Int ern at i onal  Journ al of  P ower E le ctr on i cs a n d  Drive  S ystem   (I J PE D S )   Vo l.   11 ,  No.   4 ,  Decem be r 202 0 , p p.   17 75 ~ 17 84   IS S N:  20 88 - 8694 ,  DOI: 10 .11 591/ ij peds . v11.i 4 . pp17 75 - 17 84       1775       Journ al h om e page :  http: // ij pe ds .i aescore.c om   Control   of   hybri d   power   system   bas ed   re newabl e   ener gy   generati ons   using   PI D   controll er       Moham ed   Re gad 1 ,   M ’hame d   Helaim i 2 ,   R achid   T aleb 3 ,   Ah med   M . Ot hma n 4 ,   H os s am   A.   G ab b ar 5   1,2,3   El e ct ri ca l   En gine er ing   Dep artme nt ,   Hass iba   B enboua l i   Unive r sity,   Ch le f ,   Alge ria     La bora toi re   Gén ie   El e ct r ique   et   Ene rgi es   Renou vel ab le s   (LG EER)   4   El e ct ri ca l   Pow e r   and   M ac hin e   D epa rt me nt ,   Fa culty   of   Engi n ee rin g,   Z agazi g   Un iv ersit y,   Egypt   5   Facul ty   of   Ene r gy   Sys te ms   and   Nucle ar   Sci enc e ,   Univer sity   of   O nta rio   Instit u te   of   Technol ogy   (UO IT) ,     2000   Sim coe   St .   N. ,   Os hawa   ON   L1H   7K4   ON,   Cana d a       Art ic le   In f o     ABSTR A CT   Art ic le   hist or y:   Re cei ved   Dec   2 ,   201 9   Re vised   A pr   2 4 ,   20 20   Accepte d   J un   29 ,   20 20       Thi s   pap er   ad dre ss es   to   in tegrat e   an   optimal   proporti on al - integra tor - der ivative  co ntr oll er   for   fre qu en cy   r egul a ti on   in   an   isola t ed   micr ogrid   power   sys te m   base d   r e newa ble   gene r ation.   Th is   aut on omous   mi cro gr i d   sys te m   is   com posed   of  d istri bute d   en erg y  source s  li k e  wind,   solar ,   di ese l  engi ne   gene ra tor,  fu el  c el ls   sys te m ,   and   two  diff ere n t   sto rag e   dev ices  suc h  as   ba ttery   ene rgy  storag e  s ystem   and  f lyw hee l  ene rgy  stor age   sys te m .   Opt im al   tuni ng   of   the   inve st igated   cont rol le r   is   conside red   as   the   main   prob le m   to   be   resolve d   using   t he   Kri ll   Herd   algorithm   through   an   obj ective   fu nct ion .   The   obta in ed   resul ts   are   al so   a cc o mp li shed   with   and   without   th e   b at t ery   en erg y   storage   sys tem.   The   co mpa ris on   of   sys te m   p erf orma n ce   show s   tha t   the   proposed   cont ro l   sche m e   base d   Krill   Herd   a lgori th m  is bett er   tha n   t h e  gen et i c   al gorit h m in  th e im prove m ent of s ystem   per for mance .   Ke yw or d s :   Fr e qu e nc y  c ontrol   Hybr i d  s ys te m   Kr il l  He rd  al go rithm   M ic r ogrid     PI D  Co ntr oller   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 :   M oha med   Re ga d,     Ele ct rical   Eng i neer i ng   De par t ment,     Hassiba   Be nb oual i   U niv e rsity   of   Chle f,     Lab or at oi re   Gé nie   Ele ct riq ue   et   Energies   Re nouvel ables   (L GEER) ,   BP.   78C,   O ule d   Fa res   0218 0,   Chlef,   Al ger ia .   Emai l:   m.r e ga d@u niv - c hlef . dz       1.   INTROD U CTION   Ele ct rici ty   plays   an   im portant   r ole   in   al l   s ides   of   human   li fe.   The refo r e   the   inc rease   of   t he   worl d   energ y   dema nd,   due   to   the   popula ti on   gro wth,   m oder n   i ndus tria l   s ocie ty   a nd   the   e nv iro nm e nt   poll ut ion ,   is   moved   the   w orl d   t ow a r ds   re new a ble   e nerg y   s ources   as   t he   s olu ti on   of   these   issues   r el at ed   to   t he   e nerg y   dema nd,   high   f uel   co st,   a nd   gr eenho us e   pro blems,   to   e nh a nc e   powe r   qual it y   iss ues   a nd   e ne rgy   e ff ic ac y [ 1].   