Encoderless Model Predictive Control of Doubly- Fed Induction Generators in Variable-Speed Wind Turbine Systems

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1 Journal o Phyic: Conerence Serie PAPER OPEN ACCESS Encoerle Moel Preictive Control o Doubly- Fe Inuction Generator in Variable-Spee Win Turbine Sytem Recent citation - C. Dircherl an C. M. Hackl To cite thi article: Mohame Abelrahem et al 216 J. Phy.: Con. Ser View the article online or upate an enhancement. Thi content wa ownloae rom IP are on 1/3/218 at 3:47

2 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/1125 Encoerle Moel Preictive Control o Doubly-Fe Inuction Generator in Variable-Spee Win Turbine Sytem Mohame Abelrahem,, Chritoph Hackl, Ralph Kennel Intitute or Electrical Drive Sytem an Power Electronic; Munich School o Engineering Reearch Group Control o Renewable Energy Sytem (CRES). Technical Univerity o Munich (TUM), Munich, Germany. Correponing author. mohame.abelrahem@tum.e, chritoph.hackl@tum.e, ralph.kennel@tum.e Abtract. In thi paper, an encoerle inite-control-et moel preictive control(fcs-mpc) trategy or oubly-e inuction generator (DFIG) bae on variable-pee win turbine ytem (WTS) i propoe. Accoring to the FCS-MPC concept, the icrete tate o the power converter are taken into account an the uture converter perormance i preicte or each ampling perio. Subequently, the voltage vector that minimize a preeine cot unction i electe to be applie in the next ampling intant. Furthermore, a moel reerence aaptive ytem (MRAS) oberver i ue to etimate the rotor pee an poition o the DFIG. Etimation an control perormance o the propoe encoerle control metho are valiate by imulation reult or all operation conition. Moreover, the perormance o the MRAS oberver i tete uner variation o the DFIG parameter. Notation N,R,C are the et o natural, real an complex number. x R or x C i a real or complex calar. x R n (bol) i a real value vector with n N. x i the tranpoe an x = x x i the Eucliean norm o x. n = (,...,) i the n-th imenional zero vector. X R n m (capital bol) i a real value matrix with n N row an m N column. O n m R n m i the zero matrix. x y z R 2 i a pace vector o a rotor (r), tator () or ilter () quantity, i.e. z {r,,}. The pace vector i expree in either phae -, tator ixe -, rotor ixe r-, or arbitrarily rotating k-coorinate ytem, i.e. y {,,r,k}, an may repreent voltage u, lux linkage ψ or current i, i.e. x {u,ψ,i}. 1. Introuction The electrical power generation by variable pee win turbine (WT) ha increae igniicantly uring the lat year contributing to the reuction o carbon ioxie emiion an to a lower environmental pollution[1]. Among variou win energy converion ytem(wecs), WECS with oubly-e inuction generator (DFIG) have been the ominant technology in the market ince the late 199 [1]. DFIG can upply active an reactive power, operate with a partial-cale power converter (aroun 3% o the generator rating), an ulill a certain rie through capability [2]. Operation above an below ynchronou pee i poible [2]. Fig. 1 how a DFIG mechanically couple to the win turbine via a hat an gear box with Content rom thi work may be ue uner the term o the Creative Common Attribution 3. licence. Any urther itribution o thi work mut maintain attribution to the author() an the title o the work, journal citation an DOI. Publihe uner licence by IOP Publihing Lt 1

