Full expandable model of parallel self-excited induction generators

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1 Full expndle model of prllel self-exited indution genertors FA Frret, B Plle nd MG Sim *oes Astrt: Self-exited indution genertors (SEIG) offer mny dvntges s vrile-speed genertors in renewle energy systems Smll hydro nd wind generting systems hve onstrints on the size of individul mhines, nd severl indution genertors must e prlleled in order to ess fully the potentil of the site SEIGs onneted in prllel my lose exittion momentrily owing to lrge trnsient urrents used y differenes in individul instntneous voltges nd frequeny This phenomenon nnot e esily simulted using the onventionl models euse it hs suh fst trnsient nture An innovtive nd utomti numeril solution for stedy-stte nd trnsient nlysis of ny numer of SEIGs operting in prllel is presented Experimentl results onfirm the ury of the proposed model nd open new possiilities for inorporting dvned ontrol to monitor nd optimise prllel instlltion of SEIGs The proposed SEIG model is pplied to two-turine se, whih n e extended to simulte wind generting system 1 Introdution There hs een huge inrese in energy demnd, during the lst few dedes, whih hs elerted the depletion of world fossil fuel supplies Environmentl onerns nd interntionl poliies re supporting new interests nd developments for smll-sle power genertion Therefore, the study of self-exited indution genertors hs regined importne, s they re prtiulrly suitle for wind nd smll hydro power plnts [1, 2] They hve dvntges over onventionl synhronous genertors in their redued instlltion ost, lower mintenne requirements, sene of power supply for exittion nd nturl protetion ginst system fults The pplitions of self-exited indution genertors (SEIGs) re limited, sed on eonomi resons depending on the omined osts of mhine, exittion pitors nd stti swithes Typil SEIG lods inlude eletriity for rurl residenes [], heting, lighting nd smll indution motors Typilly, genertors rted 1 kva re ost effetive; ut 1 kva [] ws found to e the upper limit where genertor prie is in the rossover prie urve A stnd-lone SEIG is unlikely to supply the energy demnd of ordinrily growing lods for long time Thus, multiple genertors operting in prllel my e required to hrvest the mximum energy ville t site Also, in the lst few yers, the trend hs hnged from instlling few wind turines to plnning lrge wind frm instlltions with mny indution genertors onneted eletrilly in prllel [, ] With inresing penetrtion of wind power into power networks, n urte dynmi model of the overll wind frm system is required to nlyse the intertion etween the wind frm nd the power system A system of prllel-operted SEIGs, in wind or smll hydro power plnt, is sujeted to vrious trnsient onditions, suh s initil self-exittion, lod trnsient nd genertor/pitor swithing Trnsient intertion nd resonnt sttes my lso e resons for onern, in smll power plnts, s they my rete unstle osilltions, use mehnil elements deteriortion nd trigger protetion iruits Therefore, it is importnt to perform modelling nd simultion nlysis of prllel-operted indution genertors under trnsient onditions Referenes [ 9] developed wind frm model thtneusedinpowersystem dynmi simultions with stedy-stte representtion of the genertor, nd do not del with the trnsient ehviour of SEIGs Severl ppers [1 1] hve een pulished on stnd-lone opertion of selfexited genertors, ut only few referenes re ville on prllel opertion of SEIGs Stedy-stte nlysis of prllel-operted SEIGs hs een disussed [1, 1], ut previous work relted to trnsient nlysis does not present ler numeril modelling nd experimentl oservtions [1, 18] The urrent literture does not pproh prllel opertion