ALENAIVE MODEL OF HE DOUBLY-FED INDUCION MACHINE FO POWE YEM DYNAMIC ANALYI oc, F., ewaega, F. an Ec, I. Unvety of Dbg-Een, Inttte of Eectca Powe Engneeng an Atomaton, D-4757 Dbg, Gemany Abtact e pape foce on te tabty of atenatve moe of te oby-fe ncton macne (DFIM fo te ty of cowba acton. e qa-tatonay moe ega te fnamenta feqency tanent n te macne cent an, a a et, can ea to ncoect pecton of te eqence of cowba acton, weea te etae maton of te ente netwok comptatonay nfeabe. Fo te focng pmay on te nfence of te DFIM on te nteconnecte ytem, te qa-tatonay moe can t be e. Fo te etae ty of te macne tanent, oweve, te fft oe moe wt te et of te netwok epeente by a nge-macne opeatng on an nfnte b neceay. maton et ave eveae tat te cowba oe not gnfcanty affect te ea powe otpt of te macne ng fat. Howeve, te effect of te cowba on te eactve powe moe pononce, patcay te econ wtcng tat may take pace afte fat ceaance. taton can mpee te potfat votage ecovey poce n te netwok an a to be conee neabe fom te pont of vew of te netwok. eywo Cowba, Incton geneato, Powe ytem, anent tabty, Wn powe geneaton. INODUCION Wn powe geneaton a expeence a ap gowt n te ecent pat. Wtn a pace of a ecae age mt megawatt nt ave become commonpace. fact ae a ange of opeatona e, wc pevoy wee not of nteet e to te mte abty of te ma wn tbne cattee ove a we geogapc aea to affect te ovea ytem pefomance n any gnfcant way. e potecton ytem of c ma nt wa egne wt meey ef-potecton n mn. In te event of a mao fat n te netwok, fo exampe, wn nt can connect temeve fom te netwok an t own, eavng te tak of eang wt te fat an t aftemat to te conventona pant n te nteconnecte ytem. In gt of te eve nceang ae of te wn powe n te ovea eectc enegy ppy an te ze of te nva nt (aeay n e o ne eveopment, t ot of aocaton of te becomng nceangy ntenabe [1]. Accongy, many powe tte ave fon t neceay to e gene fo te nteconnecton of wn tbne wt te pbc g 1
ettng ot te eqement, wc te wn nt ave to ff ng noma opeaton an fat conton []. e nceae gnfcance an ffon of wn nt togete wt te pcomng new eponbte v-à-v te g ca fo new conto an egn concept tat wo pt te wn geneato n a poton to epon to tee nee n paae opeaton wt te conventona pant. fact necetate a eepe netanng of te ynamc nteacton of wn tbne wt te nteconnecte ytem. pape foce on te moeng of te oby-fe ncton macne n te context of t appcaton a a geneato n vaabe pee wn tbne an t mpcaton on te et of fat maton. MAHEMAICAL MODEL OF HE INDUCION MACHINE e ncton geneato te mot commony e evce fo wn powe geneaton. e two bac atenatve ae te qe-cage type opeatng on a ta-contoe wn tbne an te oby-fe p-ng macne. ee two type ae ao efee to a fxe pee an vaabe pee macne, epectvey. In a fxe pee macne, te no-oa pee of te macne etemne by te g feqency an egn paamete, an te pee o coen tat te wn enegy at te expecte oca wn pee can be optmay expote. Dng noma opeaton of te macne, te pee vae wtn a naow ban n te pe-yncono ange. In a fy vaabe pee macne, oweve, te pee ange may vay omewee between -5% to 5% of te yncono pee. e powe eectonc eqpment pove a vaabe oto votage tat atabe bot n magnte an pae ange. A a et, te oto pee can be vae to matc te optmm opeatng pont n te poweeffcency cve at any pactca wn pee. capabty of te macne to cange t pee a neceay can ea to an nceae n anna enegy pocton of p to 5% [3]. Befoe te maton et of a ot cct n te netwok obtane ng te atenatve ncton macne moe ae ce te genea matematca eatonp govenng te eectomecanca enegy conveon poce w be mmaze. Fft oe moe Eqaton (1-(5 epeent te compete et of matematca eatonp tat ecbe te ynamc beavo of te macne. e pecpt enote an abtay efeence fame otatng at te pee. (If coen to be, te
