INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN 48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME ENGINEERING AND TECHNOLOGY (IJARET) ISSN 97-48 (Prnt) ISSN 97-499 (Onlne) Volume 4, Issue 5, July August 2, pp. 24-4 IAEME: www.eme.com/jret.sp Journl Impct Fctor (2): 5.87 (Clculted by GISI) www.jfctor.com IJARET I A E M E DESIGN OF PSS USING BEES COLONY INTELLIGENCE R.sheeb *, Dr.M.Jyrju, Dr. K. Sundreswrn b Deprtment of Electrcl & Electroncs engneerng, T.K.M.college of Engneerng, Kollm, Kerl, Ind b Deprtment of Electrcl & Electroncs engneerng, Ntonl Insttute of Technology, Thruchrpll, Ind ABSTRACT Ths pper report the development of new optmzton technque bsed on the bologcl behvour of colony of honey bees. The optmzton method s prepred by closely mttng the forgng pttern of bees. The development of the lgorthm nd ther vldton s well documented n ths work. The optmzton scheme s then ppled for clsscl problem of desgn of Power System Stblzer (PSS). Smulton results re crred out to vldte the proposed lgorthm. Key words Optmzton, Bees, Power System Stblzer. I. INTRODUCTION The stble opertons of synchronous mchne, ts blty to mntn the qulty of electrcl power delvered to the consumers nd the economy n the generton cost wth mxmum possble power trnsfer re some of the requrements to be consdered n the desgn of electrcl power system. One of the effectve mens of chevng the bove requrements s by provdng n effcent exctton controller for synchronous mchne. The relzton of power system stblzer (PSS) s bsed on the de tht the use of supplementry control sgnl n the exctton system of the genertng unt cn provde extr dmpng for the system nd thus mprove the mchne dynmc performnce []. Ths s the esy, economcl nd flexble wy to mprove power system stblty. Over the pst few decdes, mny types of PSSs hve been extensvely studed nd some of them hve been successfully used n the feld. The conventonl PSS ws bsed on lner model of the power system t some opertng pont nd clssc control theory ws employed s the desgn tool [2]. Wth the ncresng demnd for qulty power, modern control technques lke optml control theory [] nd hgh-gn control theory [4] hve been proposed for supplementry exctton controllers. Power systems re dynmc systems nd the opertng pont of the system wll chnge wth vryng system lod. 24
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME To mprove the dmpng chrcterstcs of power system over wde opertng ponts, dptve stblzers or self-tunng controllers hve been proposed [5-8]. In these controllers the system model s frst dentfed n rel tme usng the mesured system nput nd output vrbles. The gn settngs re then computed bsed on the model nd the dptton lw. Even though better dynmc response cn be cheved by self-tunng controllers, the mjor hurdle s the need to dentfy system model n rel tme, whch s very tme consumng. Recently rtfcl neurl networks (ANN) [9] nd fuzzy logc prncples [] re ppled for the relzton of dptve PSS. It s shown tht ANN bsed PSS cn provde good dmpng of the power system over wde opertng rnge nd sgnfcntly mprove the dynmc performnce of the power system. Fuzzy exctton controller lso mproves the dynmc response of the power system t dfferent opertng ponts. In ddton, fuzzy controller does not requre model dentfcton nd thus cn be esly mplemented on mcrocomputer. The contrbuton of ths pper les n the development of new optmzton lgorthm developed by the uthors whch closely mmc the behvor of honey bees []. Lterture survey shows tht ttempts hve been mde recently by the reserchers to utlze the behvor of honey bees for few pplctons [2-8]. The forgng behvor of honey bees s lso used for optmzton lgorthms for vrous pplctons such s trnng of lernng vector quntzton networks [5], job schedulng [], optmzng neurl networks [7] etc. In ths work, we hve developed lgorthm whch fundmentlly mtte nturl behvor of colony of honey