Load Frequency Control in Interconnected Power System Using Modified Dynamic Neural Networks

Transcription

1 Prceedgs f the 5th Medterraea Cferece Ctrl & Autmat, July 7-9, 007, Athes - Greece 6-0 Lad Frequecy Ctrl tercected Pwer System Usg Mdfed Dyamc Neural Netwrks K.Sabah, M.A.Neku, M.eshehlab, M.Alyar ad M.Masur kamel_sabah@ee.ktu.ac.r Maeku@eetd.ktu.ac.r teshehlab@eetd.ktu.ac.r M.alyar@eetd.ktu.ac.r Masur@ee.ktu.ac.r -K.N.ss Uversty f techlgy/ ctrl departmet, ehra, ra Abstract ths paper preset pwer system lad frequecy ctrl by mdfed dyamc eural etwrks ctrller. he ctrller has dyamc eurs hdde layer ad cvetal eurs ther layers. Fr csderg the sestvty f pwer system mdel, the eural etwrk emulatr used t detfy the mdel smultaeusly wth ctrl prcess. have valdat f prpsed structure f eural etwrk ctrller the results f smulat demstrated that the prpsed ctrller ffers better perfrmace tha cvetal eural etwrk ctrller. Key wrds: pwer system, lad frequecy ctrl, eural etwrk ad dyamc eural etwrk.nroducon he pwer system lad frequecy ctrl (LFC) prblems are caused by small lad perturbats whch ctuusly dsturb the rmal perat f pwer system [. herefre the geerat rate f geeratrs must be chage utl the frequecy ad te-le pwer mata clse t specfed values. t s desrable that the devats f frequecy ad te-le pwer system becme zer. he utput pwer f geeratr ctrlled wth mechacal put. Als, the LFC prblem s very mprtat tercected pwer system because the lad perturbat ay areas dsturb the frequecy f thers [. May researches have bee de the past abut lad-frequecy ctrl tercected pwer system. the lterature, sme ctrl strateges have bee suggested based cvetal ad fuzzy, eural etwrk ctrllers [-3. Fxed ga ctrllers are desged at mal perat cdts ad fal t prvde best ctrl perfrmace ver a wde rage f perat cdts. S, t keep system perfrmace ear ts ptmum, t s desrable t track the peratg cdts ad use updated parameters t cmpute the ctrl. Classcal based adaptve ctrller prpsed by [3, despte the prmsg results acheved by ths ctrller, the ctrl algrthms are cmplcated. Fuzzy ga schedulg ctrllers prpsed by [4-6. these ctrllers, ctrller parameters ca be chaged very quckly sce parameter estmat s t requred. Hwever, the same methd, the traset respse ca be ustable because f abruptess system parameters. Adaptve fuzzy ga schedulg ctrller used [7. ths ctrller, the parameters f prprtal ad tegral (P) ctrller acheved ff-le by chagg perat cdts ad saved, ad the the - le applcat fuzzy expert adjusted the P ctrller by mtrg the perat cdts. Als [8 lha ad et al. prpsed self tug fuzzy PD ctrller, whch maly deped the peak bserver dea. Neural etwrk based ctrller s used [9 ad have gd result fr LFC. Because f the ucertates the parameter f the pwer system ad because f the chage the lad demad, adaptve ctrl referred t be used fr LFC. ths study, a mdfed dyamc eural etwrk (MDNN) ctrller was desged t LFC applcat tw-area pwer system fr geeratg electrcty wth gd qualty. Als, ths paper t acheve the sestvty f pwer systems mdel, eural etwrk emulatr (NN-emulatr) used fr detfcat the pwer system. he prpsed ctrller was cmpared wth cvetal eural etwrk (CNN) ctrller, ad t was shw that the prpsed MDNN ctrller geerally has better perfrmace tha the CNN ctrller..a WO ARA NRCONNCD POWR SYSM MODL Blck dagrams f tw-area tercected pwer system fr the uctrlled case s shw Fgure(). Where D detes devat frm the mal values ad f s the system frequecy (Hz), R s regulat cstat (Hz per u, g s speed gverr tme cstat (s), t s turbe tme cstat (s), p s pwer system tme cstat (s) ad D pd s lad demad cremet. he verall system ca be mdeled as mult-varable system the fllwg frm: x ( = Ax( + Bu( + Ld( () whch A s the system matrx, B ad L are put ad dsturbace dstrbut matrces, x(, u( ad d( are state, ctrl ad lad chages dsturbace vectrs, respectvely. x = [ Df DPg DPv DP Df DPg DPv u( = [ D Pc D d( = [ DP Pc d DP = [ u d he u ad u are the ctrl utputs Fgure [8. u

