Controllers using Evolutionary Optimization for PID Tuned Synchronous Generator Excitation System

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1 FrS. nng o Frconl Orr P D Conrollr ng Evolonry Omzon or PD n Synchrono nror Econ Sym Llh mr Prwnr kmr Syj Dk rng Ajy mr rg Engnrng Collg Polchnc nk JSS Acmy o chncl Econ ll898@homl.com rwnrk7@gml.com yjy.onln@gml.com nrng8@gml.com Abrc: h r h roon h noon o h gn o cc ngr orr O PD - rconl orr FO P D conrollr by volonry ml-objcv b omzon roch or ynchrono gnror con ym. h hr conrcng rormnc nc hv bn rm n m omn wll n rqncy omn o mnmz rror cl h rob bly n o mnmz h nrgy conmon. h r roon h o conrcon n mnmzng rror clon o rob bly n mnmzon o nrgy conmon by rmng cc O PD - FO PD conrollr ml-objcv omzon roblm. h omzon roblm olv o gnr h gn rmr h m h comv ml-objcv ccon rlng o rormnc rob bly n o oml conrol by mkng r-o bwn hm n rcv wghg gvn o ch objcv ncon. h olon gnr h non-omn o Pro-oml olon n llow h gnr o lc rclr conrollr congron wh rcv wghg. Wh h lcon o h roo gn o h con ym o ynchrono gnror o owr ln h ynmc rob bly nhnc lcly wh mnmm nrgy conmon. ywor: Frconl Orr Clcl Mlobjcv Omzon PD Conrollr Pro Fron Snchrono nror Econ Sym.. RODUCO h work roon h noon o gn o cc O PD-FO PD conrollr or con ym o ynchrono gnror or owr gnron. o mnn h rmnl volg n bly n oron or ynchrono gnror n owr gnron h bc n o n conomc owr ym oron. Flcon volg cn b rc by h con conrol ym o h ynchrono gnror lo blncng o ncv owr rbon n-nrrnc non n rn oron mrov by con conrol ym o h ynchrono gnror. PD conrollr h mo common conrollr or h conrol ro o h con ym o h ynchrono gnror. Howvr conmorrly h gn o FOPD nw-ngl n rononc. h rong bly robn chvmn bl oron n convnn bggng o rconl orr FOPD conrollr mk lcbl bnlly or rc conrol. mro gn chnq n lgorhm or FOPD conrollr hv bn ror n h hory. An mrov rnl volon lgorhm or r rmr omzon h bn roo or FOPD conrollr gn n [].. Polbny h roo h noon o FOPD conrollr n monr h ccon o ho conrollr or rggrng h ron o FO ym n []. nng o h rooronly conn ngrl rmr rvv rmr h orr o ngrl conrollr n orr o rnl conrollr comlc roc comr o O convnonl PD conrollr. nng o rmr o P D conrollr h bn on or Mgnc Brng Sym o ol cor wh h lcon o nmrcl rch mho n h commnory ynmc rormnc h bn chv comr o O PD conrollr []. Loo Shng r-o roo or FOPD conrol wh h hl o ml-objcv omzon or AR ym n [] n whch h objcv ncon ormlon on n h rqncy omn n zzy logc chnq h bn o n h b olon rom h o non-omn olon. Conrol ym or rjcory rckng h bn roon or - DOF rlll roboc mnlor n [] h P D conrollr h bn gn o chv h r rormnc. P conrollr gn roo ml-objcv omzon roblm or rmr jmn n []. n [7] n O PD conrollr gn h bn roo or conrollng ro o con ym o h ynchrono gnror ng gnc lgorhm. h rn rrch work mov by h roo n [7] [] n [] whr n lr c cc FO P conrollr gn ng nrnl mol conrol roch n rqncy omn n h gn n or cc OPD-FOPD conrollr wh h ml-objcv conrcng roblm ormlon or rc conrol hn ohr ng mho. Frconl orr clcl gn m or rrch n h y n h conc or h lng o h rconl orr conrollr gn. n [] rconl conrol hory bow or MALAB mlon. h rmnng r o h r r orgnz 8 nrnonl Fron o Aomc Conrol 89