under trnsient nlysis with limittions due to pproximted representtion of the indution mhine models In this pper, n utomti proedure to uild up mtrix model for stedy-stte nd trnsient nlysisfvlid for ny numer of self-exited indution genertors operting in prllel nd supplying ommon R L lodfis proposed [19] Figure 1 shows n indution r IEE, 2 IEE Proeedings online no 2 doi:119/ip-ep:2 Pper first reeived 12th June nd in revised form 22nd Otoer 2 G1 G2 Gn FA Frret is with the Federl University of Snt Mri, Ru Dr Bozno, 91 Apto 2, Snt Mri RS 91, Brzil B Plle nd MG Sim*oes re with the Colordo Shool of Mines, 11 Illinois St, Golden, Colordo , USA Fig 1 C1 lod C2 Indution mhines supplying ommon lod Cn 9 IEE Pro-Eletr Power Appl, Vol 12, No 1, Jnury 2

2 mhines redy to e onneted in prllel ording to lod requirements or when more energy eomes ville Suh si ssoition of genertors seems to ope with the vst mjority of prtil ses sine it is lwys expeted to hve new genertor onneted or disonneted from n lredy existing prllel ssoition It should e noted tht eh mhine needs self-exittion pitne, euse eh mhine hs its own mgnetistion urve A omputer lgorithm is developed to simulte the prllel opertion of SEIGs Simulted results for onnetion of two genertors re ompred with experimentl results on two lortory mhines Individul vrition in the mgnetising indutne is inorported in the nlysis A model is then developed for wind turine with n SEIG s the AC genertor Prllel opertion of two wind turines is simulted using rel wind onditions This model llows us to reprodue severl onditions enountered in smll power plnts 2 Model for prllel SEIGs The model to e presented ords with the representtion of n SEIGs s shown in Fig 1 A generlised stte spe eqution for n genertors operting in prllel is shown in (1) Genertor, exittion pitne nd lod prmeters ofthegenertionsystemreseprtedtootinmtrix representtion of prllel genertors in wind or hydro power plnt Inoming genertors n e inorported into the model y ppending the genertor mtrix G digonlly, s shown This mtrix representtion llows us to simulte the ehvior of n genertors in prllel during the self-exittion proess nd in the stedy stte It lso llows us to nlyse the trnsient performne under vrying lod onditions nd genertor swithing Eigenvlue nd eigenvetor nlysis n lso e performed using (1), s it is in the form of the lssil stte spe eqution A detiled SEIG model is developed in Setion : 2 2 i G1 G 1 L 1 i G2 G 2 L 2 p ¼ i Gn G n L n v L C G C G C G C T i L L 2 ð1þ i G1 2 i B 1 2 G2 v G1 B 2 v G2 i Gn v L i L þ B n v Gn where 2 2 i dsi v dsi i i Gi ¼ qsi i dri ; v v Gi ¼ qsi v dri ; v L ¼ v Ld ; i v L ¼ i Ld Lq i Lq i qri v qri SEIG modelling Through () nd Fig 2, lssi mtrix formultion [2] using d q xis modelling is used to represent the dynmis of onventionl indution mhine operting s genertor For n isolted genertor, the prmeters re lelled ording to Fig 2 The representtion inludes the self nd mutul indutnes s oeffiients widely used in mhine theory Using suh mtrix representtion, one n otin the instntneous voltges nd urrents during the self-exittion proess, s well s during lod vritions At this point, it must e sid tht the trditionl d q xis model is not onvenient for the utomti uilding up of generl model of prllel-operted indution genertors, euse it does not isolte the mhine prmeters from the self-exittion pitor nd lod prmeters To isolte those prmeters, () hs een formulted using eight firstorder differentil equtions tht relte the sttor nd rotor urrents nd voltges The simultneous solution of this system of equtions n e otined using the Runge Kutt fourth-order integrtion method with utomti djustment of step This gives the instntneous vlues of d q xis voltges nd urrents for sttor