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.  45 3 ~ 46 2   IS S N:  20 88 - 8694 ,  DOI: 10 .11 591/ ij peds . v12.i 1 . pp 45 3 - 46 2          453       Journ al h om e page :  http: // ij pe ds .i aescore.c om   Fuzzy   l ogic   co ntro l   of   acti ve   and   reacti ve   power   f or   a   grid - connect ed   photo voltai c   system   using   a   t hree - lev el   neutr al - point - clamped   invert er       Ghrissi   Ta hri 1 ,   Zou bir   Ah m ed   F oitih 2 ,   Ali   Tahri 3   1,2 LE PES A   La bo rat ory ,   E le c tronics   depa r tment,   E le c tri c al   Engi n eering   Facu lt y,   De par tment   of   E lec troni cs   Engi ne er ing   of   the   Univer si ty   of   Sci ence   and   Te chno logy   of   Oran,   Moha me d   Boudia f   US TO - MB,   Oran,   Alge ria   3 El e ct ri ca l   Eng in ee ring   L abor at or y,   E lectr i ca l   Eng ine er ing   Facu lt y   of   the   Univer si ty   of   Sci ence   and   Te chno logy   of   Oran,   Mohame d   Boud i af   US TO - MB,   O ran ,   Alg eria       Art ic le   In f o     ABSTR A CT   Art ic le   hist or y:   Re cei ved   M a y   3 ,   20 20   Re vised   Jan   19 ,   20 21   Accepte d   Fe b   3,   2021       Thi s   pape r   aims   to   pre sent   a   fu zzy   logi c   cont ro l   ( FLC)   of   active   a nd   react iv e   power   for   a   grid - conne c te d   phot ovolt aic   sys tem.   The   PV   sys tem   is   connect ed   to   th e   gr id   ut il i ty   using   a   thr ee - level   n eut r al   po int   cl a mpe d   inve r te r   (3L - NP C)   and   LC L   f il t er.   Two   cont ro l   str a te gi es,   fu zz y   log ic   cont rol ,   and   c onvent ion al   PI   cont ro l   ar e   a ppli ed .   The   d esi gn   of   th e   two   c ontrol   strategi es   is   base d   on   ca l cul a ti ng   th e   i nstant an eous   ac t ive   and   re active   power   from   th e   measured   grid   vol ta g es   an d   cur r ent s   to   al l ow   the   sys te m   to   hav e   a   dyn am i c   robustn ess   per forma n ce   ag ai nst   a   sudden   cha nge   in   r eact ive   power   and   sati sfac tory   ac t ive   power   tr ac king   under   r api d   sol ar   rad i at ion   ch ange s.   The   cont ro l   strat eg ie s   can   trans fer   the   to ta l   active   power   g ene r at ed   by   the   PV   a rra y   to   th e   grid   u ti lity   with   high   power   qu ality   and   a   uni ty   p ower   fa ct or .   The   simul at io n   result s   using   th e   Mat la b - Simu li n k   env ironm en t   show   that   the   FL C   stra te gy   has   a   b et t er   dy nam i c   per f ormance   wi th   l ess   sett l ing   ti m e,   an d   over shoo t   com par ed   to   th e   conve nt iona l   PI   cont rol .   Ke yw or d s :   Acti ve   a nd   rea ct ive   powe r   Fu zz y   lo gic   c ontr ol   NP C   in ve rter   Pertu rb   an d   ob serv   PV   a rr a y   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 :   Ghrissi   Ta hr i   LEPES A   La bo ratory,   Ele ct r onic s   Dep a rtme nt,   Ele ct rical   E ng i neer i ng   Fac ulty     Un i ver sit y   of   S ci ence   a nd   Tec hnolog y   of   O ra n,   Moha me d   B oudiaf ,   US T O - MB   BP   1505   El   M ’ naoue r,   Or a n,   31000,   Alge ria   Emai l:   ghrissi.t ahr i@ univ - us t o.dz       1.   INTROD U CTION   Photo vo lt ai c   e nerg y   is   now   r ecognize d   as   one   of   t he   prom isi ng   ren e wa ble   energ y   s ourc es   that   can   ens ur e   e nergy   transiti on   in   t he   f uture.   P hoto vo lt ai c   e ne rgy   is   kn own   to   be   saf e,   poll utio n - fr ee   a nd   doe s   not   require   e xpen sive   mai ntena nc e,   s uch   as   fo s sil   fu el s   [ 1] .   Larg e   ph otov ol ta ic   sy ste ms   are   now   c onne ct ed   to   the   ut il i ty   gri d   a nd   co ntribute   to   the   gr ow i ng   dema nd   f or   el ect rical   energy   [2].   