3 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/1125 Gear Box i i r RSC I m I g GSC R L u o DFIG Cc uc i u c αβ DC-link φ ω q r Preiction i r Cot Moel 7 Function q i ωˆr φˆr r, re i r, re u MRAS 2ω L Oberver ω Lm 3n plmu αβ αβ i u * r m e 2L MPPT 3u L αβ i m Cot Function PI i, re u c i q i q i, re 7 Gri φ ω Preiction u c Moel q i q u o / q i φ u o ωˆm Q, re u c, re Figure 1: Propoe encoerle FCS-MPC or DFIG in variable pee WECS. ratio g r 1. The tator wining o the DFIG are irectly tie to the gri, wherea the rotor wining i tie via a back-to-back partial-cale voltage ource converter (VSC), an a ilter to the gri. The gri ie converter (GSC) an the rotor ie converter (RSC) hare a common DC-link. Currently, iel oriente control (FOC) an irect torque control (DTC) metho ominate both acaemic an inutrial application or RSC [3]. For GSC, voltage oriente control (VOC) an irect power control (DPC) are two popular metho [3]. However, with the evelopment o ater an more powerul igital ignal proceor, the implementation o new control trategie uch a uzzy logic an preictive control i poible [4]. One o the mot promiing preictive controller in power converter an electric rive i the inite-control-et moel preictive control (FCS-MPC) [4] [6], which exploit the inite number o witching tate o the power converter or olving an optimization problem. Lately, the interet in encoerle control technique i increaing ue to cot eectivene an robutne, which mean that the controller mut run without the inormation o mechanical enor (uch a encoer or tranucer) mounte on the hat [3]. The require rotor pee/poition mut be etimate via the inormation upplie by electrical (e.g. current/voltage) enor which are cheap an eaier to intall than mechanical enor. Furthermore, mechanical enor ecreae the rive ytem reliability ue to their high ailure rate, which mean horter maintenance perio an, conequently, higher cot [3]. Encoerle vector control technique or DFIG have been propoe by everal reearcher [7]- [1]. The encoerle metho preente in [7] i open-loop an relie on rotor current etimator in which the etimate an meaure current are compare to get the rotor poition. The application o moel reerence aaptive ytem (MRAS) oberver or encoerle control o DFIG ha been reporte in [8], where MRAS oberver are iveriie with ierent error variable, e.g. tator an rotor current an luxe. The encoerle control approach in [9] relie on ignal injection. Another alternative i the ue o an extene Kalman ilter (EKF) [1]. However, encoerle FCS-MPC i rarely preente in the literature [11]. In thi paper, a FCS-MPC trategy or DFIG bae on variable-pee WTS i propoe. The propoe control ytem ue a MRAS oberver or etimation o the DFIG rotor pee an poition. Etimation an control behavior o the propoe encoerle control metho are illutrate by imulation reult or all operation conition. Moreover, the behavior o the propoe MRAS oberver i invetigate uner variation o the DFIG parameter. 2

4 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/ Moeling o the WECS with DFIG The block iagram o WECS with DFIG i hown in Fig. 1. The RSC an the GSC hare a common DC-link with capacitance C c [A/V] with DC-link voltage u c [V] Win turbine (WT) The output mechanical power o a WT i given by [1, 12] p t (t) = c p (λ,β) 1 2 ρπr2 tv 3 w(t) (1) where ρ > [kg/m 3 ] i the air enity, r t > [m] i the raiu o the win turbine rotor (πrt 2 i the turbine wept area), c p [1] i the power coeicient, an v w (t) [m/] i the win pee. The power coeicient c p i an inication or the eiciency o the WT. It i a nonlinear unction o the tip pee ratio λ = ωm(t)rt g rv w(t) [1] (2) an the pitch angle β [ ] o the rotor blae. In reality, the power coeicient range rom.4 to.48 [1, 12] Doubly-Fe inuction generator (DFIG) The tator an rotor voltage equation o the DFIG can be written a ollow [2]: u (t) = R i (t)+ t ψ (t) an u r (t) = R r i r (t)+ t ψ r (t) (3) where (coniering