Control strategy of a variable speed wind turbine with multipole permanent magnet synchronous generator

Transcription

1 Control trategy of a varable pee wn turbne wth multpole permanent magnet ynchronou erator Gabrele Mchalke, Anca D. Hanen*, Thoma Hartkopf Unverty of Technology Darmtat, Department of Renewable nerge, Inttute for lectrcal Power Sytem, LangrafGeorgStraße 4, 648 Darmtat, Germany * Rø Natonal Laboratory, Wn nergy Department, P.O. Box 49, DK4000 Rokle, Denmark mal: gmchalke@re.tuarmtat.e, anca.anela.hanen@roe.k, thartkopf@re.tuarmtat.e Summary: The paper preent a control trategy of a varable pee wn turbne wth multpole permanent magnet ynchronou erator (SG) an full cale IGBT power converter. A comprehenve ynamcal moel of the wn turbne an t control trategy mplemente n the power ytem mulaton tool DIgSILNT. The control trategy compre both the wn turbne control telf an the power converter control. The ablty of the control trategy aee an cue by mean of mulaton. It alo emontrate, that the varable pee SG wn turbne able to upport actvely the gr, ue to t capablty to control nepenently actve an reactve power proucton to mpoe reference value. Keywor: permanent magnet ynchronou erator, varable pee wn turbne, rect rven wn turbne, wn turbne control, ynamc mulaton, DIgSILNT 1. INTRODUCTION An aupcou but not yet very popular wn turbne concept for moern wn turbne the varable pee wn turbne wth multpole permanent magnet ynchronou erator (SG) an fullcale power converter (Fg. 1). A multpole ynchronou erator connecte to a power converter can operate at low pee, o that a gear can be omtte. Snce a gearbox caue hgher weght, loe, cot an eman mantenance [1] a gearle contructon repreent an effcent an robut oluton, whch can be very benefcal epecally for offhore applcaton. Moreover, ue to the permanent magnet exctaton of the erator the DC exctaton ytem can be elmnate reucng agan weght, loe, cot an mantenance reurement []. The effcency of a SG wn turbne thu aee to be hgher than for other concept [], [4]. However the avantage of the permanent magnet exctaton are the tll hgh cot for permanent magnet materal an a fxe exctaton, whch cannot be change accorng to the operatonal pont. Neverthele, a full cale IGBT backtoback voltage ource converter, a ncate n Fg. 1, by whch the erator connecte to the power gr, allow full controllablty of the ytem. Due to the ntenfe gr coe, wn turbne wth full cale power converter mght be favoure n future compare to wn turbne concept wth oublyfe nucton erator. A the power converter ecouple the erator ytem from the gr, faultre through an gr upport can be eaer accomplhe. The paper focue on the control trategy of the varable pee wn turbne concept llutrate n Fg. 1. A comprehenve ynamcal moel of the entre ytem mplemente n the power ytem mulaton oftware DIgSILNT. The whole moel nclue moel for both the aeroynamc an mechancal part of the turbne a well a for the electrcal ytem an t control tructure. The control of the SG wn turbne realze by a coornate control of the converter control an the wn turbne control. The power converter control compre the erator e converter control an the gr e converter control, whle the wn turbne control contan the blae angle control. Wn Moel v w θ rotor_po Aeroynamc Moel θ T rot Ω rot Blae Angle Control Drve Tran Moel ω Τ mech ω Generator Moel SG U tator,ref Generator Se Converter Moe ~ Control Sgnal Generator Se Converter: DClnk voltage Control Stator voltage Control U DC,ref Dampng ω rate Gr Se Converter Moel ~ ωmpp Trackng rate P Gr,ref Tranformer Moel Control Sgnal Gr Se Converter: Actve Power Control Reactve Power Control Q Gr,ref xternal Gr Moel Fg 1: Moellng cheme an control concept of the varable pee wn turbne wth permanent magnet ynchronou erator