bees n nectr collecton nd reproducton. The frst proposl mmcs the forgng behvor of honey bees. The rndomly generted worker bees re forced to move n the drecton of the elte bee, whch loctes the best possble soluton. The movement s mde bsed on probblstc pproch nd the step dstnce of flght of bees s mde s vrble prmeter n the lgorthm [9-25]. The lgorthm s used for the desgn of PSS for sngle mchne connected to nfnte bus system nd the results re dscussed. It s shown tht the newly proposed scheme s dervtve-free, effcent n loctng the globl optm wth reduced number of tertons, ndependent of ntl vlues, nd re robust n ther convergence chrcterstcs. II. BRIEF DESCRIPTION ABOUT THE BIOLOGY OF HONEY BEES [] The honey bees re beleved to be orgnted n Tropcl Afrc nd spred from South Afrc to Northern Europe nd Est n to Ind nd Chn. A typcl smll hve contns pproxmtely 2, bees nd the bees n hve re dvded n to three dfferent types: Queen, Drone nd Worker. The functons, sex, lfe spn nd physcl sze of these three ctegores re lrgely dfferent. The sole functon of the queen s re-producton; t s femle, nd cn lve up to two yers. The queen s the mother of ll bees n the hve. The sze of queen s lrger wth ts bdomen notcebly longer thn the other bees. Drone s mle bee whch survves bout 2-2 dys n sprng or 9 dys n summer. Drones re medum n sze nd re desgnted for mtng only. Drone s eyes nd ntenne re speclly desgned for seeng, followng nd mtng wth queen. They cn fly fst to ctch up wth queen. Queens nd drones do not hve effectve body prts for hrvestng honey or pollen for self feedng. Worker bees re sterle femles nd they hve numerous functons. Worker bees mke comb, clen nd defend hve, gther honey nd pollen, nd tend queen nd young drones. They re smll n sze nd survve up to 2-4 dys n summer nd 4 dys n wnter. II.. Forgng behvor of honey bees The forgng behvor of honey bees s qute nterestng nd t s found tht bees re frly dept t effectve communcton of food sources. In the hve, the worker bees re responsble for food collecton. A few worker bees re sent to dfferent rndom drectons nd sngle bee vsts mny dfferent flowers n the mornng. If there s suffcently lrge food, the bee mkes mny trnsts 25
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME between the flowers nd ts hve. The florl fndngs re communcted to other worker bees n the hve through dncng. A bee whch returns from n re whch hs mny flowers producng much honey/pollen performs dnce on the comb. The orentton of her movements together wth frequency of vbrtons ndctes the drecton nd dstnce of flowers from the hve. Ths dnce serves s n effectve wy of communcton mong worker bees. The other worker bees wtng n the hve wll observe ths dnce nd wll come to know the locton nd quntty of food source. All the worker bees, who hd found flowers, wll perform dnces; but mjorty of worker bees wll follow the elte bee- the bee whch hd locted better nd nerer food source thn the remnng. Ths mechnsm helps the colony to gther food quckly nd effcently. II. 2. Development of optmzton lgorthm bsed on forgng behvor As cn bee n the prevous secton, worker bees perform the tsk of food collecton n n optmzed mnner. Ths mkes t possble to buld n optmzton lgorthm. The bees cn be plced ntlly t rndom loctons n the soluton spce; the bee t the best locton- the locton where the objectve functon s mnmum- cn be treted s elte bee. In nture, mjorty of worker bees follow the elte bee, whle remnng bees fly to other less ttrctve loctons. Ths cn be perceved s probblstc pproch. Thus, t cn be ssumed tht, bsed on probblty, some fly towrds the locton of the elte bee nd the left out bees to other loctons. The complete lgorthm developed by the uthors s gven n the followng steps: Let the optmzton tsk s defned s follows: Mnmze: F (x) () subject to, x x. (2) l x u In the bove, F (x) s sclr vlued objectve functon nd x l nd bounds of the vrble. xu re the lower nd upper Step : Deployng bees ntlly t rndom loctons The ntl step nvolved s deployng the bees n fesble soluton spce subject to the constrnts mposed on the soluton vrbles. Here, poston of bee refers to one complete soluton set to the problem. For generlty, let the bees be descrbed s B, B,... 2 B... Bn where n s the number of bees nd cn be termed s populton sze. For n = 4, ntl rndom poston of bees s shown n fgure (). () (b) 2
