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1 Control of a Wnd Turbne wth a Doubl Fed Inducton Generator after Tranent Falure Jorun I Marvk, Torten Bjørgum, Bjarne I Næ, Tore M Undeland,2, Terje Gjengedal, NTNU wwwntnuno 2 CHAMERS wwwchalmere Statkraft SF wwwtatkraftcom Abtract arge Wnd turbne are often equpped wth doubl fed nducton generator In numerou paper the tablt problem are ponted out and there are alo man paper decrbng control tratege for wnd turbne equpped wth doubl fed nducton generator Th paper focue on tablt after a tranent falure for wnd turbne equpped wth a doubl fed nducton machne, ome of the propoed control oluton are teted n PSCAD/EMTDC I INTRODUCTION There are everal tpe of adjutable peed generator ued n wnd turbne [] The mot common the doubl fed nducton generator (DFIG), hown n Fg There are everal advantage b ung adjutable peed generator Some of the advantage are: the reduce mechancal tree b torng the energ from wnd gut n the mechancal nerta of the turbne, creatng an elatct that reduce torque pulaton B reducng the torque pulaton alo the power qualt wll be mproved The tem effcenc can be lghtl mproved b adjutng the turbne peed to maxmze output power The converter can alo uppl reactve power to the grd f the converter are rated for th purpoe Gear Inducton Generator Rotor connected Converter dc-lnk Fg Doubl Fed Inducton Generator (DFIG) Grd connected Converter Electrcal Grd The doubl fed nducton generator an nducton machne wth wound rotor and a four-quadrant ac-to-ac converter etup connected to the rotor wndng Onl the power flow n the rotor wndng converted, thu the converter can be rated to approxmatel 25% of the total power Then the peed range wll be approxmatel ±% around the nchronou peed [] The doubl fed nducton generator tem preented n th paper baed on the model decrbed n [2], [] and [4] A ponted out n [5] flux ocllaton wll occur f the tator voltage contan tranent, th wll reult n torque pulaton arge torque pulaton wll reult n mechancal tree n the gear and alo pulaton n the power delvered to the grd In addton torque ocllaton wll caue power ocllaton trough the dclnk In th paper a controller to reduce the flux ocllaton preented When tranent falure occur, large current wll be nduced n the tator and rotor wndng The propoed controller wll reduce the large current nduced n the rotor wndng after tranent falure b applng a large voltage over the rotor wndng To acheve th, the voltage ratng of the generator connected converter mut be larger than necear n normal operaton The nducton machne wll tolerate the large current n the tator wndng and thu doe not need to be overzed due to the tranent tator voltage The haft and gear wll act a a trng between the blade and the rotor The haft and gearbox together wth the heav turbne blade wll have gnfcant nfluence durng a tranent falure f the generator operate wth contant peed However, b not dconnectng the rotor converter durng tranent falure, the rotor current wll be controlled and the mpact from th tem on the grd tablt can be reduced [6] For th project the mpact from the blade, gear and rotor tem neglected for mplfng the mulaton and reult The grd connected converter controlled a a STATCOM When ung park tranformaton to decouple the actve and reactve current n the grd, there wll be a problem due to the cro-couplng of the decoupled current A fat repondng controller for the grd connected converter mportant to mantan a contant dc-lnk voltage An dturbance n the dc-lnk voltage wll nfluence on the rotor current controller A