linear lux linkage relation) ψ (t) = L i (t)+l m i r (t) an ψ r (t) = L r i r (t)+l m i (t). (4) Here u = (u,u a,u b ) c [V], ur = (ur,u a r,u b r) c [V], i = (i,i a,i b ) c [A], ir = (ir,i a r,i b r) c [A], ψ = (ψ,ψ a,ψ b ) c [V], an ψr = (ψr a,ψr,ψ b r) c [V] are the tator an rotor voltage, current an lux linkage, repectively, all in the -reerence rame (three-phae ytem). L, L r, an L m [V/A] are the tator, rotor an mutual inuctance. R [Ω] an R r [Ω] are tator an rotor wining reitance. The DFIG rotor rotate with mechanical angular requency ω m [ra/]. Hence, or a machine with pole pair number n p [1], the electrical angular requency o the rotor i given by ω r = n p ω m an the rotor reerence rame i hite by the rotor angle φ r (t) = t ω r(τ)τ + φ r, φ r R, with repect to the tator reerence rame (φ r i the initial rotor angle). Equation (3) can be written in the tationary/rotating reerence rame a ollow x k = T P (φ) 1 x = T P (φ) 1 T C x by uing the Clarke an Park tranormation (ee, e.g., [12]), repectively, given by (neglecting the zero equence) [ 1 x = ] [ ] x an x k co(φ) in(φ) = x in(φ) co(φ) (5) 2 }{{}}{{} =:T C =:T P (φ) 1 where x k = (x,x q ), an x = (x α,x β ). The rotor voltage equation (3) with repect to the tationary reerence rame (i.e. u r = T P (φ r ) 1 T C u r ) can be expree a u (t) = R i (t)+ t ψ (t), an u r(t) = R r i r(t)+ t ψ r(t) ω r (t)jψ r(t), (6) [ ] 1 where J := T P (π/2) = [12]. The tator voltage orientation (SVO) i realize by 1 aligningthe-axiotheynchronou(rotating)reerenceramewiththetatorvoltagevectoru 3

5 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/1125 which rotate with the tator (gri) angular requency ω (uner ieal conition, i.e. contant gri requency >, it hol that ω = 2π i contant). Applying the (invere) Park tranormation with T P (φ ) 1 a in (5) with φ (t) = t ω (τ)τ + φ, φ R, to the voltage equation (6) yiel the ecription in the rotating reerence rame u k (t) = R i k (t)+ t ψk (t)+ω Jψ k (t), an u k r(t) = R r i k r(t)+ t ψk r(t)+ω l (t)jψ k r(t), (7) where ω l (t) := ω ω r (t) i the lip angular requency. Since, e.g., ψ k = T P (φ ) 1 ψ = T P (φ ) 1 T C ψ, the lux linkage are given by ψ k (t) = L i k (t)+l m i k r(t) an ψ k r(t) = L r i k r(t)+l m i k (t). (8) For a ti hat an a tep-up gear with ratio g r 1, the ynamic o the mechanical ytem are given by ( ) t ω m(t) = 1 Θ m e (t) mt(t) g }{{} r =:m m(t), ω m () = ωm R (9) where m e (t) = 3 2 n pi (t) Jψ (t) = 3 2 n pl m ( i q (t)i r(t) i (t)i q r(t) ). (1) i the electro-magnetic machine torque (moment), m t [Nm] i the turbine torque prouce by the win (ee Sec. 3) an m m = mt g r [Nm] i the mechanical torque acting on the DFIG hat. Θ[kg/m 2 ] i the rotor inertia an n p [1] i the pole pair number Back-to-back converter an DC-Link A hown in Fig. 1, a balance generator an gri are aume in thi paper. The output voltage o the RSC an GSC can be calculate a ollow [12]: u r (t) = 1 3 u c(t)t r (t) an u (t) = 1 3 u c(t)t (t) (11) where r = ( a r, b r, c r) {,1} an = ( a,b,c ) {,1} are the witching tate vector o the RSC an GSC, repectively, an T i the tranormation matrix [12] T = (12) ecribing the relation between witching tate vector an output phae voltage vector o the converter. Coniering all the poible combination o the witching tate vector r or, eight witching tate, an conequently, eight voltage vector are obtaine. Note that two ierent zero voltage vector are available, ee Fig. 2. The DC-link ynamic are given by [12] (neglecting reitive loe) where t u c(t) = 1 C c (I g (t) I m (t)), u c () = R (13) I m (t) = i (t) r (t) an I g (t) = i (t) (t). (14) are the rotor an gri ie DC-link current (ee Fig. 1). 4

