ADAPTIVE BACKSTEPPING CONTROL FOR WIND TURBINES WITH DOUBLY-FED INDUCTION GENERATOR UNDER UNKNOWN PARAMETERS

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1 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: ADAPTIVE BAKSTEPPING ONTROL FOR WIND TURBINES WITH DOUBLY-FED INDUTION GENERATOR UNDER UNKNOWN PARAMETERS MOHAMMED RAHIDI, BADR BOUOULID IDRISSI, Depamen of Eleomehanial Engineeing, Moulay Imaïl Univeiy, Eole Naionale Supéieue d A e Méie, BP 44, Majane II, Beni Hamed, 5, Meknè, Mooo moahidi@yahoo.f, ibad.bououlid@enam.umi.a.ma ABSTRAT Thi pape deal wih an adapive, nonlinea onolle fo wind yem onneed o a able eleial gid and uing a doubly-fed induion mahine a a geneao. The udy foue on he ae wheein he aeodynami oque model and winding eiane of he geneao ae unknown and will be updaing in eal ime. Two objeive wee fixed; he fi one i peed onol, whih allow u o foe he yem o ak he opimal oque-peed haaeii of he wind ubine o exa he maximum powe, and he eond deal wih he onol of he eaive powe anmied o he eleial gid. The mahemaial developmen, boh fo he model of he global yem and he onol and updae law, i examined in deail. The onol deign i inveigaed uing a bakepping ehnique, and he oveall abiliy of he yem i hown by employing he Lyapunov heoy. The eul of he imulaion, whih wa buil on Malab-Simulink, onfim when ompaed wih onol wihou adapaion, he validiy of hi wok and he obune of ou onol in he peene of paamei fluuaion o uneainy modeling. Keywod: Wind powe geneaion, doubly-fed induion geneao, unknown winding eiane, unknown aeodynami oque, adapive onol, bakepping onol, Lyapunov heoy.. INTRODUTION Fom all oue of eleiiy geneaion, ha whih ha he wind a oigin ha peened he highe gowh ae fo moe han yea, and hi hould oninue in he fuue []. Thu, wind geneaion hould be he geae onibuion o eduing he geenhoue effe in he oming yea. The aue fo hi ineae lie in he high poliial will o pomoe hi eo and alo in poduion o, whih ae beoming ineaingly ompeiive. The mo ued uue in hi aea, epeially in high powe, whih i alo he ubje of hi wok, i hown in Figue [-]. I ue a doubly fed induion mahine a a geneao. In geneal, he ao i diely onneed o he eleial gid, bu he oo i onneed hough wo bak-o-bak powe onve and an RL file. The apaio i onideed a a D egulaed volage oue fo he onve. The oo ide onvee (RS) i uually ued o onol he aive and eaive powe anmied fom he ao o gid. Howeve, he gid ide onvee (GS) i ued o egulae he D volage a a fixed value and, a he ame ime, onol he eaive powe anmied he fom he RL file o he gid. The pinipal benefi of hi onfiguaion i he poibiliy of vaying he oo peed in a lage ange aound he ynhonou peed of abou ±% [-4]. Thi allow u o deign a peed onol ha foe he yem o oninuouly ak he opimal oque-peed haaeii of he wind ubine [- ]. The pupoe of hi wok i o ake pa of hi eeah aea by examining he ubje of he obune of he onol in ae of paamei and modeling uneainie. Indeed, we have ageed he peinen paamee ha ae uepible o vay wih he empeaue, uh a he eiane of he oo and ao winding. We alo inveigaed he ae of he aeodynami oque, fo whih auae modeling i no an eay ak. We deigned adapive onolle ha allow u o eah he fixed pefomane and, a he ame ime, o updae he peviou paamee ha ae aumed o be 58

