The Fuzzy Tracking Control of Output vector of Double Fed Induction Generator DFIG via T S Fuzzy Model

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1 Receved: Augut 25, he Fuzzy ackng Contol of Output vecto of Double Fed Inducton Geneato DFIG va S Fuzzy Model Fouad Abdelmalk 1 * Najat Ouaalne 1 1 aboatoy of Engneeng, Indutal Management and Innovaton Faculty of cence and technology, Haan ft unvety, Moocco * Coepondng autho Emal: f.abdelmalk@gmal.com Abtact: he pupoe of th pape to enue a tackng contol of output tate epecally the actve and eactve powe of doubly fed nducton geneato (DFIG) by ung the appoach of Paallel Dtbuted Compenaton (PDC) of the fuzzy contol type akage-sugeno (-S) whch detemne the contol law contanng fuzzy tackng and etun tate. h tackng ha been bult to convege the output vecto of the DFIG to a deed tate. In th wok, the quadatc functon of lyaponov and a lnea matx nequalty (MI) ae ued to obtan the gan of the tackng contol and the contolle.he mulaton eult of law contol baed on the tackng and contolle gan allow the actve and eactve powe obtaned mut follow the efeence popoed. Keywod: Fuzzy model, Nonlnea ytem, akage-sugeno (-S), DFIG, PDC, MI, yapunov, Quadatc tablty, ackng contol, Matlab MI toolbox. 1. Intoducton he doubly fed nducton machne (DFIM) ha been the ubject of much eeach manly n nduty uch a geneato DFIG fo wnd enegy applcaton [1, 2] and moto fo ventlaton ytem and pump, nce t featue mple tuctue, hgh-enegy effcency, elable opeaton and can opeate vaable peed. he dynamc model of the DFIG not lnea and that ome tate cannot be meaued due to the lack of eno whch caue dffculte to contol and know the evoluton of th nonlnea ytem [3]. A lot of eeache have been done on the modelng and contol of DFIG [4-6] epecally by the fuzzy model popoed by the appoach akag- Sugeno (-S) [7, 8] and the Paallel Dtbuted Compenaton (PDC) [9]. he akag-sugeno (S) fuzzy modelng ue the fuzzy IF-HEN ule fo epeentng a local nputoutput elaton of a dffeent cla of non-lnea ytem model [7]. he objectve to epeent the local dynamc of each ule by a lnea ytem model. Fo aung the global tablty and tackng contol of DFIG by the akag-sugeno fuzzy model, we ue a quadatc yapunov functon to all ubytem founded by the vaable tanfomaton n to lnea matx nequalte MI [10, 11]. We obtan the contolle and tackng gan fo local fuzzy model by ung the poweful computatonal Matlab MI oolbox. he tackng contol ha be een n vaou ndutal ytem [12, 13], the objectve of th contol to degn a tackng contolle and to convege the output to the deed efeence model wthout a tackng eo. Compaed wth tablty contol degn and tablzaton poblem, the tackng contol poblem moe dffcult epecally fo nonlnea ytem. In th peent wok, the appoach baed on fuzzy contol akag- Sugeno peented wth Paallel Dtbuted Compenaton (PDC) technque and popoed to mpove the pefomance of cuent tackng contol and tablty fo dynamc model of nonlnea ytem the doubly fed Inducton Geneato (DFIG). Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 DOI: /je