2 . TH MULTIPOL PRMANNT MAGNT SYNCHRONOUS GNRATOR Drect rve wn turbne, characterze a hgh effcent an low mantenance oluton, offer hgh potental for future applcaton [5], epecally offhore. In orer to elmnate the gearbox the erator mut be bult for low pee operaton (max. 150 rpm). Aynchronou erator cannot be bult for low pee a a mall pole ptch together wth a large argap yel a too large reactve power eman of multpole aynchronou erator. Therefore ynchronou erator are the only opton for low pee wn turbne applcaton [6]. In a ynchronou erator the magnetc fel prove by the rotor exctaton. In cae of a permanent magnet ynchronou erator the DC exctaton ytem can be elmnate, whch ental a reucton of loe an the omon of lp rng an thu mantenance reurement. A rect rven multpole permanent magnet ynchronou erator mounte n a wn turbne hown n Fg. [5]. a varable tator freuency accorng to the actual rotor pee, no relatve movement between tator an rotor fel ext, whch coul nuce a voltage n the amper wnng [7]. Moreover, ue to the mall pole ptch of the multpole erator a amper wnng woul prove nuffcent ampng [8]. Hence, n cae of tranent nether amper nor fel wnng can contrbute to ampng. The SG connecte to a freuency converter therefor a ytem wthout nherent ampng. Thu, no tranent or ubtranent reactance, a known for woun rotor SG, can be efne for the SG. x x x x x x x x x Synchronou reactance Tranent reactance Subtranent reactance X h I j X h I () j ω Ψ U U δ ϕ Ψ I Fg : One phae euvalent crcut an phaor agram of a SG Fg : Wn turbne wth multpole SG, upple by Veny [5] The erator can be electrcally repreente by the one phae euvalent crcut hown n Fg. If a urface mounte SG ue, the magnetc flux trbuton n the rotor approxmately nuoal. Wth th aumpton the flux can entrely be ecrbe by a vector an thu the electromotve force nuce n the tator by the permanent magnet flux Ψ can be expree a follow: j ω Ψ j π f Ψ (1) The nternal voltage epen on the actual rotor pee of the erator ω p Ω. Uner loa conton, the tator current I an the tator reactance X h alo caue a magnetc fel, whch uperpoe to the fel of the rotor. The voltage rop over the machne reactance X h provoke a phae elay (the loa angle δ) between the nternal voltage an the tator voltage U, whch are eual only for noloa. SG are normally not euppe wth a amper wnng. In the cae when the SG connecte to a freuency converter, whch prove Veny The voltage euaton of the SG, expree n the rotororente reference frame (RRF) (the reference frame ax algne wth the vector of the permanent magnet flux Ψ ), can be expree a follow: u u R R ω ω ψ ψ ψ& ψ& wth the tator flux component: ψ ψ L L Ψ () (4) where u an u are the termnal tator voltage, an are the tator current, L an L are the tator nuctance n the reference frame. In tablty tue, the tator tranent ψ& an Ψ & can be neglecte. If the permanent magnet erator aume to be a rounrotor machne, whch a goo approxmaton for urface mounte SG [9], the electrcal torue of the erator can be expree n RRF wth: T e Im * [ ψ ] [ ψ ψ ] [( L L ) Ψ ] [ Ψ ] (5)

3 . POWR CONVRTR CONTROL The power converter control ve nto two controller: a control for the erator e converter an a control for the gr e converter. Whle the gr e converter mut be an actve nverter, nce t convert the DClnk voltage to the AC gr voltage wth fxe freuency of the power ytem, the erator e converter can optonal cont of pave element, e.g. a oe rectfer, or actve element a IGBT or GTO. However, the bet utlzaton an controllablty of a SG can be acheve f an actve nverter alo ue at the erator e, e.g. an IGBT voltage ource converter a ncate n Fg 1. However, IGBT converter are expenve an mut be protecte agant overcurrent an overvoltage. Dfferent control tratege can be apple to the power converter. a) Maxmum torue control Accorng to euaton 5 the torue, expree n rotororente reference frame, etermne by the current component only. If the tator current controlle to have a component only, the