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME p p t p < p t p p t p < p t (c) (d) p p t p < p t (e) (f) Fgure. Bee movement. () Intl poson of bees. (b) Indcton of durton of dnce. (c) Probblty of movement. (d) Bee flght for p pt. (e) Bee flght for p < pt. (f) Fnl poston of bees 27
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME Step 2: Evluton of objectve functon vlue The objectve functon vlue, F ( φ) t ech bee poston s evluted usng equton. Step : Computton of durton of dnce of ech bee In ths step, dependng on the florl fndngs, ech worker bee performs dnce on the comb. The durton of dnce s mesure of quntum of food nd let D d represent the durton of dnce. The durton of dnce of the -th bee n the j -th locton t t -th terton s gven n equton. D d( j) ( t) = () F ( φ) + ( j) The durton dnce of bees s ndcted n crcles nd the sze of the crcle s used to mesure D d. Ths s llustrted n fgure (b). Step 4: Identfcton of elte bee. The bee, whose locton gves mxmum vlue for n the t -th terton s gven by equton (4). B e Mx ( D ( t )) ( t ) = d ( j ) (4), j D d s desgnted s elte bee. Thus elte bee, In fgure (c), B4 s the dentfed s the elte bee. Step 5: Movement of bees Mjorty of bees follow the elte bee; however, few bees my fly to other flower ptches too. Hence the movement of bees cn be thought of bsed on probblty. Ths wll mke the serch more probblstc nd my yeld better results. A term nmed s threshold probblty s therefore ntroduced nd s denoted s p t. The vlue of p t s fxed t sutble vlue between nd. In order to fnd the drecton of flght of prtculr bee, rndom number between nd s generted denoted s p nd s compred wth p. t For p pt, then the bee fles dstnce of R towrds the elte bee. The dstnce of flght, denoted s R s vrble n the problem nd s to be judclly chosen. In fgure (c), for bees B nd B 2, p pt nd hence wll move towrds the elte bee. The flght of B nd B 2 s shown n fgure (d) where B fles dstnce of R towrds the elte bee, B4 nd reches the pont, Y. Smlrly, bee B2 fles dstnce of R towrds B 4 nd reches the pont, X. For p < p t, then tht bee fles dstnce of R towrds ny other bee locton, whch s rndomly decded between nd n. Ths s demonstrted n fgure (e). The bee, B flls n the ctegory of p < p t nd hence fles dstnce of R towrds ny other bee locton. For ths, rndom number between nd n s generted. Let the number be so tht B moves towrds the pst locton of B. Thus, B reches pont Z. When ll bees mke flght of dstnce R, one terton s completed. The fnl poston of ll bees fter one terton s shown n fgure (f). Step : End the progrm, f termnton crteron s reched; else go to step 2. B e 28
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME III. APPLICATION OF THE ALGORITHMS FOR PSS DESIGN III.. Sngle mchne nfnte bus system model For developng dynmc model, sngle mchne synchronous genertor connected to nfnte busbr s consdered [] nd s shown n fgure (). E fd ' E q Fgure. Component of torque produced by voltge regultor cton n response to speed-derved sgnl Fgure shows the effect of speed through the stblzng functon G( through the voltge regultor loops ffectng, whch produces component of torque T. In fgure (b) speed ' E q devtons ω s gven s nput of PSS. It produces n output, whch s voltge sgnl Vs. The output from the PSS s gven to AVR, whch produces correspondng chnge n torque. In other words stblzng sgnl derved from mchne speed s processed through devce clled the power system stblzer (PSS) wth trnsfer functon G(S) nd ts output connected to n nput of the excter. Contrbuton of PSS to the torque ngle loop [] s gven by T ω ( G( K2K = ' 2 ' ( (/ K + KK ) + s( T / K + Td ) + s Td T () For the usul rnge of constnts, ths functon cn be pproxmted by For lrge vlues of T s ω ( ) G( K2K ' ( (/ )[ ( / )]( ) K + K K + s T d K K K t cn be further pproxmted by T ( K2 G( = ' ω s K [ + s( T / K K )]( + st T ω ( ) ) ( ( K2 = K [ + s( T ' d d + st G( = G( GEP( / K K )]( + st ) (7) (8) (9) The trnsfer functon of PID controller s K G( = ( K p + + sk d ). s 29