2 Receved: Augut 25, he man advantage of th contol tategy ove othe to mpove the pefomance of DFIG by dmnng the epone tme of the convegence of actve and eactve powe to a deed value. h pape tuctued a follow. In Secton II, the dynamc tate-pace model of doubly fed nducton geneato and tudy of -S fuzzy modellng wth Fuzzy tate tackng ae peented and a decpton of MI-baed degn pocedue, fnally we applcate the fuzzy S method to the dynamc model of DFIG wth the eult obtaned and mulaton. 2. akage Sugeno 2.1 Model akage Sugeno he tate pace of the Double Feed Inducton Geneato DFIG dynamc model [8-11] expeed b followng Eq. (1): Wth and x( t ) A x( t ) B u( t ) y( t ) C x( t ) x( t ) [ I d,i q,i d,i q ] u( t ) [V d,v q,v d,v q ] y( t ) [ P,Q ] R M 2 RM pm p + M 2 R pm RM -p + A= RM pm R p - pm RM R p - M M B= 1 M M (1) (2) MV C= V 2 1 MV w I d Whee,,M : Stato, Roto and Mutual nductance. R, R : Stato and Roto etance., : Stato and Roto peed. I,I : Stato and Roto cuent n ax q. q q I d,i d : Stato and Roto cuent n ax d. x( t ),u( t ) : he tate ytem and contol vecto : he gan of the fuzzy obeve K : he gan of the fuzzy egulato. : he numbe of local model. p : he Numbe of pole. V : Stato voltage magntude. A akag-sugeno fuzzy model fo a dynamc ytem cont of a fnte et of fuzzy IF... HEN ule expeed a follow: Model ule : If z 1(t ) F p((z 1(t )) HEN F 1((z 1(t )) and and z p (t ). x( t ) h ( z( t )) ( A x( t ) B u( t )) 1 (3) y( t ) h ( z( t )) ( C x( t ) ) 1 Befoe F 1 (j=1, 2... p) the fuzzy membehp functon aocated wth the th ule and j th paamete component z 1(t )...z p(t ) ae known peme vaable. Whee fo each ule..e., And gven by h (z(t )) the nomalzed weght h ( z( t )) 1 1 (4) h ( z( t )) 0 Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 DOI: /je

3 Receved: Augut 25, and h ( z( t )) 2.2 ackng contol 1 w ( z( t )) w ( z( t )) p j j j1 (5) w ( z( t )) F ( z ( t )) (6) Fo each ule of a akage-sugeno model, we ue the concept of Paallel Dtbuted Compenaton (PDC) to degn fuzzy contolle to tablze fuzzy ytem n the Eq. (3). he Stablty analye baed on the quadatc yapunov tablty uch a the followng defnton: Defnton 1: he ytem n Eq. (1) ad to be quadatc ally table f thee ext a quadatc functon: WthV( 0) 0, V( x(t )) x (t ) P x(t ) (7) Satfyng the followng condton: V( x(t )) 0, x(t ) 0 P 0. (8). V( x( t )) 0, x( t ) 0. (9) If V ext, t called a yapunov functon. x (t ) I I I I (12) ef ef ef ef d d q d q he cloed-loop model of Eq. (3) wth the global contol law Eq. (11) epeented a follow [11]:. x( t ) x( t ) h ( z( t )) h j( z( t )) Gj Hj x 1 j 1 d ( t ) y( t ) h ( z( t )) C x( t ) 1 Wth G A B K Hj B N j j j (13) (14) We conde that e(t ) the functon eo whch the dffeence between the tate vecto x( t ) of - S fuzzy model Eq. (13) and the deed tate vecto x (t ), uppoed contant, a: d e( t ) x( t ) x d ( t ) (15) Combnng the Eq. (13) and Eq. (15), the eo dynamc. e(t ) Can be wtten a:. e( t ) e( t ) h ( z( t )) h j( z( t )) Gj Zj x 1 j 1 d ( t ) (16) he objectve of fuzzy tackng contol to acheve Wth Zj Gj Hj (17) lm x( t) x ( t) 0 (10) t d By applyng fuzzy contol law u (t) [11], whch wtten n the followng fom: Contolle Rule : If z 1(t) F 1 (z 1(t)) and and z p(t) F p (z 1(t)) HEN u( t ) h ( z( t )) ( K x( t ) N x ( t )) (11) d 1 Whee x () t : the deed tate vecto. d he eo dynamc n Eq. (16) can be epeented a follow:. 2 e( t ) e( t ) h ( z( t )) Gj Zj 2 h ( z( t )) x 1 d ( t ) j (18) Gj G j Zj Z j e( t ) h j( z( t )) 2 2 x d ( t ) Ung the defnton 1 n equaton Eq. (18), we obtan: And. V( e( t )) Become V(e(t ) e (t )P e(t ) 0 (19) Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 DOI: /je