nd rotor The following ssumptions re mde in this nlysis: (i) Core nd mehnil losses in the mhines re negleted (ii) All mhine prmeters, exept the mgnetizing indutne, re ssumed to e onstnt (iii) Sttor windings, self-exittion pitors nd the lod re wye onneted The vrition of the mgnetizing indutne is the min ftor in the dynmis of the voltge uild up nd stiliztion in SEIGs When multiple SEIGs re operting in prllel, the mhine with the lowest sturtion voltge will ontrol the voltge of the whole group So, with mhines of different rtings, the lrger mhines will hve to e de-rted so s to stop them driving the smller mhines The reltionship etween mgnetiztion indutne, L m, nd the mgnetiztion urrent for eh indution mhine ws otined experimentlly The non-liner reltionship etween mgnetising indutne nd mgnetising urrent for the genertor G1 (see Setion ) used in the experimentl setup is shown elow: L m ¼ :89 1 Im þ 1:8 1 Im 1:22 1 Im 2 þ 1:28 1 I m þ :2 1 2 H ð2þ exittion R r1 + L Ir1 L Is1 R s1 pitne R s2 L Is2 L Ir2 + R r2 i qdr1 jω r1 ψ qdr1 i qds1 R i qds1 jω r2 ψ qdr2 i qdr2 ψ qdr1 L m1 ψ qds1 C ψ qds2 L m2 ψ qdr2 L SEIG1 lod SEIG2 Fig 2 Two self-exited indution genertors in prllel represented in d q model IEE Pro-Eletr Power Appl, Vol 12, No 1, Jnury 2 9

3 2 v ds v qs v dr v qr 2 RþLp R s þ L s p þ RCpþLCp 2 þ1 ¼ L m p o r L m L m p R s þ L s p þ L m p RþLp RCpþLCp 2 þ1 2 o r L m R r þ L r p o r L r L m p o r L r R r þ L r p ðþ Eqution () n e expressed s stte vrile mtrix tht tkes the following form: 2 2 i ds R s L r o r L 2 m R r L m o r L m L r i qs o r L 2 m R s L r o r L m L r R r L m i dr R s L m o r L m L s R r L s o r L s L r i qr o r L m L s R s L m o r L s L r R r L s p ¼Kf v Ld 1=CK v Lq 1=CK i Ld i Lq 2 L r i ds L r i qs L m i dr L m i qr 1=CK v Ld 1=CK v Lq 1=LK R=LK i Ld 1=LK R=LK i Lq L r L m L r L m 2 L m L s v ds L m L s v qs þ v dr g ðþ v qr whih is in the form of lssil stte-spe eqution p[x] ¼ [A][x]+[B][u], or: i G G p v C ¼ C i G v C þ ½BŠ½v G Š ðþ i L L i L where G, C nd L refer, respetively, to the prtition of mtrix [A] into mtries for the indution genertor prmeters, the self-exittion pitne nd the lod Vetor [x] is the trnsposed mtrix [i G v C i L ], nd the sumtrixes [G], [C] nd[l] re defined s: 2 R s L r o r L 2 m R r L m o r L 2 m R s L r o r L m L r ½GŠ¼K R s L m o r L m L s R r L s o r L m L s R s L m o r L s L r o r L m L r L r R r M L r o r L s L r L m R r L s L m i ds i qs i dr i qr phse voltge, V rotor speed, simulted time,s 1=C 1=C ½CŠ¼½C G C r Š ¼ 1=C 1=C 1=L R=L ½LŠ¼ 1=L R=L nd K ¼ 1=L 2 m L sl r The exittion vetor [u] ¼ [v G ] of () is multiplied y the exittion prmeter mtrix [B] shown elow Therefore, [B][u] defines the voltges orresponding to the residul mgnetism in the mhine ore: 2 L r L m L r L m L m L s L ½BŠ¼ m L s Figure shows the experimentl nd simulted plots of the trnsient self-exittion proess of stnd-lone SEIG Lod is swithed on t s The indution genertor ws operted t 18 with DC motor s prime mover A pitor nk of 1 mf in str onnetion supplied out VAR/phse of retive power for the mhine, nd 12 O 22 mh str lod ws onneted fter the genertor ws ompletely exited Vrition of speed oserved in the lortory when lod ws pplied is inorported in the numeril simultion seen in Fig, whih depits simulted nd pproximted shft speed Remnent mgnetism in the mhine ore is lso tken into ount nd is explined in Setion The omplete simultion proess is detiled in the following setions Figure shows n SEIG onneted in str with n exittion pitor nk with neutrls isolted The nturl onsequene of this type of onnetion is third hrmonis in phse voltges Simultion nd experimentl results do not show ny signifint third-hrmoni ontent s the mhine ws run under light sturtion High urrents n flow through the pitors when run under deep sturtion Also, the exittion pitor long with the mhine indutne ts s lowpss filter ttenuting the thirdhrmoni voltges present in the phse voltges Figure pproximted shft speed Fig Self-exittion nd lod response of stnd lone SEIG Rotor Vrition in phse voltge mesured during self-exittion nd lod swithing on genertor G1 (see Setion ) Vrition in phse voltge simulted using MATLAB 98 IEE Pro-Eletr Power Appl, Vol 12, No 1, Jnury 2