2 low repondng grd current controller could however be compenated b enlargng the dc-lnk capactance II CONTRO OF GRID CONNECTED CONVERTER Fg 2 how a mplfed repreentaton of the grd connected converter The nverter block treated a an deal, lole power tranformer In hunt wth the DCde capactor a retance whch repreent the nverter wtchng loe AC-de ere nductance account for tranformer leakage reactance, and ere retance repreent nverter and tranformer conducton loe [7] Thu, actve power controlled trough d whlt reactve power controlled trough q Negatve q-ax current mean potve reactve power delvered b the STATCOM Eqn () can be wrtten a a block dagram a hown n Fg ed v b br b d b l C v dc dc R p VSI P = P Fg 2 Grd connected Converter ac dc e a e b e c R R R a b c The AC-de equaton can be wrtten a follow: a a e v a a d R = e v () b b b b dt e v c c c c Eqn () converted to per-unt ung the followng defnton: b x R x =, C =, R = x x x z C z z bae b x bae bae (2) x v v x bae =, v =, z = x x bae v bae bae bae Subequentl, ung the Park tranformaton, the equaton tranformed to a reference frame rotatng nchronoul wth the grd voltage: R b d d e v d b d = () dt e d R b d q Under balanced tead-tate condton the current and voltage n Eqn () are DC-quantte v the DCvalue of the grd voltage The d- and q-ax current are coupled b the factor aumed to be contant equal to the grd frequenc n rad/, that = b The ntantaneou actve power p and reactve power q generated b the STATCOM gven n the equaton below [9]: p = ( v v d d q q) = v d 2 2 (4) q = ( v v d q q d) = v q 2 2 v a v b v c eq b br Fg Tranfer functon between voltage and current Baed on the block dagram n Fg tranfer functon between voltage and current etablhed The tranfer functon between e d - v to q gven below: ( ) ( R b) e v = b d b q 2 q b 2 q b = d b b 2 ( ) e v 2R R The equaton can be rewrtten to: q K = 2 e v d ( R ) 2ζ q (5) (6) R R K = = ζ = R 2 2 b The parameter value R = 2 pu and = 5 pu are choen Then, the contant n eqn (6) become: K =655 = 7 ζ= 2 (7) In a mlar manner the tranfer functon between e d - v and d, e q and d and between e q and q found All four tranfer functon have the ame reonance frequenc and dampng factor Baed on thee equaton bodeplot hown n Fg 4 and Fg 5 are drawn From the plot t can be een that, at lower frequence, the cro gan from e d - v to q much greater than the drect gan to d, and the cro gan from e q to d much greater than the drect gan to q Thu, the tead-tate d-ax current predomnantl controlled b the q-ax voltage, wherea the tead-tate q-ax current controlled b the d-ax voltage [8] There a 8 degree phae hft between 2

3 the tead-tate q-ax current and the d-ax voltage, o a potve voltage e d - v wll reult n a negatve current q At the reonance peak the gan of the ame ze n both ax-drecton Magntude (db) q d fra e d - v tl d og q d q q_ref Phae (deg) q 9 d Frequenc (rad/ec) Fg 7 Step repone of the cro couplng controller (contant dc voltage) Becaue of the large cro-gan, uch controller do not need a large gan However, due to the weak dampng of the tem, a large ntegral tme contant needed to damp the tranent ocllaton Thu the tep repone qute low It dffcult to acheve a better performance b adjutng the controller parameter Fg 4 Input e d - v 4 fra e q tl d og q Decouplng controller Decouplng between the two current loop can be acheved b feedng forward the term Magntude (db) d q d,ref d T Kp T v e d q -6 9 STATCOM Phae (deg) -9 q d q,ref q T Kp T e q d -8 Fg 5 Input e q 2 4 Frequenc (rad/ec) Cro-couplng controller Accordng to the above anal t enble to ue the d-ax voltage to control the q-ax current, and the q- ax voltage to control the d-ax current A block dagram of th control tem hown n Fg 6 Fg 8 Decouplng controller Wth th control trateg the tep repone fat, and the decouplng between the current almot perfect, a hown n Fg d q q_ref q,ref K T T p v e d STATCOM q d,ref Kp T T e q d Fg 9 Step repone for the decouplng controller (contant dc voltage) Fg 6 Cro-couplng controller