3 votage, cent an fx nkage pace-pao coepon to te fama compex pao. Votage eqaton: (1 ( ( Fx nkage: (3 (4 wt σ an σ Eqaton of moton: { } ' Im 1 m k m (5 wee σ σ an k σ. e nomencate of a ymbo e n te above eqaton an te eqaton to foow ae gven at te en of te pape. Eqaton (1 an ( eove nto ea an magnay pat togete wt te eqaton of moton (5 conttte te 5 t oe moe of te oby-fe ncton macne. e temna votage fom te nk to te et of te netwok. Qa-tatonay moe (t oe moe e qa-tatonay moe eve ne te ampton tat te tanfome votage n te tato wnng can be negecte agant te mc geate pee votage,.e. (6 eotng to te netwok coonate (coong a efeence fame otatng at a contant pee coeponng to te netwok aan feqency an ng te
fama notaton fo votage an cent pao, we obtan fom (1 fo te tato fx nkage: (7 By btttng (4 nto eqaton (3, te oto cent can be emnate to ye: ( - (8 Eqatng eqaton (7 an (8 et n: ( - - ( k (9 e votage eqaton (9 coepon to te foowng eqvaent cct. z' ' k Fge 1: Qa-tatonay eqvaent cct of te ncton macne e ntena votage n Fge 1 ( a fncton of te oto fx, wc a tate vaabe. btttng (4 nto (, te oto fx can now be bogt to te tate-pace fom: 4
( 1 wee ( k 1 k k L z ' z' L an z' (1 Eqaton (1 togete wt te foowng eqaton of moton conttte te qa-tatonay moe of te ncton macne. 1 ( k Im{ } m (11 m e etemnaton of te oto fx nkage an t te tato cent eqe te nmeca ntegaton of (1 an (11 an te oton of te oa fow eqaton of te netwok on wc te macne opeatng n an atenatng poce. It o be note at t pont tat te matematca eatonp ae va fo bot ncton macne type n eqa meae, wt te ony mofcaton beng tat fo te qe-cage macne te oto votage ( nee to be et zeo. e teay tate moe Befoe te con of te ynamc moe pe fte, te teaytate pefomance of te macne w be evewe befy wt te obectve of entfyng te ange of conto opton an te opeatona capabte of te macne. Negectng te tanfome votage n (1 an ( an n netwok coonate: (1 ( (13 Emnatng te fx nkage ng eqaton (3 an (4, we obtan: ( (14 x x 5
6 x x ( (15 wt Eqaton (14 an (15 can ao be tate ng te eqvaent cct gven n Fge. Fge : Eqvaent cct of te oby-fe ncton macne n teay-tate Eqaton (14 an (15 can ten be wtten n a matx fom an e (afte matx nveon to expe te tato an oto cent n tem of tato an oto votage. y y y y 1 1 11 (16 Eectomagnetc toqe, ea an eactve powe e eectomagnetc toqe eveope by te macne a we a expeon fo te ea an eactve powe eve ng te foowng powe eatonp: (17 btttng te eatonp (1 an ( fo te tato an oto votage n (17: ( ( (18 x σ / x σ / x
7 e at tem n eqaton (18 (epeentng te cange n magnetc fe enegy can be negecte n teay-tate. Afte emnatng te fx nkage ng te appopate eatonp n eqaton (3 an (4, we get: (19 Afte e-aangng an ntocng te p (, we get: 444 4 3 444 14 44444 4 3 444 44 14 G G L L Q P Q P ( ( x x x x ( wee te compex powe at te temna of te macne, P L Q L epeent te oe an te eactve powe conme by te macne. P G Q G ecbe te ntena actve an eactve powe geneaton. epaatng te ntena powe tem nto t ea an magnay component et n: { } (1 Im G x P (1 { } (1 e G x Q ( { } P G Im (3 It now a tagtfowa pocee to eate te powe an toqe eatonp ((1-(3 to te magnte an pae ange of te oto votage by ng (16. e expeon fo te eectomagnetc toqe, fo exampe, : γ δ ϑ β α - co( (4 wee ϑ te ffeence between tato an oto votage pae ange. e ote coeffcent (α, β, δ an γ (efne n te appenx ae fncton of te temna votage an macne paamete, an, a a et, eman contant wen te macne opeate on a contant votage b. ma expeon can be gven fo P G an Q G. γ (n (4 coepon to te ncton toqe an nepenent of te oto votage. On te ote an, te ncton toqe tem (γ zeo wen te macne n at yncono