Out   of   al l   re ne wab le   e ne rgy   unit s ,   wind   a nd   s olar   s ys te ms   are   co ns i de red   as   sec ure d   a nd   reli able   so urces   a nd   be ing   i ns ta ll ed   widel y.   T hes e   ge ner at i on   un it s   ha ve   ob ta ined   popula r it y   beca us e   of   the   env i ronme nt - fri end ly   c har act e risti cs   an d   the y   are   ine xhau sti ble   e nerg y   s ou rces   as   well   as   fast   dev el opme nt   in   the   te ch nolo gies   [ 2].   T he   use   of   t hese   s ourc es   rece ntly   at te nd e d   a   sal ie nt   increase   acco r ding   to   t he   c ountries'   dev el opment   a nd   e nv ir onme ntal   poll utio ns.   T he   ge ner at i on   powers   fro m   this   re ne w able   gen e rati on   a re   intermit te nt   t ha t   cause s   s ome   mismat c hes   betwee n   pro du ced   powe r   an d   dem an de d   one .   T his   a ff ec ts   the   micro gr i d   oper at ion   a nd   ca use s   instabil it y   in   the   f reque nc y   a nd   po wer   of   t he   hy br id   e nerg y   s ys te m   [ 3].   To   ta ckle   this   pro blem,   s om e   st orages   e nerg y   s ys te ms   li ke   BE SS   an d   FE SS   a long   with   c onve ntion al   s ource s   li ke   Diesel   E ngine   an d   F uel   C el l   s ys te ms   are   i nteg rated   into   the   c oncept   of   the   hybr i d   en ergy   syst em   t hat   is   consi der e d   as   t he   micro gri d.   M a ny   ty pes   of   resea rch   inter est   in   t he   m od el ing   a nd   c on t ro l   of   the se   kin ds   of   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 .  11 , N o.   4 ,  D ecembe r  2020   :   17 75   –   17 84   1776   hybri d   syst ems   as   in   [ 4 - 7 ]   w hi ch   hav e   bee n   accom plishe d   to   a ddres s   t he   c on t ro l   of   micr ogrid   us in g   va rio us   cases   of   c onfig ur at io ns .     In   t his   pa per,   a   micro gr i d   sy ste m   is   c onsidere d   to   ov e rcome   the   c ha ll eng es   faci ng   the   us e   of   ren e wa ble    ge ner at io n .   T his   pro posed   mi crogr i d   incl ud es   two   re ne w able   ge ne rati on   s ys te m   su c h   as   photov oltai c   (P V)   pa nels   a nd   wind   gen e rator   with   die sel   eng i ne ,   a nd   f uel   cel l   syst em   as   ad diti on al   gen e rato rs ,   the   Ba tt ery   a nd   F lywheel   s ys te ms   a re   i nteg rated   i nto   the   mi crogr i d   sy ste m .   F r om   ma ny   s tud ie s ,   th is   micro gri d   config ur at io n   is   consi de red   as   the   most   imp ort ant   so l ution   f or   pro du ci ng   e le ct rici ty   in   iso la te d   areas.   Howe ve r,   the   maj or   c halle ng e   t hat   f aci ng   the   e xp l oiti ng   the   mic rogr i d   is   to   re gu la te   the   po wer   a nd   fr e qu e nc y   fl uc tuati on   in   an   i sla nd e d   a nd   c onnected   mod e   of   mic rogr i d   becau s e   of   the   diff ic ulty   of   desig n   con t ro l [ 8 - 9] .   A utonomo us   op erati on   of   the   micro gr i d,   t hro ugh   c on t ro ll in g   the   s ys te m   frequ e nc y,   will   enh a nce   the   pe rfo rma nc e   of   the   micr og rid.   Due   to   its   sim plici ty   a nd   facil it y   to   im plem ent   t he   PID   co ntr oller   bec ome s   the   mo st   c ontr oller   us e d   to   mainta in   the   sy ste m   f re quenc y   unde r   f luctuat io ns   in   gen e rati on   po wer   a nd   l oad   dema nds [ 10 - 11 ].   