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME III. 2. SIMULATION RESULTS A generlzed controller structure s consdered for the PSS wth the objectve of chevng the best dynmc response t ll opertng ponts. Let the controller structure be n n G K n s () ( = n In the bove equton Kn represents the controller prmeters nd n decdes the order of the controller. For smplcty PID controller s chosen,.e., n =. The tsk s to dentfy the prmeters of the controller so s to obtn optmum performnce t ll opertng ponts usng the bove mentoned method. Thus the problem s formulted s follows: Fnd ( φ) F such tht Mnmze F φ = ω + t () Subject toφ ( ) rp s mn Where ( φ) φ φ mx F s the objectve functon, ωrp nd t s denotes the pek overshoot nd settlng tme respectvely. φ s set of controller prmeters to be determned nd s denoted s [ K, K K ], the subscrpts P I, mn nd mx represent the lower nd upper bounds of the vrbles. The mnmzton of the objectve functon n equton () s now crred out usng the two new optmzton method descrbed n the prevous secton. For ths, typcl opertng pont gven n tble s consdered. Mchne Dt(p.u) Xd=.97 X'd=.9 Tble-. Prmeters of sngle mchne system Trnsmsson lne(p.u) Excter Opertng Pont Xq=.55 Re=. K A =5 Vto=. T'do=7.75s Xe=.997 T A =.5 Po=.8 p.u D=. Qo=.4 p.u H=4.2 δ =72.88 D Tble-2. Prmeters of bee food forgng pproch Bee populton sze 5 Threshold probblty.7 Step sze of movement of bees, R 8.2
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME Dedcted softwre Mtlb s developed for the optml desgn of the PSS t the bove mentoned opertng pont usng the bees lgorthm. The computed results re delneted n fgure 4. The prmeters employed n ech lgorthm re tbulted through tbles 2 nd. All the prmeters re obtned by trl nd error nd no ttempt hs been mde to optmze them. Fgure 4() shows the vrton of objectve functon t ech tertve step of the two novel optmzton lgorthms. Ths fgure lso shows objectve functon vrton employng GA whch s ncluded for comprson. It s mportnt to menton tht for frness of comprson the ntl populton s tken s sme for ll the three optmzton methods to commence wth. Tble-. Prmeters of genetc lgorthm pproch populton sze 5 Crossover probblty.8 Mutton probblty. Fgure 4. Convergence chrcterstcs Fgure 5 llustrtes the convergence chrcterstcs of two novel optmzton methods. The vrton of objectve functon of ech bee gnst tertve step s shown n fgure 5() s cler ndcton of effectve communcton through wggle dnce. Whle ech bee strts t rndom locton they ll converge coherently to the best poston of hgh qulty flower btches. However such mechnsm s bsent n the reproducton lgorthm nd ths scheme reles on the survvl of the fttest mechnsm. For completeness, the vrton of controller constnts wth ech tertve step s lso ncluded n fgure 5. At the end of terton the optml PSS structure dentfed nd s gven n tble 4. Tble-4. Optmum PSS structure K P K I K D OBF 22.72. 4.2 GA 22.2.782.2 The dynmc response of sngle mchne connected to nfnte busbr wth optmzed PSS s now studed nd s vlble n fgure. Fgure () shows the vrton ω of the mchne, when subjected to.5 p.u. step dsturbnce n Tm t rted opertng condtons. From ths dynmc response the pek vlue s lmted to. nd settlng tme s. seconds. Fgure (b) shows the vrton of termnl voltge of the genertor delverng rted lod when subjected to dp n Tm of mpltude.5 p.u. step.