2 ollow: h n con oc on h ym mollng n O PD bly conrn gn o cc OPD- FOPD mlobjcv omzon n rconl orr clcl h bn rn n Scon Scon l wh h mlon rl o gn conrollr n con concl h r.. SYSEM DESCRPO AD SABLY COSRAS FOR O PD COROLLER. Mhmcl Mol o h Sym For h mhmcl mollng o h ym h block grm o bck ym hown n gr conr. nror rnr ncon conr or h rnnng conon o h gnror no lo n crrn h or wnng crrn m o b zro. Sron c h bn gnor n h mmm volg m nr o h r volg. Snc only con volg n gnror volg h bn conr o rnr ncon rv rom no-lo chrcrc gvn ollow: Whr h no-lo volg o gnror R R L R n L r h con crrn rnc n l wnng rcnc rcvly. olg mrmn n n r orr lg lmn n h rnr ncon kn h rnr ncon o h owr mlr mol kn ollow: c Whr b *. n b b whr h o volg n h conrol gnl cv conry volg o con rnormr n b h ynchrono volg k vl rocr by h ynchrono rnormr.. Sbly Conrn wh O PD Conrollr h rcr o O PD h bn kn gvn n qon whr n r rooronl rvv n ngrl conn n lrg vl o wll b bl. Sbly conrn hv bn rmn rom h Roh- Hrwz bly ccorng o whch ncry n cn conon or ym o b bl h ch n vry lmn o h r colmn o Roh rry o chrcrc qon hol b ov. ow h chrcrc ncon o h ym wh O PD conrollr gvn blow: Eqon rrn h chrcrc qon o h ym wh O PD conrollr whr r h ncon o. ow h Roh rry cn b wrn ow ccorng o Roh h ym wll b bl ll h lmn o h r colmn m hv ov gn: Hnc Whr PD. CASCADED O PD - FO PD DES US MOO Frconl orr ynmcl ym n conrollr gn non or rrch n rcn yr. b on h rconl-orr clcl. n rconl-orr PD conrollr h orr o ngrl n rvv conrollr r lly n rcon. So n rconl-orr conrollr w hv wo mor rmr o n n on o norml O PD conrollr: rconl orr o ngron λ n o rvv µ. h rormnc o h rconl orr D P or h con ym conrol o h ynchrono h gnror long wh O PD conrollr nc o b lbl n br hn O PD conrollr c lon. Howvr nmbr o rmr n cc rcr wol b mor 8

3 comr o nvl nng o O PD n FO PD rcr. h mn rwbck o h cc gn h h ym bcom vry coml comr o nvl O PD conrollr or FO PD conrollr. B o rconl r o h ngrl n rvv conrollr n P D rc conrol o h ym cn b obl n cc O PD-FO PD wll b hn boh ngr n rconl orr conrol wll mk h ym bly bly bggng cbly robn n bly o oron mor rc n l rrono o cn b chv n h c. So hr rqrmn o rov longr ly or lrg lo chng hn cc conrol cn b or br conrol. Frhr n h con cc gn o O PD FO PD conrollr roon h ml-objcv roblm wh h nknown rmr o h ym. h roblm ormlon h bn on n h m omn wll n rqncy omn. h gn rmr o h mlobjcv roblm r h Z Z Z λ μ rmr o h con ym volg mrmn n n owr mlr mol. h rnr ncon or h FO PD h bn kn Z P D Z Z By bng =jω rqncy omn rrnon o h P D cn b rrn gvn blow: P D j = Z j Z Z j j Hnc convnn orm gvn j co j n n j co j n hnc P D Z j co j n Z Z co j n j