Int ern at i onal  Journ al of  P ower E le ctr on i cs a n d  Drive  S ystem s   ( IJ PEDS )   Vo l.   12 ,  No.   1 ,  M a r 202 1 , p p.  404 ~ 412   IS S N:  20 88 - 8694 ,  DOI: 10 .11 591/ ij peds . v12.i 1 . pp404 - 412     404       Journ al  h om e page :  http: // ij pe ds .i aescore.c om   Synthesi s   of   SM C   alg or it hms   appli ed   to   wi nd   ge nerator       Ho u aria   A bde ll i 1 ,   Ab delk ader   Mez ouar 2 ,   Mokhtar   B en dj ebb ar 3 ,   Khe ir a   Be lg acem 4   1,3 Diagnosti c   gro up   LDEE,   Univ e rsity   of   Sc ie n ce   and   T ec hnolo gy   Mohame d   Boud i af ,   Or an,   Alger i a      2 ,4 La bora tory   of   El e ct ri ca l   Eng in ee ring ,   Ta he r   M oula y   Univ ersit y ,   Said a,   Alger ia       Art ic le   In f o     ABSTR A CT   Art ic le   hist or y:   Re cei ved   M a y   26 ,   20 20   Re vised   J an   2 7 ,   20 2 1   Accepte d   Fe b   3 ,   20 2 1       The   use   of   th e   class ic al   (SM C)   a ppli ed   to   cont rol   of   sta tor’s   powe rs   of   DF IG,   give s   th e   prob lem   of   chatt eri ng,   the ref or e   to   avoid   thi s   phenomen on   a   robust   al gorit h m   (STSM C)   is   appl ied.   Thi s   pap er   pre sents   a   co m par ison   of   conve nt iona l   SMC   with   th e   pr oposed   strategy   of   STS MC   al g orit hm .   Th e   result s   ar e   ob t ai ned   using   MA TL AB   and   dem onstr at e   stabi lity   and   robustness   of   this   al gori thm .   Ke yw or d s :   DF I   ge ne rato r   Power   co ntr ol   SM C   al gorith ms     Synthesis   Win d     This   is   an   open   acc ess   arti cl e   un der   the   CC   BY - SA   l ic ense .     Corres pond in g   Aut h or :   A bdel li   H ou a ri a   Dep a rtme nt   of   Ele ct rical   Eng i neer i ng ,   Un i ver sit y   of   S ci ence   a nd   te chnolo gy   Moh a med   B oudiaf   US T O   ( 31 0 00 )   Oran ,   Al ger ia .   Emai l:   abd el li _houa ria@y a ho o. c om       1.   INTROD U CTION   Energ y   c onsumpti on   has   increase d   ove r   the   la st   de cades   c onside rab l y   due   to   massi ve   industrial iz at ion .   A   go od   al te rn at ive   is   to   use   ren e wa ble   e nergies,   wh ic h   offer   t he   poss ibil it y   of   pro duci ng   el ect rici ty   pro per l y   [1].   A m ong   the   re ne wab le   ene r gies   we   fin d   t he   wi nd   tu rb i ne,   w hich   is   bec om in g   com petit ive   in   te rms   of   pro duct ion   costs .   It   is   reducin g   the   emissi ons   of   gr ee nhouse   ga ses.   T od a y,   va riable   sp ee d   wind   t urbi nes   base d   on   ( DFI G)   of fer s   ma ny   be nef it s,   suc h   as   their   ef fici en t   powe r   de ns i ty,   t he   dimensi onin g   of   the   co nverte r   on   the   r otor   s ide   is   reduce d   to   30 %   of   the   nominal   powe r   of   t he   mac hi ne   [ 2],   [3].   To   ha ve   m aximum   wind   powe r   we   us e   var ia ble   sp e ed   wind   tu r bin es   [ 4],   so   to   achie ve   this   goal ,   t he   pea k   tur bin e   s peed   r at io   mu st   be   m ai ntained   at   its   op ti m um   valu e   des pite   the   va riat ion   in   wind   spe ed   [5],   [6].   To   so lve   t he   pr ob l em   of   trac king   the   ma ximum   powe r   point,   di ff e ren t   c on t ro l   te chn iq ues   ha ve   bee n   us e d,   a mong   them   c onve nti on al   ( SM C ).   T his   c ontrolle r   offer s   s om e   a dv a ntage s:    rel at ive   sim plici t y   of   im pleme nt at ion ,   rob us tness   an d   exter nal   disturbance s   [ 7].     