Electrical and Control Aspects of Offshore Wind Farms II (Erao II)

Transcription

1 ECN-C Electrical an Control Apect of Offhore Win Farm II (Erao II) Volume : Dynamic moel of win farm J.T.G. Pierik (ECN) J. Morren (TUD) E.J. Wiggelinkhuizen (ECN) S.W.H. e Haan (TUD) T.G. van Engelen (ECN) J. Bozelie (Neg-Micon) June 004 ECN-C

2 Erao II, Volume : Dynamic moel for win farm Ditribution Novem: J. t Hooft 5 TUD: J. Morren 6 S.W.H. e Haan 7 P. Bauer TenneT: W. Kling J. Bozelie 4 Kema: R. e Groot 5 P. Vaeen 6 Eent: H. Slootweg 7 C. Houben 8 Continuon: M. Bongaert 9 Nuon: M. van Riet 0 Neg-Micon: A. Winnemuller ICE: J.C. Montero R. Jimenez Sintef: J.O. Tane 4 Chalmer: O. Carlon 5 T. Thiringer 6 Rioe: P. Soerenen 7 VTT: B. Lemtrom 8 NREL: Y-H. Wan 9 E. Muljai 0 Ineti: A. Lopez Etanquero Univerity College Dublin: A. Mullane M. O Malley UMIST: N. Jenkin 4 O. Anaya-Lara 5 Hyro Quebec: R. Gagnon 6 ECN: A.B.M. Hoff 7 C.A.M. van er Klein 8 W.C. Sinke 9 G.J.H. van Ne 40 G. Peppink 4 H.J.M. Beurken 4 L.W.M.M. Raemaker 4 H. Snel 44 B.H. Henrik 45 G.P. Corten 46 E.J. Wiggelinkhuizen 47 B.H. Buler 48 P. Schaak 49 P. Heke 50 P. Lako 5 T.J. e Lange 5 T.G. van Engelen 5 E.L. van er Hooft 54 J.T.G. Pierik 55 ECN Win Energy Archive ECN Central Archive 70 ECN-C

3 ABSTRACT To invetigate ynamic interaction of win farm an the electrical gri, ynamic moel of win farm are neee. Thee moel are not available however. The objective of the Erao- project ha been () to evelop thee moel, () to emontrate their ue by evaluating win farm with ifferent type of electrical ytem an () to eign an emontrate controller that can cope with gri coe requirement. Four type of win farm moel have been evelope bae on ifferent type of turbine: Contant Spee Stall turbine with irectly couple Inuction Generator (CSS-IG); Contant Spee Stall turbine with Cluter Controlle inuction generator operating in variable pee moe (CSS-CC); Variable Spee Pitch turbine with Doubly-Fe Inuction Generator (VSP-DFIG); Variable Spee Pitch turbine with Permanent Magnet generator an full converter (VSP-PM). For each type of win farm, three cae have been evaluate: normal operation incluing flicker prouction; repone to a gri frequency ip; repone to a gri voltage ip. For the win farm which are able to upport gri voltage or gri frequency, controller for thee purpoe have been evelope an emontrate. Reult an concluion The repone of a win farm to a gri frequency ip trongly epen on the preence of a converter. A full converter, in the CSS-CC an VSP-PM win farm, ecouple the turbine from the iturbance. But alo the ytem with a partial converter (VSP-DFIG) i harly affecte by the frequency ip. The contant pee win farm (CSS-IG) on the other han ha eriou problem with a frequency ip an the correponing voltage ip. The contant pee win farm can tay connecte uring the voltage ip that have been applie. The high amount of reactive power that i require by thi win farm uring a voltage iturbance can be problematic. The Cluter Controlle win farm (CSS-CC) can hanle voltage ip if a reitor i place in parallel to the c-link capacitor an the urplu of energy uring the voltage ip i iipate. Win farm uing oubly-fe inuction machine (VSP-DFIG) are the mot problematic concept when voltage ip are coniere. A olution i to provie a controlle by-pa for the high current in the rotor. In the variable pee pitch win farm with permanent magnet generator (VSP-PM) goo voltage ip rie-through i achieve. The contant pee tall controlle win farm (CSS-IG) can not ait in gri frequency control. The cluter controlle win farm in the Erao- tuy i bae on a tall controlle turbine (CSS-CC). Therefore it can not ait in gri frequency upport either. Both variable pee pitch win farm (VSP-DFIG an VSP-PM) can upport gri frequency, which ha been emontrate by imulation. Only ytem with converter are uitable for gri voltage control. The imulation emontrate the feaibility of voltage control for win farm with oubly-fe inuction generator. There i no large ifference between voltage control by win farm with oubly-fe inuction generator an voltage control by the other win farm with IGBT converter: CSS-CC an VSP-PM. Recommenation With the completion of the win farm moel bae on iniviual turbine, verification of moel houl now have a high priority. ECN-C

4 Erao II, Volume : Dynamic moel for win farm Keywor: win farm moel, win farm ynamic, electrical ytem, fault rie through, gri upport Acknowlegement Erao- i a continuation of the Erao- project, in which a teay tate (loa flow) an economic moel for offhore win farm ha been evelope [8]. The Erao project have been upporte by the Dutch Agency for Energy an Environment (NOVEM) in the "Programma Duurzame Energie" of the Netherlan, execute by Novem by orer of the Minitry of Economic Affair. Novem project number: ECN project number: ECN-C

5 EXECUTIVE SUMMARY In The Netherlan offhore win power i on the brink of implementation. Plan exit for two offhore win farm of about 00 MW, locate an 5 km from the coat of the province of North Hollan. In 00 an invetigation ha been tarte to quantify the effect of 6000 MW offhore win power on the high voltage gri. Only the teay tate behaviour ha been coniere, reulting in uggetion for gri reinforcement. Thi invetigation nee to be complemente by a tuy on the ynamic interaction of win power an the electrical gri. Objective of Erao- To invetigate ynamic interaction of win farm an the electrical gri, ynamic moel of win farm are neee. Thee moel will be of great help in the evaluation of the behaviour of win power uring normal gri operation a well a uring gri fault an in the eign of controller that enable win farm to upport the gri. Dynamic moel of win farm, incluing the relevant electrical component an ection of the gri, are not available however. The objective of the Erao- project i () to evelop thee moel, () to emontrate their ue by evaluating win farm with ifferent type of electrical ytem an () to eign an emontrate controller that can cope with gri coe requirement. Part : Moel evelopment The win farm moel are bae on moel of electrical component an controller evelope in thi project an alreay exiting moel of win, rotor, tower, mechanical rive train an pitch controller. The moelle electrical component an controller are: inuction generator oubly-fe inuction generator permanent magnet generator IGBT converter an converter controller tranformer cable ynchronou generator conumer loa win farm controller for gri frequency upport converter controller for gri voltage upport A imple gri moel an a moel of the flicker meter ha alo been evelope. An important apect of ynamic moel of electrical ytem i computational pee. Electrical tranient have very mall time contant, reulting in mall time tep an long computation time. In Erao- pecial attention ha been pai to computational pee. An important increae in pee can be realie by the ue of the q0-tranformation, which ha been applie to all moel of electrical component in the Erao- component library. Volume of thi report give a mathematical erivation of the electrical component moel, followe by the implementation of the moel in Simulink, a computer program uitable for ynamic imulation. Turbine are moelle by connecting the electrical component moel to ECN-C

6 Erao II, Volume : Dynamic moel for win farm the moel of the rotor, tower, mechanical rive train an pitch controller. In the econ tep, iniviual turbine moel are connecte by cable moel to prouce the win farm moel. Reult an concluion from moel evelopment Dynamic moel of win farm bae on iniviual turbine moel are large an complicate. The number of tate variable i high an ome of the time contant are mall, leaing to a relatively long imulation time. The level of etail i high however, which make thee moel uitable for the evaluation of win farm ynamic an win farm-gri interaction a well a for the eign of controller. The application of the q0-tranformation ignificantly reuce the imulation time uring normal operation of the win farm, when tranient from electrical witching operation have ie out. Part : Moel emontration The econ part of the Erao- project emontrate the ue of the evelope win farm moel. In a number of cae tuie, four type of win farm have been compare. The win farm type ue ifferent turbine an ifferent control metho, viz.: Contant Spee Stall turbine with irectly couple Inuction Generator (CSS-IG, reference cae); Contant Spee Stall turbine with Cluter Controlle inuction generator operating in variable pee moe (CSS-CC); Variable Spee Pitch turbine with Doubly Fe Inuction Generator (VSP-DFIG); Variable Spee Pitch turbine with Permanent Magnet generator an full converter (VSP- PM). The layout of a propoe offhore win farm, the Near Shore Win farm (NSW), ha been taken a reference. The Near Shore Win Farm i planne in the North Sea near the town of Egmon in The Netherlan. One tring of turbine ha been moelle with each of the four type of turbine. A implifie gri moel ha been inclue to enable imulation of win farm-gri interaction. For each type of win farm, three cae have been evaluate: normal operation incluing flicker prouction; repone to a gri frequency ip; repone to a gri voltage ip. For the win farm which are able to upport gri voltage or gri frequency, a converter controller or a win farm controller uitable for thi purpoe ha been evelope an emontrate. Volume of thi report ecribe the cae tuy reult. Reult an concluion from cae tuie Normal operation of the win farm ha been imulate by the repone to a win gut. The imulation emontrate proper operation of the generator an converter moel, the converter controller an proper overall behaviour of the win farm. A limite flicker evaluation ha been execute. Intantaneou flicker value have been etermine over the complete range of operating conition for the four type of win farm. Flicker 6 ECN-C

7 value of a ingle turbine have been compare to the value of a tring of twelve turbine uner the ame operating conition an fictitiou gri parameter. The contant pee tall win farm generate the highet flicker, the flicker prouction of the win farm with partial an full converter i lower. Win farm repone to gri frequency an gri voltage ip The repone of a win farm to a gri frequency ip (5 Hz, 0 ec) trongly epen on the preence of a converter. A full converter, in the cae of the CSS-CC an VSP-PM win farm ecouple the turbine from the iturbance. But alo the ytem with a partial converter (VSP- DFIG) i harly affecte by the frequency ip ue to the effective ajutment of the rotor current by the rotor converter. The contant pee ytem on the other han ha eriou problem with a frequency ip an the correponing voltage ip: epening on the epth an the conition at the tart of the ip, current, power an reactive power peak may excee rate value an may lea to a win farm hut own. The farm with contant pee tall turbine an irectly connecte inuction generator (CSS- IG) can tay connecte uring the voltage ip that have been applie (0%-0 ec, 50%-0.5 ec an 85%-0. ec). High current are flowing uring the voltage rop. Due to the high thermal capacity of the inuction machine thee current will be no problem. The current may trigger protective evice in the gri. The high amount of reactive power that i require by the win farm uring a voltage iturbance can be more problematic. When the ip lat too long thi may lea to voltage collape. The Cluter Controlle win farm (CSS-CC) can hanle voltage ip if a reitor i place in parallel to the c-link capacitor an the urplu of energy uring the voltage ip i iipate. Win farm uing oubly-fe inuction machine (VSP-DFIG) are the mot problematic concept when voltage ip are coniere. Large current will flow in the rotor circuit an in the converter. Due to the limite thermal capacity of the power electronic evice in the converter, thee current may etroy the converter. A poible olution i to limit the high current in the rotor by proviing a by-pa over a et of reitor connecte to the rotor wining. With thee reitor it i poible to urvive gri fault without iconnecting the turbine from the gri. One of the cae tuie emontrate thi olution. Manufacturer of DFIG ytem are working on thi olution an are making progre in meeting the voltage rie-through requirement. In the variable pee pitch win farm with permanent magnet generator (VSP-PM), all the eential parameter can be controlle. Therefore goo voltage ip rie-through can be achieve. The power upplie by the generator i reuce by the controller uring the ip. Thi i require becaue otherwie the current in the converter or the c-link voltage become too high. To avoi overpeeing the pitch controller i activate. Win farm aiting gri frequency or gri voltage The contant pee tall controlle win farm (CSS-IG) can not ait in gri frequency control. The cluter controlle win farm in the Erao- tuy i bae on a tall controlle turbine (CSS-CC). It can not control aeroynamic power irectly an therefore it can not ait in gri frequency upport either. Both variable pee pitch win farm (VSP-DFIG an VSP-PM) can be controlle to upport gri frequency, which ha been emontrate by imulation. The controller conit of two part: elta-control to realie a power margin an frequency fee-back to act on a frequency eviation. Since frequency control capability for win farm implie maintaining a power margin, thi feature may not be cot-efficient. Only ytem with converter are uitable for gri voltage control. Different voltage an reac- ECN-C

8 Erao II, Volume : Dynamic moel for win farm tive power control trategie have been invetigate for the VSP-DFIG win farm. It ha been hown that it i poible to control the power factor an that the win farm can follow reactive power etpoint. Two voltage control option have been invetigate. In the firt option each turbine control the voltage at it own terminal, in the econ option the voltage at the gri connection point i controlle. Droop control ha been implemente on each turbine. With thi type of control, the win farm behaviour uring voltage eviation i imilar to conventional power plant behaviour. The reult epen on the X/R ratio of the gri: low X/R ratio require large amount of reactive power to control the voltage an the win farm converter are limite in current an thu in reactive power. Nonethele, the imulation emontrate the feaibility of voltage control for win farm with oubly-fe inuction generator. There i no large ifference between voltage control by win farm with oubly-fe inuction generator an voltage control by the other win farm with IGBT converter: CSS-CC an VSP-PM. Thi ha been emontrate by imulation with a cluter of CSS-CC turbine an a tring of VSP-PM turbine. The reult are imilar to thoe of the VSP-DFIG win farm. Economic evaluation The loa flow program an the atabae with electrical an economic parameter evelope in the Erao- project ha been ue in an economic evaluation of the four win farm electrical ytem. For a win regime repreentative of the North Sea, the power prouction incluing the electrical loe, ha been etermine for the layout of the Near Shore Win farm. Thi reult in the contribution of the electrical ytem to the Levelie Prouction Cot (LPC). The VSP-DFIG farm perform bet:.4 Eurocent/kWh. The CSS-IG farm i of the ame magnitue:.6 Eurocent/kWh, while the other two farm have relatively expenive electrical ytem:.60 Eurocent/kWh (VSP-PM) an 4.57 Eurocent/kWh (CSS-CC). The high price for the Cluter Controlle ytem i caue by the expenive converter. Recommenation With the completion of the win farm moel bae on iniviual turbine, verification of moel houl now have a high priority. The Erao- project ha been tarte with moel valiation a one of the objective. For the incorporation of ynamic moel of win farm in moel of national gri, the complexity of the win farm moel ha to be reuce. Aggregate win farm moel, in which all turbine are repreente by a ingle equivalent moel are more uitable for thi purpoe. However, aggregate moel looe the wie range of applicability of the win farm moel bae on iniviual turbine moel. It i recommene to evelop aggregate win farm moel, tailore to application in power ytem moel. The win farm moel evelope in Erao- can erve a reference in the evelopment of thee aggregate moel. Sytem with DC cable to hore have not been inclue in the Erao- cae tuie. The Erao- component library inclue all moel neceary to invetigate DC connection, with the exception of the thyritor converter. Thi converter however, i a le likely option for the connection of offhore win farm than the IGBT converter, ue to it limite controllability an large footprint. DC connection are currently more expenive than AC, but may offer a number of avantage. It i recommene to inclue thee ytem in a future tuy an for comparion purpoe alo evelop a thyritor converter moel. 8 ECN-C

9 Symbol Subcript C capacitance a aeroynamic, phae a E electromagnetic force abc abc reference frame f frequency b phae b G tranfer function c phae c i current conv converter I unit matrix -axi J inertia c c-link K contant, tranfer function q0 q0 reference frame L inuctance e electrical N number of turn f fiel, filter p number of pole pair g gri, groun P (active) power, intantaneou or average i integral Q reactive power, intantaneou or average m mechanical, mutual R reitance p proportional Laplace operator q q-axi S aturation function r rotor T torque tator T tranformation matrix 0 zero-equence component u voltage v voltage V Velocity W energy x arbitrary ignal Z impeance α banwih of control loop θ angle τ time contant ω angular velocity ψ flux ECN-C

10 Erao II, Volume : Dynamic moel for win farm. 0 ECN-C

11 CONTENTS Introuction Mathematical moel of electrical component 6. Moelling in a q0-reference frame Introuction Park Tranformation Moelling of baic component Moel of win turbine generator Introuction Doubly-Fe Inuction Machine Inuction machine Permanent Magnet Synchronou Machine Converter Other electrical component Tranmiion line an cable Tranformer Gri moel Zero-equence component Introuction Zero-equence component Star an elta connection Three-phae tranformer NSW-park ERAO-II Moel of win an win turbine 50. Win moel Longituinal turbulence moel, tower paage an win hear Turbine moel Aeroynamic converion, rotation an torion Tower mechanical moel Pitch control an electrical torque etpoint Dynamic moel of win farm in Simulink Contant pee tall controlle win farm Contant pee tall controlle WF with cluter controlle inuction machine Variable pee pitch controlle WF with oubly fe inuction machine Variable pee pitch controlle WF with permanent magnet machine Gri moel ECN-C

12 Erao II, Volume : Dynamic moel for win farm 5 Flicker meter Introuction Flicker meter Implementation in Simulink Teting the flicker meter in Simulink Repone to calibration input ignal Repone to moulate gri voltage an loa tep Concluion Concluion an remark 6. Concluion Remark A Summary of Erao I project 5 B Contribution to International Conference 6 B. Noric Win Power Conference B. 4th International Workhop on Large Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm B. EPE 00 Touloue ECN-C

13 INTRODUCTION Problem ecription Offhore win farm have to be large to be economical an with the increae of the contribution of win energy to the electric power prouction, the interaction between the win farm an the gri will be an important apect in the eign an planning of win farm farm [7]. It i eential to enure that the gri i capable of taying within the operational limit of frequency an voltage for all foreeen combination of win power prouction an conumer loa [9]. A econ apect i to enure appropriate tranient an mall ignal tability of the gri []. Aequate gri control play an important role but the electrical control an protection of large win farm i alo an important iue. Large win farm are a ource of fluctuating power an ometime of reactive power a well. The repone of win farm to voltage an frequency ip i a caue for worry: the farm may hut own intantaneouly. The ip itelf i a ign of a eriou gri control problem, an the problem may become wore if win power hut own on a large cale. For conventional power tation the requete behaviour uring a gri ip i to tay in operation an upply (reactive) power. Thi behaviour i precribe in gri coe. It i likely that large offhore win farm alo have to comply with thee rule. In Germany, gri operator E.On Netz alreay require pecific behaviour of win farm uring ip []. Depening on the type of win turbine, viz. contant or variable pee, an the eign of the turbine an win farm control, a win farm will have more or le problem to comply with thee rule. Objective of Erao II In orer to invetigate the ynamic interaction of win farm an the electrical gri, ynamic moel of win farm are neee. Dynamic moel of win turbine an win farm will be of great help in the eign an evaluation of the behaviour of win power uring normal gri operation a well a uring gri fault. Dynamic moel of win farm, incluing the relevant electrical component an ection of the gri, are not reaily available however. The Erao- project ha been tarte with the objective to evelop thee moel an to emontrate their ue by eigning controller to cope with gri coe requirement an evaluate ifferent type of electrical ytem in win farm. Metho An important apect of ynamic moel of win farm i computational pee. Electrical tranient have very mall time contant, reulting in mall time tep an long computation time. In Erao- pecial attention ha been pai to computational pee. An important increae in pee can be realie by the ue of the q0-tranformation (alo known a Park tranformation). Thi tranformation i mainly ue in electrical machine theory, in Erao- it i applie to all electrical component. The main characteritic of the imulation moel for the electrical component are: Reult all electrical component are moelle in q0-coorinate; AC-DC-AC converter are moelle by controlle voltage ource; the component moel are implemente in Simulink. The component moel evelope in the Erao- project are lite in table. ECN-C

14 Erao II, Volume : Dynamic moel for win farm Table : Dynamic moel of component of win farm evelope in the Erao- project Mechanical an aeroynamic (turbine): turbine rotor Electrical (turbine & win farm): Electrical (gri): Control (turbine & win farm): input from ECN control tool [5] mechanical rive train tower rotor effective win inuction generator oubly-fe inuction generator permanent magnet generator voltage ource converter tranformer cable ynchronou generator frequency an voltage controller conumer loa tranformer cable converter controller win turbine pitch controller overall win farm controller Volume of thi report give a ecription of the moel. In chapter a ecription of the Park tranformation i given, followe by a erivation of moel of ifferent electrical component in the q0-reference frame. Moel of the electrical generator are erive, together with the power electronic converter moel. The chapter conclue with a ecription of moel of the other electrical component that are neee an a icuion of the zero-equence component in the moel. Chapter give a ecription of the moel that ha been ue for the win, the turbine, aeroynamic converion, pitch control, etc. In chapter 4 the Simulink implementation of the four type of win farm i ecribe. Chapter 5 give the flicker meter that ha been ue. The final chapter lit concluion an remark an contribution to international conference can be foun in appenice. Volume of the Erao- report the focu i on the ue of the four type of win farm moel in a number of cae tuie. It emontrate how the moel can be ue to calculate the flicker contribution of a win farm, imulate a repone to a gri fault an evelop win farm control to upport the gri. Valiation The electrical component moel have only been valiate partially, viz. by comparing abcmoel with witching converter to q0-moel with controlle voltage ource converter [0], []. For extenive teting an valiation the Erao- project ha been tarte, which take part in the IEA Annex XXI (Dynamic moel of Win Farm for Power Sytem Stuie). Thi Annex i a joint effort of nine countrie to et up a atabae of win farm meaurement an to ue thee meaurement for valiation of ynamic moel. The participating countrie are Norway (Coorinator), Sween, Finlan, Denmark, USA, UK, Portugal, Irelan an the Netherlan. Oberving countrie are Canaa an Irelan. 4 ECN-C

15 Future work INTRODUCTION In the context of the implementation of large amount of offhore win power in the Netherlan [6], a conortium of partie involve in offhore win power ha been forme uner the name We@Sea. Thi group comprie win farm eveloper, electricity companie, gri operator, reearch intitute an univeritie. We@Sea ha efine a number of reearch activitie aiming to reolve the remaining bottleneck for large cale offhore win in the Netherlan. One of the activitie will be win farm control, optimalization an the interaction between large offhore win farm an the gri. ECN an TUD will make the ynamic win farm moel evelope in the Erao- project available for thi project an execute the reearch together with ome of the We@Sea partner. ECN-C

16 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS. Moelling in a q0-reference frame.. Introuction The moel of all electrical component are erive in the q0-reference ytem. To obtain thee moel from the tanar abc-moel, the Park Tranformation i ue. The Park tranformation (ometime calle Blonel-Park tranformation) i well-known from it ue in electrical machinery. The electrical ignal are tranforme to a tationary rotating reference frame. A thi tationary frame i choen to rotate with the gri frequency, all voltage an current in the q0-reference frame are contant in teay tate ituation. Therefore, moelling in the q0-reference frame i expecte to increae the imulation pee ignificantly, a a variable tep-ize imulation program can apply a large time tep uring quai teay-tate phenomena. In the ERAO- project, ynamic moel have been erive for: electrical generator (inuction generator, oubly-fe inuction generator, permanent magnet generator), power electronic converter, tranformer, cable, turbine rotor, mechanical rive train an rotor effective win. All moel of electrical component are in the q0-reference frame. In thi chapter firt a ecription will be given of the way in which moel of ifferent electrical component in the q0-reference frame can be obtaine. The moel erivation will be hown for two baic component: a three-phae RL line egment an a three-phae hunt capacitance. Next, the moel of the electrical generator will be erive, together with the power electronic converter moel. In thi part alo the control of the generator will be ecribe. Thi i followe by a ecription of the other electrical component moel neee for win farm moel. Thi chapter conclue with a icuion of the zero-equence component in the moel... Park Tranformation In the tuy of power ytem, mathematical tranformation are often ue to ecouple variable, to facilitate the olution of ifficult equation with time-varying coefficient, or to refer all variable to a common reference frame []. Probably the mot well-known, i the metho of ymmetrical component, evelope by Fortecue. Thi tranformation i motly ue in it time-inepenent form an applie to phaor, when it i ue in electrical power ytem tuie [5]. Another commonly-ue tranformation i the Park tranformation, which i wellknown from the moelling of electrical machine. The Park tranformation i intantaneou an can be applie to arbitrary three-phae time-epenent ignal. The electrical ignal are tranforme to a tationary rotating reference frame. A thi tationary frame i choen to rotate with the gri frequency, all voltage an current in the q0-reference frame are contant in teay tate ituation. Therefore, moelling in q0-omain i expecte to increae the imulation pee ignificantly, a the variable tep-ize imulation program can apply a large time tep uring quai teay tate phenomena. For θ =ω t+ϕ, with ω angular velocity, t the time an ϕ initial angle, the Park tranformation i given by: with: [x q0 ] = [T q0 (θ )] [x abc ] () 6 ECN-C

17 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS an [x q0 ] = [x abc ] = x x q x 0 x a x b x c () () an with the q0-tranformation matrix T q0 efine a: [T q0 (θ )] = an it invere given by: [T q0 (θ )] = co θ in θ ( co θ π ( in ) θ π ) ( ) co θ + π ( ) in θ + π co θ in θ ( ) ( ) co θ π in θ π ( ) ( ) co θ + π in θ + π (4) (5) The poitive q-axi i efine a leaing the poitive -axi by π/, a can be een from figure. Some aitional propertie of the Park tranformation can be erive. A the tranformation i orthogonal: [T q0 (θ )] [T q0 (θ )] = [T q0 (θ )] [T q0 (θ )] T = [I] (6) Figure : Relationhip between abc an q With equation 6 it can be hown that the Park tranformation conerve power an therefore i a vali tranformation. The power conervation principle can then be hown a follow: ECN-C

18 Erao II, Volume : Dynamic moel for win farm P (t) = [v abc ] T [i abc ] [ = [ T q0 (θ )] T [v q0 ]] [ Tq0 (θ )] [i q0 ] = [v q0 ] T [ [ T q0 (θ )] ] T [ Tq0 (θ )] [i q0 ] = [v q0 ] T [ T q0 (θ )] [ T q0 (θ )] [i q0 ] = [v q0 ] T [i q0 ] (7) The tranformation of (4) an (5) are unitary, a i hown in (6) an conerve power a i hown in equation (7). Note that by replacing the factor / by a factor / in (4) an (5) the tranformation will be amplitue-invariant, implying that the length of the current an voltage vector in both abc- an q0-reference frame are the ame, however in that cae the conervation of power i lot. Thi amplitue-invariant tranformation i motly ue in moelling of electrical machine [5]. The voltage an current in the q0-reference frame are contant in teay-tate ituation. Be aware that alo non-funamental harmonic are correctly tranforme a x a, x b an x c are time ignal, incluing all harmonic. In teay tate a non-funamental frequency component with frequency ω h will appear a a inuoial ignal with frequency (ω h -ω ) in the q0-omain. The highet frequency that can be repreente accurately in the q0-frame epen on the time tep that i ue. With electric machine the -axi i motly choen along the tator flux, which implie that i q correpon to real power an i to reactive power (ee (8)), ince ieally v = 0. In general the voltage will be phae hifte with repect to the -axi which mean that active an reactive power cannot be relate irectly to the an the q axi component (v q 0). The intantaneou active an reactive power can be obtaine irectly from the voltage an current in the q0-reference ytem [Aka 84]: P = v i + v q i q Q = v q i v i q (8).. Moelling of baic component In thi ection the q0-moel of two relevant circuit, a three phae line with erie RL an a three phae line with hunt capacitance, are obtaine. With the moel of thee baic circuit all further moel, uch a tranformer, machine an cable, that are require can be obtaine. The erivation of the baic moel tart by efining the voltage rop acro the impeance of the a-phae. The a-phae equation i then tranforme to a q0-equation with (4). The b an c phae equation are written a a function of the a-phae an the zero-equence component, in orer to eliminate thee component. After ome mathematical manipulation, the moel for the, q an 0 phae can be obtaine. Firt the q0-equation for a three-phae erie RL line with a groun return will be given an afterwar the q0-equation for hunt capacitance will be erive. Serie RL In thi ection the q0-equation for a three-phae erie RL line with groun return, hown in figure, will be preente. The q0-equation for the uniformly tranpoe line can be obtaine by coniering the reitive an inuctive rop of the a-phae equation. The en en voltage with repect to local groun i given by: 8 ECN-C

