POWERS CONTROLS OF A DOUBLY- FED INDUCTION GENERATOR USED IN A CHAIN OF WIND POWER CONVERSION

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1 POWERS CONTROS OF A DOUBY- FED INDUCTION GENERATOR USED IN A CHAIN OF WIND POWER CONVERSION Jean N. RAZAFINJAKA (a), ANDRIANANTENAINA Tory Patrck (b), Jean Claude RAKOTOARISOA (c), Hervé MANGE (d), Charle Berna ANDRIANIRINA (e) (a),(b),(c) aboratore d Automatque, Ecole Supéreure Polytechnque d Antranana, Dego Suarez, Madagacar (d) aboratore Breto de Mécanque et de Sytème, Unverté de Bretagne Occdentale (Bret), France (e)aboratore d Electronque de Puance, Ecole Supéreure Polytechnque, Madagacar (a) razafnjaka@yahoo.fr, (b) otantkroyt@gmal.com, (c) rajeanclaude@gmal.com, (d) Herve.Mangel@unv-bret.fr (e) nr_cha@yahoo.fr ABSTRACT Th paper deal wth a tudy of ome control appled on a Doubly-Fed Inducton generator (DFIG) dedcate n a chan of wnd power converon. Two method are propoed: ung a PI controller whch ynthe done by a new method called generalzed method (GM) and ung a polynomal controller RST one. The object to apply thee technque to control the actve and reactve power generated by the DFIG. Smulaton how that thee controller lead good reult on trackng behavor, load dturbance rejecton and how robutne followng of varaton parameter. Keywo: wnd power, Doubly-Fed Inducton generator, PI controller, RST controller, vector control 1. INTRODUCTION The development anhe explotaton of renewable energe met a great growth thee lat year. Among thee ource of energe, the wndmll repreent a gnfcant potental to gve oluton for the demand, whch alway ncreae (Allam, Dehba, Abd, Djerr and Adjoudj 214). The wnd power can contrbute wth a gnfcant part for the new ource of energy not emttng a ga for purpoe of greenhoue (Ajoun, Abd Aaou, Ramdan and Bounoua 21) In th paper, a DFIG modelng and t vector control are howed. Several method are been already tuded (Adjoudj and Abd 212, Benbouzd, Beltran and Mangel 213) for the DFIG whch gve good performance. Here, the control of the actve and reactve power generated by the DFIG are gven. For th purpoe, a generalzed method (GM) for PI controller ynthe propoed. A polynomal RST controller alo appled. It may be notehat thee two method neehe functon tranfer of the ytem. Th paper organzed a follow: frt, a preentaton of the wnd power converon gven. The DFIG modelng follow th generalty. For PI controller ynthe, a generalzed method preented. The applcaton of the polynomal controller RST then howed. Dcuon from varou reult and a concluon wll fnh the paper. 2. WIND POWER CONVERSION SYSTEM The ytem, howed by fgure 1 compoed of a turbne, multpler, the DFIG anwo converter (Ajoun, Abd, Aaou and Nacr 212, Meroufel, Maoum and Hammoum 21). The turbne tranform the knetc wnd power n mechancal energy. The total knetc power of the wnd : P ρ π R T V C (1) p 2 For wndmll, the coeffcent of energy extracton Cp whch depend both of the wnd velocty anhe turbne peed uually defned n the nterval [,35,59] (Adjoudj, Abd, Aaou, Ramdan and Bouboua 21). The DFIG tranform th latet n electrcal energy. The converter are ueo tranfer the maxmal energy delvered by the wndmll to the grd accong the wnd velocty. Fgure 1: General cheme of a wndmll baed on DFIG 3. DFIG MODEING AND VECTOR CONTRO The model of the DFIG decrbed n Park referental. The dfferent equaton gve the global modelng of the machne Electrcal equaton Te electrcal equaton gve the voltage expreon. 56

d φ V R + - ω co o rφ q d φ q V q R q + + ω co o rφ d φ V R r + - ( ω co o r ω ) φ d φ rq V rq R r rq + + ( ω co o r ω ) φ 3.2. Magnetc equaton Relaton (3) gve the expreon of dfferent flux. φ. + M. φ. + M. φ. + M. φ. + M q q rq r rq r rq q rq (2) (3) Wth, r, M degn repectvely the tator nductance, the rotor nductance anhe mutual.