SM C   is   a   r obust   co ntro l   met hod   [ 8] ,   w hich   guara ntees   t he   pe rformance   of   the   dy nami c   sy ste m   by   reject ing   a ny   distu r ba nce   ac ti ng   on   it.   De sp it e   the   sim pl ic it y   of   its   c oncepti on,   the   disco ntin uity   of   t his   comma nd   gi ve s   rise   to   the   ph enomen on   of   c hatte rin g.   Se ve ral   researc he rs   hav e   pro pose d   so l utio ns   to   avo i d   this   phe nomen on   an d   guara nt eed   sta bili ty   in   ste ady   sta te .   [ 9],   [10 ].     This   pap e r   pre sents   a   r obus t   su pe r - twist ing   sli din g   m od e   c on t ro l   of   doub ly   fe d   i nductio n   gen e rato r   (D F I G)   base d   wind   tur bine s.   The   sim ulati on   res ults   show ed   a   go od   S TS M C   co ntr ol   co mp a red   to   the   SMC   al gorithm.   T he   rest   of   this   a r ti cl e   is   or ga ni zed   as   f ollows :   Sect ion   2   pr esents   the   wi nd   tu r bin e   a nd   DF I G   modeli ng.   T he   Sect ion   3   desc r ibes   the   f unda mental   f ormula ti on   of   t he   pro po s ed   STS M C   app li ed   to   t he   powe r   Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Syn t hesis  of SMC   algorit hms  app li ed  to  wi nd  gen e ra t or   ( H ouar i a   A bd el li )   405   base d   on   D FIG.   Sect io n   4   presents   the   simulat ion   res ults   to   dem onstr at e   the   perfor mance   of   the   pro po se d   con t ro l   sc he me .   At   t he   e nd,   c oncl us i on   is   gi ve n   in   Sect io n   5.       2.   MA TE RIA L   AND   METH OD   2.1.   The   ge nera to r   m ode1   Bl ock   dia gr a m   of   a   wi nd   t urb ine   base d   on   D FI G   is   giv e n   in   fig ure   1.   The   model   co ntain s   of   a   wind   tur bin e,   DFIG ,   co nv e rters ,   and   a   gea rbo x.   T he   sta to r   is   connecte d   to   the   netw ork   via   a   th re e - phase   trans forme r   a nd   the   r otor   via   ano t her   thre e - phase   c urre nt   source   [ 11].           Figure   1.   Sc he me   dia gr a m   of   DF I G - base d   w ind   t urbine       2.2.   Turbi ne   m od e li ng   The   e xpressi on   of   the   aer odyn amic   powe r   is   pr ese nted   by   t he   ( 1)   [ 12 ]:     = 1 2 ( )    2 3   (1)     The   ( )   is   power   coeffic ie nt,   is   a   nonlinea r   f unct ion   of   the   r el at ive   sp eed   r at io   =  ,   with     is   wind   s pee d   ( m/s),   is   the   ai r   den sit y   (kg/ m3),     is   t he   r adius   of   t he   r otor   blades   (m ),     is   the   a ngul ar   fr e qu e nc y   of   the   blade s   the   m echan ic al   ro ta ti on   spe ed   an d   (rad/s) .   The   po wer   c oe ff ic ie nt   of   the   wind   t urbine   is   s how n   in   the   Fi gure   2.   This   fig ur e   in dicat es   that   the   tip   sp ee d   rati o   is   ke pt   eq ual   to opt ⋅ ,   the ( )   captu re   t he   m aximum   powe r   [ 12],   [ 13].     + + = − + = ds s qs qs s qs qs s ds ds s ds dt d i R v dt d i R v   (2)     − + + = − − + = dr s qr qr r qr qr s dr dr r dr dt d i R v dt d i R v ) ( ) (   (3)     + = + = qr qs s qs dr ds s ds Mi i L i M i L   (4)     + = + = qs qr r qr ds dr r dr i M i L i M i L   (5)     Evaluation Warning : The document was created with Spire.PDF for Python.