4 C V n of only smll soure of pplied voltge to the rel mhine, for reovery of its tive stte during the ourrene of fortuitous ore de-exittion Turine model Fig ttenution, db Fig C 1 1 Frequeny response of SEIG Tle 1: Genertor rtings nd prmeters Genertor G1 C db t 18 Hz frequeny, Hz Genertor G2 P ¼ 1HP R s ¼ 2 O P ¼ 1HP R s ¼ 9 O 1, Hz X ls ¼ 8 O 1, Hz X ls ¼ 9 O V ¼ 12/22 V R r ¼ 1 O V ¼ 12/22 V R r ¼ O I ¼ 11/ A X lr ¼ 8 O I ¼ 11/ A X lr ¼ 9 O V n V n SEIG onneted in str with exittion pitors Wind energy systems re usully omposed of the turine, gerox, genertor nd lod The wind turine power is given y: P w ¼ rv pr 2 CP =2 ðþ where r ¼ ir density V ¼ wind speed r ¼ propeller rdius CP ¼ wind turine power oeffiient (usully expressed s funtion of tip speed rtio l) Power oeffiient is not onstnt, ut vries with the wind speed, rottionl speed of the turine nd turine lde prmeters The torque generted y turine is given y: T w ¼ rv 2 pr CT =2 ðþ where CT ¼ CP/l is the torque oeffiient nd the eletromgneti torque generted y the indution generted is: T g ¼ :PMði ds i qr i qs i dr Þ ð8þ The mhine swing eqution is given y: dw r ¼ P dt 2J ðt w T g 2 P Bw rþ ð9þ where P is the numer of poles of the genertor, M is the mgnetising indutne, nd J nd B re the overll system inerti nd visous frition oeffiient, respetively Eqution (9) represents the wind turine s single lumped inerti; ut, if required, (9) my e expnded to inlude the msses of the genertor, gerox nd ldes with the ssoited prmeters A mtrix eqution similr to (1) for the rotor speeds of n SEIGs operting in prllel n e otined from (9) Using n itertive proess, the instntneous prime mover speeds n e lulted Simultion of prllel-operted SEIGs shows the frequeny response of the SEIG for the prmeters shown in Tle 1 The SEIG model presented ove is for the onfigurtion in Fig, nd further work is required to inorporte other onfigurtions, lthough, in prtie, it hs een oserved tht ross-onnetion is not desirle euse of the floting neutrl nd voltge imlnes At this point, it is interesting to note tht, to egin the self-exittion proess of the indution genertor, ertin mount of residul mgnetism must e present, tht is, it is ondition sine qu non This effet lso needs to e tken into ount in the numeril simultion of the selfexittion proess, without whih it is not possile to strt the numeril integrtion proess At the eginning of the integrtion proess of () nd (), n impulse funtion ws used to represent the trnsient existene of the residul mgnetism tht fdes wy fter the first itertive step Any other representtion of the wy the residul mgnetism fdes wy my e eptle This oservtion is very importnt in the dynmi understnding of the selfexittion phenomenon, euse it would justify the use Simultions hve een developed in MATLAB The routine shown in Fig is used to predit the generted voltge from two given self-exited indution genertors operting in prllel This routine n e extended for ny numer of genertors operting in prllel Remnent mgnetism in the mhine is tken into ount, without whih it is not possile for the genertor to self-exite As stted ove, n impulse funtion is used to represent the remnent mgneti flux in the ore The min routine lls for the suroutine shown in Fig, to solve the differentil equtions Results nd disussion The model proposed for prllel-operted SEIGs is investigted in the lortory using two identil indution mhines driven y two different DC motors Figure shows experimentl mgnetistion urves for eh indution genertor A fourth-order polynomil urve fitfdesriing the non-liner reltionship etween irgp voltge nd mgnetizing urrentfws otined from experimentl dt The prmeters in Tle 1 were used for simultion In ddition to the stnd-lone opertion of n SEIG IEE Pro-Eletr Power Appl, Vol 12, No 1, Jnury 2 99