T o   ens ure   maxim um   tr ansmissi on   of   el ect rical   energy,   the   phot ov oltai c   (P V )   s ys te m   m us t   mai ntain   the   PV   ar ray   to   operate   at   its   ma ximum   powe r   po i nt   ( M P P).     M ore ov e r,   the   gri d - co nnect ed   PV   sy ste m   mu st   be   hi gh l y   c on t ro ll ed   to   guara ntee   t he   secu rity   a nd   reli abili ty   of   the   powe r   s ys te m   [ 3].   Acti ve   a nd   reacti ve   co nt ro l   is   a   c r ucial   ta sk   to   mai ntain   the   sta bili ty   of   t he   powe r   s ys te m   netw ork.   T herefo re,   the   re ne wab le   ene r gy   so urces   c onne ct ed   to   the   el e ct rical   util it y   mu st   be   well   co ntr olled   to   a void   an y   instabil it y   of   t he   powe r   flo w   [ 4] .   Durin g   t he   la st   deca des,   ma ny   stu dies   hav e   been   ca rr ie d   out   to   im pro ve   act ive   an d   re act ive   power   con t ro l   of   gri d - c onnecte d   PV   sy ste m s.   Re centl y,   Laag oubi   et .   al .   [ 5]   propose d   act ive   an d   reac ti ve   pow er   c on trol   strat e gy   of   PV   gri d - c onne ct ed   s ys te m   ba sed   on   two   fu zz y   l og ic   co ntr oller s.   T he   first   one   f or   MPPT   an d   the   sec ond   one   for   act ive   a nd   reacti ve   c urren ts.   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   :   45 3   –   46 2   454   The   main   wea kn e ss   of   t he   pro posed   strat e gy   is   that   t he   sy ste m   is   not   sensiti ve   to   ch ang e   in   a   loca l   load   connecte d   to   t he   AC   si de.   Nag a raja   Ra o   et .   al .   [ 6]   de velo ped   a   c on trol   strat e gy   a pp li ed   to   a   PV   gr i d - connecte d   sy st em   us i ng   a   mul ti le vel   inv erter.   In   the   pro po sed   strat e gy   t he   act ive   an d   re act ive   curre nts   of   t he   AC   side   are   not   meas ur e d.   T her e fore,   th e   st abili ty   an d   r el ia bili ty   of   the   powe r   s ys te m   c annot   be   gu a ra nteed   especial ly   wh e n   c hanges   occ urre d   in   the   wea ther   par a mete r s.   A meer ul   et .   al .   [ 7]   pro pose d   a   nonlinea r   c on t rol   of   a   PV   gri d - c onnected   s ys te m   that   us es   in sta ntane ou s   ac ti ve   an d   reacti ve   powe r   c ompone nts   as   dy namic   var ia bles.   T he   method   has   some   ad va ntages   to   the   af oreme ntion e d   meth ods   but   in   a   pres ence   of   a   th ree - phas e   fau lt ,   t he   s ys te m   ex hib it s   a   hi gh   volt age   pea k   at   the   AC   sid e.   H oweve r,   ac ti ve   an d   reacti ve   powe r   c on tr ol   is   a   crit ic al   ta sk   in   po wer   ma na ge ment   f or   the   powe r   s ys te m .   Us ually ,   el ect rical   co mp a nie s   gua ran te e   an   act ive   powe r   fl ow   for   in dustria l   us e rs   wit h   ma ndat ory   that   us e rs   mu st   c on t ro l   r eact ive   powe r   in   the   AC   side .   Any   def ic it   in   reacti ve   powe r   will   hav e   a   gr eat   im pact   on   t he   volt age   pr of il e   a nd   powe r   s ys te m   reli abili ty   [8] - [12].   In   t his   pa pe r,   f uzzy   lo gic   co nt ro ll ers   (F LCs )   for   act ive   a nd   reacti ve   power   are   pro po se d.   The   go al   of   the   pro po se d   c on t ro l   strat eg y   is   to   t ransfe r   t he   act ive   powe r   ge ne rated   by   a   PV   a rr a y   to   the   gri d   util it y   with   a   un it y   po wer   fa ct or .   The   c on tr ol   strat eg y   des ign   is   base d   on   cal culat in g   t he   in sta ntane ous   act ive   an d   r eact ive   powe r   f rom   t he   meas ur e d   gr i d   vo lt age s   a nd   curre nts;   there fore,   t he   c on t r ol   syst em   giv e s   dyna mic   r ob us tness   performa nce   a gainst   a   s udde n   cha nge   in   re act ive   powe r   a nd   sat is factory   act ive   powe r   trackin g   under   rap i d   so la r   ra diati on   changes .   