MODELING AND STEADY-STATE PERFORMANCE ANALYSIS OF A BRUSHLESS DOUBLY FED TWIN STATOR INDUCTION GENERATOR

Transcription

1 MODELING AND STEADY-STATE PERFORMANCE ANALYSIS OF A BRUSHLESS DOUBLY FED TWIN STATOR INDUCTION GENERATOR Duo Basi 1, Jian Guo Zhu, and Gad Boadman 1 PDL Eltonis, 81 Austin Stt, Onkawa Faulty of Engining, Univsity of Thnology, Sydny PO Box 741, Nai, Nw Zaland PO Box 13 Boadway NSW 007, Austalia Phon: (Ext Phon: Fax: Fax: duo.basi@dl.o.nz jo@ng.uts.du.au Abstat This a snts an imovd stady-stat modl and foman study of a bushlss doubly fd twin stato indution gnato (BDFTSIG. Th oosd stady-stat modl is modifid to tak into aount magnti satuation and stato and oto o loss. Ths modifiations a ssntial fo alisti sults in th BDFTSIG aliations as th ontol stato mahin woks at vaiabl flux lvls and an asily om into magnti satuation whil th oto fquny is nomally muh high than that in standad indution mahins so that oto o losss annot b ngltd. Th modl is vifid by ximnts and th foman analysis indiats th fasibility of th BDFTSIG fo vaiabl sd gnato aliations. 1. INTRODUCTION Doubly fd indution mahins hav a gat advantag in high ow vaiabl-sd gnato aliations as indndnt ontol of ativ and ativ ow an b ahivd by using a ow ltoni onvt onntd to th oto iuit so that it handls only th sli ow and onsquntly an b atd fo a fation of th stato VA ating [1,]. To ombin this gat advantag of doubly fd gnatos with high liability and low maintnan quimnts by avoiding th us of th sli ings and bushs a nwd sah ffot has bn mad to dvlo altnativs fo lassial sli-ing doubly-fd indution mahins. Fo xaml, th us of two asadd indution mahins and assoiatd ontol statgis a invstigatd by Hofnsg [3,4] whil th ontol of two asadd mahins unifid in on with a sial oto ag dsign is xtnsivly xamind by th sah gou at th Ogon Stat Univsity [5]. In this a w will fous ou attntion on so alld th Bush-lss Doubly Fd Twin Stato Indution Gnato (BDFTSIG. Basially th BDFTSIG onsists of two asadd indution mahins, magntially and ltially insulatd, with ommon shaft and intonntd otos lad in a ommon housing. Th fist stato winding (ow winding is ditly onntd to th ow systm gid whil th sond stato winding (ow winding is sulid fom a ontolld voltag o unt sou of vaiabl V s f, I s ow mahin I IM 1 IM - - squn inthang ontol mahin I Figu 1. BDFTSIG ont. I s V s f, fquny. In ou study a funtional quivalnt of th BDFTSIG omising of two wound oto indution mahins (Fig. 1, ow and ontol mahin is usd with th otos mhanially and ltially ould though th sli-ings & bushs similaly as in [3,4]. Th sli ings and bush gas not ndd in al BDFTSIG systm. In a sial oation mod (synhonous mod th oto unt fquny in th both mahins is th sam so that th ow winding an b ontolld though th otos fom th ontol stato in a bushlss mann. BDFTSIG is abl to gnat th ow at th ow systm sid at onstant (ow systm fquny and vaiabl oto sds oviding that th ontol sid is fd by an aoiat fquny so that th synhonous oation is maintaind. By adjusting th has and magnitud of th ontol mahin stato unt (xitation unt th amount of th ativ and ativ ow flowing though th ow systm an b dynamially ontolld. Fo this a vto ontol shm with ointation on th ow mahin stato flux is favouabl [3] whih is basially th sam as th shms in [1,] usd fo standad doubly fd sli ing mahins. Majo aa fo th aliation of th BDFTSIGs is onsidd to b high ow wind gnatos wh vaiabl-sd oation, high liability and low maintnan of th gnatos lad on high tows a vy imotant. As all vaiabl-sd onstantfquny gnatos th BDFTSIG an b ontolld to maximis th systm ffiiny by atuing maximum wind ow at th oto sd tund aoding to th wind sd (maximal ow taking, mitigat mhanial stsss on th shaft and gas ausd by wind gusts (i.. to sto wind ngy in th mhanial intia of th tubin, omnsat fo ow ulsation ausd by bak ssu of th tow o to adjust th gnato ow fato [].

