I P O S VAR A I N S T

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1 I nternatonal Journal of En gneerng Research And Management (IJERM) ISSN : Volume-0 Issue-0 8 Novemb er 4 Comparatve analyss of PSO varants for Voltage c ontrol mnmzaton R Pradeep Sudha Ch.V.S.R..Krshna Ch Rambabu A bstract In ths paper two varants of partcle swarm optmzaton (PSO) algorthms namely Coordnated A ggregaton PSO (CAPSO) Adaptve PSO (APSO) are compared wth the conventonal PSO algorthms for the optmal steady- state performance of power system. The proposed methods are used for loss mnmzaton voltage control. Smulaton results of stard IEEE t est system s presented to llustrate the effectveness of t he proposed approaches under smulated condtons. I ndex Terms Coordnated aggregaton (CA) partcle swarm optmzaton (PSO) Adaptve partcle swarm o ptmzaton (APSO). I. I NTRODUCTION T he Optmal Power Flow (OPF) s an mportant crteron n today s power system operaton control due to scarcty of energy resources ncreasng power generaton cost ever growng dem for electrc energy. As the sze of the power s ystem ncreases load may be varyng. The generators should share the total dem plus losses among themselves. The sharng should be based on the fuel cost of the total generaton wth respect to some securty constrants. The securty c onstrants are real reactve power generaton lmts tap changng transformers lne flow lmts. Snce the dependence each generator fuel cost on the load t supples the objectve of the OPF algorthm s to allocate the total electrc power d em losses among the avalable generators n such a manner that t mnmzes the electrc utlty s total fuel cost whle satsfyng the securty constrants. But t s very dffcult t as consderng all the constrants. Natural creatures sometmes behave as a swarm. One of the m an streams of artfcal lfe research s to examne how natural creatures behave as a swarm reconfgure the swarm models nsde a computer. Reynolds developed bod as a swarm model wth smple rules generated complcated s warm behavor by computer graphc anmaton. Boyd Rcherson examned the decson process of human bengs developed the concept of ndvdual learnng cultural transmsson. Accordng to ther examnaton human bengs mae decsons usng ther own experences other p ersons exper ences []. Manuscrpt receved Nov 4 R Pradeep Sudha Electrcal Electroncs Engneerng Department Sr Vasav Engneerng College Tadepallgudem A ndhra Pradesh Inda C h.v.s.r..krshna Asst.prof n Sr Vasav Engneerng College Tadepallgudem A ndhra Pradesh Inda C h Rambabu Professor at Sr Vasav Engneerng College T adepallgudem Andhra Pradesh Inda A new optmzaton technque usng an analogy of swarm behavor of natural creatures was started n the begnnng of the 990s. Dorgo developed ant colony optmzaton (ACO) based manly on the socal nsect especally ant metaphor [ ]. Each ndvdual exchanges nformaton through pheromones mplctly n ACO. Eberhart Kennedy developed partcle swarm optmzaton (PSO) based on the analogy of swarms of brds fsh schoolng. Each ndvdual exchanges prevous experences n PSO. These r esearch efforts are called swarm ntellgence []. In the recent years the effort s contnued by the same other researchers [3- ] generatng more effectve EAs. The reason for the growng development of EA s that c onventonal optmzaton methods have faled n hlng non-convextes non- smoothness n engneerng optmzaton problems [6]. However ther man problem remans the same achevng the global best soluton n the p ossble shortest tme. I n recent years varous PSO algorthms have been successfully appled n many power- engneerng problems [ 7] [8]. Among them the hybrd PSO satsfactorly hled problems such as dstrbuton state estmaton [8] loss power mnmzaton [9] performng better convergence c haracterstcs than conventonal methods. However these PSO algorthms are based on the orgnal concept ntroduced b y Kennedy Eberhart []. In ths paper we proceed to the effort of developng more e ffectve PSO algorthms by reflectng recent advances n swarm ntellgence [9] n addton by ntroducng new concepts. Under these condtons two new hybrd PSO algorthms are proposed whch are more effectve capable of solvng non- lnear optmzaton problems faster a nd wth better accuracy n detectng the global best soluton. In ths paper the APSO CA are appled n two nonlnear optmzaton problems of power systems namely the loss mnmzaton voltage control problems. The results o btaned are compared wth conventonal PSO algorthm for demonstratng a lgorthms. mproved performance of the proposed I I. P ARTICLE S WARM O PTIMIZATION Swarm behavor can be modeled wth a few smple rules. Schools of fshes swarms of brds can be modeled wth s uch smple models. Namely even f the behavor rules of each ndvdual (agent) are smple the behavor of the swarm can be complcated. Reynolds utlzed the followng three v ectors as smple rules n the researches on bod. S tep away from the nearest agent o toward the destnaton o t o the center of the swarm w ww.jerm.com