19 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS With v g = v g v g. i a v a = R a i a + L a + L i b ab + L i c ac + L i g ag + v a + v g (9) v c i c R c L c v c L ac v b i b R b L b L bc v b v a i a R a L a L ab v a v ag L ag v ag R g L g v g i g v g Figure : Three-phae RL line with groun return Uing the relation i g =-(i a +i b +i c ), the voltage rop acro the three phae of the line can be expree in matrix form a: Where [L] = [v,abc ] [v,abc ] = [R] [i abc ] + [L] [i abc] (0) [v,abc ] = [R] = v a v b v c [v,abc ] = v a v b v c R a + R g R g R g R g R b + R g R g R g R g R c + R g L a + L g L ag L ab + L g L bg L ag L ac + L g L cg L ag L ab + L g L ag L bg L b + L g L bg L bc + L g L cg L bg L ab + L g L ag L cg L bc + L g L bg L cg L c + L g L cg The equation of the voltage rop acro the groun path i: i g v g = v g v g = R g i g L g L i a ag L i b bg L i c cg = R g (i a + i b + i c ) + (L g L ag ) i a + (L g L bg ) i b + (L g L cg ) i c () For a uniformly tranpoe line, R a =R b =R c, L ab =L bc =L ca, an L ag =L bg =L cg. Letting L =L a +L g - L ag, L m =L ab +L g -L ag =L -L a +L ab, R =R a +R g, an R m =R g, the reitance an inuctance matrice implify to: [R] = R R m R m R m R R m R m R m R () ECN-C

20 Erao II, Volume : Dynamic moel for win farm an [L] = L L m L m L m L L m L m L m L () The q0-equation for the uniformly tranpoe line can be obtaine by coniering the reitive an inuctive rop of the a-phae equation. The reitive rop in the a-phae i given by: Subtituting i o =(i a +i b +i c )/ to eliminate i b an i c, we obtain: R a i a + R m (i b + i c ) (4) (R R m ) i a + R m i 0 (5) Expreing i a in term of the q0-current, the reitive rop in the a-phae become: (R R m ) (i co θ i q in θ + i 0 ) + R m i 0 (6) Similarly, for the inuctive rop in the a-phae, we have: Eliminating i b an i c : i a L + L (i b + i c ) m (7) (L L m ) i a + L i 0 m Uing the invere q0-tranform of (5) to expre i a in term of the q0-current, the inuctive rop in the a-phae become: (8) Knowing that for x=x(t): (L L m ) (i co θ i q in θ + i 0 ) + L m i 0 (9) an (9) can be written a: in x = co xx co = in xx (0) () [ θ (L L m ) i in θ + co θ i i θ q co θ in θ i q + i ] 0 i 0 +L m () The q0-tranform can alo be applie to the voltage ifference v a = v a v a, reulting in: 0 ECN-C

21 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS Combining (6), (), an (), (9) can be written a: v co θ v q in θ + v 0 () v co θ [ v q in θ + v 0 = (R R m ) (i co θ i q in θ + i ] 0 ) + R m i 0 + θ (L L m ) i in θ i + co θ i θ q co θ i in θ q + i 0 i + L 0 m (4) By equating the coefficient of the coθ, inθ, an contant term, we obtain: v = (R R m ) i + (L L m ) i (L θ L m ) i q v q = (R R m ) i q + (L L m ) i q + (L θ L m ) i v 0 = (R + R m ) i 0 + (L + L m ) i 0 When the mutual inuctance between phae an between phae to groun are zero, that i L ab =L bc =L ca =0 an L ag =L bg =L cg =0, then L =L a +L g, an L m =L ab +L g. With ω =θ / the final reult i: (5) i v = R a i + L a ω L a i q i v q = R a i q + L q a + ω L a i v 0 = (R a + R g ) i 0 + (L a + L g ) i 0 The reulting equivalent q0-circuit are hown in figure. (6) i R a w L a i q L a v v -axi circuit i q R a w L a i L a v q v q q-axi circuit i 0 R a +R g L a +L g v 0 v 0 0-axi circuit Figure : Equivalent q0-circuit of a erie RL line ECN-C

22 Erao II, Volume : Dynamic moel for win farm Shunt C The next tep i to erive the q0-equation for the voltage rop acro the hunt capacitance of the three-phae line hown in figure 4. Beie the phae to neutral capacitance of the phae, we have alo inclue the mutual capacitance between the phae. Figure 4: Shunt capacitance of a three-phae line Let C ab = C bc = C ac = C m, C an = C bn = C cn, an C = C an + C ab. The equation of the a-phae current in figure 4 may be expree a: i a = C an v an + C ab (v an v bn ) + C ac (v an v cn ) (7) i a = (C an + C ab + C ac ) v an C m v bn C m v cn Exchanging the b an c phae voltage with v 0 = (v an + v bn + v cn )/ give: i a = (C + C m ) v an C m v 0 Applying the q0-tranformation to the current an the voltage of the a-phae we obtain: (8) (9) i co θ i q in θ + i 0 = (C + C m ) (v co θ v q in θ + v 0 ) C m v 0 (0) In analogy to equation (9) to (5), by equating the coefficient of the coθ, inθ, an contant term, the following et of equation i obtaine for the q0-current: i = (C + C m ) v i q = (C + C m ) v q i 0 = (C C m ) v 0 (C + C m ) v q θ + (C + C m ) v θ When the mutual capacitance between the phae are zero, that i C ab =C bc =C ac = 0, then C m = 0 an C =C an = C. With ω =θ / the final reult i: ECN-C ()

23 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS i = C v i q = C v q i 0 = C v 0 ω Cv q + ω Cv The reulting equivalent q0-circuit are hown in figure (6). () v i C v q i q C v 0 i 0 C w Cv q w Cv -axi circuit q-axi circuit 0-axi circuit Figure 5: Equivalent q0-circuit of hunt capacitance of a three-phae line Summary The equation for the erie reitor, erie inuctor, an hunt capacitor are erive in the previou ection. The voltage-current relationhip for the baic component are ummarie in table. Thee reationhip can be ue to erive moel of the ifferent component that are neee. Example of how thi can be one can be foun in ome of the following ection in which moel of tranformer an cable are erive. Uner the aumption that are given uring the erivation of the moel, i.e. uniformly tranpoe line an the mutual inuctance/capacitance between phae an phae to groun are zero, the R, L, an C given in the table are equal to the line reitance, line inuctance an hunt capacitance. Three-phae reitor R [i q0 ] = [u q0 ] Three-phae inuctor L [i q0] + ω Y L [i q0 ] = [u q0 ] Three-phae capacitor C [u q0] + ω Y C [u q0 ] = [i q0 ] [R] = R a R a R a + R g [C] = C C C [L] = [Y] = L a L a L a + R g Table : Voltage-current relationhip in q0-reference frame for baic component. Moel of win turbine generator.. Introuction In thi ection a ecription will be given of the electrical moel that have been evelope for the win turbine that are ue in the ERAO- project. The ection tart with a thorough ECN-C

24 Erao II, Volume : Dynamic moel for win farm ecription of the Doubly-Fe Inuction Generator (DFIG). The moel of an Inuction Machine (IM) can eaily be erive afterwar. The ection continue then with the moelling of the Permanent Magnet Synchronou Machine (PM). At the en of the ection a ecription i given of the converter moel that i ue for the DFIG an the PM. The converter moel i alo ue for the Cluter-Couple (CC) park concept... Doubly-Fe Inuction Machine Introuction In thi ection a ecription will be given of the Doubly-Fe Inuction Generator. Thi type of generator ha a converter connecte to the rotor wining intea of the tator wining. The avantage i that variable pee operation of the turbine i poible wherea the converter can be much maller, an therefore alo much cheaper. The power rating of the converter i often choen about / of the generator rating. A chematic rawing of a win turbine with Doubly- Fe Inuction Generator i hown in figure 6. Firt a ecription of the generator moel will be given. Afterwar, the controller moel will be ecribe. gear box Generator ASM Converter Gri Control Figure 6: Win turbine with Doubly-Fe Inuction Generator Generator moel In thi ection two ifferent moel of a oubly-fe inuction generator will be evelope. The firt moel inclue all ynamic term wherea in the econ moel the tranient flux term of the machine are neglecte. A q reference frame i choen to moel the oubly-fe inuction generator. The moel that i obtaine i well known an can be foun in literature [], []. The generator convention will be ue, which mean that the current are output intea of input an real power an reactive power have a poitive ign when they are fe into the gri. Uing the generator convention, the following et of equation reult: v = R i ω ψ q + ψ v q = R i q + ω ψ + ψ q v r = R r i r ω r ψ qr + ψ r v qr = R r i qr + ω r ψ r + ψ qr () 4 ECN-C

25 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS with ψ = (L + L m ) i L m i r ψ q = (L + L m ) i q L m i qr ψ r = (L r + L m ) i r L m i ψ qr = (L r + L m ) i qr L m i q (4) with v the voltage [V], R the reitance [Ω], i the current [A], ω an ω r the tator an rotor electrical angular velocity [ra/] repectively, L m the mutual inuctance [H], L an L r the tator an rotor leakage inuctance [H] repectively an ψ the flux linkage [V]. The inice an q inicate the irect an quarature axi component of the reference frame an an r inicate tator an rotor quantitie repectively. All voltage, current an fluxe in () an (4) are function of time. Sometime the tranient in the fluxe, repreente by the erivative term in equation (), are neglecte. The mot important reaon to o thi i computational pee uring imulation. Another reaon i that taking into account the rotor tranient woul require etaile moelling of the converter []. When the tranient are neglecte, the following et of equation reult: v = R i + ω ((L + L m ) i q + L m i qr ) v q = R i q ω ((L + L m ) i + L m i r ) v r = R r i r + ω r ((L r + L m ) i qr + L m i q ) v qr = R r i qr ω r ((L r + L m ) i r + L m i ) (5) The electrical angular velocity of the rotor, ω r, equal: ω r = ω pω m (6) with p the number of pole pair [-] an ω m the mechanical angular velocity [ra/]. The electrical torque of the generator i given by: T e = p (ψ r i q ψ qr i ) (7) A ynchronouly rotating -q reference frame i ue with the irect -axi oriente along the tator flux vector poition. In thi way a ecouple control between the electrical torque an the rotor excitation current i obtaine. Thi reference frame i rotating with the ame pee a the tator voltage an auming that the tator reitance i negligible, i.e, R «ω (L +L m ), the angle of the tator flux vector can be calculate a: θ = ω (8) The reference frame of the rotor i rotating with the electrical frequency of the rotor ω r. The angle of the rotor can be obtaine a: θ r = ω r = (ω pω m ) (9) With the q0-tranformation ue in (4) the active power elivere by the tator i given by: an the reactive power by: P = v i + v q i q (40) ECN-C

26 Erao II, Volume : Dynamic moel for win farm Q = v q i v i q (4) Due to the choen reference frame, ψ q an v are zero. Therefore the reactive power an the active power elivere by the tator can be written a: an: P = v q i q = v q ( Lm L r + L m ) i qr (4) Q = v q i = ω ( (L + L m ) i L m i r ) i (4) A the tator current i equal to the upply current, it can be aume that it i contant. If the frequency i alo contant, the reactive power i proportional to the irect component of the rotor current i r : With contant K an K : Q = K + K i r (44) an K = ω (L + L m ) i (45) K = ω L m i (46) Spee an current control of the generator The electrical an mechanical ynamic of a win turbine have ifferent time cale. The electrical ynamic are much fater than the mechanical. Therefore, it i poible to control the machine in a cacae tructure, a hown in figure 7. The fat electrical ynamic can be controlle in an inner loop an a pee controller can be ae in a much lower outer loop. w ref K T ref J i ref K c v ref Inv i IM w Figure 7: Cacae control; IM=Inuction Generator, Inv=Inverter, K c =current controller, J=inertia of turbine, K =pee controller The internal moel control (IMC) principle [] ha been ue to eign the controller K an K c. The iea behin internal moel control i to reuce the error between the ytem G(), an the moel of the ytem G () by a tranfer function K(). In figure 8 the principle i hown for the current controller. 6 ECN-C

27 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS i ref K u G() i G() C() Figure 8: Internal Moel Control (IMC): ytem G() an ytem moel G () One common way of chooing the tranfer function K() i [5]: K () = ( ) α n G () (47) + α where n houl be at leat one larger than the number of zero of G (), o that K() become proper (alway converging to zero). The parameter α i a eign parameter that i equal to the cloe loop banwih of the ytem. The ytem G() houl be minimum phae, i.e. it houln t contain right half-plane zero, a thee will become untable uner feeback. The controller C(), inie the ahe line in figure 8, become [5]: C () = ( K () G ()) K () (48) For a firt orer ytem, n= i ufficient an the controller become then a PI controller. With (48) an G () = G() the controller become [5]: C () = k p + k i = α G () (49) Where k p i the proportional gain an k i i the integral gain. The cloe loop ytem with parameter exactly equal to the real parameter become: G cl () = G () K () = α + α Since the tator flux i almot fixe to the tator voltage, the flux i practically contant. Thi implie that the erivative of the tator flux an of the tator magnetizing current are cloe to zero, an can be neglecte [6], [7]. The voltage equation of the rotor which have previouly been given in () can then be written a: (50) i v r = R r i r L r r ω r ψ qr i v qr = R r i qr L qr (5) r + ω r ψ r The lat term in both equation caue a cro-relation between the two current component. Reference voltage to obtain the eire current can be written a [6]: v r = v r ω r ψ qr (5) v qr = v qr + ω r ψ r (5) ECN-C

28 Erao II, Volume : Dynamic moel for win farm with v r = R ri r L r i r v qr = R r i qr L r i qr (54) The i r an i qr error are procee by a PI controller to give v r an v qr repectively. To enure goo tracking of thee current, the cro-relate flux term are ae to v r an v qr to obtain the reference voltage. Treating ω r Ψ r an ω r Ψ qr a a iturbance, the tranfer function from the rotor voltage v r to the rotor current i r an from the rotor voltage v qr to the rotor current i qr i given by: G () = Uing the IMC, the current controller become: L r + R r (55) C () = k p + k i = α c G () (56) Where α c i the banwih of the current control loop, k p i the proportional gain an k i i the integral gain. The two gain become [7]: Spee control: k p = α c L r (57) k i = α c R r (58) The rotational pee follow from: ω m = J (T m T e ) (59) It i aume that the current controller i much fater than the pee controller, which implie that for the evaluation of (59) electrical torque i than T e =T e,ref. The reference torque i et to: T e,ref = T e,ref B a ω m (60) where B a i an active amping torque [7]. Now the tranfer function from rotational pee to electrical torque become: G () = J + B a (6) Uing again the internal moel control metho, the following gain of the pee controller are obtaine: k p = α J (6) k i = α B a (6) 8 ECN-C

29 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS Where α i the eire cloe-loop banwih of the pee controller. When B a i choen to be B a =Jα change in the mechanical torque are ampe with the ame time contant a the banwih of the pee control loop [7]. Converter A can be een from figure 6, the Doubly-Fe Inuction Generator, ha a converter connecte to it rotor wining. The generator ie converter i ue to control the rotor current of the machine, accoring to (5)-(58). With thi rotor current, the active power (or inirectly the rotational pee) an reactive power of the machine can be controlle accoring to (40)-(4). The gri-ie converter raw or upplie power to the rotor-ie converter an i operate to keep the DC-link voltage contant. A further ecription of the converter i given in ection Inuction machine The moel of the inuction machine can be obtaine very eaily now, a it i the moel of the Doubly-Fe Inuction machine, with the rotor wining hort-circuite. Equation () moifie to: with v = R i ω ψ q + ψ v q = R i q + ω ψ + ψ q 0 = R r i r ω r ψ qr + ψ r 0 = R r i qr + ω r ψ r + ψ qr (64) ψ = (L + L m ) i L m i r ψ q = (L + L m ) i q L m i qr ψ r = (L r + L m ) i r L m i ψ qr = (L r + L m ) i qr L m i q (65) To obtain electrical torque an power of the machine, (6)-(4) can be ue. In win turbine the inuction machine are normally irectly connecte to the gri. Thi mean that no converter i neee an that there i no poibility to control the torque irectly...4 Permanent Magnet Synchronou Machine Introuction The next generator type that i often ue for win turbine application i the permanent magnet ynchronou machine. It i epecially ue in irect-rive win turbine, which have the avantage that no gearbox i neee, which i favourable with repect to lifetime an maintenance. In thi ection the baic equation ecribing the machine behaviour will be given, followe by the way in which controller can be obtaine. ECN-C

30 Erao II, Volume : Dynamic moel for win farm Generator moel Uing the generator convention, the tator voltage equation are, in analogy to (): v = R i ω ψ q ψ v q = R i q + ω ψ ψ q (66) with v the voltage [V], R the reitance [Ω], i the current [A], ω the tator electrical angular velocity [ra/] an ψ the flux linkage [V]. The inice an q inicate the irect an quarature axi component. All voltage, current an fluxe in () are function of time. The flux linkage in (66) can be calculate uing the following et of equation: ψ = (L + L m ) i + Ψ f ψ q = (L q + L m ) i q (67) With Ψ f the excitation flux of the permanent magnet linke with the tator wining, L m the mutual inuctance [H], an L an L q the tator leakage inuctance [H]. The electrical torque T e of the permanent magnet ynchronou machine i given by [0]: T e = p i q [i (L L q ) + Ψ f ] (68) Here p i the number of pole pair. For a non-alient-pole machine the tator inuctance L an L q are approximately equal. Thi mean that the equation become: The tator electrical angular velocity i given by: T e = pi q Ψ f (69) ω = pω m (70) with ω m the mechanical angular velocity [ra/], which can be obtaine from: ω m = J (T m T e ) (7) with J the inertia contant of the rotor [kg m ] an T m an T e the mechanical an electrical torque [Nm] repectively. Control of the generator From the voltage equation in (66) it can be een that there i a cro relation between the two axe. The -axi voltage equation ha a flux term that epen on the q-axi. Vice-vera the q-axi ha a flux term epening on the -axi. In orer to apply inepenent controller for the two coorinate the influence of the q-axi on the -axi-component an vice vera mut be eliminate. Thi can be one by ecoupling the two component, in the way hown in figure 9. The fault in the current component can be procee by the (PI) controller an afterwar the ecoupling component houl be ae to the voltage reference ignal. 0 ECN-C

31 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS i L * ω Ψf u qec L q * u ec i q Figure 9: Decoupling of the generator axe With the ecoupling applie, the linear tranfer function of i to u i given by: i () u () = (7) L + R The proportional an integral contant for the PI-controller can be obtaine in the ame way a for the oubly-fe inuction machine: k p = α c L (7) k i = α c R (74) With α c i the banwih of the current control loop. The proportional an integral contant for the pee controller are given by [0]: k p = p ψ f J (75) k i = p ψ f R JL (76)..5 Converter Introuction Some of the generator ecribe in the previou ection ue a power electronic converter. A ecription of thi converter will be given in thi ection. For the oubly-fe inuction generator it houl be poible to tranport power in both irection, an therefore a back-to-back converter coniting of two Voltage Source Converter (VSC) an a DC link i ue. The converter i hown in figure 0. The DC link eparate the two Voltage Source Converter, an therefore they can be controlle inepenent of each other. Therefore, only one converter ha to be coniere. To obtain inuoial line current, a filter can be place between the converter an the gri. The phae voltage are referre to the noe n. The value of the arbitrary voltage reference noe n epen on the circuit configuration. It houl not be confue with the neutral. The line voltage can be erive from the phae voltage. For example the voltage v ab i: ECN-C

32 Erao II, Volume : Dynamic moel for win farm v ab = v an v bn (77) I c i a i a i b V c C i b i c i c n v cn v bn v an v cn v bn v an n Figure 0: Back-to-back converter The controller of the converter will be bae on a q0-reference frame, implementing the vector control metho. All ignal will be contant in teay-tate an therefore PI controller can be ue to realie the reference value without teay-tate error. A triangular carrier bae Pule Wih Moulation cheme i ue to control the witche of the converter. The controller i bae on two control loop. The inner loop i a current controller, which get it reference from the outer loop controller, which can be for example a reactive power or torque controller. A block iagram of a PWM converter with a vector controller i hown in figure. i a v g C Filter i b i c 6 PWM ample an hol ab q ab q ab q v q * Current Controller v q i q i q * Figure : Scheme of PWM Voltage Source Converter with controller Switching Function Concept The witching function concept ha been ue to moel the converter [7]. Uing thi concept, the power converion circuit are moele accoring to their function, rather than to their circuit topologie. The witching function concept will be ecribe hortly with reference to the circuit configuration of a VSC a hown in figure an the type of voltage that are generate at the AC ie. It i well known that with voltage ource converter pulating voltage are generate at the AC ie. In figure 5 an example of the voltage V an i hown. Thi voltage i obtaine by alternatively witching the upper an the lower witch in phae a. The ON/OFF ECN-C

33 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS control ignal for the witche are generate in ome type of Pule Wih Moulator (PWM). An example of the principle of uch a moulator i hown in figure 5, where the eire output voltage V ref i compare with a triangular carrier. Whenever V ref >V tri the upper witch i cloe, an when V ref >V tri, the lower witch i cloe. In thi way the output waveform ha the ame hape a the output ignal of the comparator. For each phae leg a eparate moulator i ue, where the reference voltage are iplace over 0 or 40 egree repectively. The output voltage of a phae can mathematically be ecribe a the prouct of the logical output ignal of the comparator, alo calle witching function SF a of phae a, an the DC link voltage [7]: V an = SF a V (78) i a V i b i c v cn v bn v an n V ref V tri Comparator 0 Figure : Voltage ource converter i a i b i c V v cn v bn v an n V ref V tri Comparator V 0 Figure : Voltage ource converter, witching function equivalent ECN-C

34 Erao II, Volume : Dynamic moel for win farm i a i b i c V v cn v bn v an n V ref V V / Figure 4: Voltage ource converter, inuoial voltage equivalent The voltage V an can alo be obtaine with the circuit from figure, where controllable voltage ource are applie intea of witche in phae leg. The controllable voltage ource are controlle by the ame ignal a with the phae leg after multiplication by V. The moe of figure i obtaine then. The witching function can be expree a Fourier erie. SF = A n in (nωt) (79) n= It can be hown that in the lower frequency range the frequency component of SF V an V an are equal if the frequency of the carrier i ufficiently large [9]. Figure 5: Pule Wih Moulation (l) an witching function (r) for one phae of the voltage ource converter When the complete PWM-operation, or even the witching function, of the VSC ha to be taken into account, the moel of the converter become complicate, an imulation will become very low. If the filter i eigne well, the higher harmonic that are generate by the witching proce will be attenuate. It can be hown that, with a well-eigne filter, in the lower frequency range the frequency component of the reference voltage an the practical obtaine voltage are equal if the witching frequency i ufficiently large [9]. A further aumption i that the c-link voltage V i contant. In reality thi in t true, cauing ome higher frequency term in the output ignal. The reulting moel i then hown in figure 4. The whole ytem can then be replace by a ytem, creating inuoial waveform, exactly equal to the reference waveform. One houl be aware that thi i only vali for frequencie far below the reonance frequency of the filter. In cae of a gri-connecte converter, with a gri-frequency of 50Hz, thi requirement will be met an the moel can be ue for applica- 4 ECN-C

35 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS tion like voltage regulation, a long a normal gri operation i aume. Converter moel behaviour uring voltage iturbance It ha been explaine in the previou ection that if the filter i eigne well, the higher harmonic that are generate by the witching proce will be attenuate. With a well-eigne filter, in the lower frequency range the frequency component of the reference voltage an the practical obtaine voltage are equal if the witching frequency i ufficiently large, i.e. f >> f 0 (80) with f the witching frequency an f 0 the funamental harmonic of the voltage. During fat phenomena the voltage will alo have higher harmonic term an the conition (80) will no longer be vali. When there i no current control or voltage control applie, the harmonic will not be preent in the reference voltage an the voltage that i mae by the converter i till a goo repreentation of the reference voltage. When control i applie, the reference voltage will alo have the higher harmonic in mot cae, an the repreentation between the voltage that i mae an the reference voltage in t correct any longer. To invetigate whether the moel bae on the witching function concept can be ue uring iturbance the reuce moel ha been compare to a reference moel. The SimPower- Sytem Blocket [8] of Matlab ha been ue to obtain thi reference moel of the converter. The univeral brige moel with IGBT ha been ue. Thi block of the SimPower Sytem Blocket implement a -phae brige converter with 6 IGBT witche with antiparallel ioe. RC-nubber circuit are inclue in the IGBT-moel. Typical parameter uch a rie an fall time an voltage rop can be efine in the moel. The voltage an current are meaure an tranforme to the q0-reference ytem. Sample-an-hol circuit are implemente in the meaurement loop. The meaure voltage an current are filtere with low-pa filter with a cut-off frequency of 00 Hz. Orinary PI controller are ue to obtain the eire current. The reuce moel ecribe in the previou ection, ha been compare to the full moel. A three-phae balance voltage ip of 70% (the RMS value of the gri voltage i reuce to 0% of it pre-fault voltage) ha been imulate. The gri voltage i hown in figure 6. The converter current upplie to the gri i hown in figure 7. ECN-C

36 Erao II, Volume : Dynamic moel for win farm Figure 6: Ieal voltage ip Figure 7: Converter current The behaviour of the reuce moel of the converter ha been compare to the behaviour of the full converter. In orer to make comparion eaier, the current have been compare in the q0-reference frame. Thee current are contant in teay-tate ituation, which make it eaier to compare them to each other. The -axi current for the reuce an the full moel are hown in figure 8: on average the current of the two moel are the ame an the initial peak at the moment of the tep in voltage are alo equal. The ifference i ue to the witching of the converter in the full moel. When the witching frequency i ufficiently high, thee highfrequency term will be attenuate by a filter. More information on the comparion can be foun in [] an in appenix B. 6 ECN-C

37 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS Figure 8: Converter current in -axi for complete moel (oli line) an reuce moel (ahe line) Gri current control The controller of the VSC will be obtaine with reference to the converter hown in figure 9. A vector-control approach i ue for the upply ie converter, with a reference frame oriente along the gri voltage vector. Such a reference frame enable inepenent control of the active an reactive power flowing between the converter an the gri. I c i a L f R f i ga v g V c C i b i gb i c i gc v cn v bn v an n v gcn v gbn v gan n Figure 9: Three-phae full-brige Voltage Source Converter Conier the ytem of figure 9. The voltage balance acro the inuctor an reitor i: v a = v an v agn = L f i a + R f i a v b = v bn v bgn = L f i b + R f i b (8) v c = v cn v cgn = L f i c + R f i c With the Park tranformation thi equation can be tranforme to the q reference frame: ECN-C