erator prove the maxmum poble torue. A phaor agram of th control trategy llutrate n Fg. 4: j ω Ψ Q 0 δ j ω U L Ψ ~ Te RRF j ω Ψ Q 0 δ RRF j ω U Ψ ~ Te L RRF Fg 5: Phaor agram for unty power factor control of the erator n rotororente reference frame (RRF) c) Contant tator voltage control In orer to avo the rk of overvoltage ue to overpee, the tator voltage can be controlle ntea of reactve power. The tator voltage then controlle to t rate value. The control typcally one n the tator voltageorente reference frame SVRF (ax algne to the tator voltage vector), o that U u (Fg. 6). Th mple that the actve power epen on the tator current component, whle the reactve power epen on the component only. P u Q u (6) Whle the tator current component etermne by the actve power proucton of the erator, the tator current component can be ue to control the tator voltage to t rate value. RRF Fg 4: Phaor agram for maxmum torue control n rotororente reference frame (RRF) j ω L SVRF Fg. 4 ncate, that the reactve power eman of the erator not zero, whch ncreae the converter ratng (S>P). δ U SVRF b) Unty power factor control of the erator In orer to operate the erator wth unty power factor the tator current component can be ue to compenate the reactve power eman of the erator (Fg. 5). Man avantage of th control trategy, that the erator operate wth unty power factor, whch mnmze the converter ratng. However, a the tator voltage not rectly controlle the tator voltage vare epenng on the pee, whch coul caue overvoltage for the converter an the erator n cae of overpee. A the reactve power upply to the gr nepenent from the erator reactve power, t le mportant to control the reactve power at the erator e. Q 0 Fg 6: Phaor agram for contant tator voltage control n tator voltageorente reference frame (SVRF) The avantage of th control trategy are, that erator an converter alway operate at rate voltage, for whch they are egne an optmze. It furthermore benefcal f the converter ha a contant ratng of U DC /U AC. Due to the contant tator voltage there no rk of overvoltage an aturaton of the converter at hgh pee. A avantage of th control agan the reactve power eman of the erator, whch ncreae the converter ratng.

4 Generator e converter control A contant tator voltage control aee to be mot benefcal, th control trategy mplemente n the preent mulaton moel. In orer to guarantee, that the erate actve power fe va the DClnk to the gr, the DClnk voltage mut be kept contant. Th aure that no energy pate n the DClnk. If a lole converter aume, the followng euaton can be erve: P AC PDC U DC I DC u (7) The euaton mple that the actve power a well a the DClnk voltage are etermne by the component of the tator current only. Thu, the DClnk voltage controlle to t contant reference value by the tator current component. A mentone before the tator voltage then controlle by the component current. The control organze a llutrate n Fg 7. Dampng ω,mea BP LP DCvoltage control U DC,ref U DC,mea U tator,ref Stator voltage control U tator,mea current control I,tator,ref I,tator,mea current control I,tator,ref I,tator,mea Fg 7: Generc control of the erator e converter ach control loop ha a cacae tructure: a fat nner current control loop, controllng the tator current I,tator n an ax, combne wth an outer lower control loop for DClnk voltage an tator voltage, repectvely. Both tator voltage an DClnk voltage are controlle to ther rate value. However, mall varaton of the DClnk voltage can be allowe, when electrcal ampng of the ytem become neceary. The DClnk voltage reference value can then be prove by a ampng block, a llutrate n Fg. 7. The ampng ecrbe n ecton 5. The nner current control loop prove a control gnal n an ax (P m, P m ), whch ent to the PWMcontrolle power converter. Gr e converter control If the DClnk voltage kept contant by the erator e