2 Most ntly ublishd as hav invstigatd th ontol asts of th bush-lss mahins [3-5] whil stady-stat foman analysis hav not bn disussd in dtail. Ou goal in this a is to snt a siml stady-stat modl of th BDFTSIG whih inluds magnti o satuation and stato and oto o loss into aount to b usd fo th valuations of th BDFTSIG stady stat foman, atiulaly th gnato ffiiny. Suh a modl is imotant fo th BDFTSIG baus th ontol stato is nomally fd fom a ontolld unt sou so that th flux lvl in th ontol mahin an vay onsidably. Also, as th oto fquny is nomally muh high than that in standad indution mahins, oto o losss must b inludd into modl. Stady stat foman of a laboatoy BDFTSIG st-u is valuatd by using this modl and analysd. Th ximntal sults sntd oma vy wll with th thotial and simulation sults and onfim th fftivnss of th BDFTSIG modl. Ovall stadystat foman suggst that th us of th BDFTSIG fo vaiabl sd gnato aliations is fasibl.. DYNAMIC MODEL As th BDFTSIG onsists of two saat indution mahins onntd ltially and mhanially, its modl an b adily dvlod by ombining two of th wll known modls of an indution mahin (ow and ontol mahins. Th voltag quations fo ow mahin ( stands fo ow, fo oto and s fo stato: vs ( R + ( s + j L i + ( s + j L i s s ( R s L i v s Lm i s + + (1 Th voltag quations fo ontol mahin ( stands s m v v and i i (4 wh stands fo onjugation. Finally, fom Eqs. 1-4 th following modl of th BDFTSIG an b divd: v s ( R + ( s + j L i + ( s + j L i s s s m ( ( m is + R + R + s L + L i s Lm s ( R + ( s + j L i ( s + j L i 0 s L i (5 v s s s s m with th total toqu: ( i i T T + T 3 Lm imag s 3 Lm imag( is i 3. STEADY STATE MODEL Fo th stady stat analysis w will suos sinusoidal baland xitations at th both statos. With sinusoidal baland sulis at th both statos th sa vtos hav onstant magnituds and thy otat at th osonding sli fqunis in th oto fn fam. Fo xaml, in th as of th stato voltags, w hav: vs vs j V s jφ V s j V s jφ V s ( t+ φ j( t j( Vs t ( ( t+ φ j( t j( Vs Synhonous oation an ou if th both stato xitations odu th sam oto fquny and squn. Taking into aount that th two otos a mutually onntd with inthangd hass (Eq. 4, th following quation must b satisfid to obtain th synhonous oation: fo ontol: j ( t j ( vs ( Rs + ( s + j Ls is + ( s + j Lm i ( ( R s L i v s Lm i s + + ( Th toqu quations a: 3 ( T Lm imag is i 3 ( T Lm imag is i (3 wh all sa vtos a tansfomd into oto oodinats ( and a numbs of th ow and ontol mahin ol ais. Th two oto a mhanially onntd and thi windings a ltially intonntd so that th oto unts hav oosit squn. With a suh oto intonntion, th oto voltag and unt quations an b linkd by using th following idntitis (it is also ossibl to us a bak-bak onntion without th hang in th has squn []: t t (6 (7 (8 so that th synhonous sd is givn by: + synh (9 + In th synhonous mod th gnal dynami modl givn by Eqs. 5 and 6 an b tansfomd into th following stady stat modl: V s ( R + j X I + j X s s s m I ( + + j j R+ R 0 + j X X I X m Is X m Is s Vs Rs j X s Is j X m I s + (10 s ( ( T 3 Lm imag Is I 3 Lm imag Is I