U nd e r   a   sim ulati on   study   with   M at la b   Sim ulin k   S impowe rsyste ms   t oo l box,   it   can   be   no ti ced   that   the   pro posed   f uzzy   lo gic   c ontr ol   ( FLC)   strat eg y   has   a   f ast   dyna mic   pe rformance   re sp onse   com par e d   to   c onve ntion al   PI   con t ro l.       2.   RESEA R CH   METHO D   2.1.   Ma in   str uct ur e   of   grid - c on n ected   PV   syste m   The   gr id - c onne ct ed   PV   sy ste m   is   show n   in   Figure   1.   It   con sist s   of   a   PV   ar ray   rated   to   80   kW   an d   com posed   of   40   par al le l   an d   10   series - co nn ect ed   K yocera   so la r   KC 200GT   mod ules.   The   par a mete r s   of   the   Kyoce ra   so la r   KC200GT   modu le   a re   ta ke n   as   giv e n   by   the   man uf act ur e r   [13].   Pe rtu rb   and   obse rv e d   ( P&O )   base d   M P PT   c on t ro l   strat eg y   is   im pleme nted   us in g   a   boos t   DC - DC   c onve rter   to   mainta in   the   PV   ar ra y   to   op e rate   at   its   maxim um   power   po i nt.   T he   (P & O)   method   us ed   in   this   w ork   is   as   stud ie d   in   previ ou s     work   [14 ] - [ 16] .   A   t hr ee - le vel   neu t ral   point   cl ampe d   in ve rter   (3L - NP C)   is   c onnected   to   t he   gr i d   util it y   thr ough   an   LCL   filt er   to   e nha nce   t he   AC   powe r   flo w   qual it y.   A   lo cal   reacti ve   loa d   is   c onnecte d   to   t he   gr i d   w hi ch   can   be   c hange d   fro m   10   kVAR   in du ct ive   m ode   to   10   kV AR   ca pacit ive   m ode   and   vice   ve rsa.   The   local   reac ti ve   load   is   us ed   to   check   t he   reac ti ve   con t ro l   ca pab il it y   of   the   sy ste m   to   pro vi de   a   unit y   po wer   facto r   at   the   AC     bus   ba r.       PV I PV V D C - D C   B O O S T   C O N V E R T E R G r o u p   o f   P V   M o d u l e s out I P & O   M P P T   C o n t r o l P W M n dc V p dc V 1 C 2 C p c o 3 - l e v e l   n e u t r a l   p o i n t   c l a m p e d   ( N P C )   f R f L s R s L f C C R G r i d a e b e c e + - + - + - a i b i c i P L L gd v gq v d q a b c gd i gq i I n s o l a t i o n ( ) 2 W m T e m p e r a t u r e ( ) 0 C G a t e   s i g n a l s P W M   g e n e r a t o r - 3   l e v e l s d q a b c * d i * q i B l o c k   o f   c u r r e n t   c o n t r o l id v iq v B l o c k   o f   a c t i v e   a n d   r e a c t i v e   p o w e r   c o n t r o l Q P d   q P   Q gd v gd i gq v gq i * P * 0 Q = - + - + i a b c v A B C a b c A B C A B C a b c A B C I n d u c t i v e   l o a d C a p a c i t i v e   l o a d G r i d B u s   b a r   Figure   1.   G rid - connecte d   PV   sy ste m       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       Fuzz y  lo gic control  of  activ e a nd r eacti ve  powe r fo r  a grid - co nnect ed p hotovoltaic  …   ( G hr issi  T ahri )   455   The   i ns ta nta ne ou s   act ive   a nd   reacti ve   powe r   fl ow i ng   to   the   AC   gr i d   a re   cal culat ed   as   gi ven   by   (1)   and   ( 2) :   = 3 2 (     +     )   (1)     = 3 2 (     −     )   (2)     Wh e re:     v gd ,   v gq :   AC   gr i d   util it y   side   volt age   in   dq   f ra me.   i gd ,   i gq :   act ive   and   reacti ve   cu r ren t   in   dq   f ram e.   Takin g   int o   ac count   that   the   d   a xis   is   de finite ly   al ign e d   with   the   gri d   vo lt age   w hich   means   t ha t     v gq   =   0,   the   c ur ren ts   in   the   dq   fr ame   are   cal culat ed   as   ( 3)   an d   (4)   [17],   [18] :       = ( 2 3 ) ( )   (3)     = − ( 2 3 ) ( )   (4)     As   sho wn   in   Figure   2,   the   act ive   an d   rea ct ive   po wer   c on t ro l   pro vid e s   as   outp ut   t he   act ive   a nd   reacti ve   c urrent s   set po i nts   us e d   in   the   dec ou pled   c urre nt   c ontr ol.   