2 Prceedgs f the 5th Medterraea Cferece Ctrl & Autmat, July 7-9, 007, Athes - Greece 6-0 Fgure. Structure f dyamc eur Fgure. A tw area tercected System he fal utput f ths eur ca be wrtte as fllw: he system utput, whch depeds area ctrl errr (AC), s wrtte as fllw: O ( = O ( O ( + (4) y ( AC y ( = = Cx( y ( = AC () Ad AC = DP + b Df (3) Where y( s the utput vectr, AC s area ctrl errr, b s area frequecy bas cstat, Df s area frequecy chage, DP, s the chage te-le pwer ad C s the utput matrx..dynamc NURAL NWORK the cvetal structure f a artfcal eural etwrk, a eur receves ts puts ether frm ther eurs r frm the eural sesrs. A weghted sum f these puts csttutes the argumet f a fxed lear actvat fuct. he weghts crrespd t the syapses a blgcal eur whle the actvat fuct s asscated wth the tercellular curret cduct mechasm the sma. he resultg value f the actvat fuct s the eural utput. hs eural utput s brached ut t ther prcessg uts. hs s a versmplfed but useful frst apprxmat f the blgcal eur. hs smple mdel f the artfcal eur gres may f the characterstcs f ts blgcal cuterpart. Fr example, t des t take t accut tme delays that affect the dyamcs f the system [0. he dyamc eural etwrk fr the frst tme prpsed by Gupta wth applcat t ctrl f lear systems 993[. he basc structure f dyamc eur (DN) depcted Fgure (). ach eur cmpsed f tw uts: the hbtry (egatve) ut (Net ) ad exctatry (pstve) ut (Net ). he hbtry uts receved the summat f pstve. puts ad a delay f w utputs ad abstract a delay f exctatry utputs by multple t the determed weghts. he exctatry uts receved the summat f egatve puts ad a delay f w utputs ad abstract a delay f tatry utputs by multple t the determed weghts. Where O, O represet the utput f exctatry ad hbatatry uts, respectvely ad ca be wrtte as : O ( = a X O ( = b X 0 0 e ( + a ( + b ( t ) b ( t ) a ( t ) ( t ) Ad O ( = Net (, O ( Net ( (6) = Where the parameters f a,a,a, b,b, b are the weghts f dyamc eurs ad X e, X are the pstve ad egatve puts, respectvely. Wth csderat the structure f DN, the Archtecture f prpsed mdfed dyamc eural etwrk (MDNN) shw Fgure (3). he MDNN csst f three layer :( ) put layer: ths layer the puts f MDNN dvded tw parts, tatry (egatve) ad exctatry (pstve) puts. () Hdde layer: the eurs f ths layer csst f DN, whch trduced abve. (3) Output layer: the eurs f ths layer are cvetal eurs. he fal utputs f MDNN ca be wrtte as fllw: m O ( = W. O ( Where the O are utputs f hdde layer, matrx frm, ad ca be wrtte as fllw: O ( = F( O ( ) Ad F s the lear sgmd fucts. (7) (8) ( 5)