2 C omparatve analyss of PSO varants for Voltage control mnmzaton The behavor of each agent nsde the swarm can be modeled wth smple vectors. The research results are one of the basc b acgrounds of PSO. Each agent decdes ts decson usng ts own experences t he experences of others. The research results are also one of the basc bacground elements of PSO. Accordng to the above bacground of PSO Kennedy Eberhart developed PSO through smulaton of brd flocng n a two- dmensonal s pace. The poston of each agent s represented by ts x y axs poston also ts velocty s expressed by vx (the velocty of x axs) vy (the velocty of y axs). Modfcaton of the agent poston s realzed by the poston velocty nformaton. B rd flocng optmzes a certan objectve functon. Each agent nows ts best value so far (pbest) ts x y poston. Ths nformaton s an analogy of the personal experences of each agent. Moreover each agent nows the best value so far n the group (gbest) among pbests. Ths nformaton s an analogy of the nowledge of how the other agents around them have performed. Each agent tres to modfy ts poston u sng the followng nformaton: T he current postons (x y) T he current veloctes (vx vy) T he dstance the cur rent poston pbest T he dstance the current poston gbest Ths modfcaton can be represented by the concept of velocty (modfed value for the current postons). Velocty of each agent can be modfed b y the followng equaton: v wv c r ( pbest s ) c r *( gbest s ) () * v s velocty of agent at teraton w s weghtng functon c c are weghtng factors r r are rom numbers 0 s s current poston of agent at teraton pbest s the pbest of agent gbest s gbest of the group. Namely velocty of an agent can be changed usng three vectors such le bod. The velocty s usually lmted to a certan mum value. PSO usng () s c alled the best model. w w ( w w ) /( ter ))* ter () ( mn T he follow ng weghtng functon s usually utlzed n (): Where wm ax s the ntal weght w n s the fnal weght ter ax s mum teraton number ter s curren teraton number. m m t The RHS of () conssts of three terms (vectors). The frst t erm s the prevous velocty of the agent. The second thrd terms are utlzed to change the velocty of the agent. Wthout the second thrd terms the agent wll eep on flyng n the same drecton untl t hts the boundary. As shown below for example wm ax wm n are set to Therefore at the begnnng of the search procedure dversfcaton s heavly weghted whle ntensfcaton s heavly weghted at the end of the search procedure such le s mulated annealng (SA). Namely a certan velocty whch gradually gets close to pbests gbest can be calculated. P SO usng () () s called nerta weghts approach (IWA). Fgure : concept of modfcatons P SO s : curren t searchng pont s : modfed searchng pont v : current velocty v : modfed velocty v : velocty based on pbest pbest v : velocty based on gbest gbest of a searchng pont by The current poston (searchng pont n the soluton space) c an be modfed by the followng equaton: s s v (3) Fgure shows a concept of modfcaton of a s earchng pont by PSO Fg. shows a searchng concept wth agents n a soluton space. Each agent changes ts current poston usng the ntegraton of vectors as shown n Fg.. I II. P SO V ARIANTS A. Coordnated Aggregaton- b ased PSO T he basc system equaton of PSO [() () (3)] can be consdered as a nd of dfference equaton. Therefore the system dynamcs that s the search procedure can be analyzed usng egen values of the dfference equaton. A ctually usng a smplfed state equaton of PSO Clerc Kennedy developed CA of PSO by egen values [8 4]. The velocty of the constrcton factor approach (smplest constrcton) can be expressed as follows nstead of () ( ): v K v c * r *( pbest s ) c * r ( gbest s )](4) [ W here K w here c c 4...() 4 a nd K are coeffcents. For example f =4. then K = As w ncreases above 4.0 K gets smaller.for example f =.0 then K =0.38 the dampng effect s even more pronounced. The c onvergence characterstc of the system can be controlled by w. The whole PSO algorthms by IWA CA are the same except that CA utlzes a dfferent equaton for calculaton of velocty [(4) ()]. Unle other EC methods PSO wth C A ensures the convergence of the search procedures based on mathematcal theory. PSO wth CA can generate hgher- qualty solutons for some problems than PSO wth IWA. However CA only consders dynamc behavor of only one agent studes on the effect of the nteracton among a gents. B. A daptve PSO The followng ponts are mproved to the orgnal PSO wth I WA. w ww.jerm.com