2 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: unknown. To how he impoane of hi udy, we ompaed he pefomane of ou onol wih hoe of he onol wihou adapaion. The pape i oganized a follow. The eond eion peen a ae-pae modeling of he DFIG-baed wind powe onveion yem. The hid eion deail he popoed nonlinea adapive onolle. Thi deign wa eablihed uing bakepping ehnique and he Lyapunov appoah. In he la eion, we peen he imulaion eul and diu he impoane of ou udy. Figue. : DFIG-baed wind powe onveion yem. SYSTEM MODEL.. Modelling of he Wind Tubine The aeodynami ubine powe P depend on he powe oeffiien p a follow [5]: P = ρ πr p( λ, β) v (a) Whee ρ, v, R, p, β, Ω e λ ae he peifi ma of he ai, he wind peed, he adiu of he ubine, he powe oeffiien, he blade pih angle, he geneao peed and he Tip Speed Raio (TSR), epeively. R The TSR i given by: Ω λ = (b) G v Whee: G i he peed muliplie aio. The following equaion i ued o expe p(λ,β) [5] a: λ β = 5 p(, ) ( β 4)exp( ) + 6λ () λ λ i.5 Whee = and.8 o 6 ae λi λ+ β β + onan oeffiien given in "Appendix". The powe oeffiien eahe i maximum ( pmax ) fo β = and a paiula value λ op of λ. In hi pape, we uppoe ha he wind ubine opeae wih β=. To exa he maximum powe and hene keep he TSR a λ op (MPPT aegy), a peed onol mu be done. i Aoding o (b), he opimal mehanial peed i: G v Ω = (d) R λ op.. Induion Geneao Model To ge he model of he induion mahine, we have applied he Pak anfomaion in he ynhonouly oaing fame, wih he d-axi i oiened along he ao-volage veo poiion (v d =V, v q =). In hi efeene fame, he eleomehanial equaion ae [6]: d[ φ] [ V] = [R][I] + + [ ω][ φ] d (a) [ φ ] = [M][I] (b) dω J = T Tem fω d () T = pl (i i i i ) (d) em Whee m q d R [R] = L [M] = Lm d q R L Lm R Lm L ; R Lm ; L ω ω [ ω] = ω ω [V], [I] and [Φ] ae he volage, he uen and he flux veo. The ubip,, d and q and fo ao, oo, die and quadai, epeively. R, L, L m, ω, J, f, p, T and T em ae eiane, induane, muual induane, eleial peed, oal ineia, damping oeffiien, numbe of pole pai, mehanial oque and eleomagnei oque, epeively. By hooing uen and peed a ae vaiable, he yem () an be pu ino he following aepae fom: x (a) x (b) x () x (d) = g(x,r,r) + βu = g(x,r,r) + βu = g(x,r,r) + αu 4 = g4(x, R, R) + αu 59

