Direct Torque Control of Saturated Doubly-Fed Induction Generator using High Order Sliding Mode Controllers

Transcription

1 (IJACSA) Intenatonal Jounal of Avance Compute Scence an Applcaton, Vol. 7, No. 7, 6 Dect Toque Contol of Satuate Doubly-Fe Inucton Geneato ung Hgh Oe Slng Moe Contolle Elhaj BOUNADJA Depatment of Automatc Ecole Natonale Polytechnque Elhaach, Alge, Algea Mohan Oulhaj MAHMOUDI Depatment of Automatc Ecole Natonale Polytechnque Elhaach, Alge, Algea Abelkae DJAHBAR Depatment of Electcal Engneeng Unvety HASSIBABENBOUALI Chlef, Algea Mohame MATALLAH Depatment of Technology Unvety DJILALI BOUNAAMA Kh Melana, An efla, Algea Abtact The peent wok examne a ect toque contol tategy ung a hgh oe lng moe contolle of a oublyfe nucton geneato (DFIG) ncopoate n a wn enegy conveon yt an wokng n atuate tate. Th eeach cae out to each two man objectve. Ftly, n oe to ntouce ome accuacy fo the calculaton of DFIG pefomance, an accuate moel coneng magnetc atuaton effect evelope. The econ objectve to acheve a obut contol of DFIG bae wn tubne. Fo th pupoe, a Dect Toque Contol () combne wth a Hgh Oe Slng Moe Contol (HOSMC) apple to the DFIG oto e convete. Conventonally, the ect toque contol havng hytee compaato poee majo flux an toque pple at teay-tate an moeove the wtchng fequency vae on a lage ange. The new metho gve a pefect ecouplng between the flux an the toque. It alo euce pple n thee ganeu. Fnally, mulate eult how, accuate ynamc pefomance, fate tanent epone an moe obut contol ae acheve. Keywo Doubly Fe Inucton Geneato (DFIG); Magnetc atuaton; Dect Toque Contol (); Hgh Oe Slng Moe Contolle (HOSMC) I. INTRODUCTION Recently, wolwe awaene fo enewable enegy eouce ha been nceang. In patcula, wn enegy ha been lagely conee becaue of t economy an elablty. Wn tubne contbute a cetan amount of the wo electcty conumpton []. They uually ue a Doubly-Fe Inucton Geneato (DFIG) fo the electcal enegy conveon poce. A euce fom lteatue, many woke nvetgate the DFIG fom vee apect. Howeve, n thee wok, many mplfyng hypothee ae conee n the moellng of the DFIG, wth the neglect of magnetc atuaton beng the mot mpotant a n [-]. Howeve, the phenomenon of atuaton peent n all electcal machne. In aton, the exact calculaton of the machne ynamc pefomance epen coneably on the atuaton of the mutual an leakage fluxe [-7]. Becaue of th eaon an n oe to ealze an accuate epeentaton of the DFIG, atuaton mut be taken nto account n the mathatc moellng. Conequently, an accuate DFIG moel takng nto account the atuaton effect both n mutual flux an n leakage fluxe ue n th pape. Afte majo avance n powe electonc an mateal technologe, many wok have peente the DFIG wth ffeent contol algothm. One of the conventonal contol che ue actually fo the DFIG-bae wn tubne the Dect Toque Contol bae on wtchng table an hytee compaato [8]. Th tategy, howeve, ha a few avantage whch lmt t ue, uch a vaable wtchng fequency an toque pple [9, ]. In many eeach wok on, thee avantage ae euce by ung SVM che, but wth the pce of cafyng the obutne of the contol []. To ncopoate a obut wthout toque an flux pple, we popoe, n the peent wok, a ect toque contol bae on hgh oe lng moe contolle (-HOSMC) fo a DFIG n atuate tate. Popoe by Levant n [] the HOSMC tategy ha many attactve featue uch a t obutne towa paametc uncetante of the DFIG, an moeove, t euce the chatteng effect. The peent wok pove the mpotant featue of the -HOSMC an peent mulaton eult fo a DFIG yt. We compae the popoe tategy wth a conventonal. The peent pape oganze a follow: we peent the moellng of the wn tubne an the DFIG ung the atuate moel n ecton II. In ecton III, the popoe -HOSMC, apple to contol the atuate DFIG. The mplentaton an the eult obtane fom the popoe contolle ae hown n ecton IV. Fnlay, t wll be hown that ung the evelope DFIG moel an the popoe contolle, the ynamc epone of the yt can be etne accuately an moe pece obut contol acheve P a g e

2 (IJACSA) Intenatonal Jounal of Avance Compute Scence an Applcaton, Vol. 7, No. 7, 6 II. MODELING OF WIND ENERGY CONVERSION SYSTEM The wn enegy conveon yt aopte n th wok bae on wn tubne ven a DFIG. In uch confguaton, the tato ectly connecte to the netwok, wheea, the oto fe by the g va two convete (AC/DC) an (DC/AC). In aton, the oto e convete (DC/AC) ue to contol nepenently the DFIG actve an eactve powe. A. Moelng of the wn tubne The mechancal powe captue fom the wn tubne, ue n th nvetgaton, expee a below: Wth: P t P 3 λ,βr. 5C ρ v R: au of tubne (m), ρ: enty of a (kg/m3), v: pee of wn (m/) an C P : the powe coeffcent. Accong to [3], the powe coeffcent C p functon of the tp pee ato λ an the blae ptch angle β (eg), a follow: Wth: 6 C p. 59(. 4β 5) exp( ). 68 λ λ λ The tp pee ato λ gven by:.35 λ λ.8β 3 β Ω λ tr v In (4) Ω t epeent the otatonal pee of the wn tubne. B. Moelng of the DFIG Below, we evelop the conventonal moel of the DFIG wthout atuaton. Accong to th moel, both mutual flux an leakage fluxe atuaton ae conee. In thee moel, the DFIG conee a a genealze woun oto nucton machne takng the tato etance nto coneaton. The latte neglecte n many wok e.g. n [-9]. ) Lnea DFIG moel The an q equvalent ccut fo the DFIG ae hown n Fg. [5]. Bae n thee cha, the voltage equaton of the DFIG n the -q ynchonou efeental ae gven by: v R ψ ωψq vq Rq ψq ωψ v R ψq ωψq v q Rq ψq ωψ Whee the oto fequency ω gven by: ω ω ω The flux lnkage n (5) ae obtane fom the followng equaton yt: q q L L q L L q m L m L m q L m L m q The equaton yt n (7) ue to calculate the an q component of tato an oto cuent: Wth: L m ( L ) L L q ( L q q) L L ( L ) L L ( ) q L q q L L (7) (8), L L, L L L L (9) The magnetzng cuent m gven a follow [4, 5]: Whee: m m m mq (), mq q q () In teay tate an by algnng the q-ax of ynchonou otatng efeence fame on tato flux vecto, the followng equaton can be wtten [, 8]: v v q R R ψ q ψ V, ψ q () V L (3) L L gωl q L gωl T V p q L q V gω L (4) (5) 56 P a g e

3 (IJACSA) Intenatonal Jounal of Avance Compute Scence an Applcaton, Vol. 7, No. 7, 6 ) DFIG moel wth atuaton Ung the lnea moel explane n the pevou ecton, we evelop a DFIG moel takng the mutual flux atuaton nto coneaton. The coeponng atuate value L m eplace the unatuate mutual nuctance L m n th appoach, (7)-(9). Th atuate mutual nuctance calculate by multplyng the coeponng unatuate value, L m, wth a atuaton coeffcent K m, coeponng to the atuaton tate. The atuate mutual nuctance L m, whch a functon of the magnetzng cuent m, can be wtten a follow: m<i mat K m(m ). m I (6) mat The atuaton coeffcent K m can be epeente by the functon []: m<imat K m ( m ) I mat I mat acn( ), 5n(acn( ) m I mat π m m (7) Hee I mat epeent the magnetzng cuent at whch the atuaton tat. It aoun.5 pu,.e.7 I n [4,5]. In aton, n the moellng of DFIG, the epeentaton of atuaton nclue the vaaton n the tato an oto leakage nuctance caue by the atuaton n the leakage flux path. The atuaton n the leakage flux path taken nto account n the moel evelope n pevou ecton by eplacng the unatuate tato an oto leakage nuctance (L ϭ, L ϭ ) n (9) by the coeponng atuate value (L ϭ, L ϭ ). The latte nuctance ae obtane by multplyng the epectve unatuate value by a atuaton coeffcent K ϭ. Th coeffcent epen to the tato cuent o the oto cuent. The tato an oto leakage nuctance ae gven a functon of the coeponng cuent a follow: v L <Iat L ( ) (8) K( ).L Iat L <Iat L ( ) (9) K( ).L Iat R L ϭ L m m L ϭ R v The atuaton coeffcent K ϭ can be epeente by the functon []: <Iat K ( ) Iat Iat () acn( ), 5n( acn( ) Iat π Satuaton taken nto account at value of the cuent I at n the ange,3-3 pu, that,8 I n 4, I n [4,6,7]. III. DIRECT TORQUE CONTROL USING HIGH ORDER SLIDING MODE CONTROLLERS OF DFIG The goal of -HOSMC to egulate both the toque an the oto flux magntue of the DFIG. The flux egulate ung the ect ax voltage V, whle the toque contolle ung the quaatue ax voltage V q. The phenomenon of chatteng that epeent the mpotant pobl of the conventonal lng moe contol can be vey hamful fo the DFIG ue the fact that the contnuou contol can caue oveheatng of the col an the exctaton of unmoelle hgh fequency ynamc. In [8] ome oluton wee popoe n oe to avo th avantage. The man ea wa to ajut the ynamc n a mall egon of the contnuty uface o to ecape the eal contnuty meanwhle conevng the majo chaactetc of the ente yt. The lately popoe HOSMC genealze the man lng moe ea whch act on the hgh oe tme evatve of the yt evaton fom the contant n place of nfluencng the ft evaton evatve a n tana lng moe [6]. In aton to keepng the majo avantage of the ognal technque, they cu the chatteng effect an even epeent hghe accuacy n a eal mplentaton. In HOSMC algothm mplentaton, the man ffculty cont of the nceae n the neee nfomaton. In fact, the knowlege of ( n) S, S,..., S eque to acheve an n th oe contolle. A an excepton to all the algothm popoe fo the HOSMC, the upe-twtng algothm nee only the nfomaton on the lng uface [6]. A a conequence, th algothm ha been utlze fo the popoe contol metho. A mentone n [8], the tablty can be obtane fo all hgh oe lng moe contolle wth th algothm. Fgue how the popoe -HOSMC, whch ue to contol both the oto flux an the electomagnetc toque of the DFIG. In th tuy, the eo between efeence an meaue of the electomagnetc toque an the oto flux have been choen a lng moe uface, o the followng expeon can be wtten: q v q R (a) L ϭ L ϭ mq L m R q v q S _ ef () ST T ef T _ By ubttutng the oto flux an the electomagnetc toque n () by the expeon gven, epectvely, by (3) an (5), one obtan: (a) Fg.. Equvalent ccut of a DFIG: (a) on -ax, (b) on q-ax S éf L L V ST T éf p q L () 57 P a g e

4 (IJACSA) Intenatonal Jounal of Avance Compute Scence an Applcaton, Vol. 7, No. 7, 6 The ft evatve of (), gve: S éf L V (3) S T T éf p q L If we eplace the an q oto cuent evatve n (3) by the expeon gven fom (4), one obtan: S éf v R gl q V (4) S T T éf p vq Rq gl gv L L L We efne the functon G an G a follow: G Rq glq éf V (5) G p Rq g L g T éf L L L Afte ubttutng (5) n (4), the evatve of (4) gve: S v G V L S m T p v q G L L (6) Bang on the upe-twtng algothm etablhe by Levant n [,3], the hgh oe lng moe contolle contan two pat:. 5 v α gn( S ) β S ( ) gn S (7). 5 Vq α gn( S ) ( ) T β ST gn S T In oe to guaantee the convegence of the lng manfol to zeo n et tme, the contant α, β, α an β can be choen a follow [,6,8]: ( ) 4 ( ) G pv LL pv ( ) 4 LL ( ) G IV. SIMULATION RESULTS (8) (9) In th ecton, mulaton ae ealze wth a 7.5 KW DFIG couple to a (3V, 5 Hz) netwok, utlzng the Matlab/Smulnk envonment. The paamete of the machne ae hown n Table. The coneaton of atuaton nto account fo the mutual flux of the nvetgate DFIG ealze by takng I mat n (6)- (7) to be equal to.7 I n = 6 A. In th equalty, I n the ate cuent gven n Table. The mutual flux atuaton coeffcent K m ue n the etnaton of the atuate value of the mutual nuctance L m ketche n fgue 3. Lkewe, the coneaton of the leakage flux atuaton, I at n (8)-() wa aume to be equal to.8 I n =5.8 A, whee the leakage flux atuaton coeffcent K ϭ hown n fgue 4. Fg.. Bloc agam of HOSMC- apple to the DFIG Mutual flux atuaton coeffcent K m.,8,6 I mat, Magnetzng cuent (A) m Fg. 3. Mutual flux atuaton coeffcent K m Leakage flux atuaton coeffcent K Stato Se Convete DC bu Roto Se Convete ψ _ef S ψ + - _ef S T + - I at - HOSMC Cuent (A) (b) Fg. 4. Leakage flux atuaton Coeffcent K ϭ S a v S b S c PWM ψ v q I,abc V,abc Flux an Toque Etmaton DFIG G 58 P a g e

5 Ecat u C (%) Ecat u (%) Electomagnetc toque (N.m) Ecat u C Roto (%) flux (Wb) Ecat u (%) Electomagnetc toque (N.m) Electomagnetc toque (N.m) Electomagnetc toque (N.m) (IJACSA) Intenatonal Jounal of Avance Compute Scence an Applcaton, Vol. 7, No. 7, 6 The two contol tatege; clacal an - HOSMC ae mulate an compae n t of efeence tackng an obutne agant machne paamete vaaton. A. Tet of efeence tackng The goal of th tet to exploe the behavou of the two contol tatege whle mantanng the DFIG pee at t nomnal value. The mulaton eult ae hown n fgue 5 an 6. Fom thee fgue we can ee that fo the - HOSMC contol metho, the toque an oto flux tack almot pefectly the efeence value. In aton, an contay to the clacal tategy n whch the couplng effect between the two axe qute appaent, we ak that, n the peent -HOSMC tategy, the ecouplng between the axe guaantee. B. Tet of obutne In oe to check the obutne of the ue contol tatege, the machne paamete namely the tato an the oto etance R an R have been ntentonally ouble. The DFIG wokng at t nomnal pee an n tate of atuaton. Fgue 6 an 7 how the mulaton eult. Fom thee Fgue, we ee that the paamete vaaton of the machne nceae the tme-epone of the clacal tategy lghtly. Howeve the eult how that thee vaaton caue a make effect on the toque an flux vaaton an th effect moe make fo the clacal tategy than that wth -HOSMC Fg. 6. -HOSMC tategy epone (tet of efeence tackng) Tme() Wth pamete vaaton Wthout pamete vaaton Wth pa Wtout p Fg. 5. Clacal tategy epone (efeence tackng tet) Wth pamete vaaton Wthout pamete vaaton Tme () Tme () Tme () Fg. 7. Clacal tategy epone (tet of obutne) Wth pamete vaaton Wtout pamete vaaton Tme () Tp () Tp () - Tp () 59 P a g e

6 Roto flux eo (%) Electomagnetc Ecat u toque (%) eo (%) Roto flux eo (%) Electomagnetc toque (N.m) (IJACSA) Intenatonal Jounal of Avance Compute Scence an Applcaton, Vol. 7, No. 7, Wth paete vaaton Wthout paamete vaaton Wth paete vaaton Wthout paamete vaaton Tme() Fg. 8. -SOSMC tategy epone (obutne tet) V. CONCLUSION In th pape, we have nvetgate a Dect Toque Contol ung a hgh oe lng moe contolle. The goal of th contol tategy ha been to mpove the calculaton of the ynamc pefomance of atuate DFIG ven by a wn tubne ven. In the ft place, the moellng of the atuate DFIG-bae wn tubne ha been cae out. The atuaton of both the magnetzng flux an of the leakage fluxe have been taken nto account n the popoe DFIG moel. Then, the ynthe of a new combne wth HOSMC ha been pefome an th -HOSMC ha been compae wth the conventonal n t of efeence tackng. The tackng of the efeence wa acheve almot pefectly by the two tatege, howeve thee appeae a couplng effect n the conventonal epone, wheea th couplng wa elmnate n the -HOSMC. An nvetgaton of obutne tet ha alo been ealze n whch the paamete of the DFIG have been ntentonally mofe. Some tubance on the toque an flux epone have been nuce by thee change but wth a majo effect wth the conventonal tategy than wth the popoe - HOSMC. On the lght of thee eult, we conclue that the obut -HOSMC contol metho a vey attactve oluton fo thoe evce that ue the atuate DFIG a happen n wn enegy conveon yt. APPENDIX Tme() Tme() -HOSMC HOSMC Tme() Fg. 9. Eo cuve (obutne tet).5 TABLE I. LIST OF SYMBOLS Symbol Sgnfcance -HOSMC DFIG Doubly-fe nucton geneato Dect Toque Contol HOSMC Hgh Oe Slng Moe Contol.5 v, v q, v, v q an q ax tato an oto voltage, ψ, ψ q, ψ, ψ q an q ax tato an oto fluxe, ψ _ef Refeence oto flux, q,, q an q ax tato an oto cuent, R, R Stato an oto etance, L, L Stato an oto nuctance, -.5 L ϭ, L ϭ Stato an oto leakage nuctance, L ϭ, L ϭ Stato an oto atuate leakage nuctance, ϭ Leakage coeffcent - I n..4 Rate.6 cuent,.8 L m Mutual nuctance, Tme() L m Satuate mutual nuctance, p Numbe of pole pa, Geneato lp, ω, ω Stato an oto cuent fequence (/), ω m Mechancal oto fequency (/),, _ef Electomagnetc, Refeence electomagnetc toque. TABLE II. MACHINE PARAMETERS Paamete Rate Value Unt Nomnal powe P n 7.5 KW Stato voltage V n V Stato voltage ampltue V 3 V Stato cuent I n 8,6 A Stato fequency f 5 Hz Numbe of pa pole p Nomnal pee ω m 44 a/ Stato etance R. Ω Roto etance R.8 Ω Mutual nuctance L m.5 H Leakage tato nuctance L ϭ.54 H Leakage oto nuctance L ϭ.68 H 6 P a g e

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