38 Erao II, Volume : Dynamic moel for win farm v = R f i + L f i + ω el f i q v q = R f i q + L f i q ω el f i (8) The lat term in both equation caue a coupling of the two equation, which make it ifficult to control both current inepenently. Thi wa alo oberve in the control of the generator an the ame olution can be applie here. The lat term can be coniere a a iturbance on the controller. Reference voltage to obtain the eire current can be written a: with: v = v + ω el f i q v q = v q ω e L f i (8) v = R f i + L f i v q = R f i q + L f i q (84) Treating the cro-relate term a a iturbance, the tranfer function from voltage to current of (84) can be foun a (for both the - an the q-component): G () = A cheme of the controller i given in figure 0. L f + R f (85) Dv L f +R f i w e L f w e L f Dv q L f +R f i q Figure 0: Scheme of current controller Uing the Internal Moel Control principle [7] to eign the current controller yiel: K () = k p + k i = α c G () (86) where α c i the banwih of the current control loop, k p i the proportional gain an k i i the integral gain of the controller. The proportional an integral gain become [7]: k p = α c L f ; k i = α c R f (87) The active an reactive power elivere by the converter are given by: P = v g i + v qg i q Q = v qg i v g i q (88) 8 ECN-C

39 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS with the -axi of the reference frame along the tator-voltage poition, v q i zero an a long a the upply voltage i contant, v i contant. The active an reactive power are proportional to i an i q then. DC-link controller The DC-voltage controller i eigne by ue of feeback lineariation [4]. The capacitor in the c-link behave a an energy torage evice. Neglecting loe, the time erivative of the tore energy mut equal the um of the intantaneou tator power P an gri power P g : C ( ) v c = P P g (89) Thi equation i nonlinear with repect to v c. To overcome thi problem a new tate-variable i introuce: Subtituting thi in (89) give: C W W = v c (90) = P P g (9) which i linear with repect to W. The phyical interpretation of thi tate-variable ubtitution i that the energy i choen to repreent the c-link characteritic [4]. With the q-reference frame of the current controller along the -axi, (9) can be written a: C W an the tranfer function from i to W i then foun to be: = P v i (9) G () = v C A thi tranfer function ha a pole in the origin it will be ifficult to control it. An inner feeback loop for active amping will be introuce [4]: (9) i = i + G a W (94) With G a the active conuctance, performing the active amping, an i the reference current provie by the outer control loop, ee figure. Subtituting (94) into (9) give: C W = P v i v G a W (95) Which i hown in figure. The tranfer function from i q to W become [4]: G v () = (96) C + v G a ECN-C

40 Erao II, Volume : Dynamic moel for win farm Uing the internal moel control principle [7] an ince (96) i a firt-orer ytem, the following controller i propoe: F () = α G () = α C v α G a Which i jut a PI-controller. A uitable choice will be to make the inner loop a fat a the cloe-loop ytem [4]. When the pole of G () i place at -α the following active conuctance i obtaine: The PI-controller parameter are then given a [4]: (97) G a = α C v (98) k p = α C v, k i = α C v (99) The controller i complete by a feeforwar term from P to i q. Figure : DC-link controller tructure. Other electrical component Beie the moel of the win turbine generator, moel of other electrical component are neee for a complete offhore win farm moel. In thi ection the moel will be erive of the tranmiion line an cable, the tranformer an the gri. Whether zero-equence component have to be taken into account uring the imulation epen on the circuit configuration an will be icue in ection Tranmiion line an cable The general equation relating voltage an current in a tranmiion line or cable recognize the fact that all impeance of a tranmiion line are uniformly itribute along the line. For line up to about 50 km lumpe parameter can be ue however [4]. The ingle-phae equivalent circuit of a lumpe line i hown in figure. 40 ECN-C

41 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS R L C/ C/ Figure : Single-phae equivalent circuit of a tranmiion line In the moel that will be ue, the two hunt capacitance are aume to be both on one ie of the cable egment. The cable moel can then be ubivie in two ection: a three-phae hunt capacitor an a three-phae erie reitance an inuctance. The q0-moel of a threephae line with hunt capacitor an a three-phae RL line have alreay been obtaine. The voltage acro the RL line egment i given in (6) by: v = v v = R a i l + L a i l ωl ai ql v q = v q v q = R a i ql + L a i ql + ωl ai l (00) v 0 = v 0 v 0 = (R a + R g ) i 0 + (L a + L g ) i 0 The current through the hunt capacitance i given in () by: i c = C v i qc = C v q i 0c = C v 0 ωcv q + ωcv (0) The reulting cable moel for the -, q-, an 0-axi are hown in figure. ECN-C

42 Erao II, Volume : Dynamic moel for win farm i i l R a wl a i ql L a i c v C v wcv q i q i ql R a wl a i l L a i qc v q C v q wcv i 0 i 0l R a +R g L a +L g i 0c v 0 C v 0 Figure : Cable moel in q0-coorinate To obtain the moel, it i aume that the hiel of the cable i groune, which i true in mot cae. The hunt capacitor in the lumpe cable moel repreent the capacitance between cable an hiel. The q0-moel obtaine for the RL circuit aume that a groun return exit. A the cable hiel i groune the groun return exit an the moel of figure can be ue... Tranformer The tranformer moel that ha been ue will be analye in thi ection. A ingle-phae equivalent circuit of a two-wining tranformer i hown in figure 4. Normally the magnetiing current i m i mall an can be neglecte. The moel of figure 4 can then be reuce to the moel hown in figure 5, with R=R +a R an L=L +a L, with a=n /N. L R i a L a R i m a : i v R m L m N N v ieal Figure 4: Single-phae equivalent circuit of a tranformer 4 ECN-C

43 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS i R L a : i v N N v ieal Figure 5: Tranformer equivalent circuit with magnetiing current neglecte The voltage-current relationhip of the ingle-phae equivalent tranformer of figure 5 can be written a: v = Ri + L i + av (0) A capacitor ha been place at the primary ie of the tranformer. The capacitance repreent the wining capacitance of the tranformer an i primarily neee for numerical reaon. The effect on the reult i mall. The q0-moel of the tranformer are hown in figure 6. The zero-equence moel epen on the type of tranformer (tar-tart, tar-elta, etc.). The zeroequence moel repreent a tar-elta tranformer with a groun tar connection at the primary ie []. i R Li q L a : i v C N N v Cv q ieal i q R Li L a : i q v q C N N v q Cv ieal i 0 R L i 0 v 0 C v 0 Figure 6: Equivalent tranformer moel for, q an zero equence componenent ECN-C

44 Erao II, Volume : Dynamic moel for win farm.. Gri moel A imple gri moel ha been evelope to imulate the interaction between a win farm an the gri an to be able to tet the voltage an frequency control capabilitie of the ifferent type of win farm. The main requirement for the gri moel i a ynamic behaviour imilar to a large high voltage gri. The main component of the gri moel i an equivalent ynchronou machine, equipe with voltage an frequency control, to repreent the ynamic behaviour of the high voltage gri. The ynchronou machine moel that wa choen i the three wining repreentation in q coorinate. Damper wining are not taken into account. The generator convention i aopte: i L + L i f mf L m i + L f i f L q i q = u R.i ω.l q.i q (0) = u f R f.i f (04) = u q R.i q + ω.(l.i + L m.i f ) (05) L, L mf, L q, L m, L f R, R f i, i q u, u q i f, u f ω ynchronou machine inuctance tator an fiel wining reitance tator current in an q axi tator voltage in an q axi fiel current an voltage, tranpoe to tator wining ynchronou machine electrical angular pee For the voltage regulator an exciter a type moel i ue [] p. 9: τ e E f = K e E f + V r S e E f (06) V = K f + τ f E f (07) K a V r = + τ f V e (08) V a = + τ r u q (09) V e = V a V (0) τ e E f K e V r S e V e V K f, τ f K a, τ a V a τ r exciter time contant exciter output voltage exciter contant regulator output voltage exciter aturation function regulator input voltage tabilizer output voltage tabilier amplification an time contant regulator amplification an time contant filter output voltage input filter time contant 44 ECN-C

45 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS The inertia an pee controller of the ynchronou machine complete the moel: J ω = T mech T el () T mech = P mech ω () P mech = (K pw + K iw )(ω et ω ) () For the connection of the ynchronou machine moel to the win farm moel, the implementation of the cable moel ha been moifie. In the cable moel, ue to connect win turbine in the farm an the farm to the high voltage tranformer, the gri ie voltage an farm ie current are input. To connect the ynchronou machine to the win farm, gri an farm ie cable current are input an the voltage on both ie of the cable are output. Thi oe not affect the mathematical moel. The parameter of the gri moel have been choen to have a fair amount of tranient behaviour, not necearily foun in large cale gri. Thi choice i mae to emontrate the win farm control capabilitie. ECN-C

46 Erao II, Volume : Dynamic moel for win farm.4 Zero-equence component.4. Introuction A hort review of zero-equence component in voltage an current will be given here, to ee whether hort-circuit component can pa through tranformer an whether thee component have to be taken into account uring the moelling of ifferent circuit..4. Zero-equence component It i proven by Fortecue [] that each unbalance ytem of n relate phaor can be reolve into n ytem of balance phaor, calle the ymmetrical component of the original phaor. Accoring to Fortecue theorem, three unbalance phaor of a three-phae ytem can be reolve into three balance ytem of phaor. A ytem i balance when the impeance, voltage an current in all phae are equal (except for the 0 egree phae hift of voltage an current). The firt two balance et are the poitive-equence an negative-equence repectively. They conit of three phaor equal in magnitue, iplace from each other by 0 egree in phae, where the poitive-equence have the ame phae equence a the original phaor an the negative-equence have the oppoite phae equence. The zero-equence component conit of three phaor equal in magnitue an with zero phae iplacement from each other. Although Fortecue introuce them a phaor, the ymmetrical component can alo be written a time-epenent variable [5]. The time-epenent ymmetrical component are given by [5]: with the phaor: u 0 u + u = U 0 e jωt + U 0e jωt U e jωt + U e jωt U e jωt + U e jωt U 0 = (U a + U b + U c ) U = ( U a + au b + a ) U c U = ( U a + a ) U b + au c (4) (5) ( ) where a=exp j π. In literature the time-epenent component are uually expree a u 0, u +, u, while the teay-tate phaor are written a U 0,U,U [5]..4. Star an elta connection The wining of a three-phae tranformer are alway connecte in a certain way. The two mot important type are the tar connection an the elta connection, hown in figure 7 (a) an (b) repectively. Thee two configuration will firt be coniere in more etail. 46 ECN-C

47 MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS a I a a I a Z Y V an V ca V ab n V ca V ab I ab Z Z Z I ca Z Y Z Y I b I b I bc b b c V bc I c c V bc I c Figure 7: Star (a) an elta (b) connection of a three-phae ytem Conier firt the tar connecte ytem of figure 7(a). The line-to-line voltage can be written in term of line-to-neutral voltage: v ab (t) = v an (t) v bn (t) v bc (t) = v bn (t) v cn (t) v ca (t) = v cn (t) v an (t) (6) The zero-equence component of thi et of voltage can be etermine with (4): v 0 ab (t) = (v ab (t) + v bc (t) + v ca (t)) = 0 (7) Thi how that line-to-line voltage of a three-phae tar connecte circuit have no zeroequence component. Be aware that the line-to-neutral voltage can have zero-equence component. When the neutral point i not groune, it further hol that, ue to Kirchhoff current law: i a (t) + i b (t) + i c (t) = 0 (8) Conier now the elta-connecte ytem of figure 7(b). The line current are given a: i a (t) = i ab (t) i ca (t) i b (t) = i bc (t) i ab (t) i c (t) = i ca (t) i bc (t) (9) The zero-equence component of thi et of current can be etermine with (4): i 0 a (t) = (i a (t) + i b (t) + i c (t)) = 0 (0) Thi how that line current into a three-phae elta-connecte circuit have no zero-equence component. Accoring to Kirchhoff voltage law it further hol that: v ab (t) + v bc (t) + v ca (t) = 0 () ECN-C

48 Erao II, Volume : Dynamic moel for win farm.4.4 Three-phae tranformer In three-phae tranformer, ifferent combination of the tar an elta configuration can be ue. The firt point that houl be note, i that the current in the econary wining i equal to the current in the primary wining multiplie by the wining ratio, uner the aumption that the relatively mall magnetizing current can be neglecte. In the ame way i the voltage at the econary wining equal to the voltage at the primary wining multiplie by the wining ratio, uner the aumption that the voltage rop acro the wining reitance an leakage inuctance i negligible. The econ point that houl be note i the fact that in a tar-elta connecte tranformer the line-to-line voltage at one ie will become line-to-neutral voltage at the other ie an that line current at one ie will become phae current at the other ie. The zero-equence equivalent circuit of three-phae tranformer epen on the connection of the primary an econary wining. The mot common type i the tar-elta configuration with a groune tar-point. The zero-equence circuit of thi type of tranformer i how in figure 8. Z 0 Figure 8: Zero-equence equivalent circuit of tar-elta tranformer with groune tar point It i hown previouly that the line-to-line voltage of a tar-connecte circuit cannot have a zero-equence component. Therefore, in a tar-elta tranformer, the line-to-neutral voltage at the elta ie of the tranformer will have no zero-equence component, a long a the tar ie of the tranformer i groune. The tranformer will therefore caue no zero-equence voltage component at the tar-ie of the tranformer. A the neutral of the tar wining i groune, zero-equence current have a path to groun through the tar becaue correponing inuce current can circulate in the elta wining. The zero-equence current circulating in the elta magnetically balance the zero-equence current in the tar but cannot flow in the line connecte to the elta. An ungroune tar wining i a pecial cae, where the impeance between the tar point an groun i infinite. The zero-equence impeance in figure 8 i infinite then, an zero-equence current cannot flow. The line current into a three-phae elta-connecte circuit have no zero-equence component, a i hown previouly, an therefore no zero-equence current can be tranmitte through a elta-elta tranformer, although it can ometime circulate within the elta wining. The only type of tranformer in which zero-equence current can be tranferre i the tar-tar tranformer with both ie groune. Another point that houl be mentione i that there alway mut be two point that are groune in a circuit in orer to make zero-equence current poible. 48 ECN-C

49 .4.5 NSW-park ERAO-II MATHEMATICAL MODELS OF ELECTRICAL COMPONENTS We will now conier whether zero-equence voltage or current can occur in the NSW-park ERAO-II. The zero-equence network of the park i hown in figure 9 Turbine-trafo 4kV cable HV-trafo Gri Z 0 Z 0 Z 0 Z 0 Figure 9: Zero-equence equivalent network of NSW-park Conier that, for any reaon, the current in the gri will have a zero-equence component. The gri-ie wining of the HV-tranformer i elta-connecte an therefore the zero-equence current can not pa to the 4kV cable. For the ame reaon it can be een, that zero-equence current in the cable can not pa through the turbine tranformer to the turbine. The cable-ie wining of the HV-tranformer i tar connecte. Therefore, the line-to-line voltage can not have a zero-equence component. The cable-ie wining of the turbinetranformer i a elta-configuration. Therefore the line current can not have a zero-equence component. Thu, the cable oe not have zero-equence component in either the voltage or the current. The only caue for a zero-equence current an voltage in the cable, can be a ingle-phae or two-phae hort-circuit from cable to earth. Zero-equence current can then circulate through the hort-circuit an the groun-connection of the HV-tranformer. It ha alreay been ai, that thi zero-equence current will not pa through the turbine tranformer to the win turbine. Since in the Erao- tuy ingle-phae or two-phae hort-circuit in the cable will not be coniere, it i not neceary to inclue the zero-equence component in imulation. ECN-C

50 MODELS OF WIND AND WIND TURBINE Thi chapter give a ummary of the moel to be ue for: the win experience by the rotor of a ingle tan alone turbine; two type of turbine: contant pee tall (CSS) an variable pee pitch (VSP). Thee moel are ecribe extenively in the ECN-report [5] an in [6].. Win moel The change in win pee experience by the rotor of a ingle tan alone turbine are etermine by the uniturbe win pee change far in front of the turbine an by the propertie of the terrain at the location of the turbine. Long term variation ( or 0 minute average value) are etermine by the Weibull itribution of the win pee. The hort term variation, calle turbulence, epen trongly on the propertie of the location. To evaluate the effect of win turbine an win farm on the gri, the hort term variation of the win ha to be known. Since win pee variation i a tatitically etermine phenomenon, a win moel will calculate a realiation of the tochatically changing win pee in time. Furthermore, the win pee average over the turbine rotor ha to be etermine, incluing variation caue by the paing of the blae through the inhomogeneou win fiel over the rotor area. The inhomogeneou win fiel i caue by: win hear (air i being lowe own near the earth urface, cauing a win pee graient with height); the tower (in front of the tower the air i alo lowe own by tagnation). When a power meaurement of a turbine i taken, the effect of the win fiel inhomogenity can clearly be een by regular change in power with a frequency of the number of blae time the turbine rotational frequency, often calle np. The win moel aim at a realitic repreentation of thi effect. Summarizing, three effect will be inclue in the hort term win moel: turbulence, win hear an tower hae. The reulting win realiation will be calle the rotor effective win, a oppoe to the uniturbe win... Longituinal turbulence moel, tower paage an win hear The objective i to generate a ingle point win pee realiation Ū + ue (t) which give intantaneou aeroynamic torque value which are tatitically equivalent to the value reulting from the logituinal turbulence. The effect of win pee variation on the aeroynamic torque i etermine by the C p (λ, θ)-curve an the rotor iameter: T C p/ū+ue w (t) = C p (λ, θ) ρπ R (Ū + ue (t)) /Ω, () Thi implie that the realiation not only epen on the tatitical propertie of the win but alo on the ize an an aeroynamic propertie of the turbine rotor. The metho make ue of the Auto Power Spectral Denity (APSD) of the longituinal win pee change in a ingle point an i erive in the ocumentation of the ECN CONTROLTOOL [5]. It i aume that: 50 ECN-C

51 . the APSD i invariant in the rotor plane; MODELS OF WIND AND WIND TURBINE. the effect of itance on the coherence ecrement i invariant in the rotor plane;. the rotor i rigi; 4. the rotor pee i contant. Aumption - are ufficiently atifie, for aumption 4 thi i not alway true. For variable rotor pee, a tatitically equivalent win pee realiation can be mae for the average pee. Figure 0 how the epenence of the coherence of win pee variation for ifferent rotor iameter. For a given rotor iameter, the coherence of the variation ecreae with the frequency of the change, i.e. fater change are more likely to be ifferent at ifferent point in the rotor plane. For a given frequency, the coherence of the variation alo ecreae for increaing turbine iameter. The figure how that for rotor iameter larger than 0 m the coherence of variation above 0. Hz i practically zero at 0.4 m/ win pee. At higher win pee, the coherence at a given frequency will increae. coherence for Kaimal pectrum; V w (naaf) = 0.4m/ = m 0.7 = m 0.6 = m Coh [ - ] = 5m = 8m 0. =m =6m =m 0 =8m frequentie [Hz] Figure 0: Coherence pectra for turbine of ifferent ize 0 win pee pectrum fixe poition an rotor-effective; V w (naaf) = 0.4m/ 0 0 APSD [(m/) /Hz] APSD V fixe poiton (A) w 0 - APSD rotor-effective V w (C) 0-4 '0-moe' in rotor-effective APSD (B) frequentie [Hz] Figure : Effect of rotor averaging an rotational ampling on the win autopower pectra Figure emontrate the effect of the rotor epenent tatitically equivalent longituinal turbulence moel. Line (A) repreent the ingle point win pee variation. If the rotor averaging of the turbulence i applie, line (B) pectrum reult. The rotor thu act a a ECN-C

52 Erao II, Volume : Dynamic moel for win farm low pa filter: high frequencie are ampe. Thi rotor effective pectrum i calle the 0- moe pectrum, a oppoe to the nbp moe (n=,,...; B=number of blae; P=rotational frequency) caue by the ampling of the tower wake an win hear. Line (C) repreent the um of 0-moe an nbp moe an i referre to a the rotor-effective win pee. 0 win pee variation fixe poition, V w (naaf)=0.4m/ A [m/] rotor effective win pee variation complete (0p, p an 6p moe) 0 C [m/] rotor effective win pee variation rotor uniform (only 0p moe) 0 B [m/] time [] file C:\tgengel\lw50bct\SCOPE\PS\vturemo.p Nov 999 Figure : Win pee variation in a ingle point (A) an average over the turbine rotor (0-moe (B) an complete (C)). Turbine moel Mot large win turbine, intalle for electricity prouction an connecte to a utility gri, are horizontal axi turbine. Four turbine type can be icriminate:. Contant pee tall controlle;. Contant pee active tall controlle;. Contant pee pitch controlle; 4. Variable pee pitch controlle. The majority of the current turbine eign are of type or 4. Type i evelope only by a few manufacturer an type only work well with a metho to increae the lip of the generator. Thi option nowaay i abanonne in favour of (partial) variable pee eign. In the Erao- tuy only turbine type an 4 will be coniere. The turbine moel conit of ubmoel for: aeroynamic behaviour of the rotor; rotating mechanical ytem (rivetrain); tower (viz. motion of the tower top); control ytem (power limitation by pitch control, yaw control i not inclue). 5 ECN-C

53 .. Aeroynamic converion, rotation an torion MODELS OF WIND AND WIND TURBINE Figure give an overview of the aeroynamic an mechanical moel. From right to left the following apect are inclue in the moel: axial force F ax an aeroynamic torque T ae on the rotor; poition of the rotor blae (azimuth Ψ); inertia of the blae an hub J r ; gearbox ratio i; low an high pee haft torion γ; generator inertia J g an generator pee Ω g. fe = fat haft equivalalent rotor plane rotor inertia J r win pee V w generator inertia Jg fe generator pee Ω g fe T e fe haft torion parameter c, r k r gearbox ratio i fe Ω g /i γ Ψ rotor azimuthψ rotorblae F ax rotor pee Ω r T ae fe Ω r Ω g /i = - fe fe J g Ω ( g + i -) T fe ( i -) e Figure : Moel of the mechanical ytem The aeroynamic converion moel etermine the axial force F ax an aeroynamic torque T ae an i bae on the quai-teay tate rotor coefficient for power C p (λ, θ) an axial force (thrut) C t (λ, θ). For pitch-to-vane turbine a correction for ynamic inflow i ae. The rotor characteritic epen on the rotor eign an are calculate by an aero-elatic coe, for intance the ECN computer programme PHATAS. Figure 4 give an example of the rotor coefficient of a variable pee turbine a function of the pitch angle θ an the tip pee ratio λ. The mechanical moel for turbine rotor, low an high pee haft, gearbox an generator rotor conit of a two-ma pring an amper moel. The torque of the gearbox an generator on the nacelle i etermine, ince it interact with the tower naying... Tower mechanical moel Figure 5 give an overview of the force an moment acting on a turbine tower an the reulting tower top motion. At the far right the thrut F ax from the win on the rotor i hown. The reaction torque of the gearbox an generator (i )J g Ω g + it e i the econ variable. The rotor pee i repreente by Ω r. The tower top motion i ecompoe in two irection: ECN-C

54 Erao II, Volume : Dynamic moel for win farm 0.5 power coefficient curve for pitch angle from 0, tep, to 0 eg power coefficient [ ]; ah for pitch < 0g tip to win pee ratio [ ] file C:\tgengel\LW50BCT\SCOPE\PS\cpcurve.p 9 May 999 by C:\tgengel\LW50BCT\SCOPE\M\cmopar.m.5 thrut coefficient curve for pitch angle from 0, tep, to 0 eg thrut coefficient [ ]; ah for pitch < 0g tip to win pee ratio [ ] file C:\tgengel\LW50BCT\SCOPE\PS\ctcurve.p 9 May 999 by C:\tgengel\LW50BCT\SCOPE\M\cmopar.m Figure 4: Power an thrut coefficient of a pitch to vane winurbine in the irection of the win pee (front-aft motion or noing ) x no, an perpenicular to that irection (ieway motion or naying ) x nay. The yaw angle an yaw torque are given by α an T krui. The figure inclue the effect of wave on the tower, which can be neglecte for lan bae turbine. The imple tower moel conit of two ma-pring-amper moel for linear motion (tranlation): one for noing an one for naying. Thi i not ufficient if tower top rotation ha to be moelle a well. In that cae, a lumpe parameter moel for rotation i ue, coniting of a number of ma-pring-amper-moel in erie... Pitch control an electrical torque etpoint The pitch control algorithm regulate an limit the rotor pee an optimie energy yiel uner the retriction of only poitive tower tilt moment. The control tructure comprie: operation moe: partial loa an full loa actuation etpoint: pitch rate an electric torque meaurement: pitch (reference) angle, rotor pee, electric power 54 ECN-C

55 MODELS OF WIND AND WIND TURBINE T krui T tilt fe = fat haft equivalalent towertopcenter yaw angle α x nay rotor pee Ω r F ax x no tiltangle θ φ nay fe fe ( i -) J g Ω g + it fe e φ no nacelle in tower moel monopile in tower moel tower height L t elevation η itance to urface z k waterepth founation in tower moel F hyk inflow angle γ H Figure 5: Axiymmetric monopile tower moel The principle of both the pitch control an electric torque control algorithm will be icue below. Pitch control algorithm Start-up i imply realie by moving the pitch angle with contant pitching pee from feathering poition towar working poition. Shut own i out of the cope, becaue the overall control ytem will manage thi. Partial loa operation will take over a oon a the meaure pitch angle i cloe to the pitch angle etpoint for partial loa operation. Thi etpoint i epenent of the meaure rotor pee an i naturally cloe to zero. Uually, the pitch angle uring partial loa operation i relate to the theoretical maximum aeroynamic efficiency (maximum power coefficient, C p ), but in practice requirement like noie an thrut loaing coul alo be eciive. Therefore, the rotor pee epenency of the pitch angle etpoint uring partial loa operation can be manually ajute to empirical value. The etpoint value i realie by ervo control (proportional pitch angle control) uing a pecific maximum pitching pee. Becaue of the require mall pitch ajutment uring partial loa operation maximum pee i et to 0.8 g/. The tranition to the full loa control algorithm interact with the electric torque control in orer to maximie the energy yiel. A tranition to partial loa will only take place if the meaure pitch angle ha alreay reache it working poition an the rotor pee ha ecreae below rate. Reverely, tranition from partial loa to full loa operation i bae on a rotor pee threhol level, uch that too many tranition are avoie. During full loa control the rotor pee i limite to a maximum value, while rate power prouction i maintaine. The core i a linear PD control tructure, that fee the low pa filtere rotor pee (propor- ECN-C

56 Erao II, Volume : Dynamic moel for win farm tional part) an acceleration (ifferential part) back to a etpoint value of the pitching pee. The pitch actuator of each blae will then et the pitch angle imultaneouly to a uitable poition to regulate the rotor pee between it rate an maximum value. The meaure value of the rotor pee i filtere by a cacae filter which conit of a fourth orer invere Chebychev low pa filter (p effect) an two ban notch ellipe filter to reuce collective lea lag effect an tower influence. To eal with the non linear aeroynamic behaviour, ome non linear extenion are ae to meet atifactory performance: linear controller gain are cheule epenent on both the actual blae angle an rotor pee; with gain cheuling the linear controller i aapte to the whole operation envelope of the win turbine; an inactivity zone with hyterei i implemente, to avoi uneire pitch angle ajutment ue to mall controller correction caue by noie, tower haow, rotational ampling effect etc; pitching boun (pee an angle) are incorporate to limit the calculate pitch pee value; non linear compenation of the calculate pitching pee i ue to cancel foreeen amplification ue to ynamic inflow effect (rotor wake effect). To enure no exce of maximum rotor pee, a mechanim calle force rotor pee limitation i permitte to overrule the cloe loop rotor pee control loop by forcing the pitch angle quickly (g/) -but for a hort a perio of time a poible- in vane irection. Thi i only active if the actual rotor pee excee a certain afety level an i till accelerating to avoi turbine hut own. Power prouction optimiation i incorporate by a mechanim, name etimate win pee fee forwar which a a non linear control action to the pitching pee etpoint bae on the recontructe value of rotor effective win pee. The recontruction i bae on filtere meaure value of rotor pee, pitch angle, electric power an theoretical aeroynamic propertie of the rotor. In cae of ufficient banwih of electric torque actuation, the power meaurement can be replace by the electric torque etpoint. Etimate rotor pee fee forwar reult in higher energy yiel, le rotor pee fluctuation an maller pitch action. From viewpoint of tability etimate win pee fee forwar can be een a DD feeback control of rotor pee (jerk). For tability reaon an optimal ue of thi mechanim the following extenion are ae: non linear cheuling to meet rate power prouction in the whole operation region; fee forwar weakening to enure tability an ajut the amount of power optimiation; if rotor pee i below rate level then thi optimiation upport only pitch action in working irection; if rotor pee i near maximum rotor pee level then thi optimiation upport only pitch action in vane irection. A collection of Nyquit plot which cover the turbine operation area ae ytem tability. 56 ECN-C