3 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: η = Fη+Γ + Γ Whee: em 4 q x = (x, x, x, x ) = (i, i, i, i ), η = Ω Τ Γ em em = = a(xx4 xx); Γ = J u = v, u = d vq Lm α =, β = σl σll i d q d T J The funion g (x, R, R ) ae: (e) g = a R x + b x + R x + m x η+ n x 4 η+ αu g = bx arx + Rx4 mxη nxη g = R x a R x + b x 4 n x η m x 4 η+βu g 4 = R x b x a R x 4 + n x η+ m x η plm Lm a =, a =, b =ω = πf, =, J σl σll σ L m p, n p m = =, αu = V, σ σl σl Lm p Lm a =, b = πf, =, m =, n = p, σl σll σ σl L f β V; m u =β σ= ; F= LL J f and V ae epeively he onan fequeny and magniude of gid volage. Equaion (a) o (.d) an be pu ino he following ompa fom: x = g(x,r,r ) Whee + Au g = (g, g, g, g4), β A = β α α, u) u = (u,. ONTROL DESIGN.. onol objeive (f) By examining he equaion yem (), we an idenify wo degee of feedom u and u ha an be ued o onol he RS onvee. Thu, wo onol objeive wee e; he fi one i peed onol, whih allow u o foe he yem o exa he maximum powe, while he eond deal wih he onol of eaive powe anmied by he ao o he eleial gid. To ahieve hi goal, we ued he Bakepping ehnique [7-8]. Indeed, he following expeion of he ao eaive powe (4) Qg = Im(VI ) = vqid vdiq = Vx how ha he uen vaiable x an be ued o onol he eaive powe Q g. Aoding o equaion (b), i i lea ha he onol vaiable u an be deigned o ha he uen vaiable x ak i efeene. On he ohe hand, fom he yem (), we an eonu he following ubyem ha adap well o onol peed: η= Fη+ Γ + Γem Γ em = h.g + a ( βx4 αx) u + a ( αx βx) u Whee h(x) = Γem = a(xx4 xx) h h h h and h = (,,, ) x x x x 4 (5) So, in he fi equaion, he vaiable Γ em an be onideed a a viual onol fo he peed η. The eond equaion how ha he onol vaiable u an be deigned o ha Γ em ak i efeene.... onol and updae law Fo uneain model o whih he paamee ae no known wih uffiien auay, an appopiae hoie of onol and updae law mu be done o ill enue he abiliy ondiion. In hi udy, i i aumed ha he ao eiane, oo eiane and mehanial oque R, R and T, epeively, ae unknown and vay lowly wih ime. Thei oeponding eimaed em ae denoed, and ˆΓ, epeively. We define alo he eo vaiable a: z z = x x = η η z = Γem Γ R = R R = R Γ = Γ Γˆ em (6) Whee x, η and Γem ae he efeene of vaiable x, η and Γ em, epeively. Popoiion: The following updae and onol law: 6

4 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: ξ = λξ λh(x) +λ(f λ) η v ˆ Γ = ξ +λη = γ(x4z ah(x)z) = γa(xz + h(x)z) g (x,, ) k z x u + = ; β υ ˆ h.ĝ a( αx x )u u β = a( βx4 αx) Wih Γ ˆ em = (k F)z + Fη Γ + η Γem = h(x) = a(xx4 xx) v = z ( λ + k F)z υˆ = z kz + Fη + (k F)(kz + z) + η + v h.ĝ = a(xg4(x,, ) + x4g(x,, ) xg(x,, ) xg(x,, )) k, k, k, γ, λ ae poiive deign onan ahieve peed and uen aking objeive and enue aympoi abiliy depie he hange in paamee. Poof: a- onol law u Taking he deivaive of z and uing (b), we an wie: z = (7) g(x,r,r) +βu x Wih he Lyapunov andidae funion V = z and he hoiez = kz, whee k i a poiive deign onan, i poible o make negaive he deivaivev = k z. The onol law u an be obained fom equaion (7), uing he peviou hoie and he eimaed eiane, a: u g(x,, ) kz + x β = So, he dynami of he eo z i govened by: z = k z + R x a R 4 x (8) (9) Thi an be obained fom (7) by uing (8) and noing ha g (x,r,r) = g(x,, ) ar x + R x4. b- onol u and updae law Sep : Viual onol Γ em Uing equaion (e), he deivaive of z i wien a: () z = Fη+Γ +Γem η Sine Γ i unknown; i will be eplaed wih i eimaed ˆΓ. Wih he Lyapunov andidae funion z V = and he hoiez = kz, whee k i a poiive deign onan, i poible o make negaive he deivaivev = k z. Uing hi hoie, equaion () beome: k z = Fη+Γˆ +Γ η () em Thu, he viual onolγ em i: em Γ = ( k F)z + Fη Γˆ + η () Whee η ha been eplaed by z + η Subaing () fom (), we obain: z = k z z + Γ () Sep : onol and updae law We will now poeed in he ame way fo he deivaivez. z = Γ em Γ em (4) Fily, we expe Γ em aoding o (5): Uing (6), he deailed developmen of he em h.g give: h.g = h.ĝ a R h(x) Whee a R h(x) h.ĝ = a(x g (x,, ) + x g (x,, ) x g (x,, ) x g (x,, 4 4 To epaae unknown em fom he e, we wie Γ a: em Γ em = υ ˆ a R h(x) a R h(x) Whee υ ˆ = h.ĝ + a ( βx αx ) u + a ( αx βx ) (5) )) 4 u Seondly, aking he deivaive of Γem fom () and uing (), we an wie Γ ema: 6