T he   outp ut   po wer   ge nerat ed   by   t he   PV   arr a y   is   ta ken   as   the   act ive   powe r   r efere nce   w hile   the   ref e re nce   reacti ve   po wer   is   set   to   zero .   Ther e f or e,   t he   act ive   powe r   gen e rated   by   the   PV   ar r ay   is   c omplet el y   tra nsfer red   to   the   AC   gr id       P I   C u r r e n t   c o n t r o l l e r P I   C u r r e n t   c o n t r o l l e r d q a b c + + + - + + W *   L W *   L gd i gq i - + - + gq i gd i gd v gq v abc v P I   c o n t r o l l e r * P * 0 Q = Q P P I   c o n t r o l l e r gd v ( ) ( ) ( ) 2 12 3 uu ( ) ( ) ( ) 2 21 3 uu − * d i * q i d   q P   Q gd v gd i gq v gq i - + - + A c t i v e   a n d   r e a c t i v e   p o w e r   c o n t r o l D e c o u p l e d   c u r r e n t   c o n t r o l     Figure   2.   Bl oc k   diag ram   of   a ct ive   an d   reacti ve   powe r   a nd   de coupled   cu rre nt   co ntr ol       The   mathemat i cal   model   of   t he   cu rr e nts   fl owing   from   the   i nverter   to   t he   gri d   util it y   is   give n   by   ( 5) .      [   ] = [ − − − ] [   ] + 1 [  −   −  ]   (5)     wh e re :     = +   and   = +     R s ,   L s :   gr id   sid e   resist or   a nd   inducto r.   R f ,   L f :   3L - NP C   side   resist or   a nd   in du ct or.   :   gri d   an gula r   velocit y.   The   matri x   m odel   as   sho wn   in   e quat ion   ( 5)   exh i bits   cr os s - couplin g   te r ms    an d    ,   a nd   have   feed - f orwa rd   te rms      an d    .   F or   eff ic ie nt   co ntr ol,   the   two   c urr ent   co mpo ne nts   m us t   be   dec ouple d.   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   :   45 3   –   46 2   456     2.2.     Dec ou pled   PI   contr ol   desig n   In   the   la st   dec ades,   LCL   filt ers   were   e xten sively   us e d   in   a   gri d - co nnect ed   PV   s ys te m   due   to   thei r   capab il it y   to   a tt enu at e   harmo nics   a nd   prov i de   high   powe r   qual it y   [19],   [ 20] .   T he   LCL   filt er   is   an   ess entia l   dev ic e   to   el imi nate   ha rm on ic s   co ntents   pr ese nt   in   in ve rter   outp ut   cu rr e nts.   It   is   cal culat ed   ta kin g   into   a cc ount   the   power   rati ng   of   the   in vert er,   t he   s witc hi ng   f re qu e nc y,   and   the   gr id   frequ e nc y.   T he   eff ect   of   dam pi ng   can   ob st ru ct   r eso na nce   pro blems   passivel y   or   ac ti vely.   T he   po wer   rati ng   of   t he   in ver te r ,   the   switc hing   f requen c y,   and   the   gri d   fr e qu e nc y   a re   ess entia l   as   in pu ts   f or   s el ect ing   t he   LCL   filt er   pa rameters .   Since   the   eq uat ion s   ab ove,   t he   trans fer   f unct ion   of   t he   op e n - loop   c urren t   c ontr ol   f or   the   s yst em   can   be   giv e n   as   ( 6) :      ( ) = ⋅ + ( ) ⋅ 1 1 +  ⋅ 1 + ( )   (6)     Wh e re:   Kp   an d   Ki   are   the   PI   c on t ro ll er   pa ra mete rs.     is   the   ti me   de la y   due   to   t he   PWM   cal c ulati on   an d   c omp utati on   needed   in   dig it al   c on tr ol.   Tu ning   of   PI   ga in   pa ramete rs   is   justi fied   by   ( 7) :     =   (7)     Th us ,   t he   tra nsfer   f un ct io n   of   the   cl os e d - l oop   cu rr e nt   co ntr ol   for   the   s ys te m   can   be   s how n   as   ( 8) :      ( ) = 2 + ( 1 ) ⋅ +   (8)     The   cl os ed - loop   c urren t   c ontr ol   tra ns fe r   func ti on   in   a   sec on d - orde r   gen e ral   f or m   s ys te m   is   ( 9) :      ( ) = 2 2 + 2 + 2   (9)     By   ide ntify i ng   equ at io n   ( 8)   to   equ at io n   ( 9) ,   the   PI   co ntr oller   par a mete rs   a re   fou nd   to   be:     = 2     (10)     = 2     ( )   (11)     The   pro portio nal   an d   i nteg r al   gains   of   the   PI   c ontrolle r   are   cal culat ed   from   t he   e qu at ion s   a bove .     