                IS S N :2088 - 8 694   In t J   P ow  Ele c  &   D ri S ys t,   V ol .  12 , N o.   1 ,  Ma rch  20 21   :   404   –   412   406       Figure   2.   P ow e r   c oeffici ent   of   wind   t urbine       2.3.   Model ing   of   t he   D FIG   The   act ive   an d   reacti ve   sta to r   and   r otor   powe rs   a re   re present ed   as   ( 6),   (7)   [ 14] :     { =   +   =   −     ( 6 )     { =   +   =   −     ( 7 )     the   el ect romag netic   tor que   is   giv e n   by   ( 8) :      = (   −   )   (8)     3.   DFIG   C ONT ROL   S T R ATEGY   3.1.   V ect or   c ontro l   of   th e   ac tive   an d   reac tive   p ow er s   T o   i ndepe nden tl y   co ntr ol   t he   act ive   a nd   re act ive   sta to r   powe rs,   we   us e   the   vect or   c ontr ol   wh ic h   makes   the   DFI G   simi la r   to   a   DC   m otor     =    ⇒    = 0   (9)     The   t orqu e   is   s impli fied   as   s how n   belo w:     {  =  +  0 =  +    (10)     N egle ct in g   t he   sta t or   re sista nce   g iv e s   t h e   ( 12)     {  = 0  =   (11)     The   e quat ions   (12)  are   obta in ed   wh e n   re placi ng   t he   ro t or   fl ux   ( 5)   in   ( 3) ,   the   r oto r   volt age s   are:     {  =   +  −  +    =   +  +  +    (12)     wh e re :   = − = is   the   sli p   fr e quen cy,     is   the   sli p   ra nge   an d   = 1 − 2 is   the   le akage   coeffic ie nt .   T he   r oto r   volt age s   can   be   re wr it te n   as   f ollows   ( 13) :     {  =   +  +  ,  =   +  +  ,   ( 13 )     Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Syn t hesis  of SMC   algorit hms  app li ed  to  wi nd  gen e ra t or   ( H ouar i a   A bd el li )   407   with    , and  ,   are   the   co up li ng   te r ms   ( 14) :     {  , = −  + ⋅    , = −  + ⋅ ⋅    ( 14 )     The   sta to r   act i ve   a nd   reacti ve   powe rs   a re   give n   by   the   ( 15) :     { = − ⋅  = − ⋅ (  − )   (15)       The   ro t or   cu rr e nt   al ong   the   d   and   q   axe s   is   r epr ese nted   by   ( 16)   a nd   ( 17)     ̇  = 1 (  −  +  )   (16)   ̇  = (  −  −  − ) 1   ( 17 )       4.   WIN D   T UR B INE   CONTR OL   BASE D   ON   DFIG   4.1.   SMC   c on t rol   Sli din g   mode   con t ro l   is   a   m od e   of   operati on   of   va riable   structu re   c on t ro l   s ys te ms   ( VS CS ).   It   is   rob us t   in   view   of   the   i ns en sit ivit y   to   pa ramet ric   va riat ion s   a nd   to   e xter nal   disturba nces.     4.2.   Choice   of   s wit ching   s urf ace   The   sli di ng   s urface   giv e n   by   Sloti ne   is   def i ne d   as   ( 18)   [15 ]:     ( ) = (  + ) − 1 ( )   ( 18 )     wh e re :   ( ) is   the   er ror   trac king;   :    sy ste m   orde r   a nd      is   a   po sit iv e   coe ff ic ie nt.     4.3.   C ondi ti on   of   c onverge nce   The   e xistence   of   S M C   ca n   be   pro ve d   by   us i ng   a   L ya punov   f un ct io n   (19 ) .     ( ) = 1 2 2 ( )   (19)     The   der i vative   is   giv e n   by   (20) :     ̇ ( ) = ( ) ̇ ( )   ( 20 )     To   ma ke   the   L yapu nov   f unct ion   der i vative   of   (19)   t he   ne gative   de finite ,   we   ha ve   to   find   a de qu at e   con t ro l   i nput.   To   e nsure   sta bi li ty,   the   c ontrol   is   desi gn e d   as   fo ll ows   ( 21)   [16] ,   [ 17] :     ( ) ̇ ( ) < 0   ( 21 )     The   sli ding   m od e   c ontr ol   al gorithm   c onsis ts   of   two   te rm s :   a   disco ntinuou s   te rm   wh ic h   ens ures   the   sta bili ty   of   the   sy ste m   a nd   an   e qu i valent   te rm   wh ic h   bri ng s   bac k   t he   sta te   of   the   syst em   on   t he   sl idin g     su r face   [ 18 ] ,   [1 9 ] :   The   c ontrol   al gorith m   is   def i ne d   by   ( 22) :       =  +   ( 22 )     wh e re :     =  ( ( ) )   ( 23 )   Evaluation Warning : The document was created with Spire.PDF for Python.