To   achieve   t he   op t imal   con t ro l   of   fr e quenc y   in   t he   mic rogr i d   s ys te m,   dif fer e nt   op ti miza ti on   te chn iq ues   are   bein g   util iz ed   in   li te r at ur e   as   in   [12 - 17] .   T hese   res earches   ap plied   var io us   opti miza ti on   t ec hniqu es   li ke   the   Gen et i c   Algorith m,   M i ne   Bl ast   Algo rithm   ( M BA ),   Partic le   S wa rm   O ptimi zat ion   ( PS O) ,   a nd   quasi - opposit ion al   harmo ny   searc h   to   opti mize   the   c on tr oller   pa rameters .   Re c ently   fe w   resea rch es   ha ve   bee n   ac hieve d   to   present   fr e qu e nc y   c on t ro l   us in g   t he   Kr il l   He rd   te chn i qu e   [ 18].   H ow e ve r,   in   thi s   w ork,   the   Kri ll   Her d   al gori thm   is   us e d   to   opti mizi ng   t he   PID   pa ramete rs   to   co ntr ol   t he   f reque ncy   a nd   powe r   de viati on s   in   t he   propose d   micro gr i d.   T he   be st - obta ine d   par a mete rs   of   the   PID   co ntr ol le r   by   KH   a re   com par e d   with   the   oth er s   pres ented   in   [7]   us i ng   G A.   In   ge ner al ,   KH   is   a   r obust   searc h   an d   powe rful   op ti miza ti on   te ch ni qu e,   a ble   to   s olv in g   global   f unct io nal   op ti miza ti on   pr ob le m s   [ 19 - 20].   This   method   is   f oc us e d   to   sim ulate   the   beh a vior   of   kri ll   swarms   [ 21].   T he   rest   of   t he   pa per   is   orde rly   as   bellow .   Sect ion   2   descr i bes   the   pr opos e d   c onfig ur at io n   of   the   hybri d   ene r gy   s ys te m   an d   its   dif fe ren t   co mpon e nts   m odel s.   In   Sect ion   3   bri ef   int rod uction   to   t he   PI D   con t ro ll er   a nd   the   ob je ct ive   functi on   us in g   in   t his   stu dy.   Sect ion   4   e xp la in s   a   rev i ew   of   t he   Kr il l   Herd    te chn iq ue   us in g   f or   t he   op ti miza ti on   of   P I D   co ntr oller   ga ins.   Sect io n   5   dis plays   t he   resu lt s   a nalys is   and   com par is ons   with   the   pe rfo rma nces   of   the   c on tr oller   us ing   two   di ff e r ent   opti miza tio n   te c hn i qu es   and   al s o   their   r obus t nes s   co ntra   the   di sconnecti on   of   ene r gy   stora ge   dev ic es.   T he   pap e r   e nd e d   wit h   a   c on c lusio n     in   Sect io n   7.       2.   PROP OSE D   MICRO G RI D   S YS TE M     The   pr opos e d   hybri d   s ys te m   model   presente d   by   the   tra nsf er   f un ct io n   is   pr ese nted   in   Fi gure   1.   T he   PV   a rr a y   a nd   Win d   T urbine   Gen e rato r   ( W TG)   are   c onsid ered   t he   pr i ncipal   sou rces   to   ou t fit   the   loa d   dema nd.   The   Diesel   E ngine   Ge ner at or   ( DEG)   a nd   F uel   Ce ll ,   are   use d   as   c ompleme ntar y   ge nerat or s   to   e nsur e   the   sy ste m   operati on   co ntin uity   wh ic h   a ff ect ed   by   the   inter ruption   nat ur e   of   ren e wa ble   s ources.   T he   Ba tt e ry   a nd   Flywheel   de vi ces   are   ad de d   to   the   s ys te m   sta bili ty.   The   photovo lt ai c   ge ne rati on   s ys te m   and   the   wind   energ y   sy ste m   a re   c ombine d   with   oth er   source s   an d   e nergy   sto ra ge   dev ic es   to   obta in   a   m ore   c on sta nt   po wer   prof il e .   This   c onfig ur a ti on   is   us ed   in   [7].   T he   micro gr i d’ s   pa ramet ers   are   il lustrate d   in   Table. 1.   