5 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: Γ em = ( k F)( k z z +Γ) + Fη Γˆ + η Thu he dynami of eo zi: z = υ ˆ ar h(x) ar h(x) + (k z +Γ) Fη +Γˆ η F)( k z (6) To updae he oque, one popoe he dynami of eo eimaion Γ a [9]: Γ = λ Γ + v (7) Whee λi a poiive deign onan and v i a em o be deemined afe. If we ombine (7) and he equaion of moion (e), we an eablih he updae law of he oque a: Γ ˆ λη = λ(ˆ Γ λη) λh(x) +λ(f λ) η v Fo hi law, we have aumed ha he oque vaie lowly, whih eul in: Γ = Γˆ By uing ξ = Γˆ λη a inemediae vaiable, one an ewie he updae law of he oque a: ξ = λξ λh(x) +λ(f λ) η v (8) Γˆ = ξ +λη Equaion (6) an be now pu in he fom: z = A a R h(x) a R h(x) + ( λ + k F) Γ (9) Whee A = υ ˆ Fη + (k F)( k z z ) η v () To enue he oveall abiliy, one popoe he following Lyapunov andidae funion: R R Γ V = z + z + z () γ γ Uing (9), () and (9), V an be wien a follow: V = k z k z + (A z )z λ Γ + ( x z a h(x)z 4 )R + (z + ( λ + k F)z + v) Γ γ + ( axz ah(x)z )R γ The updae law ae obained by anelling he em wih R andγ : v = z ( λ + k F) z = γ ( x z a h(x)z ) 4 = γa(xz + h(x)z By hooinga = z kz, equaion (9) beome: z = z kz ar h(x) ar h(x) ( λ + k F) Γ ) () And he deivaivev edue o: V = k z k z k z λ Γ Whih implie ha he eoz, z, zandγ onvege o zeo. Equaion (9) and () how ha if h(x) i diffeen fom zeo hen, eo R and R onvege alo o zeo. Finally, by uing (5) one an eablih he onol law u a: υ ˆ h.ĝ a( αx x )u u β = a( βx4 αx) Fo hi expeion, he em υˆ i deemined, by eplaing he em A in he equaion () by z k, a: z υ ˆ = z kz + Fη + (k F)(kz + z) +η + v Remak: L a( βx4 αx) = a( σ L i m q iq) = σll σ a L φq L Sine he effe of he ao eiane i negligible epeially in high powe, he flux and he volage veo ae ubanially ohogonal. Then, wih he fame ued fo he induion mahine, he em φ q i equal o he ampliude of he ao flux. onequenly, he em a( βx4 αx) beome diffeen fom zeo a oon a he yem i onneed o he gid. 4. SIMULATION RESULTS The imulaion buil on Malab / Simulink deal wih he enie wind yem hown in Figue. In a peviou pape [], we developed he GS onvee onol and fo whih we ae ineeed fo egulaing he D volage and eaive powe anmied fom he oo o he gid. Thi powe i popoional o he quadai omponen of he phae uen, noed i q, paing hough he file RL (ee Eq(4)). To how he impoane of hi pape, we developed wo imulaion heme, whih oeponded epeively o he onvenional (wih known model) and ou adapive 6