pee. e toqe at te yncono pee (te yncono toqe can be obtane by ettng n (16. yn α yn β yn co( ϑ -δ yn (5 Opeatona capabte A a et of te appe oto votage, te macne capabe of opeatng at ove-yncono, b-yncono o yncono pee a a geneato. e ea an eactve powe otpt of te macne n eaton to oto votage pae ange wt te oto votage magnte a a paamete ae gven n Fge 3 an 4. e fge emontate te capabty of te macne to opeate n a fo qaant. 3 P n p.. 1-1 - -3 9 18 7 ϑ n 36 Fge 3: ea powe a a fncton of te oto votage pae ange 8
3. Q n p... 1.. -1. -. -3. 9 18 7 ϑ n 36 Fge 4: eactve powe a a fncton of te oto votage pae ange ANIEN ANALYI OF HE DOUBLY-FED INDUCION MACHINE Fft oe ve t oe moe It a been a common pactce to epeent te ncton macne ng t qa-tatonay moe n powe ytem tanent maton. e et obtane ng t moe pove to be atfactoy fo mot appcaton. e nee to evt te e,.e. te con a to te aeqacy of te qatatonay moe to epeent te ncton macne n tanent te o not, a been pompte by te emegng eqement on te wn pant not to connect temeve fom te g n te event of fat. It w be ecae tat a aent feate of te DFIM te fact tat t contan a pe-w moate convete n t oto, wc enabe te conto of te magnte an pae ange of te oto votage. If te DFIM not to be connecte fom te netwok ng fat, a can be foeeen fom te teno of cent con, te oto-e convete nee to be potecte agant exceve cent tat mgt ae a a et of te fat. One c potecton ceme te by-pang of te convete an te connecton of te oto cct to extena mpeance n te o cae cowba potecton. e man obectve of t ty wa to e tee two atenatve moe (te qa-tatonay moe an te moe etae 5 t oe moe to compte te oto cent ng a mao fat an ae te gnfcance of te ece accacy a a et of te e of te qa-tatonay moe an t mpcaton 9
on te pogammng of cowba acton. Ung te moe eveope, cent n te convete ng fat an at convete bockng foowe by connecton to te cowba, te effect of te cowba mpeance on te fat cent, etc. can a be te. Ftemoe, te mpact of cowba wtcng an ten te entatement of te oto-e convete on te ea an eactve powe otpt of te macne can be compte. et ytem e tet ytem, own n Fg.5, compe of a oby-fe ncton macne connecte to a g va a tanfome. Atonay, te tato-e an oto-e convete togete wt te conto ytem ave been mate n eta. e IGB mpemente by a maco moe wtot takng nto accont ete te geomety of te evce o te compex pyca pocee. Fge 5: e et ytem 1
e mate cenao A ymmetca tee-pae fat of 15 m aton ntoce at te netwok b ba on te g votage e of te tanfome. e fat mpeance o coen tat te temna votage at te fat ocaton ece to % of t pe-fat vae. e cowba ogc ate n c a way tat eac tme ng te coe of te fat te oto cent excee a cetan teo vae, te oto-e convete bock an te oto temna ae connecte to one anote tog te cowba (pe etance n t ty. It wa fon ot fom a manfacte cataoge tat te IGB capabe of wttanng a cent magnte twce te ate cent fo a tme pan of no moe tan 1 m [4]. On te ba of t nfomaton an te atng of te macne mate n t ty, a cowba wtcng take pace wen te oto cent excee 1.8 p.. e cowba a a etance eqa to 5 tme te oto etance [5]. Afte te peet tme nteva of 1 m eape te cowba emove an te ogna confgaton of te oto cct etoe. et of te maton Fge 6 an 7 ow te ea an eactve powe otpt of te macne ng fat. A expecte, te t oe moe oe not accont fo te ocatoy 5-Hz component pempoe on te qa-tatonay component an ecbe ony te aveage patten. nce te oto cannot foow te fat ocaton, te qa tatonay moe efect te eectomecanca tanent poce fay accatey. 1.5 P n p.. 1..5 5t oe moe. -.5 3t oe moe -1. -1.5 -..8.13.18.3.8.33 t n.38 Fge 6: Compaon of ea powe otpt obtane ng 3 an 5t oe moe 11
4. Q n p. 3. 5t oe moe. 1.. 3t oe moe -1. -. -3..8.13.18.3.8.33 t n.38 Fge 7: Compaon of eactve powe otpt obtane ng 3 an 5t oe moe Moe nteetng n t ty, oweve, wa to fn ot ow te cowba acton affect te ea an eactve powe otpt of te macne a we a te oto cent n eac pae of te macne. e et obtane ae mmaze n Fge 8 1. e pe-ape o ne n Fge 8 an 9 ncate te tmefame of cowba acton,.e. a vae of 1 mpe te cowba wtce on o ee te oto connecte to te convete. 1.5 P n p.. 1 Cowba.5 -.5 P wtot Cowba -1-1.5 P wt Cowba - 3 3.5 3.1 3.15 3. 3.5 3.3 3.35 t n 3.4 Fge 8: Compaon of ea powe otpt wt an wtot cowba 1