57 Electric torque etpoint MODELS OF WIND AND WIND TURBINE Electrical torque control i ue to etermine the power prouction below rate pee. It i alo a valuable actuation port to increae the energy yiel aroun rate conition if mall electrical torque variation (%) of it rate value are permitte. A mechanim to cro the firt bening moe of the tower can alo be incorporate. The electric torque control algorithm generate the torque or power etpoint for the controller of the generator ie converter an conit of four operating range:. turbine tart-up;. contant tip-pee-ratio operation (partial loa);. tranition between contant tip pee an contant power operation (full loa); 4. finally contant power operation. Figure 6 illutrate thee operating range, bet een in the plot of power an torque againt rotor pee. In the torque-win pee plot, the rectangular area inicate contant power uring pee excurion. Pel (kw) Vw (m/) Pel (kw) N (rpm) Torque (knm) Torque (knm) Vw (m/) N (rpm) Figure 6: NM9 characteritic curve If the firt bening moe of the tower i ituate aroun it rate pee equivalent, a mechanim ha been integrate to cro thi point of reonance quickly to avoi exceive tower vibration (excitation by rotor unbalance). The tranition zone from partial loa to full loa i ynamically implemente. The tranition part a hown i vali in cae of partial loa control. From full loa control, the contant power curve limit i extene until the pitch angle i in working poition. Mean rate power i guarantee by aitional correction in full loa. ECN-C

58 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK Thi chapter lit an explain the four Simulink moel of win farm evelope in the Erao- project. In thi chapter the term phaor i ue for the q0-vector repreenting voltage, current or fluxe in the Park reference frame, a icue in chapter. It houl not be confue with phaor repreenting AC quantitie with contant angular frequency. The q0- phaor angular frequency i variable. In Simulink block input an output an a certain execution orer houl be efine. The win turbine ha been coniere a the tarting point. The problem i that not both the voltage an the current can be etermine at the win turbine. It ha been aume that the voltage i etermine by the gri voltage. The voltage at the win turbine terminal can then be efine from the voltage of the gri plu the voltage rop acro the cable an tranformer impeance. For thi reaon the gri-ie voltage an the turbine-ie current ha been coniere a input for all block. Bae on thee input the turbine-ie voltage an the gri-ie current are etermine a output. 4. Contant pee tall controlle win farm 960 V 4 kv 50 kv Figure 7: Electrical layout of a tring of CSS turbine The contant pee tall (CSS) controlle win farm moel conit of tall regulate turbine with irectly connecte inuction machine, one tring of the Near Shore Win farm. The 58 ECN-C

59 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK moel inclue turbine tranfomer, cable in the win farm, cable to hore an high voltage tranformer in the ubtation on hore (figure 7). The main winow of the Simulink moel connect twelve turbine turb + cable through a tranformer 4kV/50kV trafo to the 50 kv gri moel (figure 8). Separate block generate iniviual win input for all turbine an plot imulation reult. v from HV trafo i to HV trafo w_in w_uit turb + cable v HV v LV i LV i HV w_in w_out 4kV/50kV_trafo Vgri i w_gri 50kV_gri Park with Contant pee turbine with AM q moel (c) 00 Tim van Engelen & Jan Pierik (ECN), Johan Morren (TUD) i v w Plot_figure win input Figure 8: Simulink CSS win farm moel main winow w_in v from cable i to cable w_in w_out tur + trafo v v i i w_in w_out 4kV_cable =tur v from cable i to cable w_in w_out tur + trafo7 v v i i w_in w_out 4kV_cable =tur7 v from cable i to cable w_in w_out tur + trafo v v i i w_in w_out 4kV_cable =tur v from cable i to cable w_in w_out tur + trafo8 v v i i w_in w_out 4kV_cable =tur8 v from cable i to cable w_in w_out tur + trafo v v i i w_in w_out 4kV_cable =tur v from cable i to cable w_in w_out tur + trafo9 v v i i w_in w_out 4kV_cable =tur9 v from cable i to cable w_in w_out tur + trafo4 v v i i w_in w_out 4kV_cable =tur4 v from cable i to cable w_in w_out tur + trafo0 v v i i w_in w_out 4kV_cable =tur0 v from cable i to cable w_in w_out tur + trafo5 v v i i w_in w_out 4kV_cable =tur5 v from cable i to cable w_in w_out tur + trafo v v i i w_in w_out 4kV_cable =tur v from cable i to cable w_in w_out tur + trafo6 v v i i w_in w_out 4kV_cable =tur6 v from cable w_in tur + trafo i to cable w_out v from HV trafo v i w_in v i w_out 4kV_cable =tur i to HV trafo w_uit Figure 9: turb + cable: CSS turbine an interconnecting cable The win farm block (figure 9) connect turbine an cable. The voltage q0-phaor at each cable en i input for the turbine an tranformer moel, the current q0-phaor i ECN-C

60 Erao II, Volume : Dynamic moel for win farm output. The turbine an tranformer moel calculate the current phaor, which i returne to the cable moel. The turbine current phaor an the current phaor from the cable connecting the other turbine are ae before entering the next cable. Thi i repeate for all turbine an cable. v from cable NM9 configure a CSS, 960V, 750 kw v_q i_q v i v_mach i i to cable CSS_ui_ w_in w_ w_out ignal w_in w_out tur_trafo 960V w_out U U(E) ignal_ Selector Goto Figure 40: turb + trafo : CSS Turbine an 960V/4kV tranformer Figure 40 how the turbine an tranformer moel, coniting of a NM9 turbine block an a 960V/4kV tranformer block. The cable voltage phaor an the current phaor from the turbine are the input of the tranformer block. The tranformer block calculate low voltage ie output voltage an high voltage ie current. The tranformer output voltage i fe to the turbine moel, the output current i input to the 4 kv cable. v_ w_m em v_q v_q T_e w_ w_ i_q i_q w_out T_m_h AM_q ignal [Vwin] From win Vw_out azi Rotor eff. win Vw_in OmegaR_in Cq Ct Cq Ct Vw Cq Ct Te Paero Taxi OmegaR w_m Turb_full_IM_CSS azi ignal Figure 4: NM9 configure a...: contant pee tall turbine moel The turbine block conit of the generator moel (AM q), the calculation of the rotor effective win (Rotor eff win), the aeroynamic coefficient (CqCt) an the block containing the mechanical equation of turbine haft an tower (Turb full IM CSS). 60 ECN-C

61 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v em vq P & Q i iq Stator power v_ v_ i_q i_q v_q v_q ir_q w_ w_ w_m phi_ & r 4 ignal AM_invere 4 T_m_h T_m_h w_m T_e w_m Gen. pee w wm lip lip EM Torque phi_r_q T_e T_e i_q Figure 4: AM q: inuction generator moel The inuction machine moel (AM q, figure 4) calculate the tator an rotor current phaor, the electromagnetic torque an the rotor angular pee ω m. Input are the tator voltage phaor, the electrical angular pee ω an the mechanical torque. v_q v_ v_ v_q phi_ phi_ em phi_q phi_r phi_q phi_qr em i_ i_q i_r phi_r K*u inv(m_phi) em i_q ir_q i_qr w_ w_ phi_qr w_r AM voltage eq phi_ & r 4 w_m p Gain Figure 4: AM invere: input for the voltage equation ECN-C

62 Erao II, Volume : Dynamic moel for win farm w_ 4 phi_q 7 i_ v_ R_ phi_ phi_ 8 i_q R_ v_q phi_q 0 w_r 6 phi_qr 9 i_r R_r v_r phi_r 0 5 phi_r 0 i_qr R_r v_qr 4 phi_qr Figure 44: AM voltage eq: inuction machine voltage equation The tator an rotor voltage equation in figure 44 etermine the tator an rotor flux phaor ψ q + jψ an ψ rq + jψ r (equation 64 an 65). The current phaor are calculate from the flux phaor in AM invere, figure 4. i_q em phi_r_q em Prouct T_e t Prouct t Figure 45: EM torque: calculation of the electromagnetic torque The electromagnetic torque i calculate from tator flux an tator current (figure 45), followe by the calculation of the inuction machine rotor pee (figure 46). 6 ECN-C

63 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK T_m_h p /J w_m T_e Figure 46: Gen. pee: Inuction machine pee v vq i 4 iq Prouct co fie Prouct qrt Math Function Prouct P & Q Figure 47: Stator power: Inuction machine power an reactive power Inuction machine tator power an reactive power are calculate from the tator voltage an current phaor (figure 47), which complete the inuction machine moel. win z Unit Delay azi z Unit Delay K /azimbae Tower haow Prouct Vw_out Win hear Rotational ampl Contant5 Figure 48: Rotor eff. win: Rotor effective win calculation ECN-C

64 Erao II, Volume : Dynamic moel for win farm To calculate the rotor effective win, tower haow, win hear an rotational ampling i taken into account (figure 48). A preproceor i ue to calculate a cale relation between the azimuth angle an the contribution of tower haow, win hear an rotational ampling to the effective turbulence of the pecifie rotor. In the imulation, the turbulence i cale with to the intantaneou win pee. K z OmegaR_in Unit Delay Gain Prouct Saturation K /Lb Look Up Cq [0.065] IC Cq Vw_in z Unit Delay Contant Look Up Ct [0.9] IC Ct Figure 49: CqCt: Torque an thrut coefficient The areoynamic torque an thrut coefficient are calculate by look-up table (figure 49). xa() = OmegaR OmegaG_; % gamma / 5 w_m K /itran [OmegaR] [gamma] [OmegaR] [Cq] K hrhoar/e6 Paero Cq Vw [Cq] K hrhoar/jr [gamma] K K cr/jr [OmegaR] [azi] [Vw] [xno] y() = OmegaR*Cq*turb.hrhoar*(Vw xno)*(vw xno)/e6; % Paero [Vw] [xno] C C/Jr kr/jr K Taero = Cq*turb.hrhoar*(Vw xno)*(vw xno); % Taero=Cq*/*rho*pi*R^*(Vwin xno)^ Fax = Taero*Ct/(Cq*turb.Rb); % Fax = Taero * Cthrut / (Cq * Rblae) K C/Jr xa(4) = (Taero Tlo turb.kr*(omegar OmegaG_) Thaft)/turb.Jr; % Jr* OmegaR / = (Ta Tl) kr*gamma cr*gamma % kr: rive train amping xa(7) = OmegaR; % azimuth/ = OmegaR [gamma] K cr/itran y() = turb.cr*gamma/turb.itran; % Thaft High Spee Sie Taxi Ct [xno] K kt/mt K hrhoar/(rb*mt) [xno] [xno] Goto5 [OmegaR] [azi] OmegaR 4 azi xa(5) = (Fax turb.kt*xno turb.ct*xno)/turb.mt; % mt * ^ xno / = Fa kt*xno ct*xno xa() = xno; % xno / = xno K ct/mt [gamma] 4 Te (cr/zt cr/(itran*zt))/mt K K /(Zt*mt) [xnay] Goto6 [xnay] Goto7 xa(6) = (Tnac/turb.Zt turb.kt*xnay turb.ct*xnay )/turb.mt; % mt * ^ xnay / = Tnac/Zt kt*xnay ct*xnay K kt / mt K ct / mt Figure 50: Turb full IM CSS: turbine haft an tower The motion of the turbine rotor, haft an tower i moelle in figure 50. Yaw control i not inclue in the moel. 64 ECN-C

65 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v em v v iql w il il il_out ic vq v w v_out v vq vq il w iql iql iql_out iqc v vq w vq_out i em w_in w_out i Figure 5: 4kV cable: park cable The cable moel (figure 5) calculate gri ie current an turbine ie voltage from the input variable turbine ie current an gri ie voltage. The -component of the gri ie current i etermine in figure 5, the -component of the turbine ie voltage i etermine in figure 5. v v iql 4 w K L K /L il_out 5 il K R Figure 5: il: park cable calculation i ic vq w K C K /C v Figure 5: v out: park cable calculation u ECN-C

66 Erao II, Volume : Dynamic moel for win farm v K N/N em v v iql w il il il_out ic vq v w v_out v_mach vq vq il w iql iql_out iqc v w vq iql vq_out em i w_in w_out K N/N_ i Figure 54: 4kV/50kV trafo: park tranformer The park tranformer connect the win farm to the 50 kv cable to fee the win power to the ubtation on lan. The magnetizing current of the tranformer i neglecte an a capacitor ha been place at the primary ie of the tranformer, a ha been explaine in ection... Therefore, the tranformer moel i imilar to the cable moel, ee figure 54. The only ifference i the wining ratio N N. Vwin Vwin7 Ramp Saturation Goto Ramp Saturation Goto6 Ramp Saturation Ramp Saturation Vwin Vwin8 Ramp Saturation Goto Ramp4 Saturation4 Goto7 Ramp Saturation Ramp5 Saturation5 Vwin Vwin9 Ramp4 Saturation4 Goto Ramp6 Saturation6 Goto8 Ramp5 Saturation5 Ramp7 Saturation7 Vwin4 Vwin0 Ramp6 Saturation6 Goto Ramp8 Saturation8 Goto9 Ramp7 Saturation7 Ramp9 Saturation9 Vwin5 Vwin Ramp8 Saturation8 Goto4 Ramp0 Saturation0 Goto0 Ramp9 Saturation9 Ramp Saturation Vwin6 Vwin Ramp0 Saturation0 Goto5 Ramp Saturation Goto Ramp Saturation Ramp Saturation Figure 55: win input: 0-moe win input for iniviual turbine The win pee for each turbine i pecifie eparately in the win input block, ee figure 55. Aeroynamic effect of the park layout can be inclue if the iniviual win pee are 66 ECN-C

67 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK calculate by a win farm aeroynamic coe, i.e. FinFarm. The gri moel ue in all win farm moel i ecribe in ection 4.5. win_ Pa_ em P_ Q_ [ignal_] From _ CSS_AM_ win_6 Pa_6 em P_6 Q_6 [ignal_6] From _6 CSS_AM_6 win_ Pa_ em P_ Q_ [ignal_] From _ CSS_AM_ Pg Qg v P i Q ig vg f i v w Power /(*pi) em em CSS_park_gri Figure 56: Plot figure: Collection of turbine output variable A election of variable i collecte for turbine, 6 an, a well a overall quantitie for the whole win farm, ee figure 56. ECN-C

68 Erao II, Volume : Dynamic moel for win farm 4. Contant pee tall controlle WF with cluter controlle inuction machine ω 4 kv ω 4 kv ω 4 kv ω4 4 kv 4 kv 50 kv Figure 57: Electrical layout of four tring of cluter controlle turbine One tring of the cluter controlle contant pee tall (CSS-CC) win farm conit of four cluter of three tall regulate turbine (figure 57). The Simulink farm moel conit of only one group of three turbine incluing turbine tranformer, the cluter converter, cable in the win farm, cable to hore an ubtation high voltage tranformer. The Simulink moel connect the cluter through the 4 kv cable an 4kV/50kV tranformer to the 50 kv gri moel (figure 58). Separate block generate iniviual win input for all turbine an plot imulation reult. v_gri w_gri i_out v i w_in v i w_out v HV i LV w_in v LV i HV w_out i Vgri w_gri Cluter 4kV_cable 4kV/50kV_trafo 50kV_gri Cluter with contant pee turbine with AM q moel (c) 00 Tim van Engelen & Jan Pierik (ECN), Johan Morren (TUD) i_cc v_cc w CC Plot_CC win input Figure 58: Simulink CC win farm moel: Main 68 ECN-C

69 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v_gri w_gri Vg w gri P_in v_ v from conv Pel I to conv OmegaR w_et pee controller w_ref w_ i_park Conv w_in turb + cable OmegaR v from conv Pel I to conv w_in turb + cable OmegaR Terminator v from conv Pel I to conv w_in turb + cable OmegaR Terminator i_out Figure 59: Simulink CC cluter moel: cluter The cluter block (figure 59) connect three turbine plu cable to the cluter converter. The voltage phaor at the turbine ie of the cluter converter i input for the turbine plu cable moel, the current phaor i output. The um of the three turbine current phaor i returne to the converter. f_et Saturation *pi Gain w_et f_ref f_ref OmegaR turb.rb Rb Prouct lam ifference control PI + anti winup [Vwin] From 5 Lb_et Figure 60: Simulink CC cluter moel: pee controller The pee controller (figure 60) etermine the etpoint for the common rotational pee of the turbine in a cluter. ECN-C

70 Erao II, Volume : Dynamic moel for win farm v from conv v v v from cable i to cable i i w_in w_out w_in w_out I to conv [Vwin] w_in Vw 0p ignal 4kV_cable From tur + trafo Terminator U U(E) Selector Pel CC_ CC_ U U(E) Selector OmegaR Figure 6: Simulink CC turbine moel: turbine + cable v from cable NM9 configure a CSS, 960V, 750 kw v_q i_q v i v_mach i i to cable w_in Vw 0p w_ Vw 0p w_out ignal w_in w_out tur_trafo 960V ignal w_out Figure 6: Simulink CC turbine moel: tur + trafo The turbine an tranformer moel in figure 6 contain the NM9 turbine block an a 960V/4kV tranformer block. The cable voltage phaor an the current phaor from the turbine are the input of the tranformer block. The tranformer moel calculate the low voltage ie voltage phaor an the high voltage ie current phaor. The tranformer moel output voltage phaor i fe to the turbine moel, the output current phaor i input to the 4 kv cable moel. 70 ECN-C

71 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v_ w_m em v_q v_q T_e w_ w_ i_q i_q w_out T_m_h AM_q ignal Vw 0p win Vw_out azi Rotor eff. win Vw_in OmegaR_in Cq Ct Cq Ct Vw Cq Ct Te Paero Taxi OmegaR w_m Turb_full_IM_CSS azi ignal Figure 6: Simulink CC electrical ytem moel: NM9 The turbine moel i ientical to the turbine moel in the CSS win farm moel an conit of the generator moel (AM q), the calculation of the rotor effective win (Rotor eff win), the aeroynamic coefficient (CqCt) an the block containing the mechanical equation of turbine haft an tower (Turb full IM CSS, figure 6). For the ecription of thee block i referre to ection 4.. ECN-C

72 Erao II, Volume : Dynamic moel for win farm Qref Vg w gri em Pgriconv Qgriconv Uc VgD VgQ w_in PQ_gri Ic_griconv Iq_gri Griconv IcPM IcGri Ic uit gri Pref gri Ic uit PM Uc Uc DC link P_in uc v_ v_ 4 w_ref wref w_ machine_conv w_ P_park PQ_gri U_c 5 i_park i_park v_park i_gri v_gri f_park ignal Figure 64: Simulink CC electrical ytem moel: Conv The cluter converter block in figure 64 connect the gri an machine ie converter to the DC link. The input of the cluter converter block are the gri voltage phaor, the gri angular frequency, the electrical power an current of all generator connecte to the cluter converter an the etpoint for the cluter rotational pee. The output are the voltage phaor of the generator an the cluter angular pee. wref w_ 0 uc /00 qrt() v_ Figure 65: Simulink CC electrical ytem moel: machine conv The machine ie converter (figure 65) etermine the tator voltage of the cluter generator. The q-component of thi voltage i cale with the etpoint of the cluter angular pee. The -component i zero. 7 ECN-C

73 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK K in out RL_ in out RL_q K Iq_griconv Iq_gri PQ_gri Imea kp.+ki U control L_conv G iq i em U Uq Ic_gri Ic_griconv I Iq PQ_griconv kw Uq_RL_rect Uc Power Griconv kw PQ_griconv kw kp.+ki Iqmea Uc Uq q control L_conv G 4 VgD 5 VgQ 6 w_in u i Qgriconv Pgriconv uq P Q iq Iq from PQ Figure 66: Simulink CC electrical ytem moel: Griconv The gri ie converter etermine the current phaor to the gri by generating a voltage ifference over a mall RL component between the converter an the gri. The etpoint for the current phaor i calculate from the DC power to the gri that i require to keep the DC link voltage contant an the etpoint for the reactive power to the gri. ECN-C

74 Erao II, Volume : Dynamic moel for win farm elta_i_clink Ic uit PM 000 /C Integrator eltau_clink PID Pc_ref_ kw Gain kw Prouct 00*4/0.960 Contant Switch Uc Pref gri Ic uit gri Prouct kw Gain Pc_gri_ kw Uc bepaalt via een PID e gewente waare van Pref rectifier e rectifier maakt hier een i en iq hieruit wor Ic uit rect bereken ter controle Figure 67: Simulink CC electrical ytem moel: DC-link In the DC link (figure 67) the DC current generate by the gri an machine ie converter etermine the DC voltage an the etpoint for the gri converter power. The cable an tranformer moel are ientical to thoe ue in the CSS win farm moel, ee ection ECN-C

75 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK 4. Variable pee pitch controlle WF with oubly fe inuction machine 960 V 4 kv 690 V 50 kv Figure 68: Electrical layout of a tring of DFIG turbine One tring in the variable pee pitch controlle win farm with oubly fe inuction machine (VSP-DFIG) contain twelve turbine (figure 68). The Simulink moel of thi tring inclue the turbine, the three-wining tranfomer, the converter connecte to the generator rotor, the cable in the win farm, the cable to hore an the ubtation high-voltage tranformer. v i v i v i v i v i i Vgri w_in w_out w_in w_out w_in w_out w_gri _turbine 4kV_cable 4kV/50kV_trafo 50kV_gri Park with Variable pee turbine with DFIG q moel (c) 00 Johan Morren (TUD), Tim van Engelen & Jan Pierik (ECN) i v w Plot_figure control Figure 69: Simulink DFIG win farm moel main winow The Simulink moel connect the turbine to a 4 kv cable, a 4kV/50kV tranformer an the 50 kv gri moel (figure 70). Separate block generate iniviual win input for all turbine an plot imulation reult. ECN-C

76 Erao II, Volume : Dynamic moel for win farm v i v i v i v i v i v i w_in w_out NM9_comp w_in w_out 4kV_cable w_in w_out NM9_comp7 w_in w_out 4kV_cable7 v i w_in w_out NM9_comp v v i i w_in w_out 4kV_cable v i w_in w_out NM9_comp8 v v i i w_in w_out 4kV_cable8 v i v i v i v i v i v i w_in w_out NM9_comp w_in w_out 4kV_cable w_in w_out NM9_comp9 w_in w_out 4kV_cable9 v i v i v i v i v i v i w_in w_out NM9_comp4 w_in w_out 4kV_cable4 w_in w_out NM9_comp0 w_in w_out 4kV_cable0 v i v i v i v i v i v i w_in w_out NM9_comp5 w_in w_out 4kV_cable5 w_in w_out NM9_comp w_in w_out 4kV_cable v i w_in w_out NM9_comp6 v v i i w_in w_out 4kV_cable6 v i w_in w_out NM9_comp i w_out v w_in Figure 70: Simulink DFIG win farm moel: turbine The turbine block (figure 70) connect the turbine an cable in one tring of the NSW win farm. The voltage phaor at each cable-turbine connection i input for the turbine plu tranformer moel, the current phaor i output. The turbine plu tranformer moel calculate the current phaor, which i returne to the cable moel. The turbine current phaor an the current phaor from the cable connecting the other turbine are ae before entering the next cable. Thi i repeate for all turbine an cable. Tm_SSE wm_sse Teet_SSE Tel_SSE ignal Mech+Aero v w_in Tm SSE wm SSE Tel SSE Teet SSE i v w_out w_in ignal Generator Conv ytem i w_out DFIG_Iq ignal_ Goto DFIG_Uq Figure 7: Simulink DFIG turbine moel: NM9-comp The DFIG turbine moel, figure 7), conit of two ubmoel: a mechanical an aeroynamic part Mech+Aero an an electrical part Generator-Conv ytem. 76 ECN-C

77 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK win_vw0ext_vp em rotor effective win [Vwin] From ctrpvp pitch pee turb_full_vp turbine excl. generator em ignal wm_sse Tel_SSE Tm_SSE Teet_SSE ctrgvp em e.m. torque gen con Figure 7: Simulink DFIG turbine moel: Mech+Aero The mechanical an aeroynamic part (Figure 7) conit of four Matlab S-function, which calculate the rotor effective win, the pitch control an electromagnetic torque etpoint an the turbine rotor, rive train an tower motion. See chapter for a ecription. K Tel SSE GearR K Tel Tm IGearR Tm SSE K wm wm SSE i IGearR i Teet v K Teet SSE IGearR 4 w_out v w_out 5 ignal ignal DFIG q w_in 4 w_in koppel en toerental low pee electrical, u torie langzame a aan e generatorzije Figure 7: Simulink DFIG electrical ytem moel: Generator-Converter ytem The electrical part of the DFIG turbine moel in figure 7 contain the moel of the -wining trafo, the generator an the converter connecte to the generator rotor. ECN-C

78 Erao II, Volume : Dynamic moel for win farm Tm {T_m} Goto {T_m} {T_e} [T_e] From Tel Teet {Teet} Goto {Teet} {w_m} [w_m] From wm v 4 w_in i v w_out w_in ignal Gen+conv+trafo i 4 w_out 5 ignal Figure 74: Simulink DFIG electrical ytem moel: DFIG q The input variable mechanical torque an electrical torque etpoint in figure 74 are pae to the generator an the torque controller ubytem repectively. The output variable electrical torque an rotational pee are calculate in the generator an the gen+conv ubytem repectively. Other input variable for the Gen-conv-trafo ubytem are the gri voltage phaor an the gri angular frequency. The current phaor into the 4 kv cable i calculate an the gri angular frequency i pae a an output. v v v_mach v_conv v_mach i i v_conv i i w_in w_in w_out w_in w_out _wining_trafo w_out [Qref_] From ignal Q_ref Gen+conv ignal Figure 75: Simulink DFIG electrical ytem moel: Gen+conv+trafo The three-wining tranformer moel in figure 75 i almot the ame a the two-wining moel ecribe in ection 4.. A mall inaccuracy i introuce in thi way. 78 ECN-C

79 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v_ref Qref Q w_lip 4 Q_ref phi v_mach em Generator i_r Q_controller v_conv em Vg Vgq Iref Vr Vqr v vq vr ir_qo i_qo phi w_m w_lip w_m {w_m} Goto Iqref i_conv Pr ignal w_in Converter vrq w_in Pr Q ignal i_r i_mach i_conv i_gri Current to trafo i v_qref phi w_lip w_in w_out Te_controller In Out Power_Summation ignal Figure 76: Simulink DFIG electrical ytem moel: Gen+conv The converter in figure 76 i able to control four quantitie: by changing the witching of the rotor ie converter, the rotor voltage amplitue an phae angle can be controlle; on the gri ie, the current amplitue an phae angle can be controlle by changing the witching of the gri ie converter an thu the voltage at the converter terminal. The rotor ie voltage an phae angle (or the - an q-component) are etermine by two controller: the reactive power controller etermine the -component an the torque controller et the q-component. The rotor ie converter realie thee voltage. em 4 phi w_lip v_ref i_kp.+i_ki I_controller em 5 i_r Q_kp.+Q_ki Q_controller Qref Q Figure 77: Simulink DFIG electrical ytem moel: Q-controller The reactive power controller compare the reactive power offet to generate a etpoint for the -component of the rotor current in figure 77. Thi etpoint i compare to the actual current value. A econ controller generate the etpoint for the -component of the rotor voltage, correcte for the croterm ω lip Ψ rq. ECN-C