The   dam ping   c oeffici ent     was   pro po se d   to   be   0.707 1   a nd     w as   ap pro ximate d   to   be   0.0 01   s :     { = 2 . 07 = 50   (12)     2.3.     M od el   of   PQ   FLC   c ontrolle r   The   FLC   c omp ared   to   ot her   c onve ntion al   co ntr ol   te ch nique s   does   not   requ ire   pri or   knowl edg e   of   t he   mathemat ic al   model   of   t he   s ys te m.   On   t he   oth e r   hand,   thi s   arti fici al   inte ll igence   c on tr ol   strat eg y   needs   a   set   of   ru le s   base d   essenti al ly   on   t he   kn ow le dge   of   t he   ope rator   mani pu la ti ng   the   sy ste m   [ 21] .   T he   desc ription   of   the   f uzzy   c ontr oller   sho ws   th at   the   sign ific a nt   quantit ie s   for   the   c on tr ol   ar e   the   erro r   an d   the   cha ng e   of   error   of   the   act ive   a nd   reacti ve   po wer.   The   act iv e   power   ref e re nce   P *   is   s uppl ie d   by   t he   PV   arr a y   an d   the   r eact ive   powe r   ref e re nc e   Q *   is   set   to   zer o.   F or   the   inputs   of   the   fu zz y   lo gic   con t ro ll er,   we   will   adopt   the   two   char act e risti cs   par a mete rs   no t ed   as   E   and E .   The   basic   te ch niqu e   of   F LC   is   an   associat ion   of   the   f ollo win g   three   processe s :   fu zzi ficat io n,   fu zz y   i nf e ren c e,   an d   de fu zzi f ic at ion   [ 22] .     The   f uzz y   lo gi c   con t ro l   diag r am   is   pr e sente d   in   Fi gure   3.   It   is   com posed   of   fou r   bl ock s   wh ic h   are   exp la ine d   as   f ol low:   -   The   nor mali zat ion   facto rs   ar e   ass ociat ed   with   the   er r or E ,   i ts   va riat ion E ,   a nd   the   var ia ti on   of   t he   var ia ble   co ntr ol    .   -   The   blo c k   of   F uzzifica ti on   of   the   er ror   a nd   its   va riat ion .   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       Fuzz y  lo gic control  of  activ e a nd r eacti ve  powe r fo r  a grid - co nnect ed p hotovoltaic  …   ( G hr issi  T ahri )   457   -   The   ru le s   of   the   f uzzy   lo gic   c on t ro ll er.   -   The   defuzzifi c at ion   blo c k   is   use d   to   c onver t   t he   fu zz y   c ontr ol   va riat ion   to   a   nume rical   va lue   [ 23] .       F u z z f i c a t i o n 1 Z − E E 1 Z − U U E K + - ( ) ** PQ ( ) PQ I n f e r e n c e   m e c h a n i s m D e f u z z i f i c a t i o n E K U K G r i d   p a r a m e t e r s   d e t e c t i o n + - + +     Figure   3.   The   s cheme   of   a   fuz zy   c on t ro ll er .       2.4.     Desi gn   of   PQ   Fuzzy   co nt r ol   The   PQ   f uzzy   log ic   c ontr ol   di agr a m   is   dep ic t ed   in   Fig ure   4.       1 z 1 z 1 z 1 z P   F u z z y   C o n t r o l l e r * P * Q Q P Q   F u z z y     C o n t r o l l e r gd v ( ) ( ) ( ) 2 12 3 uu ( ) ( ) ( ) 2 21 3 uu − * d i * q i d   q P   Q gd v gd i gq v gq i - + 5 2 . 1 0 − 4 2 . 1 0 − 80 + + - + 3 2 . 1 0 − 2 2 . 1 0 − 3 5 . 1 0 − + + - + - + P E P E Q E Q E       Figure   4.   PQ   f uzzy   lo gic   c on t ro l   diag ram.       Fuzzi fica tion:   This   ste p   em pl oy s   the   mem ber s hip   functi on s   ( M Fs )   to   conve rt   real   quantit ie s   to   f uz zy   va riables.   These   ( M Fs )   ha ve   dif fer e nt   s hap e s   but   tria ngle   a nd   tra pez oid   sh a pes   are   the   c om m only   us e d   ty pes .   T he   in pu t   and   outp ut   var i ables   are   re pr e sented   by   se ve n   li nguisti c   va r ia bles,   na mely:   NB   ( Ne gative   Bi g) ,   NM   ( Ne ga ti ve   M e diu m ),   NS   (N e gative   S ma ll ),   ZE   ( Zer o),   PS   ( Posi ti ve   Small ),   PM   (Posit ive   M edi um),   a nd   PB   (Posit ive   Bi g) .   