A can be een n te pot (Fge 8 an Fge 9, te cowba omewat ave te pke occng mmeatey afte fat ncepton an ate afte fat ceaance. A fa a te ea powe otpt concene, no fnamenta ffeence to be obeve a a et of te cowba. e effect of te cowba moe pononce a ega te eactve powe otpt. 4 3 Q n p.. 1 Cowba Q wt Cowba Q wtot Cowba -1 - -3 3 3.5 3.1 3.15 3. 3.5 3.3 3.35 t n 3.4 Fge 9: Compaon of te eactve powe wt an wtot cowba e cowba gnfcanty ece te oto cent ng fat, a can be een n Fge 1 a (wtot cowba an 1 b (wt cowba. 8 6 _oto n p.. 4 a b - -4-6 3-pae fat of 15 m 3-pae fat of 15 m -8 Fge 1 a, b: e oto cent ng fat wtot cowba 13
Dcon of te et e mot obvo concon to be ece fom te et obtane n t ty te fact tat te eactve powe otpt of te macne cange gnfcanty afte te econ wtcng of te cowba. In fact, te macne eot to a net eactve powe conme fom a taton wee t wo ave been a net eactve powe ppe wtot te cowba. Fo te macne ne coneaton an fo te gven pe-fat conton, te aton of t nfavoabe eactve powe fow abot.15. Howeve, t taton take pace mmeatey afte fat ceaance an can mpee te pot-fat votage ecovey poce. A c, fom te pont of vew of te netwok, te econ wtcng of te cowba a to be conee neabe. If te wtcng t pove to be neceay, t w pobaby ca fo conte meae to avo a votage ag n te g. e g-e convete wt te conto ytem appopatey egne to ppy te neceay eactve powe - may pove te oton. Anote atenatve te tatc va compenato. On cot gon, te atte opton key to be a vabe oton ony n age wn pak. CONCLUION e qa-tatonay moe ega te fnamenta feqency tanent n te macne cent. A a et, te moe oe not gve te f pcte wt ega to cent n te convete an can ea to ncoect pecton of te eqence of cowba acton. On te ote an, te e of te 5 t oe moe fo a netwok of any pactca ze wo t be qte a caengng comptatona tak n pte of te mmene comptng capabty avaabe toay. o econce tee two confctng eqement, te appoac aopte n t ty wa te maton of te extena netwok ng t evénn eqvaent wen te DFIM moee n eta to capte te fat tanent. kn of moeng can be e wen te man obectve te eveopment an tetng of nge nt. Fo te focng pmay on te nteacton of te DFIM wt a age netwok on wc te macne opeatng, te ato ae of te opnon tat te qa-tatonay moe aeqate. maton on te cowba acton ave eveae tat te econ wtcng of te cowba afte fat ceaance affect te eactve powe otpt of te macne gnfcanty. Wtot a conte meae, t eactve powe fow patten can mpee te votage ecovey n te netwok afte fat. o ae t 14
f extent an to expoe te pobe emea meae, te cowba beavo w be ncopoate nto te qa-tatonay moe n te beqent pae of te ty. NOMENCLAUE Vaabe an contant bcpt/pecpt votage pao n abtay efeence fame oto cent pao n abtay efeence fame tato Ψ fx-nkage man fe aan feqency σ eakage anga pee of an abtay efeence fame compex congate m tbne toqe m neta contant Appenx α a b β ( e{ y } Im{ y } e{ y } Im{ y } 1 1 ( e{ y } Im{ y } e{ y } Im{ y } 11 11 ( y } e{ y } Im{ y } y } e{ y } e{ y } Im{ y } Im{ y } a γ 1 b 1, δ tan 1 1 ( b a ( e{ y } Im{ y } e{ y } Im{ y } 1 11 11 1 1 11 11 x α yn ; ( x x β yn ; δ ( x yn x efeence 1. oc, F.; Ec, I.; ewaega, F.: Dynamc maton of Lage Wn Fam Integate n a Mt Macne Netwok, IEEE PE Genea Meetng, oonto, Canaa, Jy 13-17, 3. E.ON Netz GmbH: Netzancegen Hoc- n Höctpannngnetz, Bayet, 3 3. Akmatov, V.: Vaabe-pee Wn bne wt Doby-fe Incton Geneato; pat I: Moeng n Dynamc maton oo, Wn Engneeng Vo. 6, pp. 85-18 No., 4. EMION nnovaton evce: IGB Powe Eectonc eacng ytem: Pncpe fo zng powe convete, Appcaton note 5. Akmatov, V. Vaabe-pee Wn bne wt Doby-fe Incton Geneato; pat II: Powe ytem tabty, Wn Engneeng Vo. 6, pp. 171-188 No.3, 15