80 Erao II, Volume : Dynamic moel for win farm v_qref iq_kp.+iq_ki Iq_controller em i_r em phi w_lip num() wm_controller Gain K From [Teet] From [T_e] Figure 78: Simulink DFIG electrical ytem moel: Te-controller The torque controller compare the torque offet to generate a etpoint for the q-component of the rotor current (Figure 78). Thi etpoint i compare to the actual value. A econ controller generate the etpoint for the q-component of the rotor voltage, correcte for the croterm ω lip Ψ r. Qref Vg Vgq 6 w_in Prect Iq Qrect Uc Ic_rect VgD VgQ ignal w_in Rectifier i_conv 4 ignal i_rect Pref i_inv DC link Uc Uc 5 Pr Iref 4 Iqref Vr Vqr Inverter geeft e gewente V en Vq oor naar rotor van generator Figure 79: Simulink DFIG electrical ytem moel: Converter The gri ie converter (calle rectifier in figure 79) make the current phaor from the DC link to the gri, bae on a reactive power etpoint an the DC voltage. Two controller in the rectifier block (figure 80) etermine - an q-voltage by comparing the - an q-current etpoint to the actual - an q-current to the gri. The gri current component follow from 80 ECN-C

81 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK the voltage ifference over a mall impeance between rectifier an gri (figure 80). in RL_ out in RL_q out Iq Imea num() U control L_conv G iq i em U Uq I Ic_rect Ic_rect Iq PQ_q_rect Uc Power Uq num() q control Iqmea Uc L_conv G ignal 4 VgD 5 VgQ em 6 w_in u i Prect uq P em Qrect Q iq em Iq from PQ Figure 80: Simulink DFIG electrical ytem moel: Rectifier, gri ie converter ECN-C

82 Erao II, Volume : Dynamic moel for win farm i_inv K /C Integrator PID Uc Uc Prouct Contant Switch Pref kw i_rect Prouct Gain Prect_clink_ kw Uc bepaalt via een PID e gewente waare van Pref e rectifier maakt hier een i en iq hieruit wor Irect bereken ter controle Figure 8: Simulink DFIG electrical ytem moel: DC-link The DC voltage etermine the etpoint for the power to the gri, bae on the DC current from the inverter an the actual value of the DC voltage (Figure 8). The etpoint for the power to the gri i fe to the converter to etermine the current q-value. Tm v vq [T_m] From vr 4 vrq v vq vr vrq m w_ w_r T_m Comp_fig_abc i ir w_m T_e m phi P_r Q_ ignal Mea i_qo ir_qo 4 w_m phi 6 Pr 7 Q 8 ignal {T_e} Goto 5 w_in w_ w_r w_m p p 5 w_lip Figure 8: Simulink DFIG electrical ytem moel: Generator The generator moel etermine the rotor an tator current phaor bae on the rotor an tator voltage phaor, ee figure 8. The haft torque i alo an input to the generator moel. 8 ECN-C

83 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK Stator power v P_tator vq i Q_tator iq v v_ i_ vq vr 4 vrq v_q v_r v_qr i_q i_r i_qr w_m 7 T_m T_m T_e 5 w_ w_ phi 6 w_r w_r Dfig_q lip em m vr vqr ir iqr Rotor power P_rotor Q_rotor Figure 8: Simulink DFIG electrical ytem moel: Comp-Dfig-abc ECN-C

84 Erao II, Volume : Dynamic moel for win farm v_ v_q v_r 4 v_qr phi_ phi_q phi phi_r phi_qr i_ i_q i i_r i_qr emux v_ v_q v_r v_qr phi_ phi_q phi_r phi_qr i_ i_q i_r i_qr w_ w_r phi_ phi_q phi_r phi_qr phi_ phi_q phi phi_r phi_qr mux K*u inv(m_phi) i_ i_q i i_r i_qr emux i_ i_q i_r 4 i_qr 7 phi 6 w_ 7 w_r phi_ i_q T_e phi_q i_ 6 T_e Torque 5 T_m T_m w_m T_e 5 w_m pee w wm lip 8 lip lip_ Figure 84: Simulink DFIG electrical ytem moel: Dfig-q 84 ECN-C

85 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v_ v_q v_r 4 v_qr 5 phi_ 6 phi_q 7 phi_r 8 phi_qr w_ 4 w_r phi_ phi_q phi_r 4 phi_qr 9 i_ R_ 0 i_q R_ i_r i_qr R_r R_r Figure 85: Simulink DFIG electrical ytem moel: Voltage equation The voltage equation (ee equation ) contituting the generator moel are repreente by figure 85. The cable an tranformer moel are ientical to thoe ue in the CSS win farm moel. ECN-C

86 Erao II, Volume : Dynamic moel for win farm 4.4 Variable pee pitch controlle WF with permanent magnet machine 4 kv 50 kv Figure 86: Electrical layout of a tring of PM turbine One tring in the variable pee pitch controlle win farm with permanent magnet machine contain turbine (figure 86). The Simulink moel of thi tring inclue the turbine, the tranformer, the converter connecte to the generator tator, the cable in the win farm, the cable to hore an the ubtation high voltage tranformer. v i v i v i v i v i Vgri w_in w_out _turbine w_in w_out 4kV_cable w_in w_out 4kV/50kV_trafo i w_gri 50kV_gri Park with Variable pee turbine with PM q moel (c) 00 Johan Morren (TUD), Tim van Engelen & Jan Pierik (ECN) i v w Plot_figure control Figure 87: Simulink PM win farm moel: Main winow 86 ECN-C

87 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v i v i v i v i v i v i w_in w_out PM_ w_in w_out 4kV_cable w_in w_out PM_7 w_in w_out 4kV_cable7 v i w_in w_out PM_ v v i i w_in w_out 4kV_cable v i w_in w_out PM_8 v v i i w_in w_out 4kV_cable8 v i v i v i v i v i v i w_in w_out PM_ w_in w_out 4kV_cable w_in w_out PM_9 w_in w_out 4kV_cable9 v i v i v i v i v i v i w_in w_out PM_4 w_in w_out 4kV_cable4 w_in w_out PM_0 w_in w_out 4kV_cable0 v i v i v i v i v i v i w_in w_out PM_5 w_in w_out 4kV_cable5 w_in w_out PM_ w_in w_out 4kV_cable v i w_in w_out PM_6 v v i i w_in w_out 4kV_cable6 v i w_in w_out PM_ i w_out v w_in Figure 88: Simulink PM win farm moel: turbine In figure 88 the twelve variable pee turbine, equippe with permanent magnet generator an the eleven cable in one tring are connecte. The ignal flow i imilar to the DFIG moel. Tm_SSE wm_sse Teet_SSE Tel_SSE ignal Mech+Aero v w_in Tm SSE wm SSE Tel SSE Teet SSE i v w_out w_in ignal Generator Conv ytem i w_out PM_Iq ignal_ Goto PM_Uq Figure 89: Simulink PM turbine moel: PM The PM turbine moel (figure 89) conit of two ubmoel: a mechanical an aeroynamic part Mech+Aero an an electrical part Generator-Converter ytem. ECN-C

88 Erao II, Volume : Dynamic moel for win farm win_vw0ext_vp em rotor effective win [Vwin] From ctrpvp pitch pee turb_full_vp turbine excl. generator em ignal wm_sse Tm_SSE Tel_SSE Teet_SSE ctrgvp em e.m. torque Figure 90: Simulink PM turbine moel: Mech + Aero The mechanical an aeroynamic part (figure 90) i ientical to the VSP moel of the VSP- DFIG win farm an conit of four Matlab S-function, which calculate the rotor effective win, the pitch control an electromagnetic torque etpoint an the turbine rotor, rive train an tower movement. Tel SSE K GearR Tel Tm K IGearR Tm SSE wm SSE i 4 w_out 5 ignal K IGearR wm Teet i v w_out w_in ignal PM q + trafo K Teet SSE IGearR v 4 w_in koppel en toerental low pee electrical, u torie langzame a aan e generatorzije Figure 9: Simulink PM electrical ytem moel: Generator-conv ytem The electrical part of the PM turbine moel in figure 9 contain the moel of the tranformer, the generator an the back-to-back converter. 88 ECN-C

89 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK v 4 w_in Tm Teet i v w_out w_in Tel T_m wm Te_et ignal Machine+Trafo i 4 w_out Tel wm 5 ignal Figure 9: Simulink PM electrical ytem moel: PMq + trafo v_rectif_q i_q_griconv v v v_rectif 4 Te_et T_m w_gri Tel Te_et wm T_m ignal PM q + conv Tel 4 wm 5 ignal i_rectif w_in i w_out i w_out w_in 4kV/4kV trafo Figure 9: Simulink PM electrical ytem moel: Machine + trafo Vg v_rectif_q em Vgq i_q_griconv NG i_q_griconv w_gri w gri ignal Te_et 4 T_m /NG 0 /NG P_PM Te_et Tel I ref wm T_m ignal PMG + inverter NG Tel wm P_PM Griconv + DC link 4 ignal PM machine moel JM, june 00 Figure 94: Simulink PM electrical ytem moel: PMq + conv The back-to-back converter between PM generator an gri (figure 94) i able to make the voltage phaor at the generator an at the gri ie by changing the firing of the generator an gri ie converter. Thee voltage are etermine by current etpoint, which epen on the eire reactive power, electromagnetic torque an DC link voltage. ECN-C

90 Erao II, Volume : Dynamic moel for win farm Pgriconv [Qref_] Qgriconv Iq i_q_griconv From Uc Ic_griconv Vg Vgq w gri VgD VgQ w_in Griconv ignal ignal Ic uit gri Pref gri Ic uit PM Uc Uc DC link 4 P_PM Figure 95: Simulink PM electrical ytem moel: Gri conv + DC link The gri ie converter (calle Griconv in figure 95) etermine the - an q-current from the DC link to the gri, epenent on a reactive power etpoint an the power etpoint calculate in the DC link. Two controller in the gri converter block (Figure 96) etermine - an q- voltage by comparing the - an q-current etpoint by the actual - an q-current to the gri. The gri current component follow from the voltage ifference over a mall impeance between rectifier output an gri. Thi converter operate imilar to the gri ie converter in the DFIG moel. 90 ECN-C

91 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK c_v c_vq vg vgq i iq w v in out RL_ vq in out RL_q Iq Imea num() U control L_conv G iq i em U Uq I Ic_gri Ic_griconv Iq PQ_griconv Uc Power Griconv Uq num() q control Iqmea Uc em ignal L_conv G em 4 VgD 5 VgQ 6 w_in em Pgriconv Qgriconv u uq P Q i iq Iq from PQ Figure 96: Simulink PM electrical ytem moel: Griconv Ic uit PM K /C Integrator PID Uc Uc Prouct Contant Switch Pref gri Ic uit gri Prouct Pc_gri Uc bepaalt via een PID e gewente waare van Pref rectifier e rectifier maakt hier een i en iq hieruit wor Ic uit rect bereken ter controle Figure 97: Simulink PM electrical ytem moel: DC link The DC voltage controller etermine the etpoint for the power to the gri, bae on the DC current from the inverter an the actual value of the DC voltage (Figure 97). The etpoint for the power to the gri i fe to the rectifier to etermine the current an q value. ECN-C

92 Erao II, Volume : Dynamic moel for win farm ignal v vq we_pm m w_m T_e m P_PM i P_PM wm 4 ignal T_m T_m PM u_ec uq_ec Mea p Tel num() uq control K Te_et num() u control I ref u_ec en uq_ec zijn e kruitermen oor eze bij u en uq op te tellen wor alleen i en iq geregel Figure 98: Simulink PM electrical ytem moel: PMG + inverter The input ignal for the PMG an inverter are the etpoint for the electromagnetic torque an the -component of the tator current (figure 98). The two controller generate voltage v q an v which are input for the voltage equation of the PM generator moel in figure 00 an 0. U Uq P_PM I Iq Q_PM Power PM v v_ i_ i_q vq v_q w_m 4 T_m T_m T_e u_ec m w_ uq_ec PM_ we_pm Figure 99: Simulink PM electrical ytem moel: PM 9 ECN-C

93 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK i_ phi_ v_q v_ v_ v_q phi_ i_ i_ phi_q phi_q i_ i_ i_q i_q phi_calc i_q i_q w_ PM_ i_ i_q u_ec i_q 5 u_ec 4 w_ w_ uq_ec u_ecoupling 6 uq_ec i_q T_e 4 T_e T_e T_m T_m T_e w_m w_m pee Figure 00: Simulink PM electrical ytem moel: PM 4 phi_q 5 i_ v_ R_ K i_ 7 w_ v_q phi_ K i_q 6 i_q R_ Figure 0: Simulink PM electrical ytem moel: PM Figure 0 lit the voltage equation which moel the PM generator. ECN-C

94 Erao II, Volume : Dynamic moel for win farm i_ L_ w_ phi_f uq_ec i_q L_ u_ec Figure 0: Simulink PM electrical ytem moel: u-ecoupling The etpoint for the voltage phaor i correcte for the cro coupling term ω Ψ f in figure ECN-C

95 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK 4.5 Gri moel 4/50 kv 50/4 kv 5 km 4 kv 0 MW 5 MW 65 MW Voltage controller Exciter Frequency controller Figure 0: Electrical layout of the equivalent gri moel All win farm moel inclue a implifie gri moel, to imulate the effect of change in active an reactive win power a well a change in conumer power on gri voltage an frequency. The gri moel i kept imple: only one large ynchronou machine, a tranformer, a cable an two conumer loa (figure 0). The ynchronou machine control the gri frequency an the gri voltage. U_et U_et u_q Uf regulator+exciter type no aturation uf u_f u_q u_q w i_q i_q SM_el v i Power P_SM w_gri w_et w_et Pmech w_sm pee regulator Pe_SM w_sm Pm_SM SM inertia Figure 04: 50V gri: Gri moel main component Figure 04 connect the component of the gri moel in Simulink. The voltage equation of the ynchronou machine moel are evaluate in figure 05. Input variable are the fiel voltage an the tator voltage phaor. The fiel current an the tator current phaor are calculate. ECN-C

96 Erao II, Volume : Dynamic moel for win farm L.i/ + Lmf.if/ = u R.i w.lq.iq [i_] [i_] K R i_ [i_q] K K*u em w Lq [w_sm] inv_l_matrix i_f [i_f] u_f Lm.i/ + Lf.if/ = uf Rf.if i_f i_q u_q em [i_f] K Rf Lq.iq/ = uq R.iq + w.(l.i+lm.if) [i_q] K R K /Lq i_q [i_] K L [i_q] [i_f] K Lm [w_sm] Synchrone machine, wikkelingmoel: qf f betrokken op tator generatorconventie Figure 05: SM el: Synchronou machine voltage equation The exciter an fiel regulator moel on the ynchronou machine (ee figure 06) i a type moel []. It operate on the per unit value of the tator voltage amplitue an generate a per unit value of the fiel voltage. The parameter have been taken from a SimPowerSytem example an give a atifactory gri voltage behaviour. 96 ECN-C

97 4 DYNAMIC MODELS OF WIND FARMS IN SIMULINK U low pa filter U_et /Ubae Vt V > PU 0.0+ Tranfer Fcn (with initial output) amplifier / exciter Uf_bae Uf PU > V Uf u_q qrt(u()*u()+u()*u()); Fcn regulator gain e 4 Zero Pole (with initial output) 0 (+0) U_SM_top Exciter moel uit help PSB, incl. e parameter, komt overeen met Aneron & Foua Type Exciter (p. 9) Uf (PU) = an Uf (V) komt overeen met E = Un bij eze Uf en E i If (PU) = (zie Kunur, p. 4) Figure 06: Regulator + exciter type : Moel for the fiel voltage control Pmech0 w Contant w_et PI_in PI_regelaar PI_out Pmech w_sm w_sm Figure 07: Spee regulator: gri frequency controller Figure 07 how the gri frequency controller. The ynchronou machine inertia i moelle in figure 08. Pm_SM Pe_SM Prouct /J_SM Proportional Integrator w_sm Figure 08: SM inertia: Synchronou machine an conumer equivalent rotating inertia The cable moel preente in the previou ection ha been moifie to connect the ynchronou generator to the win farm moel. Since the win farm an the ynchronou generator both calculate the current phaor an nee the voltage phaor a input, the cable moel wa moifie (ee figure 09). The equation of both cable moel are the ame. ECN-C

98 Erao II, Volume : Dynamic moel for win farm i_q_a em i A i B w_gri i_lq u A u B u_q_a w_gri u_q_a u_q_b Cable_ i_l w_gri i_q_b em i_q_a i_q_b u_q_a w_gri i_l u_q_b u_q_b u A u B Cable_q i_lq cable pi moel : voor koppeling met ynchrone machine A en B zijn e beie kabeleinen i_q_a en i_q_b inganggrootheen u_q_a en u_q_b woren bereken Figure 09: Cable moel to connect gri ynchonou machine 98 ECN-C

99 5 FLICKER METER 5. Introuction Light flicker i the changing intenity of an electric light, caue by voltage variation. The frequency of the variation i important: the annoyance caue by flicker epen on the rate of change. Figure 0 give the level of voltage change a function of the frequency of the change which i jut viible by human. Thi curve, calle the flicker curve, i empirically etermine by ubjecting peron to light from a 60W lamp fe by a voltage with rectangular variation of ifferent intenity an frequency. The figure how that the human eye i mot enitive to variation in the range of 000/60=6.67 Hz an therefore thee variation will receive the mot weight in a flicker evaluation. A flicker evaluation i part of the Power Quality aement of gri connecte win turbine (IEC 6400-). The evaluation quantifie the voltage amplitue variation caue by a win turbine an compare them to the level of the flicker curve. 0 % of nominal voltage frequency [/min] Figure 0: Flicker curve: the level of voltage amplitue variation viible by the human eye Change in power an reactive power of win turbine an witching operation caue flicker. Power fluctuation in the range relevant for flicker (0.5-5Hz) are mainly cae by: turbulence; win hear; tower haow; yaw mialignment. For frequencie above Hz the blae paing frequency an it multiple ominate the power pectrum an therefore are critical in the aement of flicker. In contant pee ytem, the variation in aeroynamic power are almot intantaneouly tranmitte to variation in electric power. Figure give an example of the meaure flicker level caue by a contant pee turbine a function of the relative power P/P rate prouce by the turbine. The flicker level P t = if the voltage variation are equal to the level in the flicker curve. ECN-C

100 Erao II, Volume : Dynamic moel for win farm 0.4 NW c:\creaq\anlyprg\nw46eval\flicker\fltot.i Pt ( ) P / Prate ( ) Figure : Meaure flicker level P t a function of the relative power for a contant pee turbine The actual amount of flicker caue by a win turbine not only epen on the turbine propertie but alo on the characteritic of the gri at the point of common coupling. A high hort circuit ratio will reuce flicker, while nearby proucer or loa may increae the flicker level. The aim of a flicker meaurement i a tet reult which i inepenent of the gri conition at the tet ite. To accomplih thi, the IEC6400- tanar [4] pecifie a metho that ue current an voltage time erie meaure at the win turbine terminal to imulate the voltage fluctuation of a fictitiou gri with no ource of voltage fluctuation other than the win turbine. Prior to the ecription of the flicker meter, thi metho will be ummarize. Rfic L fic + + _ u g u fic _ i m Figure : Fictitiou gri for flicker evaluation The fictitiou gri i repreente by an ieal voltage ource with intantaneou voltage u g an a gri impeance coniting of a reitance R fic in erie with an inuctance L fic, ee figure. The win turbine i repreente by a current ource i m. The ieal voltage ource will atify two criteria: the amplitue i contant, i.e. no contribution to the flicker level of the voltage u fic ; the intantaneou angle α m between u g an i m i equal to the intantaneou angle between the meaure voltage at the PCC an i m. Thi enure that the angle between 00 ECN-C

101 5 FLICKER METER u fic an i m i practically equal to α m, ince the voltage rop over the gri impeance i mall. For the win turbine an win farm moel, the PCC voltage u an u q are known an the econ requirement can be atifie by calculating a voltage of amplitue U n an angle (u q, u ). Another option, lightly more time conuming, woul be a phae locke loop on the voltage. The three-phae hort circuit power of the fictitiou gri i given by: S k,fic = U n R fic + X fic () A proper ratio between S k,fic an S n mut be ue to aure that the applie flicker meter algorithm or intrument give hort term flicker value P t within the meaurement range require in IEC A a guie, a ratio of 50 between S k,fic an S n i uggete in IEC The actual ratio electe will affect the intantaneou flicker level but it will not affect the reulting flicker coefficient a long a it oe not bring the flicker meter outie it vali range. The flicker coefficient c(ψ k ), with ψ k the fictitiou gri impeance angle, for continuou operation of the turbine i etermine by: meauring the three line current an the three phae-to-neutral voltage with a ample frequency of 600 Hz. The cut-off frequency of the meaurement hall be at leat 400 Hz; taking 0 minute time erie of intantaneou current an voltage meaurement; meauring the win pee imultaneouly an etermining the 0 minute average. The flicker coefficient for a 0 minute meaurement i etermine by: calculating the fictitiou gri voltage u fic ; etermining the intantaneou flicker value (perceptability value) P f,fic for the turbine connecte to the fictitiou gri with a flicker meter; etermining the hort term flicker P t,fic by binning an etermination of the 99% percentile value (99% of the intantaneou flicker value are below thi value); calculating the flicker coefficient: c(ψ k ) = P t,fic S k,fic S n (4) The flickermeter ha been contructe in Simulink an can be ue for both on-line an offline evaluation. The moel conit of the ame block a the analogue flickermeter which i ecribe in the IEC an IEC tanar an i elaborate in ection 5.. The eparate bock are ecribe in ection 5.. ECN-C

102 Erao II, Volume : Dynamic moel for win farm 5. Flicker meter The analogue flickermeter a ecribe in IEC an IEC conit of 5 block, cf. figure :. input voltage aapter an calibration checking unit;. quare law emoulator;. weighting filter, quaring an moothing (electric attenuation); 4. weighting filter, quaring an moothing (human repone); 5. on-line tatitic. BLOCK BLOCK BLOCK u_fic(t) input voltage aaptor calibration ignal generator elect u_in(t) y =u_in(t) B Hz. BP-Filter B 0 fc = 8.8 Hz BP-Filter BLOCK 4 BLOCK 5 y = u B 0. Hz. LP-Filter T ZOH # ample PDF bin Figure : Block cheme of flicker meter The voltage aaptor in block i not neceary in the imulation moel a it purpoe i to match the input ignal to the limite ynamic range of the analogue flicker meter. The calibration ignal generator ha been implemente to check the proper operation of the flickermeter. Block eliminate the.c. an ouble main frequency an imulate the repone of a coil filament ga fille lamp (60W - 0V). Block 4 imulate the human perception of a flickering lamp. Finally block 5 claifie the perceive flicker level an buil a probablilty enity function by binning the meaure intantaneou flicker level. An extra block, a o-calle fictiou gri which i alo ecribe in the tanar, generate the input voltage of block from the meaure line current. 0 ECN-C

103 5 FLICKER METER 5. Implementation in Simulink Thi ection give a ecription of each of the block in the flicker meter in figure. Figure 4 how how the flickermeter ha been implemente in Simulink. Vabc Select_Va cal_ignal Cal_generator Select_mea_cal Square cale to % 00 In Out LPF Tau = 5 ec. Scaleref Offet 00.5e5/(*pi)*. en() r orer BW LPF 50 Hz. Selectbl main LPF on/off num() en() elective BPF Hz. num() en() haping BPF fc = 8.8 Hz. inuoial fluct. Square 0.+ LPF T =0.ec Pf z Unit Delay T K cale Pfcf t=tinit Input hol(0) / upate() reet(0) / upate() bin binne PDF_c_t_cum To Workpace PDF_c_lt z Unit Delay Tlt z Unit Delay Tt To Workpace PDF_c_t To Workpace Figure 4: Overview of flicker meter in Simulink Input elector an calibration ignal generator (Block ) In thi block one of the three line voltage i electe. The calibration ignal i a inewave at gri frequency which i amplitue moulate, a hown in figure 5. The moulate ignal i a quare-wave of 50/7 Hz with an amplitue equal to % of the inuoial carrier. Thi calibration ignal, which i precribe in the tanar, houl give a unity flicker level output. Sine Wave AM cal_ignal 50/7 Hz..995 Figure 5: Calibration ignal generator in Simulink Simulation of lamp-eye-brain chain (Block, an 4) Block quare the input ignal an normalize the output to unity by iviing it by the low- ECN-C

104 Erao II, Volume : Dynamic moel for win farm pa filtere ignal. Thi firt-orer filter ha a ettling time of 60 econ. In orer to pee-up the initial ettling of thi filter the ettling time of the filter can be witche to a 00 time fater rate, a hown in figure 6. /5 In /Tau /0.5 t=0 Switch Integrator Saturation > e Out /Tau Figure 6: LPF with witching time-contant in Simulink Thi block i followe by a econ orer ban-pa filter with a banwih from 0.05 Hz to 5 Hz to uppre the.c. component an ouble-main frequency. After thi, the ignal pae through a haping ban-pa filter centere at 8.8 Hz followe by a quare multiplier an a low-pa filter with a time-contant of 00 mec. The output i the intantaneou flicker level P f (ψ k ). Yet an extra low-pa filter ha to be ae to uppre the remaining ouble-main frequency ignal effectively. For thi a thir orer Butterworth low-pa filter with a cut-off frequency of 50 Hz wa choen. Without thi extra filter a flicker-free input ignal reult in an offet of the output ignal P f (ψ k ) of about 0.8 for 60 Hz main frequency (an. for 50 Hz main frequency). With thi extra low pa filter the gain ha to be tune to get a unity flicker level output for the calibration input ignal. Data analyi (Block 5) To calculate the hort-term an long term flicker coefficient c t (ψ k ) an c lt (ψ k ) for a certain gri angle ψ k, a cumulative probability enity function (PDF) over the correponing perio T t = 60 ec an T lt = 0 min ha to be built. Thi PDF i generate a follow: The intantaneou flicker level P f (ψ k ) i ample with a ample time T of.5 mec an then cale to the hort-circuit power of the win farm, a the intantaneou flicker coefficient c f (ψ k ) = P f (ψ k ) S k,fic /S n, with S k,fic being the gri hort-circuit power an S n the nominal power of the win turbine. Then all ample c f (ψ k ) over a meaurement perio T t are binne. Therefore each ample i cale with a factor No_bin/c f,max (ψ k ), with No_bin being the number of bin an c f,max (ψ k ) the maximum expecte flicker coefficient. Then the output i mappe to one of the bin by limiting the ignal between an No_bin an then generating a vector with a length equal to No_bin. The element of thi vector are zero except for one element with value at the poition which correpon to the intantaneou flicker coefficient (ee figure 7). The cumulative um of thi vector, which i upate each perio T, i the cumulative PDF. 04 ECN-C