3 Prceedgs f the 5th Medterraea Cferece Ctrl & Autmat, July 7-9, 007, Athes - Greece 6-0 emplyg the gradet descet methd, the cremet f Г deted by Г where Г cta all weghts MDNN ctrller, ca be btaed as, ( Γ( = η (0) Γ( Where the η s learg rate gve by a small pstve cstat, that s be ted the same η csdered fr learg f all parameters, ad Г s Fgure3. Archtecture f prpsed mdfed dyamc eural etwrk V.APPLCAON OF MDNN CONROLLR O LFC he trduced MDNN appled t the tw-area pwer system ctrl, whch descrbed sect tw, as a ctrller. hs strategy depcted Fgure (4). As ca be see frm blck dagram, he MDNN ctrller desged fr each area separately. hese ctrllers has fur uts the put layer, fve dyamc eurs hdde layer, ad e cvetal eur the utput layer. he put vectr f MDNN ctrller s: put()=[df(, Df(, AC(, AC( =, Where the Represet the dervatve f frequecy devats. he task f ths ctrller each area s t mmze the system frequecy devat Df ad the devat the te-le pwer by geeratg the prper ctrl sgals, U. Γ = [ W a b a b =, j =, j j herefre, the learg update equat fr Г s btaed by Γ( t + ) = Γ( + Γ( ( = Γ( η Γ( he partal dervatve f wth respect t elemets f Г, fr example W, s descrbed as fllw: e = W e W = e( ( ) ( Where O ad are the utputs f hdde layers u ad sestvty f plat, respectvely. Fr parameters f DN, the weghts f dyamc eurs ca be wrtte as fllw: Fgure4. MDNN ctrller stalled th area A. Learg Algrthm he learg prcess f MDNN fr each ctrl area s t mmze the perfrmace fuct gve by: = ( yd y) = ( e ) Where y d represets the referece sgals, y represets the actual utput (.e. frequecy devats f area). t s desrable t fd a set f weghts dyamc ad cvetal eurs that mmze the. A geeral ad useful way t acheve ths s a gradet descet methd. Learg f all set weghts MDNN ctrller by (9) ( = η. δ (. X ( = η. δ (. O e ( = η. δ (. O ( ( t ) ( t ) Where ( δ ( t ) = e(.. W (. F (.) ( Where, F (.) s dervatve f utputs f hdde layer wth respect t ts put.

4 Prceedgs f the 5th Medterraea Cferece Ctrl & Autmat, July 7-9, 007, Athes - Greece 6-0 B. Calculate the sestvty f plat Fr bta the sestvty f plat sme authrs have bee used the apprxmat f y [9. Als u y Referece [ used the sg( ) fr csderat the sestvty f plat, where the sg s sg fuct. t s clear that these apprxmats f cat cmpletely extract the Jacbea f plat ad may cause the perfrmace f system be far frm desre value. S ths paper eural etwrk emulatr (NN-emulatr) s used s that the Jacbea f plat became avalable. hs eural etwrk cssts f tw puts, e hdde layer wth fur eurs ad e utput fr every ctrl ze. he whle structure f prpsed strategy s depcted Fgure (5). he utput f NN-emulatr fr each area as fllw: y t = O t W () e( ) em ( ). e Where the Ο em ad W e are the utputs f hdde layer ad weghts f utputs layer respectvely. he Ο em are O = F( X (. W ) () em( em e Where the W e are weghts f hdde layer ad F(.) detes the sgmd fucts. X em Are the puts vectrs fr NN-emulatrs ad fr each area csst f defed as fllw: X em ( = [ U (, U ( U ( t ) Fgure5. he whle structure f pwer system ctrl wth MDNN ctrller ad NN-emulatr. V. SMULAON RSULS rder t demstrate the effectveess f prpsed strategy, sme smulats were carred ut. these smulats, the prpsed MDNN ctrllers were appled t tw-ctrl area pwer system descrbed Fgure (). he tal weghts f MDNN ctrllers ad NNemulatrs fr each ctrl area are prperly chse. he fllwg smulats fr dfferet dsturbace pwer system are beg csdered: Case: a 0. pu step lad crease the each ctrl area Fgure (6) demstrates the frequecy devats f - ctrl area, fllwg a 0. pu step lad creases the each ctrl area whe the pwer system s equpped wth MDNN ctrllers (sld le) ad CNN ctrllers (dashed le). Cmparg these tw curves Fgure (6) llustrates the effectveess ad ablty f the MDNN ctrl desgs agast the CNN -based ctrl desg. Where the U s utput f MDNN ctrller. Wth csderat f NN-emulatr that dscussed abve, the sestvty f pwer system ca be wrtte as fllw: y( e ( = We. F (.). W ( ( e (3) Fgure 6. Frequecy devats f each area wth MDNN (sld) ad CNN (dash d ctrller fr case.