4 Receved: Augut 25, j d 1 j. e( t ) V( e( t )) h ( t ) h ( t )h ( t ) x ( t ) j j e( t ) 0 2 x d ( t ) Wth P G (*) P Z (*) 0 Gj Gj Zj Zj j j P (*) P (*) 0 (20) (21) Gj G j Zj Z j P (*) P (*) P P 0 (*) (*) P Fo ( 1 j ) 2.3 nea matx nequalty (MI) (27) he MI condton ae ued to fnd the feedback gan K and the tackng gan N. In ode to mplfy the eoluton of the MI, we conde the vaable change by ntoducng matce X, U and V wth appopate dmenon: he equlbum of the ytem decbed by Eq. (18) aymptotcally table n the lage f thee ext a common potve defnte matx P uch a thee two condton: 1 X P U KX V NX (28) 0 (22) j j 0, 1 j (23) he condton Eq. (22) and Eq. (23) can be epeented a Eq. (24) and Eq. (25), epectvely a: P G (*) P Z 0 P 1 0 P0 (*) P P Gj G j Zj Z j P (*) P 2 2 (*) P 0 P P P (24) (25) Whle applyng to Eq. (24) and Eq. (25) the Schu emma, we obtan the followng equaton Eq. (26) and Eq. (27), epectvely a: P G (*) P Z 0 (*) P P 0 (*) (*) P Fo( 1, 2, 3,..., ) (26) he Condton n Eq. (26) and Eq. (27) can be ealy tanfomed nto MI a follow: A X BU (*) A X BU BV 0 (*) X X 0 (*) (*) X Fo ( 1, 2, 3,..., ) A Aj X BU j B ju (*) (*) X X 0 (*) (*) X Fo (1 j ) Wth (29) (30) A A X B U B U B V B V (31) j j j j j 3. Smulaton eult he popoed appoach n th wok wll be ued fo calculatng the contol law of the thee-phae 1.5 Mw Doubly fed nducton Geneato havng the followng chaactetc a hown n table 1: Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 DOI: /je

5 Receved: Augut 25, able 1. Doubly fed nducton Geneato 1.5 MW (DFIG) Paamete Quantty Unt and value R Ohm R Ohm 87 μh 87 μh M 2.5 μh V 690V P 2 Fgue.3 Smulaton eult of actve powe P-ef Fgue.1 Smulaton eult of Iq-ef Fgue.2 Smulaton eult of Id_ef A eult, the mulaton eult obtaned n tem of actve and eactve powe (P and Q) mut follow the eult of the deed efeence one whch ae lnked wth the cuent Iq and Id by Eq. (1). he Fgue 1 and 2 epeent the popoed eult the efeence cuent. hee eult gve u the bet method to know exactly the good pefomance of the actve and eactve powe. Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 Fgue.4 Smulaton eult of actve powe P-ef It obeved by the Fg. 1 and 2 of the efeence cuent Iq and Id, epectvely, that we have the thee dffeent cae of the each cuent functon opeatng n thee ange of epondng tme. A mentoned above that the efeence actve and eactve powe, and the efeence cuent ae lnked by Eq. (1). So, the eult of thee powe ae epeented n the followng Fg. 3 and 4. A we can ee fom the Fg. 5 and 6, t well obeved that the eult of the actve and eactve powe fed by the tato of the MADA follow the popoed eult of the efeence powe fo the thee ange of the epondng tme, Fnally, we conclude that the cuent Iq dong the tackng contol of the actve powe, and the dect Iq component dong the tackng contol of the eactve powe. Ung the MI appoach and the condton of quadatc tablty fo calculate the feedback contol and the tackng contol gan of the fuzzy contol law Eq. (11) gve the followng eult: DOI: /je

6 Receved: Augut 25, Fgue.5 Smulaton eult of actve powe P and P-ef Fgue.6 Smulaton eult of actve powe Q and Q-ef he quadatc yapunov matx P: 0,0263 3,532e-10 1,766e-08 8,125e-09 3,532e-10 0,0263 3,290e-09 1,512e-08 P 1,766e-08 3,290e-09 0,0263 4,520e-10 8,125e-09 1,512e-08 4,520e-10 0,0263 Gan value K: -15, ,41-346, ,5-886,55-15, ,8-351,09 K1-50, , , ,9-50, ,90-14,689 Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 DOI: /je