3 ( I I L imag( I I T 3 Lm imag s 3 3. Roto Pow Balan in th Psn of m s Co Losss (11 wh th slis s To sv ot ow balan at th oto sid th and s a intodud and dfind as follows: oto o looss an not b ditly modlld by intoduing th shunt sistans but it must thy hav to b sald by th oto sli. s and s (1 3.1 Co Loss Modlling Th o loss a modlld lassially by using sistos in aalll with magntising banh. In this way th o losss a ootional to th osonding magntising (volving flux squad. Contay to th lassial modl of an indution mahin, th oto o loss hav to b intodud as th fquny of th oto quantitis in th BDFTSIG is muh high than in standad indution mahins. Sin th sistan modlling th o loss is nomally found fom th no-load tst at 50Hz (ow systm fquny, to tak aoximatly into aount th ombind fquny dndn of th o losss, thy will b adjustd by th fato s 1.3, wh s is th osonding sli. Th ow mahin stato always oats at th ow systm fquny of 50Hz so that no otion to R ms is quid fo th ow mahin stato o losss modlling: Em PF s 3 (13 Rms In th synhonous mod th otos of th both mahins oat at th sam but vaiabl fquny dfind by th oto sliag with st to th ow systm fquny (s : Em PF Rm s Em PF 3 ( Rm s Th ontol mahin stato oats at vaiabl ontol fquny dfind by th s so that th osonding o loss an b found as: Em PF s 3 ( Rms s Pvolving fild T PF + PCu + T T s P PF + PCu + Pmh ( T ( T P F + P Cu ( volving fild F + P P s (16 Cu Thfo in quivalnt shms with th modlld oto o losss an quivalnt shunt sistan R m dndant on th oto sd has to b intodud (Fig., fo xaml: ' 1.3 Rm ( s s R s m (17 Eq. 16 an b viwd as a gnalisation of th taditional stady stat modl whih dos not tak into aount th oto ow losss and wh P volvingfild P Cu /s. It is woth noting that th atual oto o losss should b still alulatd as in Eqs Th diffn btwn th ow dvlod on th modifid sistan R m (s and th oto o loss ow is a lativly small amount of th oto mhanial ow odud by th ltomagnti toqu omonnt atd du to th sn of th oto o losss. Th xistn of this toqu omonnt was ximntally onfimd in no load tsts with on oto iuits and with stato windings ngisd at th nominal voltag of 40V. In th tsts a small toqu omonnt stimatd at -3 Nm was snt atd only du to th xistn of th oto o loss. 3.3 Eltomagnti Toqu in th Psn of Co Losss Toqu quations (Eqs. 11 should b also modifid in th sn of th o losss. No long th stato and oto unts I s, I o I s, I should b usd fo th alulation as in Eq. 11 but th unts I s, I o I s, I whih now mutually intat btwn th stato and oto iuits as an b sn in th modifid quivalnt shm in Fig.. I s R s jx sl jx l R /s R /s jx l I I I' I' s jxsl R s/s I's I' I s V s E m I m R ms s R m / s 1.3 I I F I Fs V V IFs ( onj. I F I m s R ms / s 1.3 V s/s E m jx m squn inthang jx m -s R m / s 1.3 Figu. Equivalnt stady-stat shm fo th BDFTSIG with inludd and ion magnti satuation and o loss

4 ' ' T 3 Lm imag Is I ' ' T 3 Lm imag Is I (18 In this way ow balan is fully satisfid what has bn hkd in simulations. 3.4 Magnti Satuation Modlling As th ontol mahin is usd fo gulating th ativ and ativ ow flows though th ow mahin it dos not wok in th onstant flux mod. Consquntly th satuation fft of th ion o an b signifiant sially whn th ontol mahin is havily xitd foing th ow mahin to gnat ativ ow (aaitiv ow fato. Thus, to obtain a asonabl agmnt btwn th thotial modl and ximntal sults, th satuation fft also has to b modlld. Fo ou stady stat modl th invs uv dsibing I m f(λ m is nssay so that th following ototy uv is usd fo th invs magntising uv modlling: I m b m ( aψ + (1 a ψ (19 m fquny. Th lowst valus of th ontol voltag a found naly at th oto sd osonding to th zo ontol fquny: ( + R s Tabl 1. No load tst sults. Vs [V] Im [A] Xm [Ω] Lm [mh] Ψm [Wb] R s Tabl. Paamts of th BDFTSIG. L sl L l [Ω] [Ω] [mh] [mh] [mh] [Ω] [Ω] modl L m R ms R m 3.5 Fition and Vntilation