The   mem ber s hip   f unct io ns   of   the   i nput   and   outp ut   var i ables   are   s how n   in   Fig ure   5.     Fuzzy   inferen ce:   The   M Fs   are   c ombine d   with   t he   c on t ro l   ru le s   to   get   the   c ontr ol   outp ut.   T he   f unda me ntal   par t   of   this   ste p   is   the   f uzz y   co ntr ol   r ules,   wh ic h   are   rela te d   directl y   to   a   human   bei ng’s   ex pe rtise .   H ow e ve r,   in   Tab le   1,   49   f uzz y   r ules   for   e rror   an d   c hange   of   er r or   are   sel ect ed   ac cordin g   to   the   M am da ni   meth od   [24 ] ,   [ 25] .   Def u zzi fica tio n:   The   de f uzzific at ion   ope rati on   al lows   us   to   c al culat e   fr om   the   f uzz y   infe r ence   the   real   va lue   of   the   ou t pu t   va riable .   Af te r   that,   this   outp ut   value   is   c onve rted   into   nume rical   value   to   be   a ppli ed   to   t he   pr ocess.   Four   defuzzifi c at ion   strat egies   are   com monly   us ed:   the   maxi mu m   meth od,   the   ave rage   ma ximum   meth od ,   the   center   of   gra vity   (cen tr oid)   m et hod,   a nd   the   weig hted   hei ght   method.   The   cente r   of   gr a vity   al so   kn own   as   a   ce ntr oid   meth od   is   the   m os t   co m monly   use d   m et hod   in   t he   fiel ds   of   fu zz y   con t ro ll ers .   Th is   meth od   cal c ulate s   the   ce nter   of   gr a vity   of   the   res ulti ng   membe rs hip   f unct ion   µ(x) .   T he   a bs ci ssa   of   t he   ce nter   of   gravit y   ΔU   is   deter mine d   us in g   (3) .      = ∫  ( )  ∫ ( )    (13)   wh e re:     s   :   the   domain   of   the   membe rs hip   f unct ion.   x:   the   de gr ee   of   me mb e rs hip   f un ct io ns.   The   inte gr al   of   the   de nominat or   giv es   the   surface,   w hile   the   integral   of   the   numerat or   c orres ponds   to   the   m om e nt   of   the   s urface.     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   :   45 3   –   46 2   458       0 0 . 2 0 . 4 0 . 6 0 . 8 1 - 0 . 2 - 0 . 4 - 0 . 6 - 0 . 8 - 1 E r r o r   E V a r i a t i o n   o f   e r r o r   ∆ E O u t p u t   ∆ U N B N M N S Z E P S P M P B 1 - 0 . 2 - 0 . 4 N B N M N S Z E P S P M P B - 0 . 6 - 0 . 8 - 1 0 0 . 2 0 . 4 0 . 6 0 . 8 0 0 . 2 0 . 4 0 . 6 0 . 8 1 - 0 . 2 - 0 . 4 - 0 . 6 - 0 . 8 - 1 N B N M N S Z E P S P M P B     Figure   5.   M e m ber s hip   f unct io n   of   the   e rror,   t he   var ia ti on   of   the   er ror   a nd   the   outp ut   of   t he   FLCs.       Table   1.   PQ   f uz zy   ru le   base   t able.   Variation   of   e rr o r          NB   NM   NS   ZE     PS   PM   PB       Er ror     NB   NM   NS   ZE   PS   PM   PB   NB   NB   NB   NB   NM   NS   ZE   NB   NM   NM   NM   NS   ZE   PS   NB   NM   NS   NS   ZE   PS   PS   NM   NM   NS   ZE   PS   PM   PM   NB   NS   ZE   PS   PS   PM   PB   NS   ZE   PS   PM   PM   PM   PB   ZE   PS   PM   PB   PB   PB   PB       3.   SIMULATI O N   RESU LT S   To   co m par e   the   performa nce   of   the   FLC   str at egy   to   t he   co nv e ntio nal   PI   con t ro l,   a   set   of   simulat io n   te st   cases   has   been   done   us i ng   M AT LAB \ Simuli nk   e nvir onment.   T he   s imulat ion   pa ra mete rs   of   the   sy ste m   are   giv e n   in   t he   simulat ion   pa rameters   i x.   F igure   6   s hows   the   outp ut   curr ent,   volt age,   a nd   powe r   of   PV   ar ray   us in g   pe rtu rb   a nd   ob s er ve   M P PT   te c hn i qu e .   A   rap i d   ste p   ch ang e s   a re   a ppli ed   to   i rr a dianc e   sta rtin g   with   100 0   (W \ m 2 )   f r om   0   to   0.3   s,   500   (W \ m 2 )   from   0. 3   to   0.6   s   a nd   e nd i ng   to   1000   (W \ m 2 )   from   0. 