105 5 FLICKER METER Input K gain map to cla Saturation 0 No_clae MATLAB Function [00000] < > ^ < > z Unit Delay T binne Figure 7: Binning the flicker ample in Simulink Thi cumulative PDF an the PDF over each conecutive perio T t an T lt a well are written to the MATLAB workpace a PDF_c_t_cum, PDF_c_t an PDF_c_lt. With thee function the hort-term an long-term flicker coefficient c t (ψ k ) an c lt (ψ k ) are etermine uing M-function. Fictiou gri u From Workpace uq From Workpace u_ u_q Ufic_a i_ i_q Fictiou gri Vfic Pf Flickermeter_IEC868 Pf i Ufic_abc From Workpace iq From Workpace Figure 8: Flicker calculation in Simulink Figure 8 connect the fictitiou gri moel to the flicker meter. In the fictitiou gri moel, ee figure 9, the meaure line current i m (t) i injecte into a gri coniting of an ieal flicker-free voltage ource u 0 (t) an a hort-circuit impeance R gri + jωl gri. The reulting voltage i: u fic (t) = u 0 (t) + R gri i m (t) + L gri i m (t)/ (5) u fic (t) houl be calculate for four angle ψ k of the gri impeance: 0, 50, 70 an 85 egree, with: ψ k = arctan(ωl gri /R gri ) (6) ECN-C

106 Erao II, Volume : Dynamic moel for win farm u_ q a q to a u_q i_ 4 a q q to a Rgri Rgri Ufic_a i_q u/ Derivative Lgri Lgri Figure 9: Fictiou gri in Simulink Initialiation The pre-loa function Init_flicker.m efine the electrical parameter an et their value. It et the input elector in block of the flickermeter: one of the line-voltage Va, Vb or Vc i electe an then either the calibration ignal or the electe line-voltage i pae a input ignal. The variou ample time an meauring time are et, followe by the number of bin an the maximum expecte flicker level for the calculation of the PDF. Pot-proceing The function calle at imulation top i Calc_flicker.m. In thi function the flicker coefficient c t (ψ k ) an c lt (ψ k ) are calculate. For c t (ψ k ) thi i one by calculating the cumulative probability p[x < c t,i (ψ k )] uing PDF_c_t with c t,i (ψ k ) increaing from 0 up to the maximum expecte flicker coefficient. The reult c t (ψ k ) i the minimum value of c t,i (ψ k ) for which thi probability i equal to or higher than 99%. 5.4 Teting the flicker meter in Simulink In thi ection the repone of the imulate flicker meter to a calibration ignal an a loa tep in a imulate tet circuit are preente. Seconly, the on-line calculation of the voltage change factor for two type of input ignal i emontrate Repone to calibration input ignal The calibration ignal i a 50 Hz ine wave that i amplitue moulate with a ymmetrical quare wave ignal, a illutrate in figure 5. Figure 0 how a etail of the calibration ignal that i witche on an off aroun t= ec an t=6 ec. The perio before t=0 ec i not hown a thi i ue for tabilizing the flicker meter output ignal. The repone of the flicker meter to the calibration ignal i hown in figure : a require it generate a value of ocillating aroun an intantaneou flicker value of. 06 ECN-C

107 5 FLICKER METER.0.0 etail of calibration ignal time (ec.) Figure 0: Amplitue moulate calibration ignal.4. Momentary flicker level P f time (ec.) Figure : Repone of the flicker meter to the calibration ignal 5.4. Repone to moulate gri voltage an loa tep The flicker meter ha been tete uing the circuit in figure, where component of the Power Sytem Blocket imulate an electrical network uring witching operation. The flicker ource in thi network i the amplitue moulate -Phae programmable Voltage Source. The amplitue of the moulate ignal i 0.5 p.u. an the frequency i 8.8 Hz. The moulation tart at t= ec an en at t=5 ec. Subequently a 50 kw loa tep i generate by cloing the -Phae Breaker at t = 8 ec an reopening it at t=9 ec. The meaure line current are injecte into the fictiou gri with a hort-circuit impeance choen equal to 5 MVA with an angle of 0 egree. The flicker level for the meaure input current i m (t) i mall a the hort-circuit power of the fictiou gri i relatively high. ECN-C

108 Erao II, Volume : Dynamic moel for win farm Phae Inuctive Loa 500 kva, co_phi =0.98 A A A A A A A B A B N B C Phae Programmable Voltage Source A B C B C A B C B C Phae Serie RL j Ohm A B C com B C B C Phae Serie RL j Ohm B C C Vabc Iabc Three Phae V I Meaurement Short pule C Vabc Iabc PQ phae Intantaneou Active & Reactive Power PQ Pf Phae loa 50 kw Phae Breaker Long pule Im_abc Ufic_abc Vabc Pf A B Single pule Fictiou gri Flickermeter_IEC868 C Phae RC Serie Loa 50kW, 0 kvar Ufic_abc Hol Ku Ku Voltage change factor Ufic_abc Figure : Tet circuit with flicker meter Figure how the repone u fic (t) of the fictiou gri for the line voltage U a. Figure 4 how the calculate intantaneou flicker P f (ψ k ) etail of fictiou gri voltage Ua fic (p.u.) time (ec.) Figure : Output voltage of the fictiou gri momentary flicker level P f time (ec.) Figure 4: Repone of intantaneou flicker level 08 ECN-C

109 5 FLICKER METER Figure 5 how the cumulative probability enity function of the flicker coefficient at t=8 ec for the input ignal of figure number of ample ( ) flicker coefficient c t Figure 5: Cumulative probability enity function Calculation of the flicker tep factor an voltage change factor The flicker tep factor an voltage change factor are calculate for the output voltage in figure. The flicker tep factor k f (ψ k ) i calculate a: The voltage change factor k U (ψ k ) i calculate a: k f (ψ k ) = 6 Sk,fic S n P t (ψ k ) (7) k U (ψ k ) = Sk,fic S n Ufic,max U fic,min U n (8) with U fic,max, U fic,max an U n being the maximum, minimum an nominal one perio RMS voltage on the fictiou gri uring the witching operation. For the calculation of U fic,max an U fic,min over a certain meaurement perio of time a eparate block ha been efine, which i hown in figure 6. max In Hol Zero Orer Hol min em Switch z MaxMin Unit Delay Figure 6: Calculation of minimum an maximum voltage Figure 7 how the repone of the voltage change factor k U (ψ k ) for all three line voltage for the imulate loa tep at t=8 ec. It how that the loa ecreae at t=9 ec contribute ECN-C

110 Erao II, Volume : Dynamic moel for win farm mot to k U (ψ k ). Further the voltage change iffer for the three line voltage, epening on the timing of the witching operation voltage change factor k U time (ec.) Figure 7: Calculate voltage change factor 5.5 Concluion A flicker meter ha been buil in Simulink by implementing the block of the flicker meter in IEC an IEC The repone of the flicker meter wa tete by applying a calibration ignal a well a a imulate gri repone. The reult emontrate proper operation. 0 ECN-C

111 6 CONCLUSIONS AND REMARKS 6. Concluion. Dynamic moel of offhore win farm have been evelope bae on iniviual turbine moel. The moel inclue aeroynamic apect an mechanical etail of the turbine, the electrical ytem of the turbine, the cable connection inie the farm an the connection to the ubtation on hore. Thee moel preent a powerful tool for the invetigation of win farm ynamic an win farm-gri interaction an for the evelopment of win farm controller.. The electrical ytem moelle in the win farm are () the irectly couple inuction generator (IG), () the cluter couple inuction generator (CC), () the oubly-fe inuction generator (DFIG) an (4) the permanent magnet generator with full converter (PM). The turbine moelle in the win farm are () the contant pee tall turbine (CSS) an () the variable pee pitch turbine (VSP).. A implifie gri moel ha been inclue to enable imulation of win farm-gri interaction. 4. All electrical moel, incluing the moel of cable, tranformer an the gri moel, are bae on the Park tranformation to increae computational pee in quai teaytate conition. 5. A moel of the flicker meter ha been evelope an tete. 6. All moel have been implemente in Simulink to enure full control over the etail by the uer an to have a powerfull graphical interface. Simulink make moification an extenion of the win farm moel very eay an efficient. 7. The win farm moel can be ue to evelop win farm control, invetigate ynamic interaction within the farm an between win farm an gri an alo to tuy win farm repone to win gut an gri fault. Thee application are emontrate in a number of cae tuie in Volume of thi report. 6. Remark. Dynamic moel of win farm bae on iniviual turbine are large an complicate. The number of tate variable i high an ome of the time contant are mall, leaing to a relatively long imulation time. For the incorporation of ynamic moel of (a number of) win farm in moel of national gri, the complexity of the win farm moel ha to be reuce. Aggregate win farm moel, in which all turbine are repreente by ome kin of equivalent moel are more uitable for thi purpoe. However, aggregate moel looe the wie range of applicability of the win farm bae on iniviual turbine.. Simulink appear to be le uitable for very large moel with many (thouan or more) tate variable. Computation of the teay tate become very time conuming an the imulation time for normal run increae more than proportional. The exact caue nee to be icue with Mathwork, the eveloper of Simulink.. With regar to imulation pee the choice of q0-variable prove ucceful. The current bottleneck i not the imulation pee of the electrical part any more but of the ECN-C

112 Erao II, Volume : Dynamic moel for win farm mechanical an control part of the variable pee turbine moel. Thi ubmoel ha to be increae in pee before comfortable full cale farm imulation can be mae for variable pee ytem. The variable pee turbine in the current verion i till programme a an S-function in Matlab. Converion to Simulink block will probably reuce CPU time. 4. In the current Simulink implementation the 0-component, which i only relevant uner pecific aymmetrical conition i not implemente. Since hort circuit calculation are increaingly relevant an aymmetrical hort circuit have a high probability of occurrence, it i recommene to inclue it in the next verion. 5. Now that the moel evelopment ha reache a certain level of completion, moel valiation i a high priority tak. A atabae with turbine an win farm meaurement i currently being et up in IEA Annex XXI: Win Farm Moel for Power Sytem Stuie. Thi atabae will erve a the bai for the valiation proce, execute in the Erao- project, which ha recently been tarte. For the concluion an recommenation from the cae tuie i referre to Volume of thi report. ECN-C

113 REFERENCES [] P.M. Aneron an A.A. Foua. Power Sytem Control an Stability. Iowa State Univ. Pre, Iowa, 977. [] J.C. Da. Power Sytem Analyi Short Circuit Loa Flow an Harmonic. Marcel Dekker, Inc., New York, 00. [] C.L. Fortecue. Metho of ymmetrical coorinate applie to the olution of polyphae network. Tran. of AIEE, Vol. 7, page 07 40, 98. [4] J.J. Grainger an Jr. W.J. Stevenon. Power Sytem Analyi. McGraw-Hill, New York, 994. [5] L. Harnefor an H.-P. Nee. Moel-bae current control of ac machine uing the internal moel control metho. IEEE Tran. In. Appl., Vol. 4, No., page 4, 998. [6] S.A. Herman an J.T.G. Pierik. Locatie en opwekkoten 6000 MW offhore winenergie. Technical Report ECN-CX , ECN, 00. [7] C.P.J. Janen an R.A.C.T e Groot. Aanluiting van 6000 MW offhore winvermogen op het Neerlane elektriciteitnet, Deel : Net op lan. Technical Report TDC B, Kema, 00. [8] The Mathwork. Uing Matlab/Simulink/Simpower. The Mathwork, Natick MA, 00. [9] N. Mohan, T.M. Unelan, an W.P. Robbin. Power Electronic Converter, Application an Deign. John Wiley & Son, New York, 995. [0] J. Morren, S.W.H. e Haan, P. Bauer, an J.T.G. Pierik. Comparion of complete an reuce moel of a win turbine uing oubly-fe inuction generator. In 0th European Conference on Power Electronic an Application (EPE 00), Touloue, 00. [] J. Morren, S.W.H. e Haan, an J.A. Ferreira. Moel reuction an control of electronic interface of voltage ip proof DG unit. In 004 IEEE Power Engineering Society (PES) General Meeting, Denver, 6-0 June 004. to be publihe. [] E.ON Netz. Ergänzee Netzanchluregeln für Winenergieanlagen. Technical report, E.ON Netz, 00. [] C.-H. Ong. Dynamic Simulation of Electric Machinery uing Matlab/Simulink. Prentice Hall, Upper Sale River, 998. [4] R. Otterten. On control of Back-to-Back Converter an Senorle Inuction Machine Drive. Technical Report no. 450, Chalmer Univerity, Goteborg, Sween, 00. Ph.D. thei. [5] G.C. Paap. Symmetrical component in the time omain an their application to power network calculation. IEEE Tran. Power Sytem, Vol. 5, No., page 5 58, 000. [6] R. Pena, J.C. Clare, an G.M. Aher. Doubly fe inuction generator uing back-to-back pwm converter an it application to variable-pee win-energy generation. In IEEE Proc.-Electr. Power Appl, Vol. 4, No., page ECN-C

114 Erao II, Volume : Dynamic moel for win farm [7] A. Peteron. Analyi, Moelling an Control of Doubly-Fe Inuction Generator for Win Turbine, Licentiate thei. Technical Report 464L, Chalmer Univerity, Goteborg, Sween, 00. [8] J.T.G. Pierik, M.E.C. Damen, P. Bauer, an S.W.H. Electrical an control apect of offhore win farm, Phae : Steay tate electrical eign an economic moeling, Vol. : Project reult. Technical Report ECN-CX-0-08, ECN Win Energy, 00. [9] J.T.G. Pierik, J.C. Montero Quiro, T.G. van Engelen, D. Winkelaar, an R. Sancho Chave. Cota Rica gri fee-in tuy: Effect of win power on gri frequency. Technical Report ECN-CX-0-080, ECN, 00. [0] I. Schiemenz an M. Stiebler. Control of a permanent magnet ynchronou generator ue in a variable pee win energy ytem. In IEEE Electric Machine an Drive Conference, IEMDC 00, page , 00. [] S. Skogeta an I. Potlethwaite. Multivariable feeback control. Wiley, Chicheter, 996. [] J.G. Slootweg. Win power moelling an impact on power ytem ynamic. Technical Report ISBN , T.U. Delft, 00. PhD Thei. [] J.G. Slootweg, H. Poliner, an W.L. Kling. Dynamic moelling of a win turbine with oubly fe inuction generator. In 00 IEEE Power Engineering Society Summer meeting, page , 00. [4] TC88. IEC6400-, E. : Meaurement an aement of power quality of gri connecte win turbine. Technical Report IEC6400-, IEC-TC88, Draft. [5] T.G. van Engelen, E.L. van er Hooft, an P. Schaak. Ontwerpgereechappen voor e regeling van winurbine. Technical report. [6] T.G van Engelen an E.J. Wiggelinkhuizen. ECN eign tool for control evelopment; revie point of eparture; tatu report. Technical report, ECN, 00. [7] P.D. Zioga, E.P. Wiechmann, an V.R. Stefanoviæ. A computer aie analyi an eign approach for tatic voltage ource inverter. IEEE Tran. on In. Appl, Vol., No. 5, page 4 4, ECN-C

115 A SUMMARY OF ERAO I PROJECT The aim of the ERAO project "Electrical an Control Apect of Offhore Win Farm" Phae "Steay tate electrical eign, power performance an economic moeling" ha been to invetigate the electrical concept for the interconnection of offhore win turbine an the tranportation of the electric power to the high voltage gri. The project tarte with an inventory of architecture to collect the electric power from iniviual win turbine in an offhore win farm an tranmit thi power to an on-hore high-voltage gri noe. The inventory inclue contant pee option, iniviual variable pee, cluter variable pee an park variable pee option uing AC a well a mixe AC-DC-AC moe. Steay tate electrical moel have been evelope for all electrical component in the architecture to calculate loa flow an electrical loe. Bae on thee moel, the EeFarm computer program (Electrical an Economic win FARm Moel) ha been evelope. The EeFarm program ha been ue in a cae tuy to compare electrical architecture. The electrical parameter voltage, current, active an reactive power have been calculate in all ytem noe. Bae on the aeroynamic performance of the choen win turbine, the electrical loe have been calculate over the entire range of operation of the win farm. From buget price obtaine from manufacturer, the invetment cot of the electrical ytem an the contribution to the cot per kwh have been etermine. In the cae tuy two win farm ize (00 an 500 MW) an two itance to hore (0 an 60 km) have been invetigate. In the contant pee concept C an C the win turbine in the farm are connecte by AC an the cable to hore i AC a well. Thee ytem have the mallet number of main component, only tranformer an cable. The cae tuy ha hown that the ytem C (tring layout) an C (tar layout), operating on AC only, have the lowet contribution of the electrical ytem to the price per kwh for both farm ize an itance to hore. For the 00 an 500 MW farm at 0 km an the 500 MW farm at 60 km, the C ytem alo give the lowet electrical loe. In thoe cae where a DC connection i require (longer itance to hore or avoiance of gri tability problem), the PV configuration with an HVDC Light or Plu connection i the bet alternative. For the invetigate itance an park ize thi currently increae the invetment cot an contribution of the electrical ytem to the price per kwh by a factor or more, but thi may reuce at longer itance to hore an by price reuction of the converter an more experience i gaine with thi new technology. The electrical loe of concept C an PV are of the ame orer of magnitue. The option with iniviual turbine pee control, IV an IV, although more expenive than the contant pee ytem C an C, houl not be icare bae on the ERAO cae tuy only. The reaon i that they may be preferre by a large number of turbine manufacturer (ue to their potential in loa reuction an increae controllability) an have a potentially better aeroynamic performance, which wa not taken into account in the ERAO cae tuy. Concluion: In the analye of the electrical ytem option for future evelopment three architecture houl be compare: contant pee (C-C), iniviual variable pee (IV-IV) an park variable pee (PV-PV). An important criterion houl be the ynamic performance of the win farm, internally a well a with repect to the gri. Thee are the ubject of the phae an of the ERAO project. ECN-C

116 B CONTRIBUTIONS TO INTERNATIONAL CONFERENCES B. Noric Win Power Conference 004 B. 4th International Workhop on Large Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm B. EPE 00 Touloue 6 ECN-C

117 B CONTRIBUTIONS TO INTERNATIONAL CONFERENCES. ECN-C

118 Erao II, Volume : Dynamic moel for win farm Date: June 004 Report No.: ECN-C Title Erao II, Volume : Dynamic moel for win farm Author J.T.G. Pierik, J. Morren, E.J. Wiggelinkhuizen, S.H.W. e Haan, T.G. van Engelen, J. Bozelie Principal() Novem, Minitry of Economic Affair ECN project number 7.46 Principal orer number Programme DEN Abtract In The Netherlan offhore win power i on the brink of implementation. Specific plan exit for two offhore win farm of about 00 MW, locate an 5 km from the coat of the province of North Hollan. The effect of the incorporation of 6000 MW offhore win power in the Dutch high voltage gri are currently invetigate. Only the teay tate behaviour ha been coniere, thu far reulting in uggetion for gri reinforcement. Thi invetigation nee to be complemente by a tuy on the ynamic interaction of win power an gri. Tool for thi invetigation, viz. ynamic moel of win farm incluing all relevant electrical component, have been evelope in the Erao- project. Thi report ecribe the win farm ynamic moel (Volume ) an emontrate their ue in a number of cae tuie (Volume ). Special concern exit about win farm behaviour uring extreme win pee change an abnormal gri conition (voltage an frequency ip); thee may caue complete win farm to hut own intantaneouly. Aiting gri voltage an frequency control i alo an iue. In the cae tuie the moel have been ue to compare four type of win farm: () contant pee tall with irectly couple inuction generator an () with cluter control, () variable pee with oubly fe inuction generator an (4) with permanent magnet generator. The cae tuie compare normal ynamic behaviour, flicker contribution an repone to gri fault. Win farm control ha been evelope to upport the gri frequency an voltage. Keywor win farm moel, win farm ynamic, electrical ytem, fault rie through, gri upport Authorization Name Signature Date Checke E.J. Wiggelinkhuizen Approve Authorie L.W.M.M. Raemaker H.J.M. Beurken 8 ECN-C

119 NORDIC WIND POWER CONFERENCE, - MARCH 004, CHALMERS UNIVERSITY OF TECHNOLOGY Dynamic moel of win farm for gri-integration tuie Cae tuy reult Jan Pierik, Johan Morren, Sjoer e Haan, Tim van Engelen, Ewin Wiggelinkhuizen, Jan Bozelie Energy reearch Centre of the Netherlan (ECN) Delft Univerity of Technology (TUD) pierik@ecn.nl Abtract In The Netherlan offhore win power i on the brink of implementation. Specific plan exit for two offhore win farm of about 00 MW, locate an 5 km from the coat of the province of North Hollan. The effect of the incorporation of 6000 MW offhore win power in the Dutch high voltage gri are currently invetigate. Until now only the teay tate behaviour i coniere, reulting in uggetion for gri reinforcement. Thi invetigation will be complemente by a tuy on the ynamic interaction of win power an gri. Tool for thi invetigation, viz. ynamic moel of win farm incluing all relevant electrical component, have recently been evelope. Thi paper give an overview of win farm ynamic moel an concentrate on their ue in a cae tuy. Special concern exit about win farm behaviour uring extreme win pee change an abnormal gri conition (voltage an frequency ip); thee may caue complete win farm to hut own intantaneouly. Aiting gri voltage an frequency control i alo an iue. In a cae tuy the moel will be ue to calculate the flicker contribution of a win farm, imulate repone to gri fault an evelop win farm control. Inex Term win farm moel, win farm ynamic, electrical ytem, fault rie through. I. INTRODUCTION Offhore win farm have to be large to be economical an with the increae of the contribution of win energy to the electric power prouction, the interaction between the win farm an the gri will be an important apect in the planning of the farm []. It i eential to enure that the gri i capable of taying within the operational limit of frequency an voltage for all foreeen combination of win power prouction an conumer loa [8]. A econ apect i to enure appropriate tranient an mall ignal tability of the gri [0]. Aequate gri control play an important role but the electrical control an protection of large win farm i alo of increaing importance. Large win farm are a ource of fluctuating power an ometime of reactive power a well. Seconly, the repone of win farm to voltage an frequency ip i a caue for worry: the farm will hut own immeiately. The ip itelf i a ign of a eriou gri control problem, an the problem may become wore if win power hut own on a large cale. For conventional power tation the require behaviour uring a gri ip i to tay in operation an upply (reactive) power. Thi behaviour i precribe in gri coe. It i likely that large offhore win farm have to follow thee rule alo. In Germany, operator E.On Netz alreay require pecific behaviour of win farm uring ip [5]. Depening on the type of win turbine, viz. contant or variable pee, an the eign of the turbine an win farm control, a win farm will have more or le problem to comply with thee rule. In orer to invetigate the ynamic interaction of win farm an the electrical gri, ynamic moel of win farm are neee. Dynamic moel of win turbine an win farm will be of great help in the eign an evaluation of the behaviour of win power uring normal gri operation a well a uring gri fault. Dynamic moel of win farm, incluing the relevant electrical component an ection of the gri, are not reaily available however. The Erao- project ha been tarte to evelop thee moel an to emontrate their ue by eigning controller to cope with gri coe requirement. The ynamic moel of turbine an win farm evelope in the Erao- project inclue the following component: Electrical: inuction generator; oubly-fe inuction generator; permanent magnet generator; voltage ource converter; tranformer; cable; Mechanical an aeroynamic: turbine rotor; mechanical rive train; tower; rotor effective win; Control: converter controller; win turbine pitch controller; overall win farm controller. To repreent the interaction between the win farm an the gri, a implifie gri moel i ue, bae on the following component moel:

120 NORDIC WIND POWER CONFERENCE, - MARCH 004, CHALMERS UNIVERSITY OF TECHNOLOGY Gri moel component: ynchronou generator; frequency an voltage controller. conumer loa; tranformer; cable. An important apect of ynamic moel for power ytem tuie i computational pee. Electrical tranient have very mall time contant, reulting in mall time tep an long computation time. In Erao- pecial attention ha been pai to computational pee. An important increae in pee can be realie by the ue of the q0 tranformation (alo known a Park tranformation). Thi tranformation i mainly ue in electrical machine theory, in Erao- moel it i applie to all electrical component. Thi paper can only give an overview of the moel. For a etaile ecription i refere to [4], [], [] an [9]. The main characteritic of the electrical moel are: all electrical component are moelle in q0 coorinate; AC-DC-AC converter are moelle by controlle voltage ource; the moel are implemente in Simulink. The electrical component moel have only been valiate partially, viz. by comparing abc-moel with witching converter to q0-moel with controlle voltage ource converter [], []. For extenive teting an valiation the Erao- project ha been tarte, which take part in the IEA Annex XXI (Dynamic moel of Win Farm for Power Sytem Stuie). Thi Annex i a joint effort of eight countrie to et up a ata bae of win farm meaurement an to ue thee meaurement for valiation of ynamic moel. The participating countrie are Norway (Coorinator), Sween, Finlan, Denmark, USA, Englan, Portugal an the Netherlan. Oberving countrie are Canaa an Irelan. AC-DC-AC converter. The converter are connecte by 4 kv ubmarine cable to a 4/50 kv tranformer tation on hore. Table : Erao- cae tuy imulation CSS VSP-DFIG VSP-PM CC-CSS 4 Normal operation X X X X Flicker X X X X Frequency ip X X X X Voltage ip X X X X Frequency upport - X X X Voltage upport - X X X Contant Spee Stall Variable Spee Pitch - Doubly Fe Inuction Generator Variable Spee Pitch - Permanent Magnet generator 4 Cluter Controlle - Contant Spee Stall For power limitation of a cluter controlle win turbine tall or pitch control can be choen. Both option are technically feaible, in thi cae tuy tall control i choen. The turbine rotational pee i ictate by the frequency of the turbine ie AC-DC converter. The effect of rotational pee variation on the aeroynamic power i illutrate in figure by plotting the power-win pee curve of the tall turbine at frequencie of 0-60 Hz ( ra/ low pee haft rotational pee). At 60 Hz the win pee at which the turbine rotor tall excee the rate win pee an the rate power of the turbine i exceee. Therefore, 50 Hz will be the upper pee limit for the cluter controlle tall turbine. ω ω 4 kv 4 kv ω 4 kv II. CASE STUDY ω4 4 kv The moel evelope in the Erao- project are ue in a cae tuy bae on the lay-out of the Near Shore Win Farm (NSWF): 6 variable pee win tubine of.75 MW, connecte in three tring of turbine. The NSWF will be equipe with Doubly Fe Inuction Generator (DFIG). In the cae tuy thi farm i compare to hypothetical win farm of the ame lay-out with Cluter Control (multiple inuction generator on a ingle AC-DC-AC converter), Permanent Magnet Generator an irectly connecte inuction generator. For each of the four type, normal operation, flicker, repone to frequency an voltage ip, an (if technically feaible) frequency an voltage upport are imulate (Table ). In thi paper, the ome of the reult for the Cluter Control option will be given. Figure how the layout of one tring of the Near Shore Win Farm (NSWF) in cluter controlle moe. The tring i ivie into four cluter of three win turbine on an Figure : Electrical layout of four cluter of turbine 4 kv 50 kv At low win pee, below rate rotational pee can increae aeroynamic efficiency compare to contant pee operation: the 0, 0 an 40 Hz curve are above the 50 Hz power curve. At high win pee a low rotational pee reuce the aeroynamic efficiency compare to contant pee operation. Pitch control can compenate thi effect. Spee control of a cluter will be bae on meaure win pee(). In the imulation, the win pee at turbine ha been choen, but a ifferent choice may be more efficient. Spee control aim at contant lamba operation for