5 Prceedgs f the 5th Medterraea Cferece Ctrl & Autmat, July 7-9, 007, Athes - Greece 6-0 Case: a 0. pu step lad crease each ctrl area at t=5s Fgure(7) demstrates the frequecy devat f - ctrl area, fllwg a 0. pu step lad creases the each ctrl area whe the pwer system s equpped wth MDNN ctrllers (sld le) ad CNN ctrllers (dashed le). Frm ths fgure ca be see the dsturbace reject prperty f clsed lp system whe the MDNN ctrller used, are effectveess. Fgure9. he errrs detfcat f -ctrller area fr Case 3 Fgure7. Frequecy devats f each area wth MDNN (sld) ad CNN (dash d ctrller fr case. Case 3: presece f a radm demad lad sgal Fally, the system respse s tested the presece f a radm demad lad sgal. A radm lad patter, shw Fgure (8), represetg expected area demad lad fluctuatg, s appled t the ctrl area. Als ths fgure demstrates the frequecy devat f -ctrl area, at presece f a radm demad lad sgal, ctrl area, whe the pwer system s equpped wth MDNN ctrllers. he dfferece betwee actual utputs (pwer system utpu ad NN-emulatrs, errr detfcat f -ctrl area, are depcted Fgure (9). As shw ths fgure, the system ca perfectly be detfed. Fgure 8. A radm lad patter st area ad Frequecy devats f each area wth MDNN ctrller fr case 3. V. Cclus he whle structure f pwer systems have lear dyamc ad ther perat pts may chage, therefre the adaptve ctrllers whch d t requre exact mdel f system shuld be used. Fr these reass ths paper we used MDNN ctrller fr LFC. hs ctrller has dyamc eurs ts structures ad demstrates that have gd results agast CNN ctrller. Als NN-emulatr was appled fr csderat the sestvty f plat. RFRNCS [ H. Saadat, Pwer System Aalyss, McGraw-Hll, 00 [ Kudur, P.:'Pwer system stablty ad ctrl', McGraw Hll, New Yrk, 994 [3 M. Zrb, M. Al-Rashed, M. Alrfa, Adaptve decetralzed lad frequecy ctrl f mult-area pwer systems, lectrcal Pwer ad ergy Systems 7 (005) [4 Cha-feg,chug-feg pwer system lad frequecy ctrl wht fuzzy ga schedulg desged by ew geetc algrthms,, Cferece pwer system, 00 [5 lha Kcaarsla, rtugrul Cam, Fuzzy lgc ctrller tercected electrcal pwer systems fr lad-frequecy ctrl, lectrcal Pwer ad ergy Systems [6 rtugrul Cam, _lha Kcaarsla, Lad frequecy ctrl tw area pwer systems usg fuzzy lgc ctrller, ergy Cvers ad Maagemet 46 (005) [7 Jawad talaq a,fadel al-basr, Adaptve fuzzy ga schedulg fr lad frequecy ctrl, rasact pwer system. February.999 [8 lha Kcaarsla, rtugrul Cam, Fuzzy lgc ctrller tercected electrcal pwer systems fr lad-frequecy ctrl, lectrcal Pwer ad ergy Systems 7 (005) [9 H.Bevra,Hyama,Mta, M.eshehlab, Lad frequecy regulat uder a blateral LFC scheme usg flexble eural etwrk, g t sys CRL publshg Ltd [0 P.D. Wasserma. Neural Cmputg: hery ad Practce, Va Nstrad, New Yrk, 989. [ M.M. Gupta ad D.H. Rae. Dyamc eural uts wth applcats t the ctrl f ukw lear systems, 7th Jural f tellget ad Fuzzy Systems, vl., N..pp. 73-9, Ja [ Myu Che, D.A. Lkes A hybrd eur-fuzzy PD ctrller Fuzzy Sets ad Systems 99 (998) 7-36