6 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/ u 3 u 2 11 i I 11 u u 7 u 5 u u 6 u 1 1 u R I ψ L φˆr r 1 î r î 1 r L TP m r i r e PI ωˆr 1 11 Figure 2: Dierent witching combination or 2-level converter. Figure 3: MRAS oberver or etimating the rotor pee an poition o the DFIG Filter an gri Fig. 1 how a gri-connecte voltage ource converter, which i connecte to the gri via an RLilter with reitance R [Ω] an inuctance L [V/A]. The gri i coniere a ieal voltage ource with gri voltage uo = (i a,ib,ic ) [A] low rom the gri to the GSC. Invoking Kirchho voltage law at the AC ie o the GSC [12] give = (u a o,u b o,u c o) [V]. The current i u o (t) = R i (t)+l t i (t)+u (t), i () = 3. (15) Here u = (u a,ub,uc ) [V] i the output voltage o the GSC. The voltage equation (15) can be expree in the rotating reerence rame (gri voltage orientation) a ollow uo(t) k = R i k (t)+l t ik (t)+ω JL i k (t)+uk (t). (16) 3. Maximum power point tracking (MPPT) For win pee below the rate win pee o the WT, maximum power tracking i the require control objective. Conequently, the pitch angle i kept contant at β = an the WT mut operate at it optimal tip pee ratio λ (a contant) where the power coeicient ha it maximum c p := c p (λ,) = max λ c p (λ,). Thu, the WT can extract the maximally available power p t := c p 1 2 ρπr2 tvw 3 [12]. Maximum power point tracking i realize by the nonlinear pee controller m e (t) m e(t) = k pˆω m (t) 2 with k p := ρπr5 t 2g r c p (λ ) 3 (17) which guarantee that the generator angular requency ω m (t) i ajute to the actual win pee v w (t) uch that ωm(t)rt! g rv w(t) = λ hol. Accoring to (17) the optimum torque m e(t) can be calculate rom the (etimate) hat pee ˆω m (t) = ˆω r (t)/n p. 4. Propoe FCS-MPC 4.1. FCS-MPC or RSC The tator (gri) voltage orientation (SVO) i achieve by aligning the -axi o the ynchronou reerence rame with the tator voltage vector u (t). The reultant tator q-axi voltage are u (t) = u (t) an u q (t) = [2]. By ubtituting the value o ψ k r(t) rom (8) in (7), the rotor voltage u k r(t) can be written a u k r(t) = R r i k r(t)+l r t ik r(t)+l m t ik (t)+ω l (t)l r Ji k r(t)+ω l (t)l m Ji k (t) (18) 5

7 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/1125 Invoking (8), the tator current i k (t) can be expree a an ubtituting (19) in (18) give i k (t) = 1 L ψ k (t) Lm L i k r(t) (19) u k r(t) = R r i k r(t)+σl r t ik r(t)+ Lm L t ψk (t)+ω l (t)σl r Ji k r(t)+ω l (t) Lm L Jψ k (t) (2) where σ = 1 L2 m L L r. Subtituting t ψk (t) rom (7) an ψ k (t) rom (8) in (2) give u k r (t) = R r i k r (t)+σl r t ik r (t)+(ω l (t)l r ω (t) L2 m L )Ji k r (t) (R L m L +ω r (t)l m J)i k (t)+ Lm L u k (t). (21) Solving (21) or t ik r (an writing out both component) yiel t i r(t) = 1 σl L r [ R r L ir(t)+(ω l (t)l r L ω (t)l 2 m)ir(t)+r q L m i(t) ω r (t)l m L i(t)+l q ur(t) L m u(t)] t iq r(t) = 1 σl L r [ R r L i q r(t) (ω l (t)l r L ω (t)l 2 m)i r(t)+r L m i q (t) +ω r (t)l m L i (t)+l u q r(t) L m u q (t)]. (22) The FCS-MPC approach ue a icrete-time moel or the preiction o the current at a uture ample perio. For icretization the orwar Euler metho with ampling time T [] i applie to the time-continuou moel (22). The icrete moel o the DFIG can be written a i r[k +1] = i r[k]+ T σl L r [ Rr L i r[k]+(ω l [k]l r L ω [k]l 2 m)i q r[k]+r L m i [k] ω r [k]l m L i q [k]+l u r[k] L m u [k] ] i q r[k +1] = i q r[k]+ T σl L r [ Rr L i q r[k] (ω l [k]l r L ω [k]l 2 m)i r[k]+r L m i q [k] +ω r [k]l m L i [k]+l u q r[k] L m u q [k] ] In thi paper, or the RSC, the choen cot unction i eine by (23) g RSC = i r,re [k +1] i r[k +1] + i q r,re [k +1] iq r[k +1] (24) where