7 Receved: Augut 25, , ,81-346, ,78-15, ,08 K2-50, ,8-0, , ,5-50, ,77-14,685-15, ,81-346, ,78-15, ,08 K3-50, ,8-0, , ,5-50, ,78-14,675-15, ,41-346, ,5-886,55-15, ,8-351,08 K4-50, , , ,9-50, ,90-14,684 Gan value N: 1, , ,6 888,95 2, ,1 23,520 N1 2, ,9-0,0893-7, ,8 3, ,27 0,8396 1, ,81 23, ,78 1, ,525 N3 2, ,7-0, , ,5 3, ,78 0,8534 1, ,81 23, ,77 2, ,521 N2 2, ,7-0, , ,5 3, ,78 0, , ,00 23, ,6 888,95 2, ,1 23,522 N4 2, ,9-0,0890-7, ,8 3, ,27 0,8449 Compang ou eult of the actve and eactve powe of DFIG 1.5 MW howng n Fgue 5 and 6, epectvely, by anothe obtaned by method A Fuzzy Sldng Mode [5]. It noted that the epone tme moe mpotant than one efeenced n [5], followng able 2 how the compaon between the two method: Notaton: A (*) A A Repone tme (ec) able 2. he compaon A Fuzzy A Fuzzy Sldng akage-sugeno Mode method method 0.2 < t < < t < 0.6 A B A B (*) C B C 4. Concluon In th wok, a fuzzy akage-sugeno contol baed on paallel dtbuted compenaton PDC appoach of output vecto tate of DFIG tuded and developed. Ftly, the nonlnea model of DFIG tanfomed nto a -S fuzzy epeentaton. Afte that, the appoach PDC have been ued to contuct the MI baed degn pocedue fo fuzzy contolle. Secondly, the tablty condton ae expeed n tem of nea Matx Inequalte MI. Fnally, a degn algothm of fuzzy contol ytem contanng fuzzy egulato and fuzzy tackng obtaned. he mulaton eult ae povded to mpove the tme epone of obtaned powe compaed to the othe eeache. Futue wok wll focu on ung of the popoed method n th wok n ode to apply n the ytem whch contan wnd tubne wth DFIG fo maxmze the poducton of electcal enegy and ue of othe type of contolle, uch a H nfnty. Refeence [1] H. Polnde, F. Van de Pjl, G. De Vlde, and P. avne, Compaon of dect-dve and geaed geneato concept fo wnd tubne", IEEE an. Enegy Conve., Vol. 21, No. 3, pp , [2] A. Naamane and N. Md, Doubly Feed Inducton Geneato Contol fo an Uban Wnd ubne, Intenatonal Renewable Enegy Conge IREC, pp , [3] J. Ekanayake,. Holdwoth, X. Wu, and N. Jenkn, Dynamc modellng of doubly fed nducton geneato wnd tubne, IEEE tanacton on powe ytem, Vol. 18, No 2, p , [4] F.Abdelmalk and N. Ouaalne, S Fuzzy obeve and contolle of Doubly-Fed Inducton Geneato, Intenatonal Jounal of Powe Electonc and Dve Sytem, Vol.7, No.3, pp , Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 DOI: /je

8 Receved: Augut 25, [5] O. Beloun and H. aba, Fuzzy Sldng Mode Contolle of DFIG fo Wnd Enegy Conveon, Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.10, No.3, pp , [6] M. Nadou, A. Eadk, and. Nae, Compaatve Analy between PI & Backteppng Contol Statege of DFIG Dven by Wnd ubne, Intenatonal Jounal of Renewable Enegy Reeach, Vol. 7, No. 3, pp , [7]. akag and M. Sugeno, Fuzzy dentfcaton of ytem and t applcaton to modelng and contol, IEEE anacton on Sytem, Man and Cybenetc, Vol. 1, No. 1, p , 1985 C. J. opez-obo and R. J. Patton, akag- Sugeno fuzzy fault toleant contol fo a nonlnea ytem, In: Poc. of the 38th IEEE Confeence on Decon and Contol, pp , [8] K. anaka and M. Sugeno, Stablty analy and degn of fuzzy contol ytem, Fuzzy Set Syt., Vol. 45, No.2, pp , [9] J. Pak, J. Km, and D. Pak, MI-baed degn of tablzng fuzzy contolle fo nonlnea ytem decbed by akag-sugeno fuzzy model, Fuzzy Set Syt., Vol.122, pp.73-82, [10] A. Abdelkm, C. Ghobe, and M. BENREJEB, MI-baed tackng contol fo takag-ugeno fuzzy model, Intenatonal Jounal of Contol & Automaton, Vol. 3, No [11] S. ong,. Zhang, and Y., Obeved-baed adaptve fuzzy decentalzed tackng contol fo wtched uncetan nonlnea lage-cale ytem wth dead zone, IEEE anacton on Sytem, Man, and Cybenetc: Sytem, Vol. 46, No 1, p , [12] H.,. Wang, H. Du, and A. Boulkoune, Adaptve fuzzy backteppng tackng contol fo tct-feedback ytem wth nput delay, IEEE anacton on Fuzzy Sytem, Vol. 25, No 3, p , Intenatonal Jounal of Intellgent Engneeng and Sytem, Vol.11, No.1, 2018 DOI: /je