121 NORDIC WIND POWER CONFERENCE, - MARCH 004, CHALMERS UNIVERSITY OF TECHNOLOGY thi win pee, limite by the 50 Hz barrier. Since the intantaneou win pee at the iniviual turbine in a cluter will iffer, there will alway be a mimatch, leaing to lower overall aeroynamic efficiency compare to iniviual variable pee. Thi reuction in energy yiel ha been etimate at.4% [6]. Maybe thi i compenate by a reuction in cot of the electrical ytem. Paero (MW) Hz 0 Hz 40 Hz 60 Hz 50 Hz Vw (m/) A. Normal Operation The Simulink moel which i ue in the cae tuy conit of the moel of a cluter of turbine incluing tranformer connecte to a ingle AC-DC-AC converter, the 4 kv cable, the 4kV-50 kv tranformer an a implifie gri moel (a large ynchronou generator with frequency an voltage control, tranformer, cable an two conumer loa). Figure 4 emontrate normal operation of the cluter. A gut from 4 to 5 m/ pae the turbine with a mall elay: vw, vw an vw. Below rate win pee, the turbine pee controller maintain a tip pee ratio of 5 with repect to vw. Rotor pee n, n an n an tator voltage v, v an v follow the changing win pee vw, reulting in imilar aeroynamic power an lip variation Pa, Pa, Pa an,,. vw, vw, vw (m/) CC turb,, time () n, n, n (ra/) CC normal oper time () Pa, Pa, Pa (MW) 0 plot CC b.m time () P (MW) Tel (knm) Figure : Steay tate power curve of a tall controlle turbine When the frequency in the tator of the inuction machine i reuce, the amplitue of the tator voltage i reuce proportional to thi frequency. The ecreae in frequency woul otherwie lea to above rate current an the activation of the thermal protection. Figure illutrate the combine effect of reuce frequency an voltage: the power-lip an torque-lip curve are imilar in hape at 50Hz-960V an 40Hz-768V, only the pull-out power i reuce. The reactive power conumption i reuce a well. = 50 Hz, 960 V, = 40 Hz, 768 V Slip ( ) Slip ( ) i (ka) amtat iq (ka) Q (MVAr) Slip ( ) Figure : Steay tate power P, current vw, I, Iq, torque Tel an reactive power Q for an inuction machine operating at 50Hz-960V an 40Hz-768V v, v, v (V) time () i, i, i (A) time (),, (%) time () Figure 4: Cluter control, normal operation, turbine, an Figure 5 give cluter power P an cluter reactive power Q, an q current to the gri ig, iqg, an q gri voltage at the converter vg, vqg, DC voltage uc an cluter frequency f for the conition in figure 4. The gri ie converter reactive power etpoint i zero. The cluter frequency i limite to 50 Hz. P cluter (WM) vg, vqg (kv) CC converter time () time () Q cluter (kva) uc (kv) CC normal oper time () time () ig, iqg (A) plot CC b.m time () f cluter (Hz) time () Figure 5: Cluter control, normal operation, converter value

122 NORDIC WIND POWER CONFERENCE, - MARCH 004, CHALMERS UNIVERSITY OF TECHNOLOGY 4 Figure 6 give the repone of the gri to the change in win power. The ynchronou machine power Pm i reuce, the total conumer loa Pcon remain contant. The frequency eviation freq are mall an there i not much voltage controller action Vexc either. freq (Hz) P SM (MW) Gri time () time () P con (MW) V exc (V) plot CSSout time () time () Figure 6: Cluter control, normal operation, gri value B. Flicker The current an voltage calculate for the cluter in the previou ection have been ue to calculate intantaneou flicker value. The hort circuit power for the flicker calculation i 50 time the rate power of the cluter an a fictitiou gri angle of 0 o ha been choen. The ample frequency in the calculation wa 400 Hz. The intantaneou flicker value have been binne uring interval of 6. The binne intantaneou flicker value for the cluter are plotte in figure CC, normal operation, one cluter f gri (Hz) Pm (MW) C. Frequency Dip A gri frequency ip i imulate by a change of the frequency etpoint of the ynchronou machine in the gri moel. At t=0 the etpoint i ecreae to 45 Hz an at 0 it i change to the normal value of 50 Hz (figure 8). Thi ip i ignificantly larger than any expecte ip in a large gri, in magnitue a well a rate, ince gri frequency change take time an corrective action will be taken before thi level i reache. The 5 Hz ip wa choen to emontate the cluter behaviour more clearly CC gri time [] time [] Pg, Qg (MW, MVA) Ploa, Ploa (MW) 4 CC fip time [] time [] u gri (kv) Uf (V) plot CC.m time [] time [] Figure 8: Repone of cluter controlle turbine to a 0% frequency ip: Gri variable The total conumer loa Ploa plu Ploa i 7 MW, which i upplie partly by the ynchronou machine an partly by the win turbine cluter (figure 8). The frequency ip caue a voltage ip u gri, which i counteracte by the ynchronou machine voltage controller Uf. The initial voltage ip i of the ame magnitue a the frequency ip: about 0%. Nr. of ample per bin Pconv (MW) CC converter Qconv (MVA) CC fip icg, iqcg (A) plot CC.m time [] time [] time [] Pt ( ) Figure 7: Binne intantaneou flicker value for three cluter controlle turbine The flicker level for a variable pee turbine i expecte to be lower than for a contant pee turbine, if the turbine control i well tune. Cluter control i a pecial cae of variable pee operation, turbine in a cluter will pee up an own an win power variation are not immeiately tranfere to the gri. The 99 percentile level in figure 7, ometime ue to claify flicker, i below the level calculate for the contant pee tall win farm uner the ame external conition. vcg, vqcg (kv) time [] uc (kv) time [] fpark (Hz) time [] Figure 9: Repone of cluter controlle turbine to a 0% frequency ip: converter variable The gri ie converter voltage vcg an vqcg follow the gri voltage ip (figure 9). The gri ie converter - component of the current icg remain almot contant, the

123 NORDIC WIND POWER CONFERENCE, - MARCH 004, CHALMERS UNIVERSITY OF TECHNOLOGY 5 v, v, v (V) q-current iqcg become more negative. The gri ie converter power Pconv an reactive power Qconv are not affecte by the frequency ip an correponing voltage ip. The DC voltage uc how no effect either. vw, vw, vw (m/) 0 9 CC turb,, time [] time [] n, n, n (rpm) i, i, i (A) CC fip time [] time [] Pa, Pa, Pa (MW),, (%) plot CC.m time [] time [] Figure 0: Repone of cluter controlle turbine to a 0% frequency ip: turbine variable The converter effectively ecouple the turbine an the gri. In pite of the frequency ip, the turbine operate a if no gri ip occur (figure 0): aeroynamic power Pa, Pa an Pa, tator current i, i, i an voltage v, v, v an turbine pee n, n, n follow the change in rotor effective win pee. D. Voltage Dip A 0% voltage ip i applie to the gri ie voltage of the cluter converter uring 0 econ (vconv, figure ). The imulation oe not inclue the gri moel in orer to realie a well efine voltage ip without ocillation in either voltage or frequency. Only the parameter of the firt turbine are hown; ince all turbine have imilar win pee, imilar behaviour of the other turbine i expecte. The rotor effective win pee Vw i about 5 m/, the turbine then operate at rate power Pa (ee figure ). The electrical variable in the next figure are per unit value. 0 by the voltage ip, for a tall controlle turbine it only epen on win pee an rotor pee. The gri ie converter power Pconv will ecreae ue to the voltage ip (ee figure ). The power ifference between turbine ie converter an gri ie converter will lea to an increae of the gri ie converter current iconv to keep the DC-link voltage contant. The current increae i limite by the current rating of the converter, an the DC-link voltage uc will alo increae. To overcome thi problem, a reitance i connecte parallel to the c-link capacitor. The reitance i connecte via a chopper. When the DC-link voltage reache a threhol, the chopper open an the energy urplu i iipate in the reitance. The uty-ratio of the chopper i etermine by the ifference between the actual DC-link voltage an the preferre DC-link voltage. The reult how that a 0% voltage ip i no problem for the cluter controller. P [pu] Te [pu] time [] time [] Q [pu] time [] time [] Figure : Repone of cluter controlle turbine to a 0% - 0 voltage ip: active power, reactive power, electric torque an lip vconv [pu] lip [ ] iconv [pu] Vw [m/] Pa [pu] time [] time [] time [] time [] Figure : Repone of cluter controlle turbine to a 0% - 0 voltage ip: rotor effective win pee an aeroynamic power At 5 m/ the turbine i kept at rate pee (equivalent to 50 Hz) by the pee controller: the lip lip i unchange (ee figure ). The turbine aeroynamic power i not affecte Pconv [pu] time [] uc [pu] time [] Figure : Repone of cluter controlle turbine to a 0% - 0 voltage ip: AC voltage, current an active power of gri-ie converter, DC-link voltage

124 NORDIC WIND POWER CONFERENCE, - MARCH 004, CHALMERS UNIVERSITY OF TECHNOLOGY 6 III. CONCLUSIONS Dynamic win farm moel bae on iniviual turbine moel have been evelope in Simulink. Detaile moel of the turbine mechanical an electrical ytem an of the gri are ue. The moel inclue contant pee tall an variable pee pitch turbine. Four type of turbine electrical ytem have been moelle, bae on oubly fe inuction generator, permanent magnet generator, irectly couple an cluter controlle inuction generator. Thee moel preent a powerful tool for the invetigation of win farm ynamic an win farm-gri interaction an for the evelopment of win farm control. The moel have been ue to evelop electrical ytem control an to invetigate ytem repone to gri fault. In thi paper, reult for the cluter controlle win farm have been preente. The reult how that gri fault o not preent a problem for the cluter controlle turbine. With regar to imulation pee the choice of q0 variable prove ucceful. The current bottleneck i not the imulation pee of the electrical part any more but of the mechanical an control part of the variable pee turbine moel. Thi ubmoel ha to be increae in pee before comfortable full cale farm imulation can be mae for variable pee ytem. Moel valiation now ha a high priority. A atabae with turbine an win farm meaurement i currently being et up in IEA Annex XXI: Win Farm Moel for Power Sytem Stuie. Thi atabae will erve a the bai for the valiation proce. ACKNOWLEDGMENT Erao- i a continuation of the Erao- project, in which a teay tate (loa flow) an economic moel for offhore win farm ha been evelope [7]. The Erao project are fune by the Dutch Agency for Energy an Environment (NOVEM) an the Minitry of Economic Affair of the Netherlan. REFERENCES [4] J. Morren, J.T.G. Pierik, S.W.H. e Haan, an J. Bozelie. Fat ynamic moel of offhore win farm for power ytem tuie. In 4th International workhop on large-cale integration of win power an tranmiion network for offhore win farm, Billun, 0- October 00. [5] E.ON Netz. Ergänzee Netzanchluregeln für Winenergieanlagen. Technical report, E.ON Netz, 00. [6] I. Nuimovich, S.W.H. e Haan, an J.G. Slootweg. Comparion of the energy yiel of win turbine with iniviual ac/c/ac converter an win turbine connecte to a common ac/c/ac converter. In EPE-PEMC, Dubrovnik, 00. [7] J.T.G. Pierik, M.E.C. Damen, P. Bauer, an S.W.H. Damen. Electrical an control apect of offhore win farm, phae : Steay tate electrical eign an economic moeling, Vol. : Project reult. Technical Report ECN-CX-0-08, ECN Win Energy, 00. [8] J.T.G. Pierik, J.C. Montero Quiro, T.G. van Engelen, D. Winkelaar, an R. Sancho Chave. Cota Rica gri fee-in tuy: Effect of win power on gri frequency. Technical Report ECN-CX-0-080, ECN, 00. [9] J.T.G. Pierik, J. Morren, E.J. Wiggelinkhuizen, S.H.W. e Haan, T.G. van Engelen, an J. Bozelie. Electrical an control apect of offhore win turbine II (Erao-). Volume : Dynamic moel of win farm. Technical Report ECN-CX , ECN, 004. to be publihe. [0] H. Slootweg. Win power moelling an impact on power ytem ynamic. Technical Report ISBN , T.U. Delft, 00. [] E.L van er Hooft, P. Schaak, an T.G. van Engelen. Win turbine control algorithm. Technical Report ECN-C-0-, ECN, 00. [] T.G. van Engelen, E.L. van er Hooft, an P. Schaak. Ontwerpgereechappen voor e regeling van winurbine. Technical report. [] C.P.J. Janen an R.A.C.T e Groot. Aanluiting van 6000 MW offhore winvermogen op het Neerlane elektriciteitnet, Deel : Net op lan. Technical Report TDC B, Kema, 00. [] J. Morren, S.W.H. e Haan, P. Bauer, an J.T.G. Pierik. Comparion of complete an reuce moel of a win turbine uing oubly-fe inuction generator. In 0th European Conference on Power Electronic an Application (EPE 00), Touloue, 00. [] J. Morren, S.W.H. e Haan, an J.A. Ferreira. Moel reuction an control of electronic interface of voltage ip proof DG unit. In 004 IEEE Power Engineering Society (PES) General Meeting, Denver, 6-0 June 004. to be publihe.

125 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm Fat Dynamic Moel of Offhore Win Farm for Power Sytem Stuie J. Morren, J.T.G. Pierik, S.W.H. e Haan an J. Bozelie Abtract--In thi contribution ynamic win farm moel uitable for fat imulation of power ytem tuie are preente. While eriving the moel, pecial attention ha been pai to increaing the computational pee of the imulation program. An important increae in pee i realie by the ue of the q0 tranformation (Park tranformation) not only for the generator but alo for all other electrical component. The Park tranformation i common ue in electrical machine moel, but not in the moelling of other electrical component. A ecription i given of the way in which moel of baic electrical component can be tranforme from the abc reference frame to the q0 reference frame. The reult are emontrate in a cae tuy of a win farm coniting of a tring of win turbine with oubly-fe inuction generator. tationary rotating reference frame. A thi tationary frame i choen to rotate with the gri frequency, all voltage an current in the q0 reference frame are contant in teay tate ituation. Therefore, moelling in the q0 reference frame i expecte to increae the imulation pee ignificantly, a a variable tep-ize imulation program can apply a large time tep uring quai teay-tate phenomena. An example i hown in Fig. where the inruh current of a three-phae inuction machine are hown in the abc an q0 reference ytem repectively. The time tep that can be applie without introucing ignificant error will be much large in the cae of the q0 reference ytem. Inex Term Dynamic moelling, Park Tranformation, Win Energy A I. INTRODUCTION tenency to increae the amount of electricity generate from win can be oberve []. A the penetration of win turbine in electrical power ytem will increae, they may begin to influence overall power ytem operation []. The behaviour of win turbine with repect to their interaction with the gri i therefore tuie at ifferent place []-[5]. In orer to facilitate the invetigation of the impact of a win farm on the ynamic of the power ytem, an aequate moel of the win turbine i require. Although peronal computer become fater an fater, computational pee i till one of the limiting factor in (ynamic) imulation of power ytem. One of the problem i the complexity of the moel that limit the computational pee. When reuce moel are ue imulation of complex ytem like win farm can be one much fater, but the reult may be le accurate [6]. The Park tranformation (ome-time calle Blonel-Park tranformation) i well-known from it ue in electrical machinery. The electrical ignal are tranforme to a Thi reearch i partially fune by Novem within the Program Renewable Energy in The Netherlan 00, an by Senter within the Program IOP- EMVT. J. Morren an S. W. H. e Haan are with the Electrical Power Proceing unit of the Delft Univerity of Technology. Mekelweg 4, 68CD Delft, The Netherlan. J.Morren@it.tuelft.nl J. T. G. Pierik i with Energy reearch Centre of the Netherlan, ection Win Energy, P.O. Box, 755 ZG Petten, The Netherlan J. Bozelie wa with NEG-Micon NL. (a) (b) Fig.. Inruh current of inuction machine in the abc (a) an q0 (b) reference ytem In a reearch project on the gri integration of large win farm, ynamic moel have been erive for: electrical generator (inuction generator, oubly-fe inuction generator, permanent magnet generator), power electronic converter, tranformer, cable, turbine rotor, mechanical rive train an rotor effective win. All moel of electrical component are in the q0 reference frame. In thi contribution a ecription will be given of the way in which moel of ifferent electrical component in the q0 reference frame can be obtaine. The moel erivation will be hown for two baic component: a three-phae RL line egment an the three-phae hunt capacitance. The imulation reult of ifferent moel are compare, in orer to how the valiity of the q0-moel. Afterwar win moel an the turbine moel are given. Thee moel are ue in a cae tuy that i performe to emontrate the effectivene of the propoe moelling metho. II. PARK TRANSFORMATION In the tuy of power ytem, mathematical tranformation are often ue to ecouple variable, to facilitate the olution of ifficult equation with time-varying coefficient, or to refer all variable to a common reference

126 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm frame [7]. Probably the mot well-known, i the metho of ymmetrical component, evelope by Fortecue. Thi tranformation i motly ue in it time-inepenent form an applie to phaor, when it i ue in electrical power ytem tuie [8]. Another commonly-ue tranformation i the Park tranformation, which i well-known from the moelling of electrical machine. The Park tranformation i intantaneou an can be applie to arbitrary three-phae timeepenent ignal. For θ =ω t+ϕ, with ω the angular velocity of the ignal that houl be tranforme, t the time an ϕ the initial angle, the Park tranformation i given by: [ x ] = [ T ( θ )] [ x ] () q0 q0 abc with: x [ ] q0 = x x q 0 x an [ ] xa x abc = xb () x c an with the q0 tranformation matrix T q0 efine a: [ T ] q0 = coθ inθ an it invere given by: [ ] π co θ π in θ π co θ + π in θ + coθ inθ π π T q0 = co θ in θ (4) π π co θ + θ + in The poitive q-axi i efine a leaing the poitive -axi by π/, a can be een from Fig.. () Some aitional propertie of the Park tranformation can be erive. A the tranformation i orthogonal, it hol that: [ ( )] T ( θ ) T [ ] = [ T ( θ )] [ T ( θ )] [ I] T q0 θ q0 q0 q0 = (5) The tranformation of () an (4) are unitary, a i hown in (5) an conerve power a i hown in (6). Note that by replacing the factor / by a factor / in () an (4) the tranformation will be amplitue-invariant, implying that the length of the current an voltage vector in both abc an q0 reference frame are the ame. Thi amplitue-invariant tranformation i motly ue in moelling of electrical machine [8]. The voltage an current in the q0 reference frame are contant in teay-tate ituation. Be aware that alo nonfunamental harmonic are correctly tranforme a x a, x b an x c are time ignal, incluing all harmonic. In teay tate a non-funamental frequency component with frequency ω h will appear a a inuoial ignal with frequency (ω h -ω p ) in the q0 omain. The highet frequency that can be repreente accurately in the qo frame epen on the time tep that i ue. With (5) it can be hown that the Park tranformation conerve power [9]: p T ( t) = [ v abc ] [ i abc ] = T ( θ ) = = = [ ] ( ) T [ q0 ] [ v q0 ] [ Tq0 θ ] [ i q0 ] T T [ v q0 ] [ Tq0 ( θ )] ] [ Tq0 ( θ )] [ i q0 ] T [ v q0 ] [ Tq0 ( θ )] [ Tq0 ( θ )] [ i q0 ] T [ v ] [ i ] q0 q0 The Park tranformation i often ue in control loop, a it offer the poibility of ecouple control between active an reactive power. Be aware however that active an reactive power cannot irectly be relate to the an the q axi component. Thee component are jut a repreentation. The intantaneou active an reactive power can be obtaine irectly from the voltage an current in the q0 reference ytem [0]: p = v i q = v i q + v i q q v i q (6) (7) III. MODEL DERIVATION Fig.. Relationhip between abc an q quantitie A. Introuction In thi ection the q0 moel of baic component (capacitance, inuctance, reitance) are obtaine. With the moel of thee baic component all further moel, uch a tranformer, machine an cable, can be obtaine. The erivation of the baic moel tart by efining the voltage rop of the a-phae. The a-phae equation i then tranforme to a q0 equation with (). The b an c phae equation are written a a function of the a-phae an the zero-equence

127 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm component, in orer to eliminate them. After ome mathematical manipulation, the moel in the, q an 0 phae can be obtaine. Firt the q0 equation for a threephae erie RL line with a groun return will be given an afterwar the q0 equation of hunt capacitance will be erive. B. Serie RL In thi ection the q0 equation for a three-phae erie RL line with groun return, hown in Fig., will be preente. The equation for the line can be obtaine by coniering the reitive an inuctive rop of the repective phae equation. The en en voltage with repect to local groun for line a i given by: ia ib i i c g v a = Raia + La + Lab + Lac + Lag + va + vg (8) With v g =v g -v g. Uing the relation i g =-(i a +i b +i c ), the voltage rop acro the three phae of the line can be expree in matrix form a: [ v ] [ v ] = [ R][ i ] + [ L][ i ],abc,abc abc abc (9) Fig.. Three-phae RL line with groun return For a uniformly tranpoe line, R a =R b =R c, L ab =L bc =L ca, an L ag =L bg =L cg. Letting L =L a +L g -L ag, L m =L ab +L g -L ag =L - L a +L ab, R =R a +R g, an R m =R g, the reitance an inuctance matrice are given by: R R [ R ] = R R R an [ L] m m R R m m Rm m R L = L L m m L L L m m Lm L m L The equation of the voltage rop acro the groun path i: v v L = R cg g v g = g g + ic ia ( i + i + i ) + ( L L ) + ( L L ) a b ic ( Lg Lcg ) = R i c g g L g g ig L ag ag ia L g bg bg ib ib (0) The q0 equation for the uniformly tranpoe line can be obtaine by coniering the reitive an inuctive rop of the a-phae equation. The reitive rop in the a-phae i given by: ( i i ) R aia + Rm b + c () Subtituting i o =(i a +i b +i c )/ to eliminate i b an i c, we obtain: ( R Rm ) ia + Rmi0 () Expreing i a in term of the q0 current, the reitive rop in the a-phae become: ( R Rm )( i co iq inθ + i0 ) + Rmi0 θ () Similarly, for the inuctive rop in the a-phae, we have: ia ( ib + ic ) L + Lm (4) Eliminating i b an i c : ia i0 m + Lm (5) ( L L ) Uing the invere q0 tranform of (4) to expre i a in term of the q0 current, the inuctive rop in the a-phae become: i0 m θ q 0 + Lm (6) Knowing that for x=x(t): x x in x = co x an co = in x (7) Eq. (6) can be written a: θ i θ ( L Lm ) i inθ + coθ iq coθ (8) iq i 0 i0 inθ + + Lm The q0-tranform can alo be applie to the voltage ifference v a =v a -v a, reulting in: v coθ vq inθ + v 0 (9) Combining (), (8), an (9), Eq. (8) can be written a: v coθ vq inθ + v0 = ( R Rm )( i coθ iq inθ + i0 ) + Rmi0 + θ i θ ( L Lm ) i inθ + coθ iq coθ (0) iq i 0 i0 inθ + + Lm ( L L ) ( i co i inθ + i ) By equating the coefficient of the coθ, inθ, an contant term, we obtain: v v q v = = i i ( R R ) i + ( L L ) ( L L ) i q ( R R ) i + ( L L ) + ( L L ) i m m q i 0 ( R + Rm ) i0 + ( L + Lm ) 0 = m m m m q θ θ () When the mutual inuctance between the phae an between phae to groun are zero, that i L ab =L bc =L ca =0 an L ag =L bg =L cg =0, then L =L a +L g, an L m =L ab +L g. With ω =θ / the final reult i:

128 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm 4 v v q v i = Rai + La ωlaiq iq = Raiq + La + ωlai i0 ( Ra + Rg ) i0 + ( La + Lg ) 0 = The reulting equivalent q0 circuit are hown in Fig. 4. () C. Shunt C In the ame way a i one for the erie line inuctance an reitance, equation for hunt capacitance can be obtaine. A line with hunt capacitance i hown in Fig. 5. Beie the phae to neutral capacitance of the phae, alo the mutual capacitance between the phae have been hown. Exchanging the b an c phae voltage with v 0 =(v an +v bn +v cn )/ give: van v0 ia = ( C + Cm ) C m (5) Applying the q0 tranformation to the current an the voltage of the a-phae we obtain: i coθ i inθ + i = q ( C + C ) ( v coθ v inθ + v ) 0 (6) v0 m q 0 Cm In analogy to (6) - (), by equating the coefficient of the coθ, inθ, an contant term, the following et of equation i obtaine for the q0 current: i i i q = = v v ( C + C ) ( C + C ) q ( C + C ) + ( C + C ) m m v ( C Cm ) 0 = 0 m m θ vq θ v (7) When the mutual capacitance between the phae are zero, that i C ab =C bc =C ca = 0, then C m = 0 an C =C an. With ω=θ / the final reult i: i i i q v = C ωcv vq = C + ωcv v0 C 0 = q The reulting equivalent q0 circuit are hown in Fig. 6. (8) Fig. 4. Equivalent q0 circuit of a erie RL line Fig. 6. Equivalent q0 circuit of hunt capacitance of a three-phae line Fig. 5. Shunt capacitance of a three-phae line Let C ab = C bc = C ca = C m, C an = C bn = C cn, an C = C an + C ab. The equation of the a-phae current in Fig. 5 may be expree a: i i a a = Can van + Cab ( van vbn ) + Cac ( van vcn ) () van vbn vcn = ( Can + Cab + Cac ) Cm Cm (4) D. Summary The equation for the erie reitor, erie inuctor, an hunt capacitor are erive in the previou ection. The voltagecurrent relationhip for the baic component are ummarie in table I. For clearne the moel have been erive bae on the phae equation. It i alo poible to tranfer complete et of ifferential equation at once. Equation to obtain thi can be foun in the appenix. TABLE I. VOLTAGE-CURRENT RELATIONSHIP IN DQ0 REFERENCE FRAME FOR BASIC COMPONENTS Three-phae reitor R[ i ] = [ u ] q0 q0 Three-phae inuctor L [ i ] +ω y [ i ] = [ u ] C q0 p q0 q0 Three-phae capacitor [ u ] +ω y [ u ] = [ i ] q0 p q0 q0

129 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm 5 IV. COMPARISON It houl be hown, that the moel in a q0 reference frame give correct imulation reult. The bet olution woul be to compare the imulation reult with meaurement. A thi wa not poible at the moment, ome imulation reult have been compare to reult of imulation with well-known an accepte moel in the normally ue abc reference frame []. Both the repone to low an fat ynamic phenomena have been compare. Therefore, the repone of a oubly-fe inuction machine to a tep in the mechanical torque (low ynamic) an to a ip in the gri voltage (fat ynamic) have been coniere. The repone of the rotor current of the machine to a tep in the mechanical torque i hown in Fig. 7 an the reone to a ip in the gri voltage in Fig. 8. A ifference in the repone in the abc an in the q0 reference frame cannot be oberve in thee figure. One houl be aware, that the high rotor current, caue by the ip, might etroy the converter, if no meaure are taken [], []. (a) (b) Fig. 7. Repone of rotor current to tep in mechanical torque for abc-moel (a) an q0 moel (b) (a) (b) Fig. 8. Repone of rotor current to a ip in the gri voltage for abc-moel (a) an q0 moel (b) In the abc-moel, the witching operation of the power electronic converter i not taken into conieration. A comparion ha been mae between the behaviour of a converter in the q0 reference frame an a complete IGBTconverter that alo take into account the witching operation of all witche. The IGBT converter that ha been ue i obtaine from the SimPower Sytem Blocket of Matlab. Again the behaviour uring a ip in the gri voltage ha been imulate. The -axi current of the converter i hown for both moel in Fig. 9. It can be een that except the highfrequency noie ue to the witching operation of the IGBT converter, the repone to the ip i almot the ame. The repone epen more on the parameter of the converter controller, then on the type of moel. Fig. 9. Repone of -axi converter current to ip in the gri voltage for reference IGBT moel (oli line) an q0 moel (ahe line) V. CASE STUDY SIMULATIONS A. Introuction A cae tuy will emontrate the effectivene of the propoe moelling metho. All imulation have been one in Simulink, a toolbox extenion of Matlab that i wiely ue in ynamic imulation. The Near Shore Win park (NSW park) that i planne to be built in the North Sea about kilometre from the Dutch coat will be ue a a cae tuy. The win farm will conit of 6 turbine with a.75 MVA oubly-fe inuction generator. The park layout i hown in Fig. 0. For convenience only one tring of turbine i imulate. Each of the turbine i connecte to the 4kV gri by a three-wining tranformer with a nominal power of.5mw. Thi tranformer ha a 960V wining connecte to the tator an a 690V wining to the rotor wining via a frequency converter. The win farm i connecte to the 50kV gri via a tranformer with a nominal power of 5MVA. To imulate the ynamic of a win farm not only moel of the electrical ytem are require, but alo ynamic moel of the win an the win turbine incluing generator. The main goal of thi paper i to how the poibilitie of uing the q0 tranformation for the moelling of win farm. Therefore, the ecription of the win an turbine moel will be limite. In thi ection a hort ecription of the win moel an the turbine moel will be given. More information on the moelling of thee part can be foun in literature [4]. B. Win moel To evaluate the ynamic behaviour of win turbine an win farm, the hort-term variation of the win ha to be known. Since win pee variation i a tatitically etermine phenomenon, a win moel i neee that will calculate a realiation of the tochatically changing win pee in time. Furthermore, the win pee average over the turbine rotor ha to be etermine, incluing variation caue by the paing of the blae through the inhomogeneou win fiel over the rotor area. Thi inhomogeneou win fiel i caue by win hear an the tower [4]. When a power meaurement of a turbine i oberve, the effect of the win fiel inhomogenity can clearly be een by regular change in power with a frequency of the number of blae time the turbine' rotational frequency, often calle np. The win moel aim at a realitic repreentation of thi effect.

130 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm 6 Fig. 0. NSW park layout The objective of win moelling in thee type of problem i to generate a ingle point win pee realiation, which give intantaneou aeroynamic torque value that are tatitically equivalent to the value reulting from the longituinal turbulence. The effect of win pee variation on the aeroynamic torque i etermine by the C p (λ,pitch angle) curve an the rotor iameter. Thi implie that a realiation not only epen on the tatitical propertie of the win but alo on the ize an aeroynamic propertie of the turbine rotor. The metho make ue of the Auto Power Spectral Denity (APSD) of the longituinal win pee change in a ingle point [5]. C. Turbine moel The turbine moel ue conit of ub-moel for: aeroynamic behaviour of the rotor; rotating mechanical ytem (rive-train); tower (viz. motion of the tower top); electrical ytem (generator, power electronic converter); power limitation by pitch control or tall; The mechanical moel for turbine rotor, low an highpee haft, gearbox an generator rotor conit of a twoma pring an amper moel. The torque of the gearbox an generator on the nacelle i etermine, ince it interact with the tower naying. The imple tower moel conit of a ma-pring-amper moel for the tranlation of the tower top in two irection: front-aft (noing) an ieway (naying). Thi i not ufficient if tower top rotation ha to be moelle a well. In that cae, a lumpe parameter moel for rotation i ue, coniting of a number of ma-pring-amper moel in erie. The variable pee turbine inclue two control loop: the turbine aeroynamic power i limite by pitch control an the electrical power i controlle to maximie energy prouction (optimal-lamba control). Thi require aitional component moel (enor an actuator moel) an the eign of two controller. How to eign controller for win turbine, can be foun in [5] an will not be preente here. D. Generator moel Moelling of a oubly-fe inuction generator i wellknown [7], [], [6], [7]. The moel of the inuction machine i bae on the fifth-orer two-axi repreentation. A ynchronouly rotating q reference frame i ue with the irect -axi oriente along the tator flux poition. In thi way, ecouple control between the electrical torque an the rotor excitation current i obtaine. Thi reference frame i rotating with the ame pee a the tator voltage. When moelling the DFIG, the generator convention will be ue, which mean that the current are output an that real power an reactive power have a poitive ign when they are fe into the gri. Uing the generator convention, the following et of equation reult: ψ v = Ri ωψ q + ψ q vq = Riq + ωψ + (9) ψ r vr = Rrir ωrψ qr + ψ qr vqr = Rriqr + ωrψ r + with v the voltage [V], R the reitance [Ω], i the current [A], ω an ω r the tator an rotor electrical angular velocity [ra/] repectively an ψ the flux linkage [V]. The inice an q inicate the irect an quarature axi component of the reference frame an an r inicate tator an rotor quantitie repectively. All quantitie are function of time. A converter i ue to connect the rotor circuit of the DFIG to the gri, wherea the tator circuit i connecte to the gri irectly. The converter mut be able to tranfer energy in both irection. The gri-ie converter ha to control the DC-link voltage, regarle of the magnitue an irection of the rotor power an the rotor-ie converter ha to control the rotor current. For the converter moel it i aume that the

131 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm 7 converter are ieal. It aume that they exactly make the reference voltage ignal that i et by the controller. It ha been hown in [] that uch a moel give goo imulation reult. E. Simulation reult The repone of one tring of the win farm to a gut in the win pee ha been imulate. The gut in the win pee are important for the gri behaviour of the park, a the gut in win pee will lea to a gut in the output power of the park an will thu caue fluctuation in the voltage at the connection point. The reactive power etting of the turbine are kept contant uring the imulation. The gut i aume to cro with a certain pee through the tring. The turbine are affecte one after another by the gut. It i aume that the gut will affect firt the turbine with the larget itance to hore, an it will come cloer an cloer to the hore, affecting each turbine. It i aume that the time between affecting two turbine will be 5 econ. The rotor effective win pee at the firt turbine that experience the gut i hown in Fig.. The win pee before the gut i about 5 m/. The win pee increae to 0 m/ uring the gut. tranformer i hown in Fig. 6. Be aware that the change in output voltage of the win farm hown in Fig. 6, i only ue to one tring. The reulting change in output voltage ue to the whole park will be omewhat higher, but it i to be expecte that it will meet the gri requirement. The oubly-fe inuction generator ue in thi imulation offer the poibility to control the reactive power output. It houl be invetigate whether or not it i poible to ecreae the voltage fluctuation by controlling the reactive power output of the turbine. Fig.. Output power of ixth win turbine Fig.. Gut in win pee Fig. 4. Output power of twelfth win turbine Fig.. Output power of firt win turbine The increaing win pee will caue an increaing output power of the turbine. The output power of the firt turbine i hown in Fig.. The output power of the ixth an twelfth turbine are hown in Fig. an Fig. 4 repectively. The output power of the whole firt tring of the win farm i hown in Fig. 5. The large change in output power of the win farm will alo affect the voltage of the 50kV gri at the point of connection. The voltage at the park ie of the 50kV Fig. 5. Output power of one tring of the win farm After completion of the win farm moel bae on four ifferent electrical ytem (irect couple inuction machine, oubly fe inuction machine, permanent magnet generator an cluter-controlle inuction machine), the next tep i to invetigate the impact of win turbine or win farm on the gri an to improve the interaction between win farm (turbine) an the gri by control of the electrical ytem.

132 4 th International Workhop on Large-Scale Integration of Win Power an Tranmiion Network for Offhore Win Farm 8 [ T ( )] [ x ] = [ x ] + ω y [ x ] q0 θ abc q0 q0 (5) with y given by: y = ω 0 0 T [ ] q0 q0 = 0 0 (6) [ ( θ )] T ( θ ) It can be een from (6) that ifferential equation will caue a cro-relation between the an the q axi. Fig. 6. Output voltage of win farm VI. SUMMARY In thi contribution it ha been hown, that the Park tranformation can be ue to tranlate moel of all electrical component of a win farm from the abc reference frame to moel in the q0 reference frame. A ecription an ome example have been given of the metho to erive the q0 moel. A cae tuy imulation howe the ue of the moel to evaluate the impact of win farm on the electricity gri. VII. APPENDIX Voltage an current of electrical ytem are often given a a et of ifferential equation. A hort ecription will be given of how thee complete et of equation can be tranforme to the q0 reference ytem. The erivative of a vector in the abc reference ytem i given by: [ x abc ] = ([ Tq0 ( θ )] [ x q0 ]) (0) With the chain-rule for erivative: [ x q0 ] = [ Tq0 ( θ )] [ xabc ] + [ Tq0 ( θ )] [ x abc ] () [ T ( θ )] [ x ] = [ x ] q0 abc q0 [ T ( θ )] T ( θ ) q0 [ T ( θ )] [ x ] = [ x ] q0 abc q0 [ ] [ x ] q0 [ T ( θ )] T ( θ ) q0 ω ω q0 [ ] [ x ] q0 q0 () () With (7) an knowing that ω =θ / the following reult i obtaine: 0 0 T [ ] = q0 q0 ω 0 0 (4) [ ( θ )] T ( θ ) An it can eaily be een that: VIII. REFERENCES [] J.G. Slootweg, H. Poliner, W.L. Kling, Dynamic Moelling of a Win Turbine with Doubly Fe Inuction Generator, in Proc. 00 IEEE Power Engineering Society Summer meeting, pp [] J.G. Slootweg, W.L. Kling, Moeling of large win farm in power ytem imulation, in Proc. 00 IEEE Power Engineering Society Summer meeting, pp [] P. Sorenen, A. Hanen, L. Janoi, J. Bech, B. Bak-Jenen, Simulation of Interaction between Win Farm an Power Sytem, Report Rioe-R- 8 (EN), Rioe National Laboratory, Rokile, Denmark, December 00. [4] V. Akhimatov, H. Knuen, A. H. Nielen, J.K. Peeren, N.K. Poulen, Moelling an tranient tability of large win farm, International Journal of Electrical Power & Energy Sytem, Vol. 5, No., Feb. 00, pp [5] J.G. Slootweg, S.W.H. e Haan, H. Poliner, an W.L. Kling, General moel for repreenting variable pee win turbine in power ytem ynamic imulation, IEEE Tran. Power Sytem, Vol. 8, No., pp. 44-5, Feb. 00. [6] V. Akhimatov, Moelling of variable-pee win turbine with oublyfe inuction generator in hort-term tability invetigation, in: Proc. r Int. Workhop on Tranmiion Network for Offhore Win Farm, April -, 00, Stockholm, Sween. [7] C.-H. Ong, Dynamic Simulation of Electric Machinery uing Matlab/Simulink, Upper Sale River: Prentice Hall, 998. [8] G.C. Paap, Symmetrical Component in the Time Domain an Their Application to Power Network Calculation, IEEE Tran. Power Sytem, Vol. 5, No., pp. 5-58, May 000. [9] B Bachmann, H. Wiemann, Avance Moeling of Electromagnetic Tranient in Power Sytem, in Proc. Moelica Workhop, -4 Oct. 000, Lun, Sween pp [0] H. Akagi, Y. Kanazawa, A. Nabae, Intantaneou Reactive Power Compenator Compriing Switching Device Without Energy Storage Component, IEEE Tran. In. Appl., Vol 0, pp. 65, 984. [] J. Morren, S.W.H. e Haan, P. Bauer, J.T.G. Pierik, J. Bozelie, Comparion of complete an reuce moel of a win turbine with Doubly-Fe Inuction Generator in Proc. 0 th European conference on Power Electronic an application (EPE), Touloue, France, 4 September 00. [] A. Dittrich an A Stoev, Gri Voltage Fault Proof Doubly-Fe Inuction Generator Sytem, in Proc. 0 th European conference on Power Electronic an application (EPE), Touloue, France, 4 September 00. [] I. Serban, F. Blaabjerg, I. Bolea, Z. Chen, A Stuy of the Doubly-Fe Win Power Generator Uner Power Sytem Fault, in Proc. 0 th European conference on Power Electronic an application (EPE), Touloue, France, 4 September 00. [4] L.L. Freri, Win Energy converion ytem, Upper Sale River: Prentice Hall, 990. [5] T.G. van Engelen, E.L. van er Hooft an P. Schaak: Ontwerpgereechappen voor e Regeling van Winurbine, ECN Report (in preparation) [6] R. Pena, J.C. Clare, G.M. Aher, Doubly fe inuction generator uing back-to-back PWM converter an it application to variable-pee win-energy generation, IEE Proc.-Electr. Power Appl., Vol. 4, No., pp. -4, May 996. [7] A. Peteron, Analyi, Moelling an Control of Doubly-Fe Inuction Generator for Win Turbine, Licentiate thei, Technical report no. 464L, Chalmer Univerity, Göteborg, Sween, 00.

133 Comparion of complete an reuce moel of a win turbine uing Doubly-Fe Inuction Generator Keywor J. Morren ), S.W.H. e Haan ), P. Bauer ), J.T.G. Pierik ) ) Electrical Power Proceing, Delft Univerity of Technology Mekelweg 4, 68 CD Delft, The Netherlan ) ECN, Petten, The Netherlan J.Morren@it.tuelft.nl Ajutable pee generation ytem, Moelling, Renewable energy ytem Abtract Win turbine equippe with a Doubly-Fe Inuction Generator are increaingly popular in the power range above MW. For power ytem tability tuie it i eirable to apply reuce moel of the machine an the converter in orer to limit the computation time. Several reuce moel have been evelope an compare with each other. With repect to the generator, moel with an without tranient term in the fluxe have been compare. With repect to the converter, moel with an without PWM operation have been ue. The whole ytem ha been moelle both in abc coorinate an in a rotating -q reference frame. Epecially a moel with tranient flux term an without PWM operation, which ha been moelle in the -q reference frame ha hown to be accurate an fat. Introuction One of the mot important contemporary win turbine i a win turbine equippe with a Doubly-Fe Inuction Generator (DFIG), hown in Fig., with a voltage ource converter feeing the rotor circuit. Compare to variable pee win turbine with the converter connecte to the tator, one of the major avantage of the oubly-fe inuction generator i the fact that the converter in the DFIG cheme only nee to hanle the rotor power. Thi rotor power i aroun 5% of the total generator power, epening on the pee range that i allowe []. Fig.. Doubly-fe inuction generator with voltage ource converter

134 A tenency to increae the amount of electricity generate from win can be oberve []. A the penetration of win turbine in electrical power ytem will increae, they may begin to influence overall power ytem operation []. The behaviour of win turbine with repect to their interaction with the gri i therefore tuie at ifferent place [], [4], [5]. To facilitate the invetigation of the impact of a win farm on the ynamic of the power ytem to which it i connecte, an aequate moel of the win turbine i require. Although peronal computer become fater an fater, computational pee i till one of the limiting factor in (ynamic) imulation of power ytem. One of the problem i the complexity of the moel that limit the computational pee. When reuce moel are ue imulation can be one much fater, but the reult may be le accurate []. In thi contribution a number of ifferent moel (from etaile complete moel to imple reuce moel) for the oubly-fe inuction generator with back-to-back converter have been evelope an compare to each other. With repect to the generator, moel with an without tranient term in the fluxe have been compare. With repect to the converter, moel with an without PWM operation have been moelle. The whole ytem ha been moelle both in abc coorinate an in a rotating - q reference frame. It will be hown that accurate moel can be evelope, which can be imulate very fat. Moelling an control Moelling the generator A -q reference frame i choen to moel the oubly-fe inuction generator. Thi o-calle Park Tranformation i ue to tranform the tator quantitie of a ynchronou machine onto a -q reference frame that i fixe to the rotor [6]. It ue i not limite to ynchronou machine however. Other quantitie can be choen a a reference a well. The -q reference frame i obtaine from the rectangular α-β reference frame by the invere Park-tranformation: x x q = C rot x x co θ in θ in θ co θ α ( θ) with C ( θ) = an C ( θ) = C ( θ) β rot The α-β reference frame i obtaine from the -phae abc ytem with the Clarke tranformation: x x x α β 0 = C xa xb x c αβ 0, abc with Cαβ 0,abc = 0 The moel that i obtaine i well known an can be foun in literature [], [6]. The generator convention will be ue, which mean that the current are output intea of input an real power an reactive power have a poitive ign when they are fe into the gri. Uing the generator convention, the following et of equation reult: v v v v q r qr = R i = R i q = R i r r = R i r qr ψ ω ψ q + ψ q + ω ψ + ψ r ω rψ qr + ψ qr + ω rψ r + with v the voltage [V], R the reitance [Ω], i the current [A], ω an ω r the tator an rotor electrical angular velocity [ra/] repectively an ψ the flux linkage [V]. The inice an q inicate the rot rot () () ()

135 irect an quarature axi component of the reference frame an an r inicate tator an rotor quantitie repectively. All quantitie in () are function of time. The flux linkage in () can be calculate uing the following et of equation: ψ ψ ψ ψ q r q = = = = ( L + Lm ) i Lmir ( L + Lm ) iq Lmiqr ( Lr + Lm ) ir Lmi ( Lr + Lm ) iq Lmiq with L m the mutual inuctance [H] an L an L r the tator an rotor leakage inuctance [H] repectively. Sometime the tranient in the fluxe, repreente by the lat term in equation (), are neglecte. The mot important reaon to o thi have to o with the computation pee uring imulation. Another reaon i that taking into account the rotor tranient woul require etaile moelling of the converter []. When the tranient are neglecte, the following et of equation can be erive: v v v v q r qr = R i = R i q = R i r r = R i r qr + ω ω + ω r ω r ( L + Lm ) iq + Lmiqr ) (( L + Lm ) i + Lmir ) ( Lr + Lm ) iqr + Lmiq ) (( L + L ) i + L i ) r m r m (4) (5) The electrical angular velocity of the rotor, ω r, can be etermine a: ω = ω pω r m (6) with p the number of pole pair [-] an ω m the mechanical angular velocity [ra/], which i given by: ω m = J ( T T ) m e with J the inertia of the rotor [kg m ] an T m an T e the mechanical an electrical torque [Nm] repectively. The mechanical torque i generate by the win turbine an epen on the win pee. The electrical torque i given by: T = p e ( ψ i ψ i ) r q qr The power invariant -q tranformation ha been ue. If the amplitue-invariant tranformation i ue, (8) houl be multiplie by a factor /. A ynchronouly rotating -q reference frame i ue with the irect -axi oriente along the tator flux vector poition. In thi way a ecouple control between the electrical torque an the rotor excitation current i obtaine. Thi reference frame i rotating with the ame pee a the tator voltage an auming that the tator reitance i negligible, i.e, R << ω (L +L m ), the angle of the tator flux vector can be calculate a: θ = ω The reference frame of the rotor i rotating with the electrical frequency of the rotor ω r. The angle of the rotor can be obtaine a: θ = ω = ω pω (0) r r m The angle θ an θ r can be ue for the Park-tranformation of the tator an the rotor quantitie repectively. (7) (8) (9) With the caling factor ue in () an () the active power elivere by the tator i given by: P = v i + v i q q ()

136 an the reactive power by Q = v i q v i q When the amplitue invariant tranformation wa ue, () an () houl be multiplie by a factor /. Due to the choen reference frame, ψ q an v are zero. Therefore the reactive power an the active power elivere by the tator can be written a: P v i v L i m = q q = q qr Lr + L () m an: q ( ( L + L m ) i L m i r ) i Q = v i = ω (4) A the tator current i equal to the upply current, it can be aume that it i contant. The reactive power i then proportional to the irect component of the rotor current i r. Control of the generator The electrical an mechanical ynamic of a win turbine are in ifferent time cale. The electrical ynamic are much fater than the mechanical. Therefore, it i poible to control the machine in a cacae tructure, a hown in Fig.. The fat electrical ynamic can be controlle in an inner loop an a pee controller can be ae in a much lower outer loop. () Fig.. Cacae control; IG=Inuction Generator, Inv=Inverter, K c =current controller, J=inertia of turbine, K =pee controller The internal moel control (IMC) principle [7] ha been ue to eign the controller. The iea behin internal moel control i to reuce the error between the ytem G(), an the moel of the ytem Ĝ() by a tranfer function K(). In Fig. the principle i hown for the current controller. One common way of chooing the tranfer function K() i [8]: K α + α () = G () n where n houl be at leat one larger than the number of zero of Ĝ(), o that K() become proper. The parameter α i a eign parameter that i equal to the cloe loop banwih of the ytem. The ytem G() houl be minimum phae, i.e. it houln t contain right half-plane zero, a thee will become untable uner feeback. The controller C(), inie the ahe line in Fig., become [8]: C = (6) ^ () K() G() K() For a firt orer ytem, n= i ufficient an the controller become then a PI controller. With (6) an Ĝ()=G() the controller become [8]: C k α i () = k + = G () p Where k p i the proportional gain an k i i the integral gain. The cloe loop ytem with ieal parameter become: (5) (7) 4

137 G cl () = G() K() = α + α (8) Fig.. Internal Moel Control (IMC) The voltage equation of the rotor are given in () a: v v r qr = R i r r = R i r qr ψ r ωrψ qr + ψ qr + ωrψ r + Since the tator flux i almot fixe to the tator voltage, it i practically contant. Thi implie that the erivative of the tator flux an of the tator magnetiing current are cloe to zero, an can be neglecte [9], [0]. Equation (9) can then be written a: v v r qr = R i r r = R i r qr ir Lr ω rψ iqr Lr + ω rψ qr r The lat term in both equation caue a cro-relation between the two current component. Reference voltage to obtain the eire current can be written a [9]: v v * r * qr with ' v r ' v qr = v = v ' r ' qr = R i = R i ω ψ r + ω ψ r r r qr r qr r ir Lr iqr Lr The i r an i qr error are procee by a PI controller to give v r an v qr repectively. To enure goo tracking of thee current, the cro-relate flux term are ae to v r an v qr to obtain the reference voltage. Treating ω r Ψ r an ω r Ψ qr a a iturbance, the tranfer function from the rotor voltage v r to the rotor current i r an from the rotor voltage v qr to the rotor current i qr i given by: G() = L + r R r Uing the IMC, the current controller become: C k α i c () = k + = G () p (9) (0) () () () (4) 5

138 Where α c i the banwih of the current control loop, k p i the proportional gain an k i i the integral gain. The two gain become [0]: k p = α L, k = α R c r i c r (5) The rotational pee i given by (7) a: ω m = J ( T T ) m e It i aume that the current controller i much fater than the pee controller. The electrical torque i than T e =T e,ref. The reference torque i et to: T e,ref = T e,ref ' B ω a m where B a i an active amping torque [0]. The tranfer function from rotational pee to electrical torque become now: G () = J + B a Uing again the internal moel control metho, the following gain of the controller are obtaine: (6) (7) (8) k p = α J, k = α B i a (9) Where α i the eire cloe-loop banwih of the pee controller. When B a i choen to be B a =Jα change in the mechanical torque are ampe with the ame time contant a the banwih of the pee control loop [0]. Moelling the converter A three-phae AC-AC converter i normally ue to connect the rotor circuit of the DFIG to the gri, wherea the tator circuit i connecte to the gri irectly. The converter that will be ue mut be able to tranfer energy in both irection, i.e. it mut be able to work a a rectifier an a an inverter. When the generator operate in ub-ynchronou moe the converter will tranfer energy to the rotor, while it i extracting energy from the rotor when the generator operate in uper-ynchronou moe []. The converter connecte to the gri ha to control the DC-link voltage, regarle of the magnitue an irection of the rotor power. A moelling an control of voltage ource converter i well known, no ecription will be given here. A etaile ecription, relate to the converter of a DFIG can be foun in [9]. Compare moel Four ifferent moel of a oubly-fe inuction generator an converter have been evelope an compare to each other. A hort ecription of the ifferent moel will be given here. The generator ytem conit of two component namely the generator itelf an the converter in the rotor circuit. Two ifferent machine moel have been ue. The firt i a 5 th orer moel, incluing all tranient flux term, bae on the equation () an (4). From now on thi moel i referre to a the complete moel. The econ moel i a reuce moel, bae on (5) in which the tranient flux term in the tator an rotor circuit are not taken into conieration. Thi lat machine moel i often ue in power ytem tability tuie []. From now on thi moel i referre to a reuce moel. A number of moel have been evelope for the converter. In the firt moel the PWM operation of the converter i moelle, which mean that the output voltage have a pulating character. The intantaneou DC-link current are erive from the power balance in the converter, o they till reflect the witching nature of the converter an are pulating too. In the econ moel the converter i moelle a a controllable three-phae inuoial voltage ource, where amplitue, frequency an 6

139 phae of the output voltage can be controlle inepenently an on both ie (rotor ie an gri ie). In thi moel both converter part can be coniere a power amplifier that convert the input control voltage (normally ue to obtain the PWM ignal) irectly to output ac waveform that are et to the gri an the rotor. The DC-link current are again erive from the power balance in the converter. In thi moel the DC-link current are contant in teay tate. The generator ha internally been moelle in a -q reference frame, bae on () an (4). Tranformation from -q to abc coorinate have been ue to connect them with the converter an the gri, which are both moelle in abc coorinate. When all ignal in the time omain are inuoial, the ignal in the -q frame are contant. Therefore, complete moelling in -q omain i expecte to increae the imulation pee ignificantly, becaue the variable tep-ize imulation program can apply a large time tep uring quai teay tate phenomena. To verify thi, a moel ha been evelope that i bae completely on -q ignal. Alo the converter an the gri are moelle in the -q reference frame. The -q moel of the machine i given in () an (4). An example of a converter moel in the -q reference frame can be foun in []. Reult A number of ifferent moel have been obtaine in Simulink. Simulink i a toolbox extenion of Matlab that i wiely ue in ynamic imulation. Some reult of four ifferent moel will be hown. The firt moel (A) i the benchmark, coniting of a complete machine moel (bae on () an (4)) an a converter moel incluing PWM. Moel B ue the complete machine moel of () an (4) an the inuoial converter moel. Moel C ue the reuce machine moel bae on (5) an the ame converter moel a B. Moel D i completely moelle in the -q reference frame. The generator i again bae on () an (4) an the converter moel i bae on inuoial operation. The four ifferent moel are chematically hown in Fig. 4. The ub-plot a, b, c an, correpon with the moel A, B, C an D repectively. (a) (b) (c) () Fig. 4. Four moel ue for the imulation The four moel have been compare for a number of event. The level of etailing that i neee in a moel, to obtain reliable imulation reult, might epen on the event that i invetigate. Epecially the time cale of the event might be important. The moel have therefore been compare for two important event with ifferent time cale. The firt i a change in the win pee, which caue a change in the mechanical torque. Fig. 5 how, for the ifferent moel, the rotor current i qr an the rotational pee ω m of the machine for a tep in the mechanical torque. The econ event i a ip in the 7

140 gri voltage. Voltage ip caue large problem for thi type of generator, an the generator might be eaily etructe [], [0]. The ip in the gri voltage will reult in a fat increaing large current in the tator wining of the DFIG. Becaue of the magnetic coupling between tator an rotor a large current will alo flow in the rotor circuit an will lea to etruction of the converter. To analye thi behaviour it important to have a moel of the Doubly-Fe Inuction Generator that eibe the fat ynamic event that occur uring the gri ip accurately. Fig. 6 how the rotor current i qr an the rotational pee ω m of the machine for a ip of 0% in the gri voltage. Moel A Moel B Moel C Moel D Repone of rotor current i qr an rotational pee w m to a tep in the mechanical torque 5400 time unit 00 time unit 800 time unit time unit (=ref) Fig. 5. Repone to a tep in the mechanical torque for moel A, B, C an D. Upper row: repone of rotor current i qr to the tep. Secon row: repone of rotational pee w m to the tep. On the lower row the relative computation time i inicate with repect to the fatet moel Moel A Moel B Moel C Moel D Repone of rotor current i qr an rotational pee w m to a ip in the gri voltage Fig. 6. Repone of rotor current i qr an rotational pee w m to a 0% ip in the gri voltage In Fig. 5 alo the time i hown that it take to imulate the ifferent moel. The imulation of the ifferent moel i relate to that of the fatet moel (D), which i et to (about 50 time fater than real time on a GHz peronal computer). A can be een, the imulation reult of moel B how a goo imilarity with the benchmark moel A. During the firt 0.4 econ the ignal of moel A are lightly ifferent from the other moel. Thi i ue to the fact that not all ignal of moel A ha reache teay tate yet, when the plot wa tarte. Further there i a high-frequency ripple in moel A 8