Toqu Th toqu latd to mhanial loss T fv is modlld simlistially as a lina funtion of th oto sd. Its valu is found to b 6Nm at 1500 m so that: T fv f ( T fvb (0 157 b 4. PERFORMANCE STUDY Th stady stat foman of th BDFTSIG systm is valuatd in th sd ang fom 600 m to 900 m fo onstant ativ ow gnatd though th ow mahin of P s -0kW fo sval ow fatos of th ow mahin of osϕ s 0.8, 0.9 ind., 1 and 0.9 a.. Th ow mahin voltag is 40V/50Hz. In od to find th magntising uv λ m f(i m no load tst was fomd on th ow mahin and th sults a shown in Tabl 1. Ths sults a usd to fit th invs magntising uv modl (Eq. I m f(λ m uv-modl by using th Cuv Ext softwa, Vsion 1.3. It has found that th following uv aamts giv th bst fit: a0.51, b6.5, 6.4 as shown in Fig.3. Th aamts shown in Tabl usd in th foman valuation and thy osond to th aamts of th mahins usd in th ximntal st-u (two naly idntial IM of 0kW/1500m. Th simulation sults shown in Fig. 4 dit how majo quantitis of th BDFTSIG a vaying with th oto oational sd. Fom ths sults it is ossibl to s that th quid ontol voltag (Figs. 4a and ontol winding VA ating (4 dnd almost linaly on th oto sd (i.. on th ontol Figu 3. Eximntal sults and fittd modl of th invs magntising uv As th ow mahin ow is kt onstant (Figs. 4, th ow mahin and ontol mahin stato unts (Fig. 4b a naly onstant but th ontol unt xhibits a high dndn on th ow fato (analogous as in synhonous mahins. Th lowst ontol unt is quid fo th indutiv ow fatos (Fig. 4b, aox. 44A fo 0.8 ind., whil it is onsidabl high if ow fato is aaitiv (Fig. 4b, aox. 61A fo 0.9a.. Du to naly onstant unts th osonding ow losss a also naly onstant (Fig. 4g. Th total ltial ow gnatd by th BDFTSIG is naly linaly ootional to th oto sd (Fig. 4 as th ow of th ontol winding is a lina funtion of th oto sd. Blow th oto sd givn by Eq. th ontol mahin uss a at of th ow gnatd by th ow mahin (uslss iulation of th ow whil abov that sd th ontol winding gnats th ow whih adds u to th ow gnatd by th ow mahin. Thus th gnato ffiiny ogssivly inass as th oto sd inass

5 (Fig. 4h. It has th highst valu fo th indutiv ow fatos sin th ontol unt has th lowst valu (8%. Th toqu in th both mahins is aoximatly onstant in th whol sd ang (Fig. 4f. It an b notid that th ontol mahin toqu is slightly high than that of th ow mahin. As th both mahins sha ommon oto unt this is th sult of a high ai-ga flux in th ontol mahin. Th ontol mahin ai-ga flux (Fig. 4i, Wb in tms of ms valus is stongly dndant on th ow fato. A lativly high lvl of th ontol flux is quid fo aaitiv ow fatos and thus th ontol mahin ion o is magntially satuatd what is fltd, as w alady mntiond, as a vy sha inas in th ontol unt and onsquntly as a high VA ating of th ontol mahin. Th ow mahin ai-ga flux is mo stabl (Fig. 4i, fom Wb as this mahin is onntd at stiff ow systm voltag. To limit VA ating of th ow ltonis onvt to aox. of ¼ of th ow mahin ating (to aox. 5kVA th gnato sd ang should b stitd to 650 m-900 m whil th ow mahin ow fato must b kt in indutiv ang (fably aound 0.9. Although ossibl, it is not onomially justifid to gnat ativ ow (aaitiv ow fatos with th xisting ontol mahin dsign. It would qui th ontol mahin/ow onvt VA atings of naly 50% (10kVA fo 0.9 a. of th ow mahin VA ating (s Fig 5 in th sd ang of 650m o 900m. Th VA ating fo th aaitiv ow fatos an b dud signifiantly but th ontol mahin must b dsignd fo th flux lvls quid fo suh aliations to avoid its havy magnti satuation. As