3 I nternatonal Journal of En gneerng Research And Management (IJERM) ISSN : Volume-0 Issue-0 8 Novemb er 4 The search trajectory of PSO can be controlled by ntroducng the new parameters (P P) based on the probablty to move close to the poston of ( pbest gbest) at the followng teraton. The w term of () s modfed as (7). Usng the v equaton the center of the range of partcle m ovements can be equal to gbest. When the agent becomes gbest t s perturbed. The n ew parameters (P P) of the agent are adjusted so that the agent may move away from the poston of ( pbest gbest). When the agent s moved beyond the boundary of feasble regons pbests gbest cannot be m odfed. When the agent s moved beyond the boundary of f easble regons the new parameters (P P) of the agent are adjusted so that the agent may move close t o the poston of (pbest gbest). The new parameters are set to each agent. The weghtng c oeffcents are calculated as follows: c c c ( 6) P P The search trajectory of PSO can be controlled by the parameters (P P ). Concretely when the value s enlarged more than 0. the agent may move close to the poston of p best/gbest. w gbest c ( pbest x) c ( gbest x) / x ( 7) Namely the velocty of the mproved PSO can be expressed a s follows: v w cr *( pbest s ) cr *( gbest s ) ( 8) The mproved PSO can be expressed as follows (steps a re the same as PSO): eneraton of ntal searchng ponts: Basc procedures are the same as PSO. In addton the parameters (P P) of each agent are set to 0. or hgher. Then each agent may move c lose to the poston of (pbest gbest) at the followng teraton. E valuaton of searchng ponts: The procedure s the same as PSO. In addton when the agent becomes gbest t s perturbed. The parameters (P P ) of the a gent are adjusted to 0. or lower so that the agent m ay move away from the poston of (pbest gbest). M odfcaton of searchng ponts: The current searchng ponts are modfed usng the state e quatons (7) (3) of adaptve PSO. I V. P ROBLEM F ORMULATION T he OPF problem s to optmze the steady state performance of a power system n terms of an objectve functon whle satsfyng several equalty nequalty constrants. M athematcally the OPF problem can be formulated as gven M n F ( x ( 9) Subject to g ( x 0 ( ) h ( x 0 ( ) x s a vector of dependent varables consstng of slac bus power power P outputs Q V load bus voltages L generator reactve the transmsson lne loadngs Hence x c an be expressed as gven T x P V... V Q... Q S... S ] ( ) [ L LNL N l lnl S l N L N n l are number of load buses number of g enerators number of transmsson lne respectvely. u s the vector of ndependent varables consstng of enerator voltages V generator real power outputs P g except at the slac bus P transformer tap settngs T shunt VAR compensatons Q C. Hence u c an be expressed as g ven T u V... V P... P T... T Q... Q ] ( 3) [ N N NT C CNC Where N T N C are the number of the regulatng transformers shunt compensators respectvely. F s the objectve functon to be mnmzed. g s the equalty c onstrants that represents typcal load flow equatons h s t he system operatng constrants ) O bjectve functons I n ths paper the objectve(s)(j) s the objectve functon to be m nmzed whch s one of the followng: ( ) Objectve functon- ( Mnmzaton) T he optmal reactve power flow problem to mnmze actve l osses can be formulated as nl J PL oss( x Pl (4) w here x s t he ve ctor o f d epended va rables u s t he v ector o f control v a rables s t he r eal pow er l osses a t lne- a nd n l s t he n umber o f t ransmsson l nes. ( ) Objectve functon- ( Voltage Control) Voltage profle s one of the qualty measures for power system. It can be mproved by mnmzng the load bus voltage devatons from.0 per unt. The objectve functon c an be expressed as NL sp J V V ( ) s p w here V s t he pre-s pecfed r eference va lue a t l oad bus- w hch s u sually s et a t t he va lue o f. 0 p.u. a nd N L s t he n umber o f l oad b u ses. ) E qualty constrants T he equalty constrants of the OPF reflect the physcs of the Power System as well as the desred voltage set ponts throughout the system. The physcs of the Power System are enforced through the power flow equatons whch requre that the net njecton of real reactve power at each bus sum to zer o n P P V V Y cos( ) 0 D j j j j j n Q -Q + V V Y sn( θ -δ +δ ) = 0 D j = j j j j (6) 3 w ww.jerm.com