The   ty pical   m odel   of   the   micr ogri d   s ys te m   util iz ed   in   this   st udy   is   as   fell ow:   [7 - 10,   22 - 25]           Figure  1. Bl oc k of t he pr opos ed hyb rid  e nergy syst em   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       Con tr ol o f  hy bri d po we r  syste m ba se d renew ab le  e ner gy ge ner ation s  usi ng P ID …   ( Mo hame d Reg ad)   1777   Table1 . Prop ose d  mic rogr i d’ s   par a mete rs    Co m p o n en t   Gain  ( K )   The tim e con stan t  (s)   W TG    = 1    = 1 . 5   PV    = 1    = 0 . 04   / = 0 . 004   FC    = 0 . 0 1    = 4   DEG    = 0 .00 3    = 2   BESSS    = 1    = 0 . 1   FESS    = 1    = 0 . 1       G WT G = K WTG   1 + S T WTG = ∆ P WTG ∆ P WTG     (1)   G PV = K PV 1 + S T PV = ∆ P PV ∆ ∅     (2)   G FC ( s ) = K FC 1 + S T FC = ∆ P FC ∆ u     (3)   G DEG ( s ) = K DEG 1 + S T D EG =   ∆ P DEG ∆ u     (4)   G BESS ( s ) = K B ESS   1 + S T B ESS = Δ P B ESS Δ u     (5)   G FESS ( s ) = K FESS 1 + S T FESS = Δ P FESS Δ u     (6)     Wh e re   Δ   is  the  s ign al   c on t ro l  act ion   of  the   PID  c on t ro ll er  in   fee db ac k  to   minimi z e  the  fr e qu e nc y  dev ia ti on   Δ .   The  powe r  ge ner at io n  from  ren e wa ble  sou rces  a nd  pow e r  de man d  is  m od el e d  in   co nsi der in g  t he  small  sto ch ast ic  f luct uations a nd lar ge dete r minist ic  d ri ft [6 - 7].       P =   ( ( ϕ . ƞ . √ β (   1 − G ( s ) )   +   β ) /   β )   Γ = χ . Γ     (7)     Wh e re  ϕ  is  the   powe r  c omp onent,   P  re pr ese nts  the   outp ut  of   wind  or  s olar  s ys te m  a nd  load,  β  giv es   the  val ue  of   t he   powe r,   ƞ  is  r enormali zat ion  co ns ta nt  of   t he   ge ner at e d  or  load.  (χ )  to  c or respo nd  the  pe r  unit   (p.u.)   le vel,   Γ  is  a  ti me - de pe nd e nt   co nverti ng  si gn al   wit h  a   gai n  t hat  tr anscr i bes   the   s udde n  cha nge  in  t he   value f or  t he p ow e r o utput [ 7, 23] .    Figure  2  sho w s  the   stoc hastic   m od el   of  ge ne rati on  po wer s   ( Pw ,   Ps ol),  the   total   powe r  (P t ),   a nd  al s o  the  dema nd  (Pl ).   Sig nificant   fluctuati ons   th at   can   in flue nc e  the   f re qu e nc y  de viati on  ca n  be   re mar ke d.  T he  stochastic   natu res  a re inde penden t  of the  con trol strate gy.              Figure   2.   Re al iz at ion   of   the   sol ar,   wind   a nd   load   po wer s   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 .  11 , N o.   4 ,  D ecembe r  2020   :   17 75   –   17 84   1778   3.   PID   CONTR OLL ER   ST R UC T UR E   AND   OB JEC TI V E   FU NC TI O N   F OR   OPTI MIZATI ON   PI D   co ntr oller   is   us e d   as   a   s pecific   re gula tor   in   loop   feedback   that   is   use d   widely   in   t he   in dustria l   regulat ion   s ys te m.   Its   sta nd a rd   str uctu re   ha s   a   ‘‘ t hr ee - te rm”   c ontr oller,   w hich   can   be   m od el e d   us in g   t he   trans fer   f un ct io n   in   its   ideal   form   by   (8)   or   in   its   par al le l   f orm   by   ( 9)   [ 11].     ( ) = ( 1 + 1 + )     (8)   ( ) = + +     (9)     Wh e re     is   the   ga in   of   propo rtion al it y   is   the   ti me   c onsta nt   of   integ ral,     the   t ime   co ns ta nt   t he   de rivati ve,     is   the   inte gr al   gain   a nd     is   the   der i vative   gain .   The   ‘‘ t hr ee - te r m”   ope rati ons   are   pr ese nted   as   f ollow s   [ 3,   12] .   - - T he   pro portion al   te rm   fur ni sh in g   a   global   re gu la ti on   act ion   pro portio na l   to   the   er ror   sign al   mean w hi le   the   al l - pass   gain .   - The   integ ral   t erm   decr e asi ng   ste ad y - sta te   e r rors   over   l ow - f reque ncy   us i ng   the   inte gr al   ac ti on .   - The   de rivati ve   te rm   e nhance s   transie nt   res po ns e   by   high - fr e qu e nc y   c ompe ns at or   us in g   di ff e ren ti al   act io n.     Propo rtion al ,   I nteg ral,   a nd   De rivati ve   te rms   consi st   of   the   P ID   co ntr oller   a ct ion s.           Figure   3.   Bl oc k   of   PID   c ontr oller   m odel       The   ob je ct ive   functi on   ( J)   is   co ns ide red   the   op ti miza ti on   pr ob le m   w hole   the   var ia bl es   are   P ID   con t ro ll er   pa ra mete rs.   It   is   an   inte gr al   of   t he   s um   s quare   fr e quenc y   de viati on   ( Δ f )   and   t he   dev ia ti on   of   the   sign al   c ontrol   dev ia ti on   ( Δ u )   as   presente d   by   ( 10)   [6 - 7].     J opt = ∫   [ w ( Δ f ) 2 + ( 1 − w Kn ) ( Δ u ) 2 T m ax T m in ] dt     (10)     Wh e re   w   tran s cribes   the   relat ive   value   of   t he   obje ct ives   f unct ion   (i. e.,   I nt egr al   of   S quar ed   E rro r — IS E   a nd   I nteg r al   of   square d   Dev ia ti on   of   Con t ro l   Ou t put — ISDCO ),   a nd   it   is   eq ual   to   0.7.   Kn   =   10 4   is   the   normali zat ion   of   scal e   in   IS E   and   I SD C O.         4.   A   REVIEW   ON   KRI LL   H ERD   OPTI MI ZATION   AL GORIT HM     A   new   meta - he ur ist ic   Algorit hm   cal le d   Kr il l   Herd   al gorith m   is   i nv est i gated   by   Gand omi   an d   Alavi   (20 12)   t hat   is   insp ire d   us in g   the   sim ulati on   of   kri ll   swa r m   be hav i or   [ 18]   T his   meth od   is   known   as   r obus t   op ti miza ti on   a lgorit hm   mimi cs   the   be ha vio r   of   K rill   swarms   in   Kr il l   Herd   us i ng   for   so l ving   diff ic ult   op ti miza ti on   issues   [ 19] .   The   kr il l   mo ti on   m os tl y   in flue nce s   the   obje ct ive   functi on   with   t he   dista nces   of   each   kr il l   swa rm   be tween   foo d   a nd   herd   densi ty.   T he   K rill   ind ivi du al ’s   ti me   posit ion   is   determi ned   by   the   bellowi ng   th re e   act ion s   [ 20,25] :   1.   The   moveme nt   pro voke d   by   kri ll   swarms;   2.   Fo r agi ng   act ivit y;   an d   3.     Sud den   pr op a gation,   the re fore .   The   pro voke d   m ov e ment   re fer s   to   the   de ns it y   c onser va ti on   of   the   he rd   by   each   s warm.   The   mathemat ic al   f ormula   is   as   f ol lows :   [18 - 20]      =  +      (11)     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       Con tr ol o f  hy bri d po we r  syste m ba se d renew ab le  e ner gy ge ner ation s  usi ng P ID …   ( Mo hame d Reg ad)   1779   Wh e re   N max   is   the   ma xi mu m   sp ee d,   a nd     is   def i ned   a s:     =  +      (12)       is   the   inerti a   w ei gh t   of   the   provo ked   move ment   in   the   int erv al   [ 0,   1],    is   the   la st   mo ve ment   pro voke d,      is   the   l ocal   i nf l uen ce   giv e n   by   the   nei ghbors   and      is   the   ta r ge t   directi on   ef f ect   giv e n   by   the   best   kr il l.     The   sec ond   m ov e ment   is   i nf l uen ce d   by   the   foo d   prese nt   lo cat ion   a nd   t he   la st   exp e rience .it   can   be   pres ented   as   fell ow   [20] :     = +      (13)     Wh e re     =  +        and     is   the   sp eed   f or a ging,   is   the   ine rtia   weig ht,      is   the   la st   forag i ng   m oveme nt.   