                IS S N :2088 - 8 694   In t J   P ow  Ele c  &   D ri S ys t,   V ol .  12 , N o.   1 ,  Ma rch  20 21   :   404   –   412   408   5.   S UPE R - TWI STING   SLI DI NG   MO DE   C ONTROL   DE SIGN   T o   re med y   the   pr ob le m   of   c ha tt ering   du rin g   the   im pleme ntati on   of   the   c ontr ol   sli di ng   m od e ,   we   us e   oth e r   m or e   ef fi ci ent   te ch nique s   cal le d   s up e r - t wisti ng   ST   al gorith m   [ 20 ],   [ 21 ] .   The   c ontrol    co ntr ol   co ntains   the   s um   of   two   te rms   (24)   [ 22 ] ,   [ 23 ] :     {  = 1 + 2 ̇ 1 = −  ( ) 2 = − | | 1 2  ( )   ( 24 )     w he re :   > 0 , > 0   T he   c onve rg e nc e   co nd it io n   is   giv e n   by   ( 25)   [ 24]   [25 ] :     {         > 2 ≥ 4 ( + ) 3 ( − )   ( 25 )     w he re   , ,   are   the const ants   value s   of   s up e r - t wis ti ng   sli di ng   m ode   c on t ro ll er .   Figure   3   s how   t he   sta te   traj ect ory   of   the   an d   ̇   ph a se   plane .           Figure   3.   Traje ct ory   ph ase   pla ne   of   ST   al gori thm       5.1.   Super - T wistin g   sli din g   m ode   contr ol   desi gn   The   e rrors   of   t he   powe rs   a re   giv e n   b y   ( 26) :     { ( ) =  = ∗ − ( ) =  = ∗ −   ( 2 6 )     w he re   ∗   an d   ∗   are   the   ref e ren ce   values   of   the   st at or act ive   a nd   reacti ve   powe r s .   The n   we   will   ha ve :     ̇ ( ) = ̇ ∗ − ̇   ( 2 7 )     ̇ ( ) = ̇ ∗ − ̇   ( 2 8 )     Substi tuti ng   ( 15)   an d   (17 )   int o   ( 27 )   le ads   to:     ̇ ( ) = ̇ ∗ + (  −  −  − ) 1   ( 2 9 )     Wh e n   t he   sta te   of   the   syst em   is   on   t he   s urfac e   of   sli ding,   th en :   Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Syn t hesis  of SMC   algorit hms  app li ed  to  wi nd  gen e ra t or   ( H ouar i a   A bd el li )   409   ( ) = 0 ; ̇ ( ) = 0 ;  = 0     so ,   t he   e quival ent   co mma nd   is   gi ven   by:       =  +  + + ̈  ⋅   (30 )   Ther e f or e :      = − | |  ( ) − ∫  ( )   (31 )     The   sta to r   reac ti ve   powe r   of   the   DF I G   is   re presente d   by   s ubsti tuti ng   ( 15)   and   ( 16)   i nto   ( 28 )   le a ds   to:     ̇ ( ) = ̇ ∗ + (  −  +  )   (32 )     wh e n :     ( ) = 0 ; ̇ ( ) = 0 ;  = 0       T he   e quivale nt   com man d   is       is   d e fin e d   as:       = − ( ̈ −  ̈  − ̇ −  +  )   (33 )     hen ce :      = − | |  ( ) − ∫  ( )   (34 )     Figure   4   s how n   the   bl ock   dia gr a m   of   t he   DFIG   co ntr olled   by   the   sec ond   order   sli ding   m ode   wh ic h   us es   t he   s uper - twist ing   al gorithm .           Figure   4.   Str uc ture   of   ST SM   con t ro l       6.   RESU LT S   A ND   DI SCUS S ION   The   blo c k   dia gr a m   (F ig ur e   4)   is   validat ed   by   a   sim ulati on   us in g   t he   pa rameters   in di cat ed   in   the   app e ndix.   A   c omparis on   between   the   two   con t ro ll ers   ST SM C   an d   cl as sic   S M C   is   a ppli ed   to   a   D FIG.   Thi s   com par is on   s hows   that   the   S TSM C   is   m ore   ef fici ent   a nd   r obus t   t han   S MC .   Fig ure   5   il lustrate s   t he   refe ren ce   of   the   act ive   an d   reacti ve   pow er .       Table   1.   DFIG   par a mete rs   no minal   7 .5   KW   4 0 0 /6 9 0 V   50   Hz   P   =   2   R s   =   0 .45 5   Ω   R r   =   0 .6 2   Ω   M   =   0 .07 8   H   L s   =   0 .08 4   H   L r   =   0 .08 1   H     Table   2 .   Para m et ers   t urbi ne   Dia meter   =   14   m   Gea rb o x   =   28   Nu mb er   of   b la d es   =   3     Table   3 .   (DFI G+T urbine )   = 50    ⋅ 2   = 0 . 071   ⋅ ⋅ /      Evaluation Warning : The document was created with Spire.PDF for Python.