converter control, the actve power of the erator tranferre va the DClnk to the gr e converter. Thu, the actve power proucton of the wn turbne can be controlle wth the gr e converter. Due to the converter ytem, the reactve power operatonal pont of erator e converter an gr e converter are fully ecouple. Th mean that the reactve power, whch fnally prove to the gr, can be nepenenly controlle by the gr e converter. P m P m The erc control of the gr e converter llutrate n Fg. 8. Agan, a fat nner current control loop control the converter current I,Conv n an ax, whle the outer lower control loop control actve an reactve power. The control one n a gr voltageorente reference frame. Thu, the ame relaton a n euaton 6 can be erve. The actve power controlle by the current, whle the reactve power controlle by mean of the component current. In orer to capture the optmal power out of the wn a maxmum power pont (MPP)trackng mplemente, contanng a charactertc Pω lookup table, whch preefne the pont of maxmum aeroynamc effcency [10]. Below rate wn pee, the optmum power can be acheve f the maxmum power coeffcent c p,opt (θ opt, λ opt ) ajute. For th reaon the ptch angle kept to the optmal value, whch zero n th cae, an the turbne pee change n uch a way that the optmal tppee rato λ opt alway obtane. A a reult a P~ω charactertc mplemente n the MPPtrackng an the reference power gnal P Gr,ref erate bae on the meaure erator pee ω,mea (Fg. 8). A hown n Fg. 8 the MPPcharactertc contnue a a rampfuncton ncreang P an ω lnearly towar rate power. In aton to that, ynamc varaton aroun rate pee are allowe n orer to aborb fat change n aeroynamc power urng wn gut. The MPPtrackng block prove the reference gnal P Gr,ref for the actve power, whch etermne the actve power proucton of the erator. The reactve power Q Gr,ref typcally et to zero but can alo be controlle to an mpoe reference value epenng on the reactve power reurement of the gr. MPPTrackng ω,mea Actve power control P Gr,ref P Gr,mea Reactve power control Q Gr,ref Q Gr,mea current control I,conv,ref I,conv,mea I,conv,ref I,conv,mea current control Fg 8: Generc control of the gr e converter 4. WIND TURBIN MODL AND CONTROL A llutrate n Fg. 1 the wn turbne moel contan moel of the wn, the aeroynamc of the rotor an the rve tran. Furthermore a control of the blae ptch mechanm mut be mplemente. Wn Moel The mplemente wn moel ecrbe n etal n [11]. A wn tme ere erate bae on the pectral energy trbuton of the wn an a uperpoe noe gnal. In a econ tep the o gane wn pee average over the whole rotor P m P m

5 area, whch take turbulence an tower haow nto account. Aeroynamc Moel Bae on the aeroynamcal euaton: T rot Prot 1 ρ π R vw c( θ, λ ) (8) Ω rot a uatatc aeroynamcal moel evelope. The aeroynamcal torue T rot rectly compute by mean of the torue coeffcent c epenng on the actual ptch angle θ an the tppee rato λω rot R/v w. The ue varable are ρ for the ar enty, R for the rotor rau, v w for the wn pee an P rot an Ω rot for the rotatonal power an pee, repectvely. Mechancal Moel A multpole erator ha a hgh number of pole an a large ameter, whch caue a hgher erator nerta compare to e.g. or 4 pole erator. It aee n [1] an [1], that the effectve haft tffne of a erator reuce wth ncreang number of pole. Th mple, that any mechancal toron of the ytem reult n larger ynamc change of the electrcal rotor angle for erator wth a large number of pole. A toronal twt of the haft connecte to a multpole erator ha thu a tronger mpact on the electrcal ytem [1] an a more etale moel of the haft ytem become neceary. It thu eental to repreent the mechancal ytem by mean of a twoma prng an amper moel n orer to get an accurate repone from the erator an the power converter. It wa mentone before, that the SG connecte to a converter ytem ha no nherent ampng epte the ampng of the haft. Thu, loa change, e.g. wn