i r,re [k +1] an iq r,re [k +1] are the reerence value o the & q-axi current. For the preiction algorithm, the cot unction (24) (an, hence, (23)) i calculate or each o the even voltage vector, proucing even ierent current preiction. The voltage vector whoe current preiction i minimizing the cot unction (24) i applie at the next ampling perio. However, the uture reerence current i k r,re [k + 1] value i unknown. Thereore, it ha to be preicte rom preent an previou value o the current reerence uing Lagrange extrapolation a ollow [5]: i k r,re [k +1] = 3ik r,re [k] 3ik r,re [k 1]+ik r,re [k 2]. (25) The value o the reerence current i r,re [k] i calculate rom the optimum torque m e[k] an the value o i q r,re [k] i calculate rom the reerence tator reactive power Q,re[k] a ollow [2] i 2ω[k]L r,re [k] = 3n pl mu [k]m e[k] an i q 2L r,re [k] = 3L mu [k]q,re[k] u [k] ω [k]l m. (26) 6

8 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/ FCS-MPC or GSC Again, applying the orwar Euler metho to (16), the icrete moel o the gri ie ilter can be written a ollow i [k +1] = (1 TR L )i [k]+ω et i q T [k]+ L (uo[k] u [k]) i q [k +1] = (1 TR L )i q [k] ω et i For the GSC, the cot unction i eine by [k]+ T L (u q o[k] u q [k]). } (27) g GSC = i,re [k +1] i [k +1] + i q,re [k +1] iq [k +1] (28) where i,re [k +1] an iq,re [k +1] are the reerence value o the - & q-axi current. Again, (27) i calculate or each o the even voltage vector, yieling even ierent current preiction. The voltage vector whoe current preiction i minimizing the cot unction (28) i applieatthenextamplinginterval. Theuturereerencecurrent i k,re [k+1]valueicalculate alo uing Lagrange extrapolation a explaine beore. The value o the -axi reerence current i,re [k] i obtaine rom an outer DC-link voltage control loop. The meaure DC-link voltage u c [k] i compare with a contant reerence value u c,re an the error i procee by a PI controller proucing the -axi reerence current i,re [k], ee Fig MRAS oberver The MRAS oberver i conit o two moel [8]: a reerence moel an an aaptive moel, ee Fig. 3. In thi paper, the reerence moel (ee let part in Fig. 3) i e by the meaure tator current i (t) an the meaure tator (gri) voltage u (t). From the reerence moel (bae on (8)) the rotor current î r(t) i etimate via î r(t) = 1 L m ( ψ (t) L i (t) ) where ψ (t) = t ( u (τ) R i (τ) ) τ +ψ (). (29) The aaptive moel (ee right part in Fig. 3) i e by the etimate rotor current î r(t) an the meaure rotor current i r r(t) in the rotor reerence rame. The objective o the aaptive moel i to etimate rotor poition ˆφ r (t) an rotor pee ˆω r (t). To achieve that the etimate an the meaure rotor current mut be compare; to o o, the etimate rotor current î r(t) (in the tator reerence rame) mut be expree in the rotor reerence rame, i.e. îr r(t) = T P (ˆφ r (t)) 1î r(t). The error between etimate îr r(t) an meaure rotor current i r r(t) i eine a e(t) := îr r(t)ji r r(t) = îr r(t) i r r(t) in ( (îr r(t),i r r(t)) ). The PI controller orce thi error to zero by ajuting ˆω r (t). It output i the etimate pee ˆω r (t) which i integrate to obtain the etimate rotor angle ˆφ r (t). For more etail ee [8]. 6. Simulation Reult an Dicuion A imulation moel o a 5kW WECS with DFIG i implemente in Matlab/Simulink. The ytem parameter are lite in Table 1. The implementation i hown in Fig. 1. The imulation reult are hown in Fig The etimation perormance o MRAS oberver are compare with the actual value or ierent win pee an parameter uncertaintie in R, R r an L m. 7