                IS S N :2088 - 8 694   In t J   P ow  Ele c  &   D ri S ys t,   V ol .  12 , N o.   1 ,  Ma rch  20 21   :   404   –   412   410       Figure   5 .   Re fere nce   of   sta tor ’s   powe rs       As   cl earl y   s hown   in   Fi gure   6   and   Fig ur e   7 ,   t he   s up e r - t wisti ng   sli ding   m od e   co ntro l - bas ed   sy ste m   has   al mo st   simi la r   trackin g   perfor mance   as   the   conve ntion al   sli ding   m od e   c on trol - base d   sy st em   of   DFIG   sta tor’s   powe rs.   It   is   f ound   t hat   cl ass ic al   sli din g   m ode   c ontr ol - ba s ed   sy ste m   s uff ers   from   c hatte rin g   e ff ect ;   w her eas   STS M C   base d   s ys te m   is   free   f rom   this   ph e nome non .   Figure   8   a nd   Fig ure   9   il lustrate   the   dire ct   an d   qu a drat ur e   r ot or   cu rr e nt.   Fig ur e   1 0   s hows   the   dynamic   re sp onses   of   t he   el ect ro ma gn et i c   tor que.   T he   con t ro l   by   the   super - t wisti ng   sli ding   mode   of   the   D FI G   gi ves   a   go od   po ur s uit   an d   is   bette r   t han   SM C   co ntr oller.           Figure   6 .   Acti ve   powe r   trac ki ng   pe rfo rma nc e           Figure   7 .   Re act ive   po wer   trac king   performa nce           Figure   8 .   Cu rr e nt   idr   Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Syn t hesis  of SMC   algorit hms  app li ed  to  wi nd  gen e ra t or   ( H ouar i a   A bd el li )   411       Figure   9.   Cu rr e nt   iqr         Figure   1 0 .   T or qu e       7.   CONCL US I O N   The   a ppli cat ion   of   the   ST S M C   al gorithm   on   a   DFIG   ha s   bee n   s hown   in   t his   a rtic le .   The   S TS MC   al gorithm   is   use d   for   sta tor ’s   powe rs   c ontrol .   T he   pro posed   ap proac h   giv e s   go od   perform ance   ( good   tra ckin g ,   disturba nce   reject ion   a nd   mi ni mize s   the   c hatte ring   phe nom enon ) .       REFERE NCE S   [1]   A.   Gupta ,   S. N.   Singhand ,   D.K .   Khatod,   “ Model ing   and   simul at i on   of   doubly   fed   induc t ion   g ene r at or   coupl ed   wit h   wind   turbi n e - an   over vi ew ”   Jou rnal   of   Engi n eer ing,   Computers   &   Appl i ed   S cienc es   (JE C &A S ) ,   vol .   2,   no.   8,     pp.   45 - 54 ,   2013 .   [2]   F.   Poiti er ,   T.   B ouaouc hi che,   M.   Mac hmou m,   “ Advanc ed   con tr ol   of   a   doubly - f ed   induction   ge ner at or   for   win d   ene rgy   conve rsi on, ”   Elec tri c   Po wer   Syste m   Re se arch. ,   vol.   79 ,   n o.   7,   pp . 1085 - 10 96, 2009.   [3]   G.   Pannell,   D.   Atkinson,   B.   Z aha wi,   Analytic al   Study   of   Gri d - Fault   Respons e   of   W ind   Tu r bine   Doubly   Fe d   Induc ti on   Gene r at or, ”   I EE E   Tr ansacti ons   on   En ergy   Conv ersion ,   vol .   25 ,   no .   4,   p p.   1081 - 1091 ,   2 010.   [4]   B.   Beltran ,   M.   Benbouz id ,   T.   Ahmed - Ali,   H.   