6 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: (wih unknown eiane and mehanial oque model) bakepping onolle. The aking and idenifying apabiliy of ou adapive onolle wee veified in he ae of ime-vaying wind peed (Figue ). To demonae he obune again winding eiane and mehanial oque hange, egulaion pefomane fo adapive and onvenional onolle wee ompaed a onan wind peed (Figue 4). Fo boh ae, one aume ha hange ou in he yem model, fi (a, R=5%) and nex in he mehanial oque (a, T =-5%). The onan value fo D-link volage file and quadai uen efeene wee onideed. To have a uniy powe fao, he efeene of q-axi uen i q and i oq have been e o zeo. The value of he deign paamee ued in imulaion ae: k =, k =5, k =, λ = and γ =γ =.. Figue a and b onfim he effeivene of he MPPT aegy ine he oo peed vaie in aodane wih wind peed o ha he ubine opeae a i opimal TSR. Figue d and e how he good aking apabiliy of he q-axi uen onolle. The ame pefomane ae ahieved in he ae of D-link egulaion (Figue f) and he viual onol vaiable (Figue ). Figue g and h illuae he wo opeaing mode of he geneao. Aound ime =55, we an ee in Figue b ha he induion mahine wihe fom upe-ynhonou o ubynhonou mode (N=5 pm). Figue g how ha gid volage and ao uen ae in phae fo boh of he wo opeaing mode; hu, he aive powe i anmied fom he ao o he gid. Figue h how ha gid volage and file uen ae in phae oppoiion fo (>55); hu, he aive powe i anmied fom he gid o he oo. Thi eul i ompaible wih he ubynhonou peed opeaion. Alo, Figue (h) how ha, fo (<55), he gid volage and file uen ae in phae; hu, he aive powe i anmied fom he gid o he oo. Thi eul i ompaible wih he upe-ynhonou peed opeaion. Aoding o Figue i, one an noie ha he unknown oo eiane quikly onvege o i ue pofile (unknown o he onolle). Likewie, Figue j how ha he eimaed mehanial oque eove pefely he applied unknown aeodynami oque. Figue 4 how he egulaion pefomane of he onvenional and adapive onolle when hee ae hange in he oo eiane R and he mehanial oque T. The imulaion aume ha hange ou in he yem model fi a, R=5% and nex in he mehanial oque a, T=-5%. Unlike he onvenional bakepping onolle (Figue. 4b, 4d, and 4f), he adapive onolle ak oely he efeene of egulaed vaiable depie he hange (Figue. 4a, 4, and 4e). Thee eul onfim he obune of he popoed onolle. 5. ONLUSION Thi pape ha hown he effeivene and obune of a nonlinea, adapive, bakepping onolle in vaiable-peed DFIG yem wih unknown aeodynami oque model and unknown eiane of oo and ao winding. The numeial imulaion how he good peed, uen aking pefomane, and he oe updae and idenifiaion of unknown paamee. Finally, he ompaion wih he onvenional onolle wihou adapaion how he upeioiy of he popoed adapive onolle and he peinene of hi wok. 6