9 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/1125 Table 1: Parameter o the WECS with DFIG. Name Nom. Value Name Nom. Value WT rate power p t 5kW Rotor inuctance L r 82.12mH WT raiu r t 4.5m Mutual inuctance L m 77.2mH Rate win pee v wrate 14 m DFIG moment o inertia Θ.1 kg m 2 Optimal tip pee ratio λ 8.36 DC-link capacitor C c 3mF DFIG rate power p nom 5 kw DC-link voltage u c 7V DFIG line-line voltage u rm 4V Gri line-line voltage u o 4V Number o pair pole n p 2 Gri normal requency e 5Hz Stator reitance R.2448 Ω Filter reitance R.16Ω Rotor reitance R r.4847 Ω Filter inuctance L 12mH Stator inuctance L 8.76mH Sampling time T 4µ ωr [ra/] [m/] ˆω r 1 [m/] 8 [m/] 14 [m/] 8 [m/] 11 [m/] ω r φr [ra/] i /q r [A] 1 7 ˆφr φ r 5 i r i r,re i q r i q r,re λ 1 λ λ 5.6 c p c p cp Time [] Figure 4: Etimation an control perormance o the propoe encoerle FCS-MPC (rom top): etimate an actual rotor pee (ˆω r, ω r ), etimate an actual rotor poition (ˆφ r, φ r ), actual an reerence & q axi current o the rotor (i r, i r,re, iq r, i q r,re ), Optimal an actual tip pee ratio (λ, λ), optimal an actual power coeicient (c p, c p ). The etimation perormance o the propoe MRAS oberver uner variable win pee i hown in Fig. 4. Thi win pee range cover almot the complete pee range o the DFIG (i.e. ±3% aroun the ynchronou pee). Fig. 4 illutrate the tracking ability o the MRAS oberver o the rotor pee an poition at low an high pee, an cloe to ynchronou pee. An acceptably high etimation accuracy i achieve a the etimation error i very mall. The FCS-MPC perormance o the rotor ie converter(rsc) uner variable win pee i illutrate in Fig. 4. It i clear that the RSC control ytem enure tracking o the maximum power rom the win turbine. The actual rotor current i /q r o the DFIG i ollowing the reerence value 8

10 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/1125 ωr [ra/] 4 R = 1.25R & R r = 1.25R r [m/] 3 ˆω r ω r ωr [ra/] L m = 1.1L m v w = 12 [m/] ˆω r ω r φr [ra] 7 ˆφ r φ r φr [ra] 7 ˆφ r φ r i r [A] Time [] i r i r,re Figure 5: Etimation an control perormance o the propoe encoerle FCS-MPC at 25% tep change in R an R r (rom top): etimate an actual rotor pee (ˆω r, ω r ), etimateanactual rotorpoition(ˆφ r, φ r ), actual an reerence axi current o the rotor (i r, i r,re ). i r [A] Time [] i r i r,re Figure 6: Etimation an control perormance o the propoe encoerle FCS-MPC at 1% tep change in L m (rom top): etimate an actual rotor pee (ˆω r, ω r ), etimate an actual rotor poition (ˆφ r, φ r ), actual an reerence axi current o the rotor (i r, i r,re ). i /q r,re. Thu, the MPPT capability i enure. The tip pee ratio λ i ollowing the optimal value λ. Subequently, the power coeicient c p (λ) i kept cloe to it maximal (optimal) value c p.48. In orer to check the robutne o MRAS oberver an FCS-MPC uner (unknown) parameter variation o the DFIG, the value o the tator reitance R an rotor reitance R r i increae by 25% (e.g. ue to warming or aging) at t =.3. For thi cenario, Fig. 5 how the etimation an control perormance o the propoe MRAS oberver an FCS-MPC uner win pee v w = 12 m. It i clear that MRAS oberver an FCS-MPC are robut againt parameter uncertaintie in R an R r. The MRAS oberver i till capable o etimating the rotor pee an poition with goo accuracy an FCS-MPC i till able to track the reerence current, ee Fig. 5. Moreover, the robutne with repect to change (ue to magnetic aturation) in the mutual inuctance L m i invetigate. Thereore, L m i increae by 1% at t =.3. Fig. 6 how the imulation reult o the propoe MRAS oberver an FCS-MPC or thi cenario uner win pee v w = 12 m. Again, MRAS oberver an FCS-MPC how a goo etimation an control perormance an are robut againt parameter uncertaintie. Figure 7 illutrate the FCS-MPC perormance o the GSC uner the ame win pee a hown in Fig. 4. Again, the GSC control ytem guarantee tracking o the contant reerence DC-link voltage an o the reerence & q current a hown in Fig. 7. Finally, the robutne o the propoe FCS-MPC with repect to change in the ilter reitance R an inuctance L i invetigate. Thereore, R an L are increae by 25% at t =.3. Fig. 8 how the imulation reult o the propoe FCS-MPC or thi cenario uner win pee v w = 1 m. Again, the propoe FCS-MPC or GSC how a goo control perormance an i robut againt parameter variation o the ilter. 