2 d φ V R + - ω co o rφ q d φ q V q R q + + ω co o rφ d φ V R r + - ( ω co o r ω ) φ d φ rq V rq R r rq + + ( ω co o r ω ) φ 3.2. Magnetc equaton Relaton (3) gve the expreon of dfferent flux. φ. + M. φ. + M. φ. + M. φ. + M q q rq r rq r rq q rq (2) (3) Wth, r, M degn repectvely the tator nductance, the rotor nductance anhe mutual Torque and power equaton The electromagnetc torque expreed a accong to current and fluxe by: M C p ( φ φ ) (4) em q rq The expreon of the actve and reactve power are: By tator de, P V S I + Vq I q (5) Q V I - V I S q q By rotor de, P V I + V I r rq rq Q V I - V I r rq rq (6) 3.4. Vector control of the DFIG In oer to control the electrcty producton, a method, whch not depend of the actve and reactve power, propoed. It cont to etablh relaton between rotor voltage delvered by the converter wth actve and reactve tator power (Ajoun, Abd, Aaou and Nacr 212, Meroufel, Djerr, Maoum and Hammoum 21). Referental d-q related of pnnng feld and a tator flux algned on the ax d adopted. So: φ d φ φ q Flux equaton become: φ φ. + M.. q + M. rq φ r. + M. φ rq r. rq + M q (7) (8) If the grd uppoed table, the tator flux φ contant. Moreover, the tator retor may be neglected; t a realt hypothe for a generator ued n wndmll. Takng nto account all thee conderaton: V V V ω φ q (9) By the equaton (8), a relaton between tator and rotor current can be etablhed: φ (1) M. M q - (11) rq Ung mplfyng hypothe, the equaton of power gve: M P - V. Q - V. + rq 2 M V. ω (12) In oer to control the generator, expreon howng the relaton between rotor voltage and rotor current are: d V R + - gω V R σ g σ r rσ rσ rq dt (13) drq MV rq r rq + r + ω r + dt ω Wth g, σ denotng repectvely the lp anhe leakage coeffcent. Ung relaton (9),(1),(11) and (12), fgure 2 how a dagram where the rotor voltage lke nput and actve and reactve power lke output. Fgure 2: Dagram of the ytem to be controlled There are generally two method to do an ndependent regulaton for the actve and reactve power: Drect method, whch cont to neglect the couplng term ano put a controller on each 57

3 axe to control actve and reactve power. In th cae, the controller command drectly the rotor voltage of the machne The econd method, whch take nto account the couplng term ano compenate them by ung two loop permttng to control the power anhe current of the rotor. It baed on the relaton (12) and (13). The dagram gven by fgure 3. Fgure 3 : Indrect vector control dagram 4. PI CONTROER The ynthe baed on the mplfed model of the DFIG. A PI controller a mple one but can offer good performance. Dfferent documentaton how everal method (Allam, Dehba, Abd, Djerr and Ajoun 214, Bühler 1998) for t ynthe. Here, a generalzed method (GM) propoeo determne the parameter of the PI controller. Uually, there are two knd of functon tranfer: n K GR ( p) GR ( p) K p + (14) p It eay to fnd relaton between dfferent parameter: Tn K p T 1 K T (15) Andranantenana T. 215). Therefore, the functon tranfer of opened loop : n K Go ( p). 1 + Relaton (18) reume the method: Tn a. T a T b. K. T b > Example: 1/ a 1 (the tme contant T cancelled) 1 1 o ( ) +. K G p pbkt (1 + ) pbt The functon tranfer for the cloed loop then Go ( p) 1 H ( p) 1 + G ( p) pbt o (17) (18) (19) (2) The functon tranfer yet a frt oer one wth the tme-contant T f b.t (<b<1, here) 2/ a 1 1 o ( ). K G p pbkt 1 + pbt.(1 + ) The cloed loop tranfer functon Go ( p) 1 1 H ( p) 1 + G ( p) pbt.(1 + ) p² bt ² + pbt + 1 o By comparng wth the canoncal form, Ho 1 1 2ζωn T 2 1 ωn bt ² Impong b gve ζ and vce vera. (b 2 ζ Fgure 4 how the power loop, * Y r n PI Ka a (21) (22) (23) 2 2 ). Yr For each loop, the functon tranfer of frt oer can be ued for the ytem. K G( p) (16) 1 + Uually, the econd knd of functon tranfer ued. The method cont to: Impoe a repone tme at ± 5% Chooe a frequency for cloed loop. Here, the GM method ung the frt expreon of the functon tranfer choen (Razafnjaka N.J. and Fgure 4: Power loop dagram Here, M. V Ka. Rr. r M ² Ta. Rr (22) 58