4 III ROTOR CONNECTED CONVERTER A DFIG act n man wa a a nchronou machne, wth the addtonal feature that t can be ued for rotatonal peed both over- and under nchronou peed Th make the ue of dampng wndng mpoble A tatonar peed dfferent from nchronou, would nduce current n thee wndng Th would agan lead to unacceptable power lo Wthout an form of dampng, the DFIG repreent a tem wth ver poor dampng The egen frequenc alo about the ame a the 5 Hz grd frequenc [5] The cclc varaton of the flux n the machne ha nfluence on the tranformed α- and β current It alo ha nfluence on the electrc torque, nce the torque gven of the flux lnkage and the β-ax current An ocllaton n the flux would lead to ocllaton n the torque Ocllaton n the torque would agan lead to horten the relablt and the length of lfe of the gear For th reaon the machne ha to be controlled n wa that prevent the flux to ocllate It normal to orentate the tate n the machne to the tator flux lnkage The flux tate equaton gven b eqn (8) d x h r n u = α α (8) dt T T It could be een that the flux can be controlled b ung the α-current Th mean that the flux could be tablzed to a predefned level wth ung th α-current The challenge to fnd a reference value for the tator flux Farada nducton law gve the relatonhp between nduced voltage and dervatve of the flux lnkage r u Fg Stator voltage and emf The voltage balance gve the relatonhp between tator voltage and electro motve force (emf) The flux level n the machne dependent on the tator voltage A utable reference for the flux level the emf If the etmated flux alo contan frequenc component of hgher order, th could be ued a a reference for the flux f t fltered through a low pa flter, a hown n Fg, ref T f u r Fg Flux reference etmator The total tem llutrated n Fg 2 p T T α ref, ref, Fg 2 Flux controller K Tv / r T r r u α T T The current controller aumed to be much fater than the flux controller, and therefore repreented wth a tranfer functon of value The flux controller optmzed under the requrement that t hould be decade lower than the current controller The voltage whch come nto the tem can be een a a dturbance The open loop tranfer functon can be wrtten a: T T h, fluk = Kp xh (9) T T It a requrement that the cro frequenc for the flux controller hould be one decade lower than the current controller, and therefore = () c, flux c, current Th gve the control parameter: T = T () K c, fluk p = (2) xh The open loop tranfer functon wll appear a: h c, fluk () = () In the frequenc doman: 4

5 h, fluk ( j ) = h ( j ) = 9, fluk c, fluk (4) The flux cannot be meaured drectl, thu t mut be etmated from known tate From the voltage balance equaton t poble to etmate the tator flux n the machne Smulaton made n Matlab how the nfluence of the flux control, ee Fg 7 If the voltage on the termnal of the machne are decreang, the voltage are not large enough to pull the tator flux further Therefore, nce the rotor wndng have rotatonal peed, nduced voltage n the rotor wndng wll appear The pace vector durng normal operaton condton are hown n Fg u β Fg Stator flux and voltage durng normal operaton (Have neglected the voltage drop over tator retance) α The equaton for the flux lnkage gven a: ( u r) d t= t = n (5) τ The voltage 9º ahead of the flux lnkage When the voltage drop, the flux lnkage not able to change value ntantaneoul, and th the reaon wh the flux relatvel fxed n pace durng a voltage drop on the grd de Th lead to hgh voltage on the rotor de A llutrated n Fg 4 β u α Smulaton Reult It developed a machne model n Smulnk The model tranformed to tator flux frame Th a full model whch nclude tator dnamc, rotor dnamc and rotatonal dnamc Two tem are teted, one wth a reactve power control, and the other wth flux control Frt, the reult from mulaton durng normal operaton evaluated At a gven tme there a change n the β-current referene How the tem repond to th change hown n