The   thi rd   moveme nt   is   def i ned   as   an   arb it ra ry   proce ss   that   is   pr es ented   with   a   di recti on al   fact or   a nd   a   pro pa gation   sp ee d.   It   is   e xpresse d   by   the   be ll ow in g   form ula   [ 20]:     =      (14)     Wh e re      is   the   maxim um   dif f us io n   s peed   a nd     is   the   random   directi onal   ve ct or ,   a nd   its   va lues   are   var ie d   in   [ - 1,   1].     Using   va rio us   eff ect ive   paramet ers   of   the   mo ti on   acco r ding   to   the   ti me,   the   posit ion   of   a   kri ll   ind ivi du al   over   the   inte rv al   t   to   ∆   is   giv e n   by   t he   bellow   f orm ula   [ 20]:     ( + ∆ ) = ( ) + ∆      (15)     It   ma y   no ti ce   t hat   ∆   is   one   of   the   m os t   e ssenti al   par a mete rs   a nd   m us t   be   c orrectl y   determi ne d   unde r   the   pr ob le m   to   be   s olv e d.   I nd e ed,   t his   par a me te r   infl uences   as   a   scal e   facto r   f or   t he   s pee d   vecto r.   Diff e re nt   al gor it hm s   ins pire d   by   kr il l   can   be   determi ned   usi ng   the   movem ent   cha racteri sti cs   of   kr il l   ind ivi du al s .   T he   KH   al go rith m   can   be   s ummari zed   by   va r iou s   ste ps   as   be low   [ 20].   1 -   Data    forms :   determi ne   the   s imple   li mit s,   re so lute ness   of   Kr il l   He rd   al go rithm   par a mete r( s ).     2 -   I niti al iz at io n:   ar bitrar y   i niti al iz e   the   kr il l   swarm   int o   the   searc h   e nv i ron ment.     3 -   Eval uatio n   of   obje ct ive   functi on :   c al culat ion   of   eac h   kr il l   swarm   ob je ct ive   f unct ion   wi th   the   kri ll   posit ion .     -   M otio n   cal c ulati on :   - Mo ve ment   provo ke d   by   oth e r   kr il l   swa rms,   - Fora ging   m oveme nt   – Phys ic al   pro pag at io n.   4 -   Im pleme nt   t he   gen et ic   oper at or s.     5 -   U pdat ing :   update   t he   kr il l   swarms   posit ion   in   the   searc h   env i ronme nt.     6 -   Re cu rr in g:   r et urn   to   ste p   3   un ti l   the   it erati on   num be r   is   a tt ai nted.     7 -   En d       5.   SIMULATI O N   AND   RES U LT S   The   pr opos e d   sy ste m   is   pe rfo rme d   a nd   anal yzed   unde r   MATL AB/ Simul ink  s of t war e.   T ime - D om ai n   analysis   of   t he   pro po se d   hybri d   s ys te m   is   i nv e sti gated   us i ng   KH   an d   GA   ba sed   PID   con t ro ll er.   The   Kr il l   Herd   al gorith m   is   app li ed   to   op ti mize   the   PI D   c ontr oller’s   pa rameters   in   the   pr opos e d   hybr i d   po wer   sy ste m   il lustrate d   in   Fi gure  1   for   f re quenc y   c on t ro l   and   t he   obta ine d   res ults   are   co mp a red   with   th os e   obta ine d   by   GA   repor te d   in   [ 7].   Re su lt s   based   on   t he   obje ct iv e   functi on   J   s ol ved   us in g   the   pro po se d   KH   is   repor te d.   Fi gure .4   disp la ys   the   c onve rg e nce   of   the   obje ct ive   functi on   us i ng   KH.   T he   co nver ge nce   cha r act erist ic s   of   t he   K rill   Herd   Algorith m   f or   the   PID   con t ro ll er   are   i ll us trat ed   in   Fi gure. 4.         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 .  11 , N o.   4 ,  D ecembe r  2020   :   17 75   –   17 84   1780       Figure   4.   Fit ne ss   co nver ge nce   of   the   pro pose d   KH   al gorith m       Figure   5  s how s  the   fr e quenc y  an d  po wer  va riat ion s   with  t he   sig nal  c ontr ol  de viati on .   