5 strt red mhine prmeters, mgnetiztion hrteristis initilize residul mgnetism; set itr = V g, V G2 G1 simulte stnd-lone opertion of genertor-1 using the su-routine in fig () swith lod when genertor is ompletely exited Fig I m, A Mgnetistion hrteristis of genertors G1 nd G2 simulte stnd-lone opertion of genertor-2 using the su-routine in fig () rotor speed, pproximted shft speed simulted lose the prlleling swith t the hosen instnt 1 simulte stnd-lone opertion of two genertors using the su-routine in fig () strt phse voltge, v 1 1 if itr < mx_itr solve the stte-spe eqution for the d-q prmeters using Runge- Kutt fourth order method lulte the mgnetiztion urrent nd updte mutul indutne N Y end simultion of two wind turines using rel wind dt operting eletrilly in prllel Fig 8 Voltge ollpse in stnd-lone SEIG under hevy lod Rotor Vrition in phse voltge mesured during ollpse of G1 Vrition in phse voltge simulted itr = itr + 1 if itr > 1 N reord instntneous genertor phse voltges Fig Min progrm to simulte prllel opertion Su-routine for numeril solution remove the initil impulse pplied for residul mgnetism supplying medium lod disussed in Setion, four other ses hve een disussed in this pper: voltge ollpse in stnd-lone self-exited indution genertor due to hevy lod trnsient phenomen of lod nd genertor swithing of two SEIGs operting t different voltges levels trnsient phenomen of lod nd genertor swithing of two SEIGs operting t similr voltge levels Y Figure 8 shows the experimentl nd simulted plots of terminl voltge ollpse of stnd-lone SEIG under pplition of hevy R L lod t time ¼ 2 s Genertor G1 ws self-exited with 1 mf pitne nk, nd O mh str lod ws pplied fter the genertor ws fully exited Speed vritions oserved in the lortory were tken into ount for simultion, s illustrted in Fig 8 It took out 2 s for the voltge to ollpse ompletely To void the ollpse, n eletroni protetion sheme n e used to detet the urrent levels If the ollpse ours, the mhine hs to e re-mgnetised Figure 9 shows the trnsient proess of lod nd genertor swithing of two SEIGs operting in prllel Genertor G1 ws self-exited with 1 mf pitne t 18, nd 1 O 22 mh str-onneted lod ws pplied t time ¼ 2 s Genertor G2 ws previously selfexited with 1 mf t 18, nd onneted in prllel t time ¼ s The sudden nd rief ollpse in voltge is due to differenes in phse voltge of the two genertors, t the prlleling instnt Full ommon voltge ws reovered t out time ¼ s The rotor speed vrition of genertors G1 nd G2, during prllel opertion, ws refully oserved in the lortory nd ws inorported in the simultion, s illustrted in Fig 9 At the preise 1 IEE Pro-Eletr Power Appl, Vol 12, No 1, Jnury 2