gut, can excte ocllaton, whch mght be nuffcently ampe by the ytem. A repreentaton by mean of a onema moel woul neglect uch ocllaton. Due to thee reaon, the mechancal moel realze by mean of a twomamoel connecte va a flexble haft characterze by a tffne k an a ampng c (Fg. 9). The two mae correpon to the large turbne rotor nerta J rot, repreentng the blae an hub, an to the erator nerta J. θ rot T rot Ω rot J rot k c θ T Ω J Fg 9: maprng an amper moel of the rve tran Blae Angle Control The blae angle control trategy, whch wa evelope n [10] an [14] for a oublyfe nucton erator wn turbne, can be aopte for the SG an wll be brefly preente here. For hgh wn pee the extracte wn power ha to be lmte va blae ptchng. Th realze by mean of a pee controller, regulatng the pee ω,mea to t rate value ω,rate (Fg. 10). The pee controlle by a PIcontroller, whch output a reference ptch gnal θ ref to the ptch ytem. In orer to get a realtc repone n the ptch angle control ytem, the ervomechanm moel account for a ervo tme contant T Servo an the lmtaton of both the ptch angle (0 to 0 eg) an t graent (± 10 eg/). The reference ptch angle θ ref compare to the actual ptch angle θ an then the error correcte by the ervomechanm. The blae angle control thu only actve, when the pee excee rate pee. Snce the pee an the power are couple va the MPPtrackng, th mple nrectly that the power lmte to t rate value, too. Furthermore, a gan cheulng control of the ptch angle mplemente n orer to compenate for the extng nonlnear aeroynamc charactertc. ω,rate ω,mea K PI θ ref 1 Rate lmt T Servo Gan cheulng Angle lmt Fg 10: Spee controller actng on the ptch mechanm 5. DAMPING OF SPD OSCILLATIONS A multpole permanent magnet erator are low pee applcaton an erally connecte to a freuency converter ytem, no amper wnng ue n the erator. However, loa change can excte ocllaton, whch are amplfe n the ytem an whch reure an external ampng of the wn turbne ytem. Dfferent ampng metho have been aee an nvetgate, e.g. ampng by mean of blae ptchng [15] or ampng by mean of a complant mountng of the erator [1]. Atonal or ubttutonal to mechancal meaure, ampng can alo be prove by the electrcal ytem,.e. by mean of the backtoback voltage ource converter. The DClnk capactor, whch erve a a buffer between erator an gr, wll be ue to prove ampng. If mall varaton of the DC voltage are allowe, pee an torue ocllaton can be aborbe by chargng an chargng of the capactor. Thu, the ampng prove a reference gnal for the DClnk voltage controller of the erator e converter, a llutrate n Fg. 1 an Fg. 7. Actng mlar a a power ytem tablzer, the ampng ytem mut prouce a component of electrcal torue, whch counteract the rotor pee ocllaton [16]. The ampng ytem llutrate θ

6 n Fg. 11. In orer to amp the fat pee fluctuaton, the erator pee meaure an fltere by mean of a ban pa flter n a way that only the freefreefreuency of the ytem tranmtte through the flter. Furthermore, the phae lag between the ampng gnal (U DC ) an the electrcal torue mut be compenate [16]. In th cae a properly egne low pa flter guarantee th phae compenaton. Fnally, the gane ampng gnal moulate on the reference value of the DC voltage, o that the mall DC voltage varaton caue a ampng torue component. ω Banpa flter Lowpa flter U p c ref U c Fg. 11: Dampng ytem by mean of U DC Gen.e converter U DC controller Fg. 1 how the mulaton reult of erator pee an actve power proucton for two cae: () wthout apple ampng an () wth ampng, after a wn pee change of 1 m/. Wthout ampng ytem the wn pee change provoke ocllaton, whch are amplfe n the ytem. In contrat to th the ocllaton are effectvely uppree by mean of the ampng. Spee [p.u.] Power [MW] tme tme wthout ampng Fg. 1: Impact of the ampng ytem on pee an power ocllaton after a wn pee change of 1 m/ 6. SIMULATION RSULTS U c wth ampng In orer to evaluate the performance of