4 For the current loop, * I r + - n PI Kr r Ir dt,15 [] Wth, 1 Kr Rr σ. Tr Rr r Fgure 5: Current loop dagram (23) (b) (c) (b) Actve power (Ω:167,5 [. -1 ] 178 [. -1 ] (c) Actve power (Rr: Rr 2*Rr) 4.1. Smulaton and reult Trackng tet, dturbance rejecton and robutne compareo the varaton parametrc, epecally varaton of the rotorque retance Rr are ued. All mulaton have the ame condton: Varaton of the power reference, P ref and Q ref t 2,5[], Ω :167,5 [. -1 ] 178 [. -1 ] t 3[], Rr 2*Rr All the parameter of the PI controller are determned by the MG method. Power : a b, 58 current : a 1 b 1 Fgure 6 preent the mulaton reult. courant rotorquee -1 Ira -15 Irb Irc temp en[] (d) Rotorque current 2 1 Va [V], a[a] P [W] Pref P t[] t [] (e) Statorque Voltage and current when Q Fgure 6: Smulaton reult wth PI controller It clear here to note that PI controller determned by the MG method allow good performance: trackng, dturbance rejecton and robutne from parameter. Fgure 6 (b)-(c) how that teady tate reached after t,125,15 []. The peak value : P 2 [W]. Va 1*a Q [VAR] Qref Q t[] (a) : Actve and reactve power curve 5. RST CONTROER Th controller prmarly a dgtal controller. It generalze the tanda PID controller.. It owe t appellaton by the three polynomal R(z), S(z) and T(z) whch defne t. The command law : R. U T. Y S. Y (24) c 59

5 Where Yc(z), Y(z) are repectvely the et pont anhe output. The dfference between T(z) and S(z) offer more poblty and t the reaon that RST controller called controller wth two degree of freedom RST ynthe The RST ynthe baed on pole placement when a dered model H m (z) n cloe loop gven. Fgure 7 how the bac dea. Uually, the dered model wth non-hgh oer. It pole mut atfy abolute and relatve condton of dampng. Yc(z) Yc(z) RST H m (z) U(z) Fgure 7: Bac cheme for RST ynthe The relaton (16) how that power loop and rotorque current loop may be preented by frt oer tranfer functon. K G( p) 1 + Relaton (25) permt to calculate the dcrete tranfer functon G(z) when G(p) gven. 1 1 G( p) G (1 z ) Z [ ] (25) p So, B b G (26) A z z Wth b K.(1 z) h (27) z T e Here h the amplng tme. The dered model n cloe loop a follow: Bm Hm Am (28) Ung the relaton (24), (26) and (28), the followed equalty can be etablhed: T. B Bm A. R + B. S A m G(z) Y(z) Y(z) (29) Reolvng the equaton (29) need zero mplfcaton. For H m (z), ome conderaton mut be taken nto account. To elmnate the poton error: e H (1) 1 p m The denomnator : d Am z. P Where d P 1 or d P 2. For the lat condton, P z² + c z + c 1 2 ζωnh c1 2. e.co( ωnh. 1 ζ ² (29) 2ζωnh c2 e Becaue of the expreon of G(z), no zero can be cancelled. All tep to determne the polynomal RST are reumed n (ongchamp 1991, Razafnjaka 1991). In th paper, a polynomal P(z) wth degree 2 and a perturbaton compenator (m1) are ued. The reult of computaton are: h 1[ m] ζ, 77 ωn 4 Power R z 1 S, 89z, 39 T,5 h 1[ m] ζ, 77 ωn 4 Current R z 1 S 3, 6z 13, 48 T 17, Smulaton reult All condton for trackng, dturbance rejecton and robutne tet are the ame lke wth the PI controller. Fgure 8 how dfferent curve. P [W] Pref P t[] Here, R(z), S(z) and T(z) are to be calculated. Uually R(z) choen a a normalzed polynomal. 6