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME Kp 5 25 2 5 5 2 No of tertons K 5 4 2 2 No of tertons () (b) Kd 2 8 4 2 2 No of tertons Objectve functon 9 8 7 5 4 2 5 5 2 25 No of tertons (c) (d) Fgure 5. Colony behvour of bees. Vrton of controller prmeters () K P, (b) (d) Convergence chrcterstcs. K (c) K nd I D The response shows tht the proposed controller effectvely stblzes the mchne termnl voltge wth settlng tme of.4 seconds. Also the mxmum dp n mchne voltge s s low s. p.u. It s evdent tht the proposed schemes re on pr wth tht of GA. () (b) Fgure () Vrton ω of the mchne, when subjected to.5 p.u. step dsturbnce n Tm t rted opertng condtons. (b) Vrton of termnl voltge of the genertor delverng rted lod when subjected to dp n T of mpltude.5 p.u. 2 m
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME V. CONCLUSION The prospectve method bsed on honey bees presented n ths pper supplements the present welth of recently developed optmzton technques nd knowledge. The novel concept promse confrmed convergence wth rndom ntl guess, smple computtonl steps, dervtve-free operton etc. Results obtned from computer smultons of sngle mchne connected to nfnte busbr ndcte tht the bee tuned exctton controller cn yeld good dmpng chrcterstcs over wde rnge of opertng condtons. REFERENCES [] F.P.Demello nd C.Concord, Concepts of synchronous mchne stblty s ffected by exctton control, IEEE Trns. Power Apprtus nd Systems, vol. PAS-88, No.4, pp. - 29, Apr99. [2] Lrsen, E.V. nd D.A.Swn, Applyng power system stblzers, IEEE Trns. PowerApp. Syst., vol. PAS-, pp. 7-4, 977. [] Ohtsuk, K., S.Yokokm, H.Tnk nd H.Do, A mult vrble optml control system for genertor, IEEE Trns. Energy Converson, vol. EC-, No. 2, pp. 88-98,988. [4] S.Pln nd K.L.P.Mshr, Desgn of hgh-gn exctton controller of synchronous genertor, Electrc mchnes nd Electro Mechncs, Vol.7, pp. 4-472, 982. [5] DX nd G.T.Heydt, Self-tunng controller for generton exctton, IEEE Trns. Power App. Syst., vol. PAS-2, pp.877-885, 98. [] C.J.Wu nd Y.Y.Hsu, Desgn of self-tunng PID power system stblzers for multmchne power systems, IEEE Trns. Power syst., vol. PWRS-, pp. 5-4,988. [7] Y.Y.Hsu nd C.J.Wu, Adptve control of synchronous mchne usng the uto-serchng method, IEEE Trns. Power Syst., vol. PWRS-, pp. 44-44,988. [8] A.Chndr,O.P.Mlk nd G.S.Hope, A self-tunng controller for the control of multmchne power systems, IEEE Trns. Power Syst., vol. PWRS-, pp. 5-7, 988. [9] Y.Zhng, G.P.Chen, O.P.Mlk nd G.S.Hope, An rtfcl neurl network bsed dptve power system stblzer, IEEE Trns. Energy Converson, vol. 8, No., pp. 7-77, 99. [] Y. Y.Hsu nd C.H.Cheng, A fuzzy controller for genertor exctton control, IEEE Trns.Syst. mn nd cybernetcs, vol. 2, No.2, pp. 52-59, 99. [] The bology of honey bees, Mrk.L.Wnston, Hrdwrd Unversty Press, Cmbrdge, MA, 