7 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: Appendix: haaeii and Paamee Induion Geneao Raed powe Raed ao volage Nominal fequeny Numbe of pole pai Roo eiane Sao eiane Sao induane Roo induane Muual induane Wind Tubine Blade Radiu Powe oeffiien Opimal TSR Mehanial peed muliplie p oeffiien Geneao and Tubine Momen of ineia Damping oeffiien Bu D MW 69V 5Hz p = R =.97e-Ω R =.8e-Ω L =.H L =.H L m =.e-h R =45m pmax =.48 λ op =8.4 G= =.576, = 6, =.4, 4 = 5, 5 = 6 =.68 J=54Kg.m F=.4 = 8 mf, v d = V File RL R =,75 Ω, L =,75 mh Eleial gid U = 69 V, f = 5 Hz [7] M. Ki, I. Kanellakopoulo, P. Kokoovi, Nonlinea and adapive onol deign, John Wiley Son, In, 995. [8] I. Kanellakopoulo, P.V. Kokoovi, and A.S. Moe, Syemai deign of adapive onolle fo feedbak lineaizable yem, IEEE Tan. Auo. onol. 99. Vol. 6, (), pp [9] Maino, Riado, Tomei, Paizio, Veelli, iiano M. Induion Moo onol Deign Spinge-Velag London,. [] M. Rahidi, B.Bououlid, Adapive Nonlinea onol of Doubly-Fed Induion Mahine in Wind Powe Geneaion Jounal of Theoeial and Applied Infomaion Tehnology May 6, Vol 87, N. [] E. Kououli and K. Kalaizaki, Deign of a Maximum Powe Taking Syem fo Wind-Enegy- onveion Appliaion IEEE Tanaion On Induial Eleoni, Vol. 5, No., Apil 6. [] Y.Hong, S. Lu,. hiou, MPPT fo PM wind geneao uing gadien appoximaion, Enegy onveion and Managemen 5 (), pp. 8-89, 9 REFERENES: [] B. Mulon ; X. Roboam ; B Dakyo ;. Nihia ; O Gegaud ; H. Ben Ahmed, Aéogénéaeu éleique, ehnique de l Ingénieu, Taié de génie éleique, D96, Novembe 4. [] R. Pena, J.. lae, G. M. Ahe, Doubly fed induion geneao uing bak-o-bak PWM onvee and i appliaion o vaiable -peed wind-enegy geneaion, IEE Po. Ele. Powe Appl., vol. 4, no., pp. -4, May 996. [] Kahikeyan A., Kummaa S.K, Nagamani. and Saavana Ilango G, Powe onol of gid onneed Doubly Fed Induion Geneao uing Adapive Bak Sepping appoah, in Po h IEEE Inenaional onfeene on Envionmen and Eleial Engineeing EEEI-, Rome, May. [4] H. Li, Z. hen, Oveview of diffeen wind geneao yem and hei ompaion IET Renewable Powe Geneaion, 8, ():-8. [5] Siegfied Heie, Gid Inegaion of Wind Enegy onveion Syem John Wiley Son Ld, 998, ISBN X. [6] J.P.aon, J.P.Hauie, 995 Modéliaion e ommande de la Mahine Aynhone Ediion Tehnip, Pai. 64

8 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: Fig. a: Time-vaying wind peed Fig. b: Roo peed and i efeene Fig. : viual onol and i efeene Fig. d: Sao q-axi uen and i efeene Fig. e: File q-axi uen and i efeene Fig. f: D-link volage and i efeene 65

9 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: Fig. g: Phae a gid volage and ao uen Fig. h: Phae a gid volage and file uen Fig. i: Roo eiane and i eimaed Fig. j: Mehanial oque and i eimaed Figue : Taking apabiliy unde ime-vaying wind peed hange ou a ( R=5%) and a ( T =-5%) Fig. 4a: Roo peed wih adapaion Fig. 4b: Roo peed wihou adapaion 66

10 Jounal of Theoeial and Applied Infomaion Tehnology 5 h Sepembe 6. Vol.9. No. 5-6 JATIT LLS. All igh eeved. ISSN: E-ISSN: Fig. 4: Sao uen wih adapaion Fig. 4d: Sao uen wihou adapaion Fig. 4e: Viual onol wih adapaion Fig. 4f: Viual onol wihou adapaion Figue 4: ompaion of aking pefomane unde unknown paamee hange ou a ( R=5%) and a ( T =-5%) 67

QUASI-EXTREMUM SCALAR CONTROL FOR INDUCTION TRACTION MOTORS: RESULTS OF SIMULATION. Rodica Feştilă* Vasile Tulbure** Eva Dulf * Clement Feştilă*

QUASI-EXTREMUM SCALAR CONTROL FOR INDUCTION TRACTION MOTORS: RESULTS OF SIMULATION. Rodica Feştilă* Vasile Tulbure** Eva Dulf * Clement Feştilă* QUAI-EXEMUM CALA CONOL FO INDUCION ACION MOO: EUL OF IMULAION odia Feşilă aile ulbue Eva Dulf Cleen Feşilă Depaen of Auoai Conol, ehnial Univeiy of Cluj-Napoa, Fauly of Auoaion and Copue iene, 6-8 Baiiu,