the followng fgure Current [pu] Flux [pu] Operaton under Normal Condton Rotor Current refered to Ψ α β 2 Tme [] Stator flux Tme [] Voltage [pu] Power [pu] 2 8 Rotor Voltage refered to Ψ ur α ur β Tme [] Aktve og reaktve tator power 2 P Q Tme [] Fg 5 Overvew of tate n the machne wth flux controller At t= there a change n the reference of rotor β-current Current [pu] Flux [pu] Rotor Current refered to Ψ 2 Tme [] Stator flux α β 2 Tme [] Voltage [pu] Power [pu] Rotor Voltage refered to Ψ 2 Tme [] ur α ur β Aktve og reaktve tator power P Q 2 Tme [] Fg 4 Stator flux behavor durng voltage drop on the grd de Fg 6 Overvew of tate n the machne wth reactve power controller At t = there a change n the reference of rotor β- current 5

6 The man dfference between thee two control tratege the nfluence of the flux Wth flux control the varaton of the rotor voltage larger than wth reactve power controllng The current are alo more table wth reactve power controllng One of the reaon for th that the flux controller ue the α- current more actve to adjut the tator flux n the machne The flux n the machne alo more table wth th control trateg The man advantage of reactve power control to regulate the conume of reactve power from the grd Operaton under Fault Condton There a change n β-current referece a before at t = At tme t = a voltage drop appear on the tator termnal from pu to 5 pu Current [pu] Flux [pu] Rotor Current refered to Ψ α β 2 Tme [] Stator flux Tme [] Voltage [pu] Power [pu] Rotor Voltage refered to Ψ ur α ur β 2 Tme [] Aktve og reaktve tator power P Q 2 Tme [] Fg 7 Overvew of tate n the machne wth flux controller under voltage dp The voltage dp happen at t = At t= there a change n the reference of rotor β-current Current [pu] Flux [pu] Rotor Current refered to Ψ 2 Tme [] Stator flux α β 2 Tme [] Voltage [pu] Power [pu] Rotor Voltage refered to Ψ 2 Tme [] ur α ur β Aktve og reaktve tator power 2 Tme [] Fg 8 Overvew of tate n the machne wth reactve power controller under voltage dp The voltage dp happen at t = At t = there a change n the reference of rotor β-current Thee mulaton llutrate the man advantage of flux regulaton Wth th control trateg t poble to tablze the flux, and thereb the electrcal torque ver rapdl even wth a voltage drop to 5 [pu] on the tator termnal The reactve power controller ha problem controllng the flux, rotor voltage and actve and reactve power exchange to the grd IV PSCAD/EMTDC SIMUATIONS The wound rotor nducton machne model n the PSCAD lbrar ued a generator A voltage ource behnd an mpedance ued a grd model The converter are modeled wth voltage ource ntead of wtche The control trateg ued for the generator connected converter the ame a decrbed earler n th paper The grd connected converter controlled b a cro couplng controller a hown n Fg 6 The mechancal peed held contant to mplf the mulaton Machne data ued n the PSCAD mulaton taken from a 22 [kva] nducton machne The turn rato between the rotor and tator 8 P Q The mplemented DFIG tem wa mulated wth a tranent drop n the ource voltage a decrbed n [] and hown n Fg 24 The frt mulaton, hown n Fg 9 and Fg 2, wa carred out wht onl current controller for the converter connected to the rotor wndng The flux wll begn to ocllate after the voltage drop; a a reult the torque ocllate a hown n Fg 9 Th reult n a large amount of power flowng n and out of the dc-lnk and the repone of the grd connected converter not fat enough to compenate for the power ocllaton A a reult, the dc-lnk voltage collape a hown n Fg 2 B ung a 6