6   to   0.9   s.   The   PQ   FLC   a nd   PI   c on t ro l   a re   de picte d   in   Figure   7.   It   ca n   be   see n   that   the   act ive   pow er   res pons e   con t ro ll ed   by   t he   f uzzy   lo gic   con t ro ll er   f ollo ws   the   act ive   powe r   ref e re nc e   ge ne rated   by   the   PV   ar ray   bette r   than   the   one   c on t ro ll ed   by   the   PI   c on t ro ll er.   It   ca n   be   al so   noti ced   that   t he   reacti ve   po wer   co ntr olled   by   t he   fu zz y   l ogic   c ontr oller   trac ks   the   r efe ren ce   s et ed   to   ze ro   with   a   fast   tra nsi ent   res ponse   com par e d   to   the   one   con t ro ll ed   by   t he   PI   c on t ro ll e r.   The refo re,   the   t otal   act ive   powe r   s upplie d   by   t he   PV   a rr a y   is   tra nsfer red   to   AC   gr i d   with   un it y   powe r   fa ct or .   Fi gure   8   sh ows   the   respon s es   of   act ive   cu rr e nt   an d   its   re fer e nce   us ing   the   two   c ontr ol   str at egies.   It   is   c le ar   that   the   PQ   F LC   te ch ni qu e   ha s   a   bette r   dynamic   pe rformance   an d   more   sensiti ve   to   a   s udde n   c hange   in   ir rad ia nce   c ompa red   to   t he   PQ   PI   c ontr ol   s trat egy.     The   reacti ve   c urren t   an d   its   re fer e nce   res pons es   a re   de picte d   in   Fig ure   9.   T he   reac ti ve   cu rr e nt   con t ro ll ed   by   fu zz y   l og ic   co ntr oller   has   a   faster   res pons e   an d   it   is   m ore   sen sit ive   to   a   sud den   c hange   in   irrad ia nce   c ompare d   to   t he   one   con t ro ll ed   by   PI   c on tr oller.   It   can   be   noti ced   that   the   rea ct ive   curre nt   al way s   after   a   s hort   tr ansient   sta te   re tur ns   to   ze r o.   Figures   10   an d   11   sho w   loa d   curre nt   an d   volt age   wav e for ms   on   the   top   a nd   t he   gri d   cu rr e nt   an d   volt age   wav e f or m s   on   the   bo tt om   c on t ro ll ed   by   PQ   PI   a nd   PQ   FLC   con t ro ll ers   res pecti vely .   The se   wav e f or m s   are   obta ine d   with   a   change   of   local   load   f rom   inducti ve   m od e   to   capaci ti ve   m ode   at   0.15   s.   It   can   be   see n   that   the   gr i d   c urren t   is   al wa ys   in   phase   with   the   gr i d   volt age.   Howe ver,   t he   powe r   facto r   is   imp r ov e d   an d   al way s   e qu al   to   unit y.   T he   propose d   f uzzy   l og ic   co ntr ol   a ppr oac h   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       Fuzz y  lo gic control  of  activ e a nd r eacti ve  powe r fo r  a grid - co nnect ed p hotovoltaic  …   ( G hr issi  T ahri )   459   al lows   the   PV   gr id - c onnecte d   sy ste m   to   tr ansf e r   the   tota l   act ive   power   gen e rated   by   the   PV   ar ra y   with   com pensat ing   the   reacti ve   power.         Figure   6.   O utput   cu rr e nt,   volt age,   a nd   powe r   of   PV   a rr a y   with   a   cha nge   in   irrad ia nce   fro m     1000   to   500   ( W/m2)           Figure   7.   Acti ve ,   reacti ve   po w er   a nd   their   re f eren ces ,   us in g   PI   c ontrolle rs   a nd   f uzz y   lo gic   con t ro ll ers     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   :   45 3   –   46 2   460       Figure   8.   Re spon s es   of   Acti ve   cu rr e nt   an d   it s   ref e ren ce   ve rs us   ti me,   us in g   PQ   PI   c on t ro ll er s   an d   PQ   Fu zz y   l og i c   co ntr ollers   ( F LCs)       Figure   9.   Re spon s es   of   reacti ve   c urren t   a nd   its   ref e ren ce   ve rs us   ti me,   us in g   PQ   PI   c on t ro ll er s   an d   PQ   Fu zz y   l og i c   co ntr ollers   ( F LCs)           Figure   10.   