7. Concluion Thi paper propoe an encoerle FCS-MPC metho or variable-pee WECS with DFIG. A MRAS oberver or etimation o the DFIG rotor pee an poition i utilize. The reult have hown that the MRAS oberver track rotor pee an poition with high accuracy even uner variation o the DFIG parameter. Alo, the reult how that the propoe FCS-MPC 9

11 The Science o Making Torque rom Win (TORQUE 216) Journal o Phyic: Conerence Serie 753 (216) 1125 IOP Publihing oi:1.188/ /753/11/1125 uc [V] 71 7 u c u c,re uc [V] 72 7 R = 1.25R L = 1.25L v w = 1 [m/] u c u c,re i i,re i q i q,re 12 i /q [A] i /q [A] 6 i i,re i q i q,re Time [] Figure 7: Perormance o the propoe FCS- MPC or GSC uner variable win pee (rom top): actual an reerence DC-link voltage (u c, u c,re ), actual an reerence & q axi current o the ilter (i /q, i /q,re ) Time [] Figure 8: Perormance o the propoe FCS- MPC or GSC at 25% tep change in R an L (rom top): actual an reerence DC-link voltage (u c, u c,re ), actual an reerence & q axi current o the ilter (i /q, i /q,re ). or RSC track the reerence current or all the operation conition an i robut againt parameter variation o the DFIG. Thu, tracking o the maximum power rom the win turbine i guarantee. Moreover, the propoe FCS-MPC or the GSC track the reerence current or all the operation conition an i robut againt parameter variation o the output ilter. Thereore, a contant DC-link voltage i enure. Reerence [1] Lierre M an et. al. 211 Overview o Multi-MW Win Turbine an Win Park IEEE Tran. on Inutrial Electronic [2] Wu B an et. al. 211 Power converion an control o win energy ytem (Wiley-IEEE Pre). [3] Carena R, Pena R, Alepuz S an Aher G 213 Overview o Control Sytem or the Operation o DFIG in Win Energy Application IEEE Tran. on Inutrial Electronic [4] Corte P an et. al. 28 Preictive Control in Power Electronic an Drive IEEE Tran. on Inutrial Electronic [5] Roriguez J an Corte P 212 Preictive Control o Power Converter an Electrical Drive (1 t eition New York: Wiley-IEEE Pre). [6] Vazquez S an et. al. 214 Moel Preictive Control: A Review o It Application in Power Electronic IEEE Inutrial Electronic Magazine [7] Datta R an Ranganathan V 21 A imple poition enorle algorithm or rotor ie iel oriente control o woun rotor inuction machine IEEE Tran. on Inutrial Electronic [8] Carena R an et. al. 28 MRAS oberver or enorle control o oubly-e inuction generator IEEE Tran. on Power Electronic [9] Reigoa D an et. al. 213 Senorle Control o Doubly Fe Inuction Generator Bae on Rotor High- Frequency Signal Injection IEEE Tranaction on Inutry Application [1] Abelrahem M, Hackl C an Kennel R 215 Senorle Control o Doubly-Fe Inuction Generator in Variable-SpeeWinTurbineSytemin Proceeing o the 5 th International Conerence on Clean Electrical Power (ICCEP) (Taormina) p [11] Davari S an Khburi D 215 Voltage moel oberver bae encoerle preictive control o DFIG or win tubine application Power Electronic, Drive Sytem & Technologie Conerence (PEDSTC) p [12] Dircherl C, Hackl C an Schechner K 215 Elektriche Antriebe Regelung von Antriebytemen e Schröer D (Springer-Verlag) Chapter 24 pp