ow [ j ] n P D j co jn Z co jn Z Z n Or P D j hn co j n Z co j n n Z Z h cc PD- P D conrollr rcr hown n gr. h clo loo rnr ncon or nnr loo n or loo r obn gvn blow: Y PD 7 R PD Y P D PD R PD P D 8 n h bov conrol ym rcr nnr loo conrol gn o rgl h rbnc rn n h loo n or loo conrol gn o chv -on rckng h rov bl ovr m ron.. Evolonry Omzon o Ml-Objcv Fncon n ml-objcv omzon roblm h objcv ncon r omz n olon o on nohr n h lbl olon b on h nvl olon n or ch objcv. n ml-objcv omzon hr no ny conc o oml olon. h olon o h roblm mll olon ch o whch lbl b on h n n rlv gncnc o h nvl objcv ncon. h ml-objcv omzon roblm cn b [8]: rmnon o * * * * h vcor... n h mnmz h gvn ollowng:... j vcor vl objcv ncon con o non-ncl nvl objcv bjc o o conrn rrn by qon -. h mn chllng n volonry ml-objcv omzon l n nng h oml olon bc ngl vcor * rrly rrn h oml olon o ll h objcv ncon. n h rgr h Pro oml olon conc whch ror o mll non-omn olon rqnly. n h con o mnmzon roblm vcor * cn b conr Pro oml olon hr no whn h bl rgon yng ll h conrn ch h: * ;.... j * q q ; q.... n h qon crb bov ml h or Pro oml olon hr no bl vcor whch c mnmzon n crn objcv ncon who mlno mmzon n ny o h rmnng objcv. A hr no ny ngl olon * h br hn ohr vcor n rm o ll h objcv mlobjcv omzon chnq rch or o omn olon n h bl c commonly rrr o Pro. h rojcon o h Pro n h objcv c n known h Pro ron. Svrl volonry lgorhm hv bn vlo n h hory or h olon o ml-objcv omzon roblm b on h rv gnron o h Pro ron. Among hm chnq b on A gnc lgorhm hv bn cclly l n mny ngnrng lcon. h olr chnq mong hm ncl MOA [9] SA [] EA [] n SA- []. n h con SA- chnq h bn ncoror rnng o h ym ncon n gn o O PD conrollr. Followng rnom nlzon o olon o z M h rv j 8

4 n SA- or obnng h Pro ron r l blow; A combn olon o h rn n orng olon or o m h conc o non-omnon. Elm nr by conmlng ll h nvl o h rvo n rn olon. All h nvl rom h omn hv bn conr n h n olon. Snc h olon z grr hn h nmbr o nvl n h omn h rmnng lmn o h ccv olon r conr rom h nonomn ron ccorng o hr rnk crr. h olon lo rom h ron ohr hn h omn r obn ng h crowng nc comron oror. h bc bhn h crowng nc chm o rmn h rmr o h rcngl n h rmr c whr h nr nghbor o rclr nvl r gonlly oo vrc [8]. h lrgr crowng nc conr or nvl hvng h m rnk. h nw olon o z M nrgo h oron o lcon croovr n mon o cr h nw orng olon. h ornmn lcon long wh crowng nc oror lz o h lc h nvl. h crowng comron oron rvn r-mr convrgnc by mnnng vry mong h non-omn olon. Sml bnry croovr o gnr chlrn rng rom wo rnomly lc rn rng rom []. Fnlly rng mon h chlrn rng r lr ng olynoml mon b on h von bo h r n lowr lm o h rn comonn.. Problm Formlon n Omzon h ml-objcv omzon roblm or cc O PD - FO PD gn orml boh n h m omn wll n rqncy omn. n m omn SE ngrl o h qr rror rormnc n h bn conr or mnmzng h qr rror. Prormnc n or SE J [ ] 9 n y y whr y r o ron wh n y cl o ron o h ym wh conrollr. h con n mo morn gol nmn