Wa veforms   of   loa d   c urren t   a nd   volt age   on   the   t op   an d   the   gri d   cu rr e nt   and   volt age   on   the   bo tt om   c on t ro l le d   by   PQ   PI   f r om   i nductive   mode   to   capaci ti ve   m od e.       Figure   11.   Wa veforms   of   loa d   c urren t   a nd   volt age   on   the   t op   an d   the   gri d   cu rr e nt   and   volt age   on   the   bo tt om   c on t ro l le d   by   PQ   FLC s   fro m   in duct iv e   mode   to   capaci ti ve   m od e .       4.   CONCL US I O N   In   t his   pap e r,   fu zz y   l og ic   c ontr ol   of   act ive   an d   reacti ve   powe r   f or   a   gri d - c onnecte d   photov oltai c   sy ste m   us in g   a   three - le vel   ne utral - po i nt - cl ampe d   in ve rter   ( 3L - N PC)   is   pr e sente d.   T he   three - le vel   ne utral   po i nt   cl ampe d   inv e rter   has   be en   use d   with   an   LCL   filt er   to   minimi ze   ha rm on ic s   c onte nts   and   i mpro ve   c urren t   and   volt age   wa ves hap i ng.   T he   goal   of   the   pro posed   co ntr ol   strat egy   is   to   trans fer   t he   act ive   po wer   ge ne rated   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       Fuzz y  lo gic control  of  activ e a nd r eacti ve  powe r fo r  a grid - co nnect ed p hotovoltaic  …   ( G hr issi  T ahri )   461   by   a   PV   ar ray   to   t he   gri d   util it y   with   a   unit y   powe r   facto r.   The   co ntr ol   st r at egy   de sig n   is   ba sed   on   cal c ulati ng   the   i ns ta ntane ou s   act ive   a nd   reacti ve   pow er   from   the   m easur e d   gri d   volt ages   an d   cu rr e nts;   the refo r e,   the   con t ro l   strat eg y   giv es   dynam ic   rob us tnes s   performa nce   to   t he   gr i d - c on nected   PV   s yst em   agai ns t   a   su dde n   change   in   reacti ve   po wer   an d   sat isfact ory   act ive   po wer   trac king   unde r   ra pi d   s olar   ra diati on   c hanges .     The   sim ulati on   res ults   of   the   gr i d - c onnecte d   PV   sy ste m   us ing   M at la b - Si mu li nk   e nv i ronme nt   s how   cl early   t hat   t he   FLC   strat e gy   has   a   bette r   dy namic   pe rformance   with   le ss   set tl ing   ti me,   a nd   ov e rsho ot   com par e d   to   the   co nv e ntio nal   PI   c ontrol.       APPE ND I X     Simulat io n   paramet ers   Para m eters   Variables   Valu es   The   g rou p   of   ( PV )   m o d u les   wh ich   co m p o rts   40   p arallel   an d   10   series   co n n ected   Kyo cera   so lar   KC 2 0 0 GT   m o d u les   Maximu m   Po we r   P ma x   80   kW   Maximu m   v o ltag e   V ma x   263   V   Cu rr en t   at   m ax im u m   p o wer   I ma x   304   A   Op en - circuit   v o lta g e   V oc   330   V   Sh o rt - circuit   cu r re n t   I sc   328   A   DC - DC   Bo o st   co n v erter   p ar am e ters   Inp u t   v o ltag e   V i   300   V   Du ty   cy cle   D   0 .6   Ou tp u t   v o ltag e   V 0   825   V   Load   cu rr en t   I 0   8   A   Ind u cto r   L   0 .00 1 1   H   Ou tp u t   capacito r   C 0   5 .28 9 3   µF   Inp u t   capacito r   C in   100   µF   Switch in g   fr eq u en cy   F s   55   kh z   Load   resisto r   R 0   1 0 3 .1250   Ω   3L - NPC   Inv erter ,   LCL   filter   an d   Loa d s   Grid   sid e   in d u cto r   L s   1 .84   mH   3L - NPC   sid e   in d u cto r   L f   2 .3   mH   Filter   c ap acito r   C f   1 1 .02   µF   Res isto r   in   series   with   th e   capacito r     R C   3 .12   Ω   Res o n an ce   fr eq u en cy     f r es   1 5 4 0 .6   hz   Total   in d u cto r   resi stan ce   R   0 .1   Ω   Ph ase   to   p h ase   RMS   v o ltag e     V ph   p h /RMS   3 8 1 .05   V   DC - Link     C 1   =   C 2   550   µF   Grid   f requ en cy   f g   50   hz   Switch in g   fr eq u en cy   f s   30   Kh z   Inv erter   co n figu rat io n   3   p h a ses   3L - 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