987. [2] Sung Hoon Jung, Queen-bee evoluton for genetc lgorthms, Electronc Letters, Volume 9, Issue, pp.575 57, Mr 2. [] Qn, L.D.; Jng, Q.Y.; Zou, Z.Y.; Co, Y.J.; A queen-bee evoluton bsed on genetc lgorthm for economc power dsptch Proceedngs of 9-th Interntonl Conference UPEC 24, Vol., pp: 45 45. [4] H.A.Abbss, MBO: mrrge n honey bees optmzton- Hplometross polygynous swrmng pproch Proceedngs of the 2 congress Evolutonry Computton, Vol., 27-, pp:27 24, My 2. [5] Sto, T.; Hgwr, M, Bee System: fndng soluton by concentrted serch Proceedngs of IEEE Interntonl Conference on Computtonl Cybernetcs nd Smulton, Volume 4, pp. 954 959, 997. [] Phm, D.T.; Otr, S.; Ghnbrzdeh, A.; Koc, E.; Applcton of the Bees Algorthm to the Trnng of Lernng Vector Quntzton Networks for Control Chrt Pttern Recognton Proceedngs of Interntonl Conference, ICTTA, Vol., pp.24 29, 2. [7] C.S.Chong, M.Y.H. Low, A.I.Svkumr, K.Leng Gy, A bee colony optmzton lgorthm to job schedulng Proceengs of 2 IEEE Wnter smulton conference, pp.954-9.
48(Prnt), ISSN 97 499(Onlne) Volume 4, Issue 5, July August (2), IAEME [8] Phm, D.T.; Sorok, A.J.; Ghnbrzdeh, A.; Koc, E.; Otr, S.; Pcknther, M.; Optmzng Neurl Networks for Identfcton of Wood Defects Usng the Bees Algorthm Proceedngs of 2 IEEE Interntonl Conference on Industrl Informtcs, pp.4 5, Aug. 2. [9] Dr.K. Sundreswrn, V.T. Sreedv, Development of Novel Optmzton Procedure Bsed on Honey Bee Forgng Behvor, IEEE Interntonl Conference on Systems, Mn nd Cybermetcs,28, [2] J.H.Hollnd, Adptton n Nturl nd Artfcl Systems, ser. MI. Ann Arbor:Mchgn Unv. Press, 975. [2] Dvd.E.Goldberg, Genetc Algorthms n Serch, Optmzton nd Mchne Lernng, Addson-Wesley publctons, 99. [22] L.Dvs, The Hndbook of Genetc Algorthms, New York:Vn Nostrnd, 99. [2] K.F.Mn, K.S.Tng nd S.Kwong, Genetc lgorthms: Concepts nd desgn," IEEE Industrl Electroncs News Letter, vol.45, No.4, December 998. [24] Z. Mchlewcz, Genetc Algorthms + Dt Structures = Evoluton Progrms, rd Ed. New York: Sprnger-Verlg, 999. [25] T.Furuhsh, Advnces n Fuzzy logc, Neurl networks nd Genetc Algorthms, Berln, Germny: Sprnger-Verlg, 995. [2] Llt Kumr nd Dr. Dheerendr Sngh, Solvng Np-Hrd Problem usng Artfcl Bee Colony Algorthm, Interntonl Journl of Computer Engneerng & Technology (IJCET), Volume 4, Issue, 2, pp. 7-77, ISSN Prnt: 97 7, ISSN Onlne: 97 75. [27] G.Vsu, J. Nncy Nmrth nd V.Rmbbu, Lrge Scle Lner Dynmc System Reducton usng Artfcl Bee Colony Optmzton Algorthm, Interntonl Journl of Electrcl Engneerng & Technology (IJEET), Volume, Issue, 22, pp. 45-55, ISSN Prnt : 97-545, ISSN Onlne: 97-55. [28] Gowrshnkr Kslngm, Effect of Genetc PID Power System Stblzer for Synchronous Mchne, Interntonl Journl of Advnced Reserch n Engneerng & Technology (IJARET), Volume 4, Issue 4, 2, pp. 8-2, ISSN Prnt: 97-48, ISSN Onlne: 97-499. 4