T he   f reque ncy   and   powe r  devi at ion s  are  a ff e ct ed  by  re ne w able  powe r  c ha ng i ng   acc ordi ng   t o  the  weather  c onditi ons.   This   eff ect   is  mit ig at ed  by  the   use   of  the  P I D  c on t ro ll er  base d  Kr il l  He rd  al gorith m  in  c omparis on  with  t he  GA .   The  PID  c on t r oller  el imi nate s   the  mismat ch es  an d  e nhance s  al so   t he  perf ormance   of  t he   sy ste m .  Howe ver,  it   can  be   s how n  t hat  t he  os ci ll at ion s   ba nd  is   le s s  with  K H  t han  with   G A.   This   is  more   imp or ta nt  to   f aci li ta t e  the   desig n  of   t he   co ntro l  si gn al   wh ic h  act ivate s  the  fee db ac k  c omp onents  su c h  as   the  FE SS,   BESS,     and DE G , etc.           Figure   5.   Fr e quenc y   a nd   pow er   var ia ti ons   with   the   c on t ro l   sign al   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       Con tr ol o f  hy bri d po we r  syste m ba se d renew ab le  e ner gy ge ner ation s  usi ng P ID …   ( Mo hame d Reg ad)   1781   Figure   6   disp la ys   the   res ponse s   of   the   va rio us   gen e rati on   dev ic es   of   the   pro po se d   micr ogrid   sy ste m   su c h   as   BESS,   FESS,   FC ,   an d   DE G   under   nominal   co ndit ion s   of   op e rati on .   It   can   be   s how n   that   ther e   ar e   few e r   fluctuati on s   wit h   P ID   c on t ro ll er   t unin g   By   KH   t ha n   with   the   P ID   c on t ro ll er   opti m iz ed   usi ng   GA.               Figure   6.   Re spon s es   of   dif fere nt   co mpo ne nts   of   the   micr og rid   s ys te m   us i ng   the   be st   PID - KH   an d   PID - GA       To  li mit   the  fr e qu e nc y  va riat ion  by  the  el imi nation  of  the unb al a nce  in  s uppl y  an d  dema nd  und e r  the   stochastic   c ha nge  of  bo t h  t he  gen e rated   pow er  a nd  loa d  de man d,  the   po w er  dev ia ti on   is   con t ro ll ed   by  a   PID  con t ro ll er.   T he   pa rameters   of   the  c on tr oller  a re  op ti mize d  usi ng  the  K rill   Herd  al gorith m  an d  co mp a r ed  with   the  res ult  obt ai ned   us i ng  G A  in   [ 7].  It  ha s  bee n  s how n  that  t he  fr e qu e nc y  respo nse   us i ng  K rill   He rd   al gorithm - base d  PID   outp e rfo rms   the   P ID  c ontr oller  opti mize d  us i ng  the   GA  al go rithm.   PI D   c ontrolle r   tun e d  by the  K rill  H e rd is validat e d as t he bett er c ontr oller ove r  th e GA - P I D  c on t ro ll er.   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 .  11 , N o.   4 ,  D ecembe r  2020   :   17 75   –   17 84   1782   The  simulat io n  of  t he  pro pose d  s ys te m   wit hout   batte r y  is   presente d  i n  Fig ur e   7  a nd  Fi gure  8.  It  c an  be  obse rv e d  th at   the  BE S S  ha s  a  high  im pa ct   on   the  fluct uation  i n  the  f reque ncy   a nd  powe r  of  the  hybri d  sy ste m.   T his  fl uctuati on  ca use d  by  the   stoc hastic   an d  i nte rmitt ent  f orm  of  wi nd  an d  sol ar  po wer s .  Also ,   th e   impact   is  obse rv e d  in   va rio us  powe r  gen e r at ion   by  dif fere nt  sou rces  li ke   FC,  DEG,  a nd  FES S.  T he   res ults   sh ow  t he  r obust ness  of   t he  P ID   c ontr oller  ba sed  KH  that  minimi zes  the  powe r  an d  fr e qu e nc y  fl uctua ti on s  i n   the  abse nce  of  the  batte r y  energ y  stora ge   dev ic e.   The  gen e rated  pow er  from  dif fe r ent  com pone nt s,  as   repor te d  in  Fig ur e   9, s hows  t he   r obus tne ss   of the c on t ro l s ch eme agai ns t t he  en e rgy  st or a ge  d isc onnecti ng.           