Mange l,   “ DF IG - Based   Wi nd   Tu rbine   Robust   Co ntrol   Us ing   High - Order   Slidi ng   M odes   and   a   High   Gain   Obs erv er, ”   Inte rnational   Revie w   on   Mod el l i ng   and   Simulat i ons ,   vol.   4 ,   no.   3,   pp.   1148 - 1155 ,   Nov.2011.   [5]   J.   A.   Moreno   an d   M.   Os orio,   “ St ric t   Lya punov   f unct ions   for   the   super - twisti ng   algorithm, ”   I EEE   Tr ansacti ons   on   Aut omatic   Contr ol ,   vo l.   57,   no.   4,   pp.   1035 – 1040,   2012 .   [6]   C.   Eva ng el ist a,   P.   Puleston ,   F.   Vale nc ia ga ,   and   L.   M.   Fridma n ,   “ Lya punov - d esi gned   super - twist ing   slid ing   mod e   cont rol   for   wind   ene rgy   conve rs ion   opti m izati on , ”   IE EE   Tr ansacti ons   on   Indust rial   Elec troni cs ,   vol.   60 ,   no.   2,     pp.   538 – 5545 ,   2 013.   [7]   K.   Be lgace m ,   A.   Me zoua r ,   A.   Mass oum,   “ Sl id ing   Mode   Contr ol   of   a   Doubly - fed   Indu ct ion   G ene ra tor   for   Wind   Ene rgy   Conv ersi on , ”   In te rnat ion al   Journal   of   En ergy   Eng ineerin g ,   vol .   3,   no .   1,   p p.   30 - 36 ,   2013 .   [8]   Utkin,   V.   I . ,   “ Sli ding   mod es   and   the ir   applic at ion   in   var ia bl e   stru cture   sys te ms, ”   Mi r,   Mos cou,   1978   [9]   S.   Benelgha li ,   M.E . H.   Benbou zi d,   T.   Ahm ed - Ali   and   J.F.   Ch arp entier ,   “ H igh - orde r   slid ing   mode   cont rol   of   a   ma rin e   cur ren t   t urbine   dr ive n   do ubly - fed   induc t i on   gene r at or , ”   I EE E   J.   Oc ean .   Eng. ,   vol .   35 ,   n o.   2,   pp .   402 - 41 1,   Apr.   2010.   [10]   B.   B el tr an,   M. E.H.   Benbou zi d ,   T.   Ahmed - Ali ,   “ Second - Order   Sl idi ng   Mode   Po wer   and   Grid   Fa ult - tolera n ce   of   a   DF IG - base d   Wind   Turbi n e , ”   Revue   of   sc ie nc es   a nd   Technol og y .   vol.   2,   no   1,   Jan uar y, 2011.   [11]   I.   Kol ey,   S.   Gho sh,   A.G.   Roy ,   P.K.   Sah a,   G.Kr.   P anda ,   “ Matlab   Modeli ng   and   Si mul ation   of   Grid   Conne ct ed   Wi n d   Pow er   Gene rati on   Us ing   Doubly   Fed   Induc ti on   Gene ra tor, ”   Int ernati onal   Journal   of   Computa t ional   Eng ineeri ng   Re search,   vol .   4 ,   no.   7,   pp.   28 - 34 ,   July   2014 .   [12]   B.   Ham ane,   M.   L.   Doumb ia,   M.   Bouham id a,   M.   Bengha n em ,   “ Control   of   Wi n d   Turbi n e   Base d   on   DF IG   Us ing   Fuzzy - PI   and   S li ding   Mode   C ontrol lers , ”   IE E E   Proce ed ings   Nint h   In te rnatio nal   Conf ere nc e   on   Ec o logi ca l   Ve hi cl es   and   R e newabl e   Ene rgi e s   (EV E R ),   Mont e - Carl o   (Monac o),   Fren ch,   pp.   4 40 - 448,   2014 .   [13]   B.   B el tr an,   A.   B enbouz id ,   “ A   Se cond - orde r   slid i ng   mod e   cont ro l   of   a   doub ly   fed   indu ct ion   g ene r at or   driv en   wind   turbi ne , ”   IEEE   T rans act ions   on   E nergy   Conv ersion ,   vol .   27 ,   no .   2,   pp.   261 - 269 ,   20 12.   Evaluation Warning : The document was created with Spire.PDF for Python.