o mr rob bly.. h clo-loo conroll ym wll rmn bl vn nc o rmrc ncrny hr. Howvr h ncrny hn nny-norm o h nvy ncon orml o cl h mrgn o rob bly. h nvy ncon h bn n S / C B whr C conrollr n B h orwr rnr ncon o h ym. h rrn rnc ncon h vcorl lngh n h yq lo rom - o h on loo rnr ncon n gvn by h qon C = C. h nny norm S mn / C j j rnr ncon m b mnmz o cl h rob bly. Hnc J mn / C j j h hr rormnc n ormlon -norm o oml conrol or ncon o nvy o mnmz h nrgy conmon n orml -norm o nglr vl o U C S R gvn by ollowng ncon: J q U j j whr =mnmn; m n n r h nmbr o n n o o h MMO ym n rrn h lrg nglr vl o C S R j h C S R mr h grn h mnmm nrgy conmon ovr h rqncy rng j q. ow h vcor vl ncon cn b wrn ollowng J. [ ] h vcor vl ncon now olv wh h hl o mlobjcv omzon lgorhm SA- crb n h rvo con wh. h olon z h bn kn nmbr o gnron h Pro rcon h bn kn. cro ovr rcon. n mon rcon... Frconl Orr Clcl Frconl orr clcl gn m n h l w c n bcom bqo or rc conrol o ym. gnrlzon o rnon n ngron oron o h rconl orr oror D whr α rconl orr n n r lowr n r rmnl o h oron rcvly. ow ngro-rnl cn b r D Whr n gnrl b col b mgnry lo. n gnrl hr r wo non o rconl orr rongrl clcl n wly. h rnwl-lnkov non n Rmnn-Lovll non [] [] gvn blow h D h h lm h whr [.] rrn ngr vl n D n n n n For n n n. h gmm ncon. h Llc rnormon ronly o olv h ngrl n rnl qon o ngnrng roblm. h cron o FO PD conrollr h bn on on h b o h bov rn conc o rconl orr clcl. 8

5 Aml Aml h coml ncon conc w o crb rqncy omn conc. Fg.. Block grm o PD- P D Fg. Pro Oml Solon or Fg. Pro Oml Solon or cc ym h m ron o h b conrollr r mkng ro wh cc FO PD-O PD hown n gr n 7 rcvly. n rom h ron h h cc PD- P D conrollr rorm br comr o ngr-orr PD conrollr lon n lmo ll h c. h lng m or h O PD conrollr gn lon wh MOO or h ynchrono gnror con ym r 9.c c n.c rcvly n or h cc O PD-FO PD conrollr rcr.7c c n.8c rcvly. From lng m w cn y h conrollng o ynchrono gnror con ym wh cc O PD n FO PD conrollr l own h ym oly comr o ngr-orr PD conrollr lon. h rqncy omn ron bo lo r lo hown n gr 8 9 n rcvly. h gn mrgn n h mrgn or h ngr-orr conroll ym r.8b B n n.7b n rcvly n or cc PD- P D conroll ym h gn mrgn n h h mrgn r.b n.7b rcvly. From h rqncy omn cn b gn h h bly n o h cc conroll ynchrono gnror con ym mor hn h o ngr-orr conroll ynchrono gnror con ym. hror wol b monr h or mrovng bly mrgn n bnwh o clo-loo ym gncnly or h low-rqncy rbnc n no rjcon FO PD conrollr vngo h O PD conrollr or ynchrono gnror con ym.. S Ron. O-PD FO-PD.. Fg. Pro Oml Solon or. RESULS AD DSCUSSOS h Pro oml olon obn r h mlon o mlobjcv omzon roblm crb rvoly n h rn work. h SA- lgorhm roc nonomn olon. hror h gnr h o mk om r-o n orr o choo h b olon whch ll h objcv ncon n conrn mlnoly. h Pro ron h bn rrn n h gr n n whch ll h normlz objcv ncon n h orm o Ecln norm on h Y n ch nvl objcv ncon c on h X ; hror ch rormnc n h own rrnon on h grh n Y rormnc n wol b h m. Fgr rrn goo SE whl conrol or n robn wor. Smlrly h ym h mnmm vl o J hn goo robn chv whl wor conrol or n SE hr n rrn by gr. J mnmm hn oml conrol or chv wh wor c o SE n robn whch h bn rrn by gr m con S Ron O-PD. FO-PD Fg. O ron y o h ym r r-o m or m con Fg. O ron y o h ym r r-o m or h omz vl o gn rmr r on o b Z.8.. Z