the control ytem for the varable pee wn turbne concept wth SG, mplemente n the power ytem mulaton tool DIgSILNT, a et of tep repone mulaton frt wth etermntc wn pee (no turbulence, no tower haow) an then wth tochatc wn pee are performe. In Fg. 1 typcal uantte of the turbne ytem, a ptch angle, erator pee an power are hown for tep n wn of 1 m/ every 0 econ. At a wn pee of 1 m/ the turbne work at rate conton. A the wn pee above t rate value (v w,rate 11.7 m/), the ptch mechanm actve an lmt the power an the pee to ther rate value. For lower wn pee below 1 m/ the ptch mechanm pave an the ptch angle kept to t optmal value (.e. zero for the conere turbne). Meanwhle, the power controller control the actve power to the actve power reference gnal prove by the maxmum power trackng lookup table. The erator pee thu contnuouly aapte to the wn pee, n uch a way that the turbne extract maxmum power out of the wn. Notce that the repone tme n the tep bgger at lower wn pee than at hgher wn pee. Power [MW] Spee [p.u.] Ptch angle [eg] Wn pee [m/] Fg. 1: Wn pee, ptch angle, erator pee an actve power for tep n wn of 1 m/ from 1 m/ own to 5 m/ The tep repone of ptch angle, pee an power for hgher wn pee preente n Fg. 14. Now, the tep n wn pee yel change n both the ptch angle an the erator pee. The tep repone of the ptch angle an erator pee oe not preent bg overhoot an ocllaton. Power [MW] Spee [p.u.] Ptch angle [eg] Wn pee [m/] tme tme Fg. 14: Wn pee, ptch angle, erator pee an actve power for tep n wn of 1 m/ from 1 m/ up to 0 m/ The power controller keep the actve power to MW. Snce the ptch mechanm react lowly compare to the power controller, ynamc varaton n the erator pee an o n the rotatonal pee of the turbne rotor are allowe n orer to aborb fat wn gut an to tore rotatonal energy n the turbne nerta. Fnally, mulaton reult uner tochatc wn conton verfy the ablty of the varable DIgSILNT DIgSILNT

7 pee wn turbne wth SG to regulate t power proucton to mpoe reference value an unerlne the feature of nepenent control of actve an reactve power. Fg. 15 llutrate the ptch angle, the erator pee a well a the actve an reactve power n cae of a turbulent wn pee wth a mean wn pee of 0 m/ an a turbulence ntenty of 10 %. Power [MW] Spee [p.u.] Ptch angle [eg] Reactve power [MVar] tme Fg. 15: Ptch angle, erator pee an actve an reactve power proucton uner tochatc wn pee wth a mean wn pee of 1 m/ The ptch angle an pee gnal reflect the tochatc character of the wn an are trackng the low varaton of the wn pee. However, nepenent of the fluctuaton of the wn, the actve power can be controlle an lmte to MW. In the preent mulaton the reference power reuce n tep of 500 kw every 0 from MW own to 1 MW an teppe up back agan to MW. Note that the actve power output followng th reference very well. Such abrupt reucton of power woul not be apple n practce. However, t hown here n orer to unerlne the feature of the control ytem. The frt 150 econ the reactve power controlle to zero an then ncreae n tep to 0.9 MVar. 0.9 MVar enote approxmately the maxmum avalable reactve power of the gr e converter f rate actve power ( MW) upple at the ame tme. After 180 the ame actve power control euence repeate. Fg. 15 pont out, that the egne control trategy of the varable pee wn turbne moel wth SG able to control actve an reactve power nepenently to mpoe value, exactly a a conventonal power plant oe. 7. CONCLUSIONS DIgSILNT The preente paper focue on the egn an nvetgaton of the entre control ytem for a varable pee wn turbne wth multpole permanent magnet ynchronou erator. Due to the gearle contructon an the permanent magnet exctaton the ynchronou erator repreent a hgh effcent an low mantenance oluton, whch can be very benefcal for offhore wn turbne. A comprehenve ynamc mulaton moel evelope n the mulaton tool DIgSILNT. The control of the wn turbne