6 rotor speed, phse voltge, v pproximted shft speed simulted d Fig 9 Prllel onnetion of two SEIGs with different voltge levels Rotor Vrition in phse voltge of G1 mesured Lod pplied t t ¼ 19 s, nd prlleling swith losed t t ¼ 8 s Simulted vrition in phse voltge of G1 d Simulted vrition in phse voltge of G2 rotor speed, phse voltge, v pproximted shft speed d simulted Fig 1 Prllel onnetion of two SEIGs with similr voltge levels Rotor Vrition in phse voltge of G1 mesured Lod pplied t t ¼ 12 s, nd prlleling swith is losed t t ¼ s Simulted vrition in phse voltge of G1 d Simulted vrition in phse voltge of G2 instnt of prllel onnetion of the two genertors, hevy dip in the overll speed of the mhines ws notied Three moments should e pointed out in those grphs The first is relted to the voltge redution ross genertor G1 s terminls when the R L lod ws swithed on The seond is the prtil voltge ollpse t time ¼ 8 s, nd its reovery up to the prllel ommon voltge level t out s The third moment to oserve is the redued voltge of genertors G1 nd G2 with respet to the no-lod voltge level of G2 lone representing n ppreile voltge differene t the prllel onneting instnt These three moments n e lerly nd losely oserved in oth theoretil nd experimentl setups Synhronistion tehniques ould e inluded so s to swith the genertors when the phse voltges re in phse The purpose of this result ws to demonstrte the possiility of representing the worst-se senrio using the proposed model Figure 1 shows the experimentl nd simulted plots of trnsient genertor swithing proess when prllel onnetion ws mde etween SEIGs operting t identil voltge levels Genertor G1 ws self-exited with 18 mf pitne, nd 1 O 22 mh str lod ws pplied t time ¼ 12 s Genertor G2 ws lredy self-exited with 1 mf nd ws onneted in prllel t time ¼ s Full ommon voltge ws reovered t out time ¼ 2 s As the voltges were similr, there ws no ollpse s oserved in the previous se, nd the voltge nd speed dips were not very pronouned Figure 11 shows the simulted plots of two 2 kw wind turines operting eletrilly in prllel Figure 11 shows the wind of the two turines The genertor egins to self-exite fter the rotor hs rehed ertin speed (1) As the wind speed inreses, the generted voltge lso inreses (2) The dip in voltge t () orresponds to lod swithing G2 is onneted to G1 t () to shre the lod, resulting in slight inrese in the G1 voltge Figure 12 shows the simulted rotor speed nd torque vritions during lod nd genertor swithing proess The torque surge experiened y the two mhines, during the swithing of the seond genertor, is very high However, it settled down in few milliseonds; therefore, the system is le to sustin its exittion wind speed, m/s phse voltge, v Conlusions v w1 vw2 An innovtive model to simulte the eletromehnil stedy-stte nd trnsient performne of ny numer of wind turines with indution genertors onneted in prllel hs een presented With this model, it is possile to hve n utomti omputer proess to generte the stte vrile mtrix representing the inorportion of ny new wind turine to the previous prllel ssoition This feture is gurnteed y the seprte prmeter representtion of the mhine model, the self-exittion nk of pitors nd the lod The pproh presented enhnes previous work sed only on eletril stedy-stte onditions tht ould not e used for rel nlysis of the trnsient phenomenon tht ours nd my hve dverse impt on system stility nd Fig 11 Simultion of two wind turines operting in prllel Wind Simulted phse voltge of G1 Lod pplied t t ¼ s, nd prlleling swith losed t t ¼ 8 s Simulted phse voltge of G2 IEE Pro-Eletr Power Appl, Vol 12, No 1, Jnury 2 11

7 torque, N m rotor speed, protetion Previous work relted to trnsient nlysis does not present ler numeril modelling nd experimentl oservtions Experimentl results prove tht the proposed mtrix prtition is in greement with the mthemtil modelling In ddition, the use of the mtrix prtition proved to e powerful numeril tool The min dvntges of this pproh re: (i) representtion of the self-exited indution genertor in the form of lssil stte equtions; (ii) seprtion of the mhine prmeters from the self-exittion pitors nd lod prmeters, to llow the utomti uilding up of the mtrix representtion of SEIG prllel opertion; (iii) n inrese of flexiility nd simpliity in generlising