet d ot opted ode to ute ot tu ehvou of oto we woud hoe gge eeget ode (MODE-). Howeve f we wt to eeve outo quky Aty efeee fe ode (MODE-) good hoe. Mutpe efeee fe ode (MODE-) outo etwee MODE- d
6 587 MODE-, whee oe get eut of uto fte the MODE- d oe pee th MODE-. REFERENCES [] P.. CHAPMAN, S. D. SUDHOFF, C. A. WHITCOMB, Mutpe Refeee Fe Ay of No-uod Buhe DC Dve, IEEE Tto o Eegy Coveto (999) [] D. C. HANSEMAN, Buhe peet-get oto deg, MGw-H, I, 994. [] P. C. RAUSE, Ay of eet hey, MGw-H Book Copy, 98. [4] J. MEISE, Ppe of eetoeh-eegy oveo, MGw-H I, NY, 9. [5] P. PIAY, R. NSHNAN, Modeg of Peet Mget Moto Dve, IEEE Tto o Idut Eeto, Vo. 5, No 4, Novee 988 [] Y. S. JEON, H. S. MO, G. H. CHOE, D.. IM, J. S. RYU, A New Suto Mode of BDC Moto Wth Re Bk EMF Wvefo, IEEE [7] S. WOFRAM, The Mthet Book 5 SYMUACJA STANU PRACY PRĄDNICOWEJ MASZYNY BEZSZCZOTOWEJ PRĄDU STAŁEGO Z MAGNESAMI TRWAŁYMI W PROGRAMIE MATHEMATICA W tykue poówo tzy odee zyy ezzzotkowej pądu tłego z ge twły (BDC) w pzypdku py pądowej. Njpotzy ode qd powdzoo do dwóh o potopdłyh zwązyh z wke []. Zkłd o uody ozkłd po w zzee. Mode opy w oh tuyh wypowdzoo w opu o foz gge [4] oże uwzgędć dowoy ozkłd po wzudzoego pzez gey twłe. Mode pośed (g. utpe efeee fe ode) [] uwzgęd euody ozkłd po wzudze pzy jedozey upozzeu odeu. Syuje tu py pądowej wykoo w poge Mthet. Wyk yuj odzweedją óży topeń upozze ode.
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