6 Ph g Mgn B Ph g Mgn B Ph g Mgn B Aml... Z S Ron..8.8 O-PD FO-PD -. m con Bo Dgrm Fg. 7 O ron y o h ym r r-o m or Frqncy r/ Fg. 8 Frqncy lo r r-o or b olon o Bo Dgrm O-PD FO-PD Frqncy r/ Fg. 9 Frqncy ron r r-o or b olon o Bo Dgrm Frqncy r/ O-PD FO-PD O-PD FO-PD Fg. Frqncy ron r r-o or b olon o. COCLUSO h rrch r bow h vng o cc O PD-FO PD conrollr rcr ovr O PD conrollr whn c lon or ynchrono gnror con ym. h roblm h bn orml mlobjcv roblm wh conrcng objcv or h chvmn o SE rob bly n oml conrol or. h roblm h bn olv or ch nvl objcv ncon wh rc o Ecln norm o ll h hr objcv ncon. h vl o rconl orr oror r kn λ< n μ<. From h m ron ccon n rqncy ron ccon o om b non-omn Pro olon h conclon h rwn h rconl-orr conrollr n cc wh ngr-orr conrollr n mor bl comr o ngr-orr conrollr whn c lon. Howvr h cc conrollr ym mor coml hn ngr orr conrollr ym or rccl mlmnon o cc rcr o PD P D b h mrovmn n h ym rormnc n bly conrm h ln o cc rcr o O PD-FO PD conrollr. REFERECES [] A. Bw S. D.l. Dgn o rconl orr PD conrollr wh n mrov rnl vlon. Engnrng Alcon o Arcl nllgnc 9 -. []. Polbny Frconl orr ym n PD conrollr. EEE rncon on Aomc Conrol [] J. Zhong n L. L nng rconl orr PD conrollror l cor mgnc brng ym EEE rncon on Conrol Sym chnology. [] S. D n. Pn On h m H /H loo hng r-o n rconl orr conrol o h AR ym EEE rncon on nrl normc. [] A Dml n Ernrk rjcory rckng conrol or -DOF rlll mnlor ng rconl orr PD conrol EEE rncon on nrl Elcronc. [] L. mr P. mr S. hoh Dgn o P Conrollr: A Ml-objcv Omzon Aroch EEE nrnonl Conrnc CACC. [7] CAO Yn n MA Jn Rrch on PD rmr omzon o ynchrono gnror con conrol ym h nrnonl Conrnc on CRS g - - mbr. [8]. Db Mlobjcv Omzon Ung Evolonry Algorhm John Wly n Son L. Engln. [9] C. M. Fonc n P. J. Flmng nc Algorhm or Mlobjcv Omzon:Formlon Dcon n nrlzon n rocng o h h nrnonl Conrnc on nc Algorhm []. Srnv n. Db Mlobjcv Fncon Omzon Ung on-omn Sorng nc Algorhm Evolonry Comon. -8 Fll 99. [] J. D Schr Mlobjcv Omzon wh cor Evl nc Algorhm Procng o h nrnonl Conrnc on nc Algorhm n hr Alcon 99. []. Db A. Pr S. Agrwl. Myrvn A n El Mlobjcv nc Algorhm: SA- EEE rncon on Evolonry Comon. [] rong L L H ng n L Lnh Frconl Orr P Conrollr nng Rl or Cc Conrol Sym WASE nrnonl Jornl o Mchncl n Mchronc Engnrng ol: o: 7. [] D.. Phn n S. Mjh Synh o PD nng or nw Prlll Cc Conrol Srcr FAC Conrnc on Avnc n PD Conrol PD Brc ly. [] Y.Q. Chn. Pr n D. X Frconl Orr Conrol- A orl Amrcn Conrol Conrnc S. Lo USA 9. []. B. Olhm n J. Snr h Frconl Clcl Acmc Pr w York 97. 8