model for n prllel-operted genertors; (iv) inlusion of eletromehnil stedy-stte nd trnsient nlysis of the prlleling of indution genertors; nd (v) eigenvlues (eigenvetor nlysis n e performed using the lssil stte spe representtion) 8 Aknowledgments The uthors sinerely thnk the Coordintion for Improvement of Advned Edution Personl (CAPES) nd the Ntionl Siene Foundtion (NSF) for their finnil support of this projet T w1 ω r 2 T w2 ω r 1 T g1 T g Fig 12 Simultion of two wind turines operting in prllel Rotor s of two genertors Turine torque nd eletromgneti torque of G1 Turine torque nd eletromgneti torque of G2 9 Referenes 1 Chn, TF, nd Li, LL: A novel exittion sheme for stndlone three phse indution genertor supplying single-phse lods, IEEE Trns Ind Appl, 2, 19, (1), pp Bnsl, RC, Bhtti, TS, nd Kothri, DP: Biliogrphy on the pplition of indution genertors in nononventionl energy systems, IEEE Trns Energy Convers, 2, 18, (), pp 9 Mrr, EG, nd Pomilio, JA: Self-exited indution genertor ontrolled y VS-PWM idiretionl onverter for rurl pplitions, IEEE Trns Ind Appl, 1999,, (), pp 8 8 Elder, JM, Boys, JT, nd Woodwrd, JL: Self-exited indution mhine s smll low-ost genertor, IEE Pro C, 198, 11, (1), pp 1 Muljdi, E, Slln, J, Snz, M, nd Butterfield, CP: Investigtion of self-exited genertors for wind turine pplitions, Thirty-Fourth IEEE IAS Annul Meeting, 1999, 1, pp 9 1 de Mello, FP, nd Hnnett, LN: Lrge sle indution genertors for power systems, IEEE Trns Power Appr Systems, 1981, 1, pp Hnsen, AD, Sorensen, P, Jnosi, L, nd Beh, J: Wind frm modelling for power qulity Pro 2th Annul Conf of the IEEE Industril Eletronis Soiety (IECON 1), 21, Vol, pp Feijoo, AE, nd Cidrs, J: Modeling of wind frms in the lod flow nlysis, IEEE Trns Power Syst, 2, 1, (1), pp Slootweg, JG, de Hn, SWH, Polinder, H, nd Kling, WL: Generl model for representing vrile speed wind turines in power system dynmis simultions, IEEE Trns Power Sys, 2, 18, (1), pp Seyoum, D, Grnthm, C, nd Rhmn, F: The dynmi hrteristis of n isolted self-exited indution genertor driven y wind turine, IEEE Trns Ind Appli, 2, 9, (), pp Seyoum, D, Grnthm, C, Rhmn, F, nd Ngril, M: An insight into the dynmis of loded nd free running isolted self-exited indution genertors Pro Int Conf on Power Eletronis, Mhines nd Drives, University of Bth, UK, 22, pp Wng, L, nd Deng, R-Y: Trnsient performne of n isolted indution genertor under unlned exittion pitors, IEEE Trns Energy Conver, 1999, 1, (), pp Alghuwinem, SM: Stedy stte nlysis of n isolted self-exited indution genertor driven y regulted nd unregulted turine, IEEE Trns Energy Conver, 1999, 1, (), pp Seyoum, D, Rhmn, MF, nd Grnthm, C: Terminl voltge ontrol of wind turine isolted indution genertor using sttor oriented field ontrol Pro 18th Annul IEEE Power Eletronis Conferene nd Exposition, Mimi Beh, Florid, USA, 2, Vol 2, pp Chkrorty, C, Bhdr, SN, nd Chttopdhyy, AK: Anlysis of prllel- operted self exited indution genertors, IEEE Trns Energy Conver, 1999, 1, (2), pp Al-Bhrni, AH, nd Mlik, NH: Stedy stte nlysis of prllel operted self-exited indution genertors, IEE Pro, 199, 1, (1), pp 9 1 Wng, L, nd Lee, C-H: A novel nlysis of prllel operted selfexited indution genertors, IEEE Trns Energy Convers, 1998, 1, (2), pp Wng, L, nd Lee, C-H: Dynmi nlysis of prllel operted selfexited indution genertors feeding n indution motor lod, IEEE Trns Energy Convers, 1999, 1, (), pp Frret, FA, Cnh, LV, Corre, JM, nd Rekziegel, M: Estudo sore ssoi-*o de gerdores de indu-*o uto exitdos usndo esp-o de estdos Pro XII Brzilin Congress on Automtion, Uerlndi, Brzil, 1998, Vol 1, pp Hnok, NN: Mtrix Anlysis of Eletril Mhinery (Pergmon Press, Oxford, New York, USA, 19) 12 IEE Pro-Eletr Power Appl, Vol 12, No 1, Jnury 2