4 C omparatve analyss of PSO varants for Voltage control mnmzaton P Q are the real reactve power outputs njected at bus- respectvely the load dem at the same b us s represented by P D Q D admttance matrx are represented by elements of the bus Y j j. 3 ) I nequalty constrants T he nequalty constrants of the OPF reflect the lmts on physcal devces n the Power System as well as the lmts created to ensure system securty. Ths secton wll lay out all the necessary nequalty constrants needed for the OPF mplemented n ths thess. ) enerators real reactve powe r outputs mn P P P N mn Q Q Q N ) Voltage magntudes at each bus n the networ mn V V V NL 3 ) Transformer tap settngs mn T T T N ( 9) 4 ) Reactve power njectons due to capactor bans mn QC QC QC S () ) Transmsson lnes loadng S S N () V. P ERFORMANCE E VALUATION ( 7) ( 8) T he man focus of ths paper s the comparson of the two alternatve PSO algorthms wth the conventonal PSO algorthm. Specfcally they need to hle two optmzaton problems namely mnmzaton of ) real power losses n transmsson lnes (Reactve Power Control) ) voltage d evaton on load buses (Voltage control). In all case studes as decson varables generator voltages transformers tap settngs reactve power compensators are chosen. In ths p aper these varables are consdered to be contnuous. T o verfy the feasblty of the proposed PSO algorthms (PSO CAPSO APSO) n the mnmzaton voltage control they are appled on the IEEE - bus system. The results are also compared wth conventonal PSO a lgorthm. All PSO algorthms are smply called compettors. T he topology the complete data of ths networ can be found n []. The networ conssts of 6 generators 4 lnes 4 transformers capactor bans. In the transformer tests tap settngs are consdered wthn the nterval[0.9.]. V oltages are consdered wthn the range of [0.9.]. C. R esults wth mnmzaton objectve TABLE - I Optmal control varable settng for m nmzaton objectve C ontrol V arables M n M ax P SO CAP SO A PSO P P P P 8 P P 3 V V V V 8 V V 3 T T T T Q C Q C Q C Q C Q C Q C Q C Q C Q C 9 C ost($/h) V oltage Devaton P loss ( MW) SO P APSO C PSO A Power loss teratons No.of I teratons No.of 4 0 Fgure Convergence c haracterstcs of PSO CAPSO Table shows the optmal settng of control varables for loss mnmzaton objectve. From Table Power loss usng APSO s 3.76MW whch s less than 3.93MW usng CAPSO a nd 4.9MW usng conventonal PSO. 4 w ww.jerm.com

5 I nternatonal Journal of En gneerng Research And Management (IJERM) ISSN : Volume-0 Issue-0 8 Novemb er 4 F gure shows the graphs plotted Power loss vs teratons varaton for PSO CAPSO APSO algorthms for IEEE- bus system respectvely. Voltage Devaton N o.of teratons I teratons 4 No.of D. R esults for Voltage Control objectve Table shows the optmal settng of control varables for v oltage devaton mnmzaton objectve. From Table Voltage devaton usng APSO s 4 p.u whch s less than 64 p.u. usng CAPSO 94 p.u. usng c onventonal PSO. Fgure 3 shows the graphs plotted Voltage devaton V s teratons varaton for PSO CAPSO APSO algorthms for IEEE- bus system respectvely. Table shows the optmal settng of control varables for voltage devaton mnmzaton objectve. From Table Voltage devaton usng APSO s 4 p.u whch s less t han 64 p.u. usng CAPSO 94 p.u. usng c onventonal PSO. Fgure 3 shows the graphs plotted Voltage devaton teratons varaton for PSO CAPSO APSO algorthms for IEEE-3 0 bus system respectvely C APSO P SO Voltage v araton(pso) Devaton Voltage Devaton v araton(capso) C ontrol V arables P P P P 8 P P 3 V V V V 8 V V 3 T T T T 36 Q C Q C Q C Q C 7 Q C Q C Q C 3 Q C 4 Q C 9 T ABLE I I OPTIMAL CO NTROL VARIABLE SETTIN FOR V OLTAE DEVIATION MINIMIZATIO N OBJECTIVE M n L mt C ost($/h) V oltage Devaton P loss ( MW) M ax L mt P SO C APSO A PSO PSO A 0 Voltage Devaton v araton(apso) F gure 3 Convergence characterstcs of PSO CAPSO A PSO for Voltage control objectve CO NCLUSIONS Ths paper proposed PSO varants such as Coordnated Aggr e gaton PSO (CAPSO) A daptve PSO (APSO) The proposed PSO algorthms competed n the optmzaton problems of Power loss mnmzaton Voltage control problems. The results of the proposed CAPSO APSO methods for dfferent objectve functons are compared wth conventonal PