Internatonal Journal of Electrcal Energy, Vol 4, No 4, December 6 Nonlnear Control of a Gr-Connecte Double Fe Inucton Generator Bae Vertcal Ax Wn Turbne: A Reental Applcaton Rha Chekh an Hocne Belml Untée Développement e Equpement Solare, UDES, Centre e Développement e Energe Renouvelable, CDER, 445 Tpaza, Algera Emal: chkhreha@uez, belmlh@yahoofr Abtract Th paper propoe a robut nonlnear feeback control approach of a reental Savonu Vertcal Ax Wn Turbne (VAWT) bae on Double Fe Inucton Generator (DFIG) an connecte to a powerful gr However, a the tue ytem non lnear, t ffcult to be controlle ung uch tratonal metho Thu, n orer to acheve an ntantaneou control of both tator actve an reactve power flow, the am of th approach to control the Rotor Se Converter (RSC) ung a robut non-lnear feeback control cheme, n whch, a robut control law bae on Lyapunov theory aocate wth a lng moe controller ue to hanle the ue of parameter uncertanty an to guarantee a global aymptotc tablty of the ytem The propoe approach ha been evaluate by mulaton reult ung MATLAB/Smulnk Inex Term oubly-fe nucton generator, Lyapunov functon, vertcal ax wn turbne, MPPT, lng moe I INTRODUCTION Wth the fat ncreang of wn energy ntalle capacty over the lat two ecae, t playng a vtal role n worl energy market at the preent It expecte that global total wn power generaton wll upply aroun % of the total worl electrcty generaton at the en of [], [] Among the fferent alternatve to obtan varable pee wn turbne, the Doubly Fe Inucton Machne (DFIM) ha become the mot preferre confguraton n wn energy nutry [], [3] However, to take avantage of the DFIM n energy generaton, a control trategy houl be acheve takng nto account the gr coe requrement, the complexty of the WECS-bae DFIG, an hence the qualty of energy [4] However, everal egn an arrangement have been mplemente to cope wth problem relate to gr ntegraton of WECS-bae DFIG, uch a the power factor ecreae an harmonc polluton [5] The prefere confguraton n Wn nutry ung DFIG (Fg ), ecrbe a the tator connecte rectly to the gr an the three phae rotor wnng are upple va lp rng from a back-to-back Voltage Source Converter (VSC), the Rotor Se Converter (RSC) & Gr Se Converter (GSC) harng a DC bu [5], [6] If the converter control carre, certanly a ecouple control of the tator e actve an reactve power reulte [7], [4] A lot of reearche have been conucte over the pat few year to egn a robut control to acheve the maxmzaton of the power capture facng to a varyng wn conton [8], [9] In th paper, a robut control bae on the Lyapunov theory preente n orer to regulate the tator actve an reactve power flow Wn power, even though an abunant ource of energy, the power that can be obtane from t change throughout the ay a wn pee change contnually The maxmum power whch a wn turbne can elver at a certan wn pee epen upon certan optmum value of pee at whch the rotor rotate Extractng maxmum poble power from the avalable wn power of utmot mportance, therefore, MPPT control an actve reearch area In orer to have maxmum poble power, the wn turbne houl alway operate at optmum tp pee rato Th poble by operatng the turbne at the optmal rotaton pee where the tp pee rato optmum [] Fgure Topology of the DFIG-bae WECS II WIND AND WIND TURBINE MODELING The geographcal te choce an the charactertc of the wn, where the prmary factor etermne the quantty of the power energy whch wll be extracte To know the properte of the te, wn velocty meaurement a well a t recton, over a great pero of tme, are neceary To acheve th work, the wn pee moele n etermntc form by a um of everal harmonc a the followng form [8]: V (t ) 6 n(47t ) n(665t ) n(93t ) n(36645t ) Manucrpt receve October 9, 6; reve December, 6 6 Internatonal Journal of Electrcal Energy o: 878/joee44-6 ()
Internatonal Journal of Electrcal Energy, Vol 4, No 4, December 6 The wn power avalable on the turbne haft, extracte from the power of the wn gven by: 3 P mec C R p () an R are the ar enty an the rau of the vertcal ax wn turbne propeller, repectvely The power coeffcent can be ecrbe a the porton of mechancal power extracte rectly from the avalable wn power an repreent the aerofol of the wn turbne Th power coeffcent Cp generally efne a a functon of the tp-pee-rato () a followng: 3 C p ( ) 99 R 68 4546 (3) R where, correpon to the pee of the wn turbne From Fg t can be een that the maxmum power extracte from a wn turbne gven by rven the wn turbne at any optmal wn pee III THE DOUBLE FED INDUCTION MACHINE MODEL It expree, n the ynchronou reference frame, by the followng equaton: Voltage equaton: u R j u r r Rr r j r r Current-Flux equaton: r r r where, -, L LLr L From (4) an (5), the all flux tate moel gven lke: M u r j T T Lr M u j r r T L T r r r r r The tator power expreon are: * P =Re u * Q =Im u Replacng (5) n (7) wth equalzaton of the real an magnary part, the followng equaton obtane: P U U r Uq q Uq rq Q Uq Uq r U q U rq The equalzaton of the Real part an Imagnary part of (6) gve the followng [6]: (4) (5) (6) (7) (8) u r q f uq q rq q f q ur 3 4 r r r rq f3 r urq 3 q 4 rq rq r r f4 rq M (9) Wth:,, 3, T T Lr Tr L 4 Tr An, f r q f q rq f3 3 4 r r () rq f4 3 q 4 rq r r The rewrte of (9) gve: fu q fu q r f3 u r rq f4urq IV VECTOR CONTROL STRATEGY OF DFIG () Vector control trategy bae on the followng coneraton, where the tator voltage are contrane n q-ax a followng [], []: u uq u Replacng () n (8) the power expreon become: P u ( rq q ) Q u ( r ) () (3) Then a Lyapunov functon can be efne a followng: V ( P P ) ( Q Q ) ref ref (4) It ervatve : V ( P P ref )( P Pref ) ( Q Q ref )( Q Qref ) (5) Subttute () an (3) n (5), t reult: V ( P Pref )( u urq Pref ) ( Q Q ref )( u u r Q ref ) (6) Wth: u f 4 ( f u ), u f 3 f Then, (6) can be efnte negatvely f we efne the followng control law: 6 Internatonal Journal of Electrcal Energy
Internatonal Journal of Electrcal Energy, Vol 4, No 4, December 6 ur ( Q ( )) ref K Q Qref u urq ( Pref K ( P Pref )) u Replace (7) n (6) we get: (7) V K ( P P ref ) K ( Q Q ref ) (8) So (8) table f K (=, ) were of coure all potve [6], an hence: lm Q Qref t lm P Pref t (9) V ROBUST NON LINEAR FEEDBACK CONTROL A large moel uncertanty ue to parameter varaton, noe, an meaurement error the man problem face the goo control behavor [] In th en we propoe a novel robut control cheme to eal wth th problem In the kn of feeback control, the moel uncertante are more globally relate to the nonlnear functon, f (=,, 3, 4), than to the parameter rft In practce, thee nonlnear feeback functon can be trongly affecte by the conventonal effect of Inucton Machne (IM) uch a temperature, aturaton an kn aocate to the fferent no lnearly caue by harmonc polluton an the noe meaurement Globally we can wrte: f fˆ f ˆ NLFF: nonlnear feeback functon f : NLFF effectve; f : NLFF varaton aroun of ˆf ˆf : the true nonlnear feeback functon The f () can be generate from all parameter an varable a ncate above We aume that all of the f are boune a follow: f, where a known boun Knowlege of the not ffcult to obtan, nce one we ue a uffcently large number to atfy the contrant f Replacng () n (), we obtan: ^ f fu ^ q f fu q ^ r f 3f3ur ^ rq f 4 f3urq () Takng nto account the f, the new law control can be choen a follow: ur ( Q ( ) ( ) ref K Q Qref K gn Q Qref u () urq ( P ref K ( P Pref ) Kgn ( P Pref ) u where, K, K an =, Then the analogue ervate Lyapunov functon etablhe from (6) ung () an () become a follow: V ( P P ref )( K gn( P P ref )) ( Q Q ref )( K gn( Q Q ref )) V (3) Hence the fˆ varaton can be aborbe when the ytem tablty ncreae f we chooe: Fnely we can wrte: K K (4) V V (5) We can conclue that the control law gvng by () to en at the convergent proce tablty for any ˆ VI MAXIMUM POWER POINT TRACKING STRATEGY Several technque can be ue to obtan an MPPT operaton of the WECS, uch a graent metho, P&O, fuzzy logc etc In th paper, an extractng the maxmum wn power through the Savonu wn turbne nee: Operatng at varable pee plu a well-known of the Savonu wn turbne aerofol a t hown n the control cheme (Fg ) Fgure Block agram of DFIG control cheme A Trackng Performance VII SIMULATION RESULTS The DFIG parameter an the vertcal ax wn turbne ata are gven n the appenx below In orer to valate our approach, a gtal mulaton ha been realze ung the general block-agram epcte n Fg 6 Internatonal Journal of Electrcal Energy 3
Internatonal Journal of Electrcal Energy, Vol 4, No 4, December 6 Aume to have a wn pee llutrate by the bac profle efne n Fg 3 Hence, the obtane reult are organze accorng to the followng pecfcaton: the Fg 4 an Fg 5 repectvely how the actve an reactve power njecte to the gr, wherea, the actve power reference generate by the MPPT bloc an the reactve power fxe at VAR, the Fg 6 how the Tp pee rato veru tme whch almot mantane to the maxmum Tp pee rato n whch the Power Coeffcent of the vertcal ax wn turbne mantane to t maxmum value a t hown n the Fg 7, fnally the tator power factor hown n the Fg 8 whch alo mantane to the unty at all the operaton moe, that reflect the goo qualty of electrcal energy njecte to the gr 9 8 Tp pee rato 5 4 3 9 8 7 6 4 6 8 Tme (Sec) 3 5 Fgure 6 Tp pee rato veru tme Generator Spee (roun/m) 7 6 5 4 3 4 6 8 Tme () x 4 Fgure 3 DFIG pee (roun/m) Cp 5 5 4 6 8 Tme (Sec) Fgure 7 Power coeffcent veru tme - - Stator Actve Power (WAT) - -3-4 Stator Power Factor -4-6 -8 - Stator Reactve Power (VAR) -5-6 4 6 8 Tme (Sec) 5 4 3 - - -3-4 Fgure 4 Stator actve power repone -5 4 6 8 Tme(Sec) Fgure 5 Stator reactve power repone 4 6 8 Tme (Sec) Fgure 8 Stator power factor B Robutne Performance The robutne of the tructure houl be checke agant the ncerttue of parameter So the followng tep taken to check the robutne agant the retance tator an rotor changng It well-known that the problem n the electrcal machne the changng of ther electrcal parameter ue to the changng of the temperature; thee change may caue ome problem Therefore, n orer to know the control tructure behavor uner thee crtcal conton, an attempt wa mae to check t by tet of robutne, when the tator an rotor retance are change a hown n Fg 9 The mulaton tet wa mae wthout the MPPT bloc n orer to how clearly the control performance, thu the tator power reference have been choen a fxe etpont a t hown n Fg The obtane reult how 6 Internatonal Journal of Electrcal Energy 4
Internatonal Journal of Electrcal Energy, Vol 4, No 4, December 6 the robutne (Fg ) of the cheme agant a % changng of the rotor an tator retance; although a mall turbance can be oberve, they o not have any notable effect on the tator actve an reactve power (fgure zoom repectvely) 4 8 3 4 5 6 7 8 t() Stator retance varaton 8 6 Rotor retance varaton 4 3 4 5 6 7 8 t() - -4-6 Fgure 9 Parameter varaton -8 3 4 5 6 7 8 t() Q (Var) 5-5 - 3 4 5 6 7 8 t() -74-745 -75 5-5 P (Wat) Fgure Stator actve an reactve power repone Zoom P -755 8 3 3 34 36 38 4 4 Zoom Q - 8 3 3 34 36 38 4 4 Fgure P an Q zoom VIII CONCLUSION Recently the reental WECS are conere a an mportant oluton of the electrfcaton ue whether n tan alone or gr ntegraton operaton The DFIM ouble acceblty an mportant avantage; t nuce a goo control of the power flow between the machne an the gr an hence permt to nject the power uch that the gr power factor cloe to unty In th paper, a robut vector control ntene for Doubly Fe Inucton Generator (DFIG) ha been nvetgate The tablty of the robut control ha been guarantee ung the econ Lyapunov approach wth a lng moe controller The tet of performance realze n two way; frt; n orer to check the trackng performance from a fluctuate power reference an then the robutne performance agant parameter uncertanty checke by tetng the control cheme uner a changng of the rotor an tator retance The obtane reult have emontrate the effcency of the propoe control when a goo reference trackng ha been hown wthout any recore effect, an a goo robutne agant the parameter uncertanty note A a concluon th propoe control can be conere a an nteretng oluton n reental wn converon ytem APPENDIX The DFIG parameter an the vertcal ax wn turbne ata are gven n the followng table: TABLE WECS DATA DFIG ata Output power Pn=75 KW Stator retance R=455 Ω Rotor retance Rr=6 Ω Stator nuctance L=84 H Rotor nuctance Lr=8 H Mutual nuctance Mr= 78 H Number of pole 4 Inerta moment j=35 Nm Rubbng factor f=673e -3 Vertcal Ax Wn Turbne Data (Savonu) Rate power KW 7 Denty of ar (ρ) kg/m 3 Area wept (Dameter heght) m 4 Rotor ameter m 4 Tp pee rato 9 Optmal coeffcent C pmax 9 Gearbox rato 4 REFERENCES [] Global Wn Energy Councl (GWEC) Global Wn Stattc 5, Report //6 [Onlne] Avalable: wwwgwecnet [] L Yu an C Xu, Rotor current ynamc of oubly fe nucton generator urng gr voltage p an re, Internatonal Journal of Electrcal Power & Energy Sytem, vol 44, no, pp 7-4, Jan 3 [3] D G Gaourak an A N Safaca, Quanttatve an qualtatve behavor analy of a DFIG wn energy converon ytem by a wn gut an converter fault, Wn Energy, vol 9, no 3, pp 57-546, 5 [4] E Özoy, et al, Moelng an control of a oubly fe nucton generator wth a turbance oberver: A tator voltage orente 6 Internatonal Journal of Electrcal Energy 5
Internatonal Journal of Electrcal Energy, Vol 4, No 4, December 6 approach, Turk J Elec Eng & Comp Sc, vol 4, pp 96 97, 6 [5] H T Jahav an R Roy, A comprehenve revew on the gr ntegraton of oubly fe nucton generator, Internatonal Journal of Electrcal Power an Energy Sytem, vol 49, pp 8 8, 3 [6] M Rahm an M Parnan, Dynamc behavor analy of oubly-fe nucton generator wn turbne The nfluence of rotor an pee controller parameter, Internatonal Journal of Electrcal Power an Energy Sytem, vol 3, no 5, pp 464-477, [7] R Pena, J C Clare, an G M Aher, Doubly fe nucton generator ung back-toback PWM converter an t applcaton to varable-pee wn-energy generaton, IEE Proc Electr Power Appl, vol 43, pp 3, pp 3-4, 996 [8] G Aba, et al, Doubly Fe Inucton Machne: Moelng an Control for Wn Energy Generaton, t e, IEEE-John Wley & Son, Inc, [9] I Munteanu, et al, Optmal Control of Wn Energy Sytem: Towar a Global Approach, Sprnger, 8 [] S K Pana an P K Dah, Applcaton of non lnear control to wtche relectance motor: A feeback lnearzaton approch, IEE Proc Elect Power Appl, vol 43, no 5, pp 37-379, Sept 996 [] F Poter, Etue 'un ytème éolen baé ur une machne aynchrone a ouble almentaton, n Jeune chercheur- JCGE'3, Par: Hermè Scence Publcaton, 3 Rha Chekh receve h BS an MS egree n Electrcal Engneerng from Bkra Unverty, Algera, n 8 an, repectvely Currently, he workng through h PhD egree wthn the LGEB lab (Electrcal Engeerng Lab of Bkra) He erve a a Reearch Aocate wthn the CDER, Renewable Energe Development Center n Algera H reearch nteret nclue Electrc Machne an Drve, Wn Energy Generaton Sytem, Gr Integraton Iue 6 Internatonal Journal of Electrcal Energy 6