                IS S N :2088 - 8 694   In t J   P ow  Ele c  &   D ri S ys t,   V ol .  12 , N o.   1 ,  Ma rch  20 21   :   404   –   412   412   [14]   K.   Bel g acem ,   A.   Mez ou ar,   N.   Essounbouli ,   “ Design   and   Analy sis   of   Adapti v e   Slidi ng   Mode   with   Expone nt ia l   Rea ch ing   L aw   C ontrol   for   Doubl e - Fed   Induc ti on   Gene rat or   Based   Wi nd   Turbi n e, ”   Inte rnat ional   Jo urnal   of   Powe r   El e ct ronics   and   Dr iv e   Syst em   (I J PE DS) ,   vo l.   9,   n o.   4,   pp .   1534   - 1 544,   2018 .   [15]   B.   Bel k acem ,   “ Hybrid   Fuzzy   Sl idi ng   Mode   Con trol   of   a   DF IG   Inte gra te d   int o   th e   Network, ”   In ter nati onal   Journ al   of   Pow er   Elec tronic s   and   Dr ive   Syste m   (I JP EDS ),   vol .   3 ,   no .   4,   p p.   351 - 364 ,   201 3.     [16]   Y.   Krim ,   D.   A bbes,   S.   Krim ,   M.   Faouzi   Mi m ouni ,   “ C la ss ical   vec tor ,   f irst - or der   slidi ng   mod e   and   h igh - orde r   slidi ng - mode   co ntrol   for   a   grid - conne c te d   var i a ble   spe ed   wind   ene rgy   conve rsi on   sys te m:   A   co mpa ra ti ve   study , ”   Wind   Eng ine erin g ,   vol .   42 ,   no .   1 ,   pp.   16 – 37 ,   2018 .   [17]   Abdedda im   S.,   Bet ka ,   “ Opti ma l   tr ac king   and   ro bust   power   con t rol   of   the   DF IG   wind   turb ine , ”   El e ct rica l   Power   and   Ene rgy   Syst ems   (ELSIVE R ),   vol.   49 ,   pp .   234 – 242,   2013 .   [18]   H.   Maji d,   H.   Abouaïssa ,   “ Co mparat iv e   Study   of   a   Super - Twisti ng   Slidi ng   Mode   Obs erv er   and   an   E xte nded   Ka lm an   Filt er   for   a   Fre e way   Traffic   Sys te m ,”   C ybe rnet ics   and   Informatio n   Technol og ie s .,   vol. 15 ,   no   2,   pp.   141 - 158,   2015.   [19]   Liu   N. ,   L ing   R. ,   Huang   Q.,   Zhu   Z.,   “ Second - Order   Super - Twist in g   Slidi ng   Mode   Control   for   Fin ite - Time   Le ad er - Follower   Cons ensus   with   U nce rt ai n   Nonli nea r   Mul ti ag en tSys te ms , ”   Hin dawi   Pub li shin g   Corpor ati on   Mathe mati cal   Proble ms   in   Engi n ee ring .,   2015 .   [20]   A.   Boua louc h ,   T.   Nass er ,   A.   Essadki ,   A.   Boukhr iss ,   A.   Frigui ,   “ A   Robust   Pow er   Control   of   a   DF IG   used   in   Wi nd   Turbi ne   Convers ion   Sys te m , ”   Int ernati onal   Ene r gy   Journal .   vo l.   17,   no .   1,   pp .   1 - 10,   2017 .   [21]   A.   Tama ara t   an d   A.   Ben akc h a,   “ Perform ance   of   Acti v e   and   Rea c ti ve   Pow er   Control   in   a   DF IG   - base d   Wind   Turbi ne , ”   Revue   des   Ene rgi es   R e nouve lab le s,   vol.   20,   no.   4,   pp.   63 5   –   647 ,   2017 .   [22]   S.   Ramtin .,   M.   Seyed. ,   A.   Mohammad. ,   M.   R.   Agha   Kashkoo li ,   “ Super - Twist ing   Slidi ng   Mo de   Dire ct   Pow e r   Control   of   Brushless   Doubly   Fe d   Induc ti on   Gen era tor , ”   I EE E   Tr ansacti ons   on   In dustrial   El e ct ro nic s ,   vol .   65,   no .   11,    pp .   9147 - 91 56,   Mar .   2018 .   [23]   S.   Hongcha ng ,   H.   Yaoz hen .,   Z. Lvyua n,   “ Maxi mum   W ind   Pow er   Tracki ng   of   Doubly   Fed   Wind   Turbi ne   Sys t e m   Based   on   Ad apt i ve   Gain   Second - Order   Slidi ng   Mode ”   Journal   of   Control   Sc ie nc e   and   Engi n ee ring ,   2018 .   [24]   H.   Yaoz h en ,   M .   Rongli n . ,   “ Ada pti ve - Ga in   Se co nd - Order   Slidi n g   Mode   Dir ect   Pow er   Control   f or   Wi nd - Turbi n e - Drive n   DF IG   under   Ba la n ce d   an d   Unbala n ce d   Grid   Volt age, ”   En ergie s ,   vo l.   12,   n o.   20 ,   pp .   1 - 18 ,   2019.   [25]   I .   EL   Kara ou i,   M.   