th ltomagnti toqu of th bot mahin a simila th amount of th ativ matials in th both mahins must b naly th sam (sam volum. It may b unxtd as w just hav shown that th ontol mahin VA ating is muh low than that of th ow mahin. Howv th low VA is th sult of a low oational fquny of th ontol mahin (onsquntly low ontol voltag whil th ontol unt and flux a vn high thn ths in th ow mahin. Thfo it is xtd that in alisti BDFTSIG th atual volum of th ontol mahin may nd to b slightly bigg than that in th ow mahin. But it dos not man that in this way w a aying a havy nalty fo avoiding th sli ings and bushs by obtaining a vy bulky gnato systm. 4a. Contol voltag 4b. Contol unt 4. Contol mahin VA ating 4d. Contol ow fato 4. Pow 4f. Toqu 4g. Co+o losss 4h. Effiiny 4i. Ai-ga flux (ms Fig.4 Simulation sults fo P s -0kW fo diffnt ow fatos in th sd ang of m

6 5a. Pow and ontol mahin unts 5b. Pow and ontol mahin unts 5. Toqu 5d. Effiiny Figu 5. Comaison of th simulation and ximntal sults fo 15kW and 0.9 indutiv Th fat is that th both mahins a abl to odu full nominal toqu. Thus in th BDFTSIG w atually doubld th total toqu whil th bas sd is halvd (Eq., th sam numb of ols:, i.. th atio btwn th toqu and sd is simly distibutd (xatly as a ga box dos. Thfo, fo th sam numb of ols of th ow and ontol mahins, th BDFTSIG has ow ating of a singl stato but it bhavs as it had twi numb of ols. Thus it is xtd that th two statos of th BDFTSIG ombind should b naly th sam in volum as th stato of an quivalnt sli ing standad indution mahin of th sam ow and with th ol numb qual +. In ou as w hav obtaind fom two naly idntial 0kW/1500m indution mahins an quivalnt of th BDFTSIG of 0kW oating at th bas sd of 750 m. Eximntal sult fo P s 15kWonst. (du stitd ow of th im mov and ow fato of 0.9 ind. a shown in Fig. 5. Ths sults oma vy wll with th simulation sults what onfims th auay of th dvlod stady stat modl. Big os in th dition of th ontol unt (4A instad 30A, toqu and ffiiny a notiabl whn th o losss and satuation a ngltd (sults makd by o, fo unsatuatd L m L m 85mH, and R ms R m R ms R m. 5. CONCLUSION Th a has sntd stady stat modl of th BDFTSIG that aounts magnti satuation and o losss. Using th oosd modl a foman study of th BDFTSIG has bn aid out. It shows that th BDFTSIG ffiiny vais btwn 70%-8% in th sd ang fom 650 to 900 m (dnding on th ow fato whil th VA ating of th ontol mahin (ow ltonis onvt is lss thn a ¼ of th ow mahin VA ating. As th BDFTSIG bhavs as a obust bushlss quivalnt of a doubly fd vaiabl sd gnato w antiiat that it will b atial fo lag wind gnatos. 6. REFERENCES [1] R. Pna, J.C. Cla, G.M. Ash, Doubly fd indution gnato using bak-to-bak PWM onvts and its aliation to vaiabl sd wind-ngy gnation, IEE Po.-Elt. Pow Al., Vol.143, No.3, 1996, [] S. Mull, M. Dik, R.W. D Donnk, Adjustabl Sd Gnatos fo Wind Tubins basd on Doublyfd Indution Mahins and 4-quadant IGBT Convts Linkd to th Roto, IEEE Industy Aliations Confn, Vol.4, 000, [3] B. Hofnsg, D.J. Atkinson, R.A. Lakin, Stato flux ointd ontol of a asadd doubly-fd indution mahin, IEE Po.-Elt. Pow Al., Vol.146, No.6, 1999, [4] B. Hofnsg, D.J. Atkinson, R.A. Lakin, Combind magntising flux ointd ontol of th asadd doubly-fd indution mahin, IEE Po- Elt Pow Al, Vol.148, No.4, 001, [5] D. Zhou, R. S, G.C. Alxand, Eximntal Evaluation of a Roto Flux Ointd Contol Algoithm fo Bushlss Doubly-Fd Mahins, IEEE Tans. on Pow Eltonis, Vol.1, No.1, 1997,.7-78