4 3 2 1-1 Qref Q -2.5 1 1.5 2 2.5 3 3.5 4 t[] (a) Actve and reactve power curve (b) (b) Actve power (Ω:167,5 [. -1 ] 178 [.

6 Qref Q t[] (a) Actve and reactve power curve (b) (b) Actve power (Ω:167,5 [. -1 ] 178 [. -1 ] (c) Actve power (Rr: Rr 2*Rr) Courant rotorque [A] Q [VAR] t[] (d) Rotorque current (c) Ira -15 Irb Irc Va[V], Ia[A] t[] dt,11[] Va [V] 15*Ia[A] (e) Statorque voltage and current when Q Fgure 8: Smulaton reult wth RST controller Fgure 8 (b) (c) how that the ytem wth RST controller ( h 1 [m]) fater but the peak power hgher ( P8 [W]) n comparon wth the PI controller one. However, t hould be notehat th peak value anhe ocllaton decreae a the amplng tme decreae. In the two cae, the reactve power Q null when tatorque voltage and current are purely are nuodal and n phae enurng good qualty of the energy njecteo the grd. The tatc error null. At leat, good performance are obtaned. CONCUSION In th paper, PI and RST controller are ueo control the actve and reactve power generated by a DFIG ued n a chan of wnd power converon. A new method called generalzed method (GM) propoed and appled. The reult how the effectvene of th new method. It mut be alo notehat the RST controller may be nerted n adaptve control. REFERENCES Allam M., Dehba B., Abd, M. Djerr Y., Adjoudj R; 214. Etude comparatve entre la commande vectorelle drecte et ndrect de l machne aynchrone à double almentaton (MADA) dédée à une applcaton éolenne. JARST. Adjoudj M., Abd M. Aaou A., Ramdan Y., Bounoua H. 21. Commande par mode glant.d une machne aynchrone à double almentaton montée dan une éolenne. Revue Nature et Technologe, pp Ajoun M. Aaou I A., Abd M., Nacer A Commande par mode glant d un ytème éolen à bae d une génératrce aynchrone à double almentaton. Internatonal Conference of Renewable Energy (ICRE), Unverté Mra. Bejaa. Ajoun M., Abd M Commande par mode de glement flou d un ytème éolen à bae de génératrce aynchrone à double almentaton. 2ème Journée Internatonale ur le Energe Renouvelable et le Devéloppement durable agouat, Algére. Benbouzd M., Beltran B., Amrat Y., Yao Gang, Jngang H. Mangel H. 213.Hgh-Oer ldng mode Control for DFIG baed wnurbne fault Rde-Trough. IEEE IECON Venne Autra. Bühler H Concepton de ytem automatque- Complément au Traté d Electrcté. Edton PPR. auanne. ongchamp R., 1991, Commande adaptatve, Cour d été, EPF, Sue. Razafnjaka N. J., Automataton de ynthèe de régulateur tanda et polynomaux- Applcaton à la commande adptatve, thèe de doctorat 3è cycle, EPF auanne (Sue), ESP Antranana (Madagacar). Razafnjaka, Andranantenana, 215.Comparaon de performance de régulateur PI et IP applqué aux ytem fondamentaux, Reearchgate. 61

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