acheve by the power converter control n coornaton wth the ptch control ytem. The converter control guarantee varable pee operaton to gan optmal power proucton. Above rate wn pee the ptch angle control control the erator pee an nrectly the power output to ther rate value. A ampng controller mplemente, whch neceary to amp toronal ocllaton of the rve tran ytem. Smulaton how that the control metho uccefully control the varable pee SG wn turbne wthn a range of normal operatonal conton. At wn pee below rate wn pee the converter eek to maxme the power accorng to the MPPtrackng. At large wn pee the pee controller permt a ynamc varaton of the erator pee n orer to avo mechancal tree, whle the converter keep the power to the rate power. The control trategy facltate furthermore nepenent control of actve an reactve power to mpoe reference value at varable pee. It can thu be conclue, that the SG wn turbne can operate n the ame manner a a conventonal power plant oe. 8. RFRNCS [1] Wetlake A. J. G., Bumby J.R., Spooner., Dampng the powerangle ocllaton of a permanentmagnet ynchronou erator wth partcular reference to wn turbne applcaton. I Proceeng, lectr. Power Appl., Vol 14, No, May, [] Polner H., e Haan S. W. H., Dubo M. R., Slootweg J., Bac Operaton Prncple an lectrcal Converon Sytem of Wn Turbne. NORPI / 004, Norc Workhop on Power an Inutral lectronc, Paper 069, Tronhem, Norway, 1416 June, 004. [] Grauer A., ffcency of three wn energy erator ytem. I Tranacton on nergy Converon, Vol. 11, No., pp , September [4] Jöckel S., Calculaton of Dfferent Generator Sytem for Wn Turbne wth Partcular Reference to LowSpee PermanentMagnet Machne. PhD the, Techncal Unverty Darmtat, 00. [5] Jöckel S., VNSYS nergeyteme GmbH, Germany, Hgh energy proucton plu bultn relablty The new Veny 70 / 77 gearle wn turbne n the 1.5 MW cla. Paper no. 058, uropean Wn nergy Conference WC, Athen, 006.

8 [6] Bner A., Schneer T., Permanent magnet ynchronou erator for reeratve energy converon a urvey. uropean Conference on Power lectronc an Applcaton, P 005, 1114 September, Dreen, Germany, 005. [7] Jauch C., Tranent an Dynamc Control of a Varable Spee Wn Turbne wth Synchronou Generator, Part I: Drve Tran Stablaton. Submtte to Wn nergy 006. Publcaton n PhD the Stablty an Control of Wn Farm n Power Sytem. Rø PhD4, Rø Natonal Laboratory, [15] Jöckel S., Hakort B., Hartkopf T., Schneer H., DrectDrve Synchronou Generator Sytem For Offhore Wn Farm wth Actve Drve Tran Dampng by Blae Ptchng. uropean Wn nergy Conference WC 001, n6th July, Copenha, Denmark, pp , 001. [16] Kunur P., Power Sytem Stablty an Control. McGraw Hll, [8] Grauer A., Degn of Drectrven Permanentmagnet Generator for Wn Turbne. PhD the, Department of lectrc Power ngneerng, Chalmer Unverty of Technology, Göteborg, Sween, [9] Spooner., Wllamon A.C., Drect couple, permanent magnet ertoar for wn turbne applcaton. I Proceeng, lectr. Power Appl., Vol. 14, No. 1, January [10] Gal G., Hanen A.D., Hartkopf T., Controller egn an analy of a varable pee wn turbne wth oublyfe nucton erator. uropean Wn nergy Conference WC 7th Februaryn March, Athen Greece, 006. [11] Sørenen P., Hanen A.D., Roa P.A.C., Wn moel for precton of power fluctuaton from wn farm. Proc. The Ffth AaPacfc Conference on Wn ngneerng (APCWV), Kyoto, Japan. Journal of Wn ngneerng, no.89, pp. 918., 001. [1] Akhmatov V., Nelen A.H., Peeren J. K., Nymann O., Varablepee wn turbne wth multpole ynchronou permanent magnet erator. Part I. Moellng n ynamc mulaton tool. Wn ngneerng, Volume 7, No. 6, pp 51548, 00. [1] Akhmatov V., Analy of Dynamc Behavour of lectrc Power Sytem wth Large Amount of Wn Power. PhD the, ØretaDTU, Denmark, 00. [14] Hanen M.H., Hanen A.D., Laren T. J., Øye S., Sørenen P., Fuglang P., Control egn for a ptch regulate, varable pee wn turbne, Rø report R1500, Rø Natonal Laboratory, Denmark, 005.