7 decouplng controller, llutrated n Fg 9, the dc-lnk voltage would mabe not collape However, there would tll be a problem due to the ocllatng torque Ira [pu] electrcal torque [pu] Ura [pu] Irb [pu] Urb [pu] 2 4 Fg 9 Rotor current, torque and rotor voltage durng a tranent voltage drop Vdc [pu] Fg 2 Dc-lnk voltage durng a tranent voltage drop A flux controller ntroduced to damp the torque ocllaton Th controller gve a reference to the alpha component of the rotor current a hown n Fg 2 Alo an extra reference added to the beta component of the rotor current n th mulaton, baed on the ame trateg hown n Fg 2 Th beta component reult n a lghtl reduced peak of the frt two torque rpple In the followng mulaton the gan from the flux controller reduced due to the lmted output voltage from the converter Th wll reult n maller rotor voltage and lager rotor current durng the tranent falure compared to the reult hown n Fg 7 Fg 2 how the reultng rotor current, torque and rotor voltage A hown n Fg 2 the dc-lnk voltage wll not collape becaue the power ocllatng n the dc-lnk reduced The controller doe not manage to damp the two frt peak of the torque rpple However, the rpple wll be damped much fater than wthout a flux controller To acheve th, the converter had to repond wth a large voltage For th tuaton the converter had to be rated for a voltage of [pu], ntead of 25 [pu] whch necear for normal operaton The reultng power flow hown n Fg Ira [pu] Irb [pu] - electrcal torque [pu] Ura [pu] Urb [pu] Fg 2 Rotor current, Torque and Rotor Voltage durng a tranent voltage drop Vdc [pu] Fg 22 Dc - lnk voltage durng a tranent voltage drop 7

8 5 P ource [kw] Q ource [kvar] be appled A hown n Fg 9 and Fg 2 the ampltude of the frt perod of the torque ocllaton where not damped However, after the frt perod the controller manage to damp the torque ocllaton effcentl -5 - VI ACKNOWEDGMENTS The work decrbed n th paper ponored b the Reearch Councl of Norwa, Statkraft, Umoe Rvng and Nork Hdro VII REFERENCES [] S Muller, M Decke and Rk W De Doncker, DOUBY FED INDUCTION GENERATOR SYSTEMS for Wnd Turbne, IEEE Indutr Applcaton Magazne, Ma- June, Fg 2 Reactve and Actve Power under a tranent Voltage drop V ource [V] Fg 24 Tranent Voltage drop V CONCUSIONS The ze of the dc-lnk capactance and the control trateg of the grd connected converter affect the qualte of the total DFIG tem Ung a flux controller make the DFIG robut agant voltage drop It alo damp the torque ocllaton rapdl, and therefore could ncreae the lfetme of the gear and the relablt of the machne The requred ratng of the rotor connected converter the man drawback Th converter ha to repond on the tator voltage drop b applng large rotor voltage The larget appled rotor voltage under th tud were [pu], and the beta component of the rotor current had a peak of 5 [pu], a hown n Fg 2 If the ampltude of the current hould be decreaed further a larger rotor voltage had to [2] R Nlen, Elektrke Motordrfter, ecture note (n Norwegan), NTNU, 2 [] H Koltad, Control of an Adjutable Speed Hdro utlzng Feld Programmable Devce, Drng The, Dept Electrcal Power Eng, NTNU, 22 [4] A Peteron, Anal, Modelng and Control of Doubl- Fed Inducton Generator for Wnd Turbne, centate The, Dept Electrc Power Engneerng, Chalmer Unvert of Technolog, Sweden 2 [5] M Heller, W Schumacher, Stablt Anal of Doubl- Fed Inducton Machne n Stator Flux Reference Frame, n proc 7 th European Conference on Power Electronc and Applcaton, 997, pp [6] V Akhmatov, Anal of Dnamc Behavour of Electrc Power Stem wth arge Amount of Wnd Power, PhD The, Electrc Power Engneerng DTU, Denmark, 2 [7] C Schauer, H Mehta, Vector Anal and control of advanced tatc VAR compenator, IEE proc C, Vol 4, No 4, Jul 99 [8] Qng Yu, Invetgaton of dnamc control of a unfed power flow controller b ung vector control trateg, Dr ng The, NTNU, 997 [9] P Garca-Gonzale, A Garca-Cerrada, Control Stem for a PWM-Baed STATCOM, IEEE Tranacton on Power Delver, Vol 5, No 4, October 2 [] Eltra, Vndmøller tlluttet net med pændnger under kv, Hørngudgave Forkrft TF 26, Doknr 77899, januar 2 8