Figure   7.   O bje ct ive   f un ct io n   conve rg e nce   of   KH   al go rithm               Figure   8.   Fr e quenc y   a nd   pow er   dev ia ti ons   with   co ntr ol   sig na l   with   a nd   wit hout   BES S   us i ng   PID - KH   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       Con tr ol o f  hy bri d po we r  syste m ba se d renew ab le  e ner gy ge ner ation s  usi ng P ID …   ( Mo hame d Reg ad)   1783         Figure   9.   P ow e r   of   va rio us   c omp on e nts   of   the   auto nom ous   sy ste m   with   wi thout   an d   BE S S       6.   CONCL US I O N   The   pap e r   pr es ented   an   a pp li c at ion   of   a   PID   con t ro ll er   sc he me   to   regulat e   the   f reque ncy   dev ia ti on   in   hybri d   pow er   s ys te m   co ns ist s   of   WT G,   P V,   DE G,   FC ,   BE SS,   an d   FES S   as   il lustrate d   in   fig ur e .1    wh i ch   a re   consi der e d   t he   mo st   promisi ng   a nd   sust ai na ble   co nfi gurati on   us e d   in   the   kind   of   hybri d   energ y   s ys te m   .   S olar   and   wind   ca use   f re qu e nc y   and   powe r   osc il la ti on s   cau s ed   by   t he   sto chasti c   natu re   of   t his   re ne wab le   gen e rati on.   T he refor e ,   f reque ncy   co ntr ol   is   pro vid e d   by   t he   inte gr at io n   of   t he   P ID   c ontr oller   base d   Kr il l   Herd.   A   co mpa rison   with   t he   resu lt s   off er ed   by   GA   as   repor te d   in   [7]   is   done.   T hes e   com par is ons   sh ow   evide nce   t hat   the   KH   outpe rformed   the   G A.   H ow e ve r,   perf ormances   of   t he   KH   base d   P I D   c on t ro ll er   is   bette r   than   P ID   bas ed   GA   restri ct ing   t he   f requen c y   an d   po wer   os ci ll at ion s.    Als o ,   the   r obus t ness   a gainst   disco nnect ing   the   Ba tt ery   e nergy   sto rag e   is   te ste d.         REFERE NCE S   [1]   Anw ar,   Md   Nishat,   and   Somnat h   Pan ,  "A   fre qu en cy   r esponse   mod el   match ing   met hod   for   PID   controlle r   d esign   fo r   proc esses   with   d ea d - t im e , " ISA   transacti ons ,   Vol .   55 ,   pp .   175 - 187 ,  2015 .   [2]   Ganguly,   Somnat h,   Chand an   K uma r   Shiv a,   an d   V.   Mukher jee .   "F req uen cy   st abi liza ti on   of   is ola t ed   and   grid   conne c te d   hybri d   power   sys tem   mode ls , "   Journa l   of   Ene rg y   Stor age ,   Vol .   19 ,   pp .   145 - 159 ,  2018 .   [3]   Raj esh,   K.   S.,   a nd   S.   S.   D ash.   " Loa d   fr eque n cy   cont rol   of   au ton omous   power   sy stem   using   ada p ti ve   fuz zy   base d   PID   cont roller   o pti mized   on   i m prove d   sine   cosi ne   a lgori th m , ”  J ournal   of   Ambient   Int el l ige nc e   a nd   Hum anized   Computing ,   Vol .   10,   no.   6 ,   pp.   23 61 - 2373 ,  2019 .   [4]   Wa ng,   Huan,   et   al.   "D esign   of   a   Frac ti on al   Orde r   Freque ncy   PID   Control l er   for   an   Islande d   Micr ogrid:   A   Mult i - Objec t ive   Ext r e ma l   Optimizatio n   Method , ”  Ene r gie s ,   Vol .   10 ,  15 02 ,  2017 .     [5]   Tom onobu   Sen j yu,   et   al ,   “ A   Hybrid   Pow er   Sys te m   Us ing   Alt er nat iv e   Ene rgy   Facilit i es   in   Isol ated   Isl and ,”   I EEE   Tr ansacti ons on Energy  Con ve rs i on ,   Vol .   20 ,   No .   2,   pp .   406 - 414 ,   J une   2005.   Evaluation Warning : The document was created with Spire.PDF for Python.
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