Maa rouf i,   “ Robust   powe r   cont rol   m et h ods   for   wind   t urbine s   using   DF IG - gene rat or , ”   Inte rnational   Jo urnal   of   Powe r   El e ct ronics   and   Dr iv e   Syst em   (I J PE DS) ,   vo l.   10,   no.   4,   pp .   2101 - 2117,   De c.   2019 .       BIOGR AP H I ES   OF   A UTH ORS       Houari aAb dell i   was   born   in   Alger ia   in   196 9.   She   i s   Ph.D   student   in   the   Depa rtment   of   El e ct ri ca l   Engi n ee ring   at   the   Univer sity   of   Sci enc es   and   T ec h nology   (US TO - MB)   of   Oran,   Alger ia.   She   r ecei ved   Magist er   degr ee   in   Indust ria l   con trol   of   e le c tri c al   driv es   and   di agnosis   from   the   Univ er sity   of   Scie n ce   and   Technol ogy   of   Oran   (US TO - MB),   Alger ia   in   2011.   Her   ma jor   r ese arc h   int er ests   a re   m odel ing ,   cont ro l   of   e lectr i ca l   ma ch ine s   and   c ontrol   of   wind   turbi nes .           Ab delk ader   M EZOUAR   was   born   in   Masc ara,   Alger i a,   in   1974 .   He   r ecei ved   the   B. S.   and   M.S.   degr ee s   in   El e ctrical   Engi n ee rin g   from   Na ti ona l   Polyt ec hni c   Sc hool,   Algi ers,   Alger i a,   in   1997   and   1999   respe ctivel y .   Subs equently,   he   re ceive d   the   Ph.D.   deg re e   and   the   unive rs it y   h abi l it a ti on   from   DjillaliLia bes   Univer sity,   Sidi   Bel   Abbès,   Alger ia,   in   200 6   and   2008   resp ec t ive ly .   He   is   cur ren t ly   th e   pr eside nt   of   the   L abor at ory   of   E lectr i ca l   Engi n ee ri ng,   T ahe r   Moul ay   Univer sity ,   Saida ,   Alg eria.   His   rese arc h   intere sts   include   e le c tri c al   ma ch in es   and   driv es,   slidi ng   mod e   cont rol ,   observ er   technique s   and   r ene wabl e   ene rgy         Mok htar   Bend j ebbar   was   born   on   Augus t,   16 ,   1 965   in   R el i za n e   Alger ia.   He   re ceive d   re ce iv ed   the   B. S   d egr e e   in   e le c trica l   enginee ring   and   the   M.S.   and   PhD   d egr ee s   in   e lectr i ca l   and   cont rol   sys te ms   from   th e   Univer sity   of   Scie nc es   and   Technol ogy   of   Or a n   M.B. ,   Alger i a,   in   1989,   1993,   and   2007,   r espe ct iv el y.   He   is   cu rre ntl y   Prof essor   of   Elec tr ical   En gine er ing   at   th e   Univer sity   of   Scie nc es   and   T e chnol ogy   of   Ora n.   His   rese ar ch   i nte rests   in cl ude   El e ct ri ca l   machi nes   and   Drive s   Control ,   Pow er   El e ct roni cs,   as   w el l   as   In te l li gen t   Control   and   Di a gnosis.         Khei ra   Bel ga cem   was   born   in   Saida   Alge ria   in   1977 .   R e cei ved   B . S.   d egr e e   in   E lectr i ca l   Engi ne eri ng   fro m   Ta h er   Moul a y   Univer sity ,   Sa ida ,   Alger i a,   in   2001   and   th e   M . S.   degr ee   from   High   Nati ona l   Schools   of   Techn ic a l   Studie s   (EN SET)   in   2009.   Subs eque ntl y ,   she   rec e ive d   the   Ph.D.   degr ee   fro m   Djilla li L ia bes   Univer sity,   Sidi   Bel   Abbès,   Alge ria ,   in   2014.   She   is   cur r ent ly   a   me mb er   of   th e   La bora tory   of   E le c tri c al   Engi n e eri ng,   T ahe r   Mo ula y   Univ ersit y   Saida ,   Alger ia .   His   rese ar ch   in t ere sts   in cl ud e   e l ec tr ic a l   ma ch ines   and   driv es,   sli ding   mod e   control,   mode l li ng   and   con trol   of   w ind   turb ine s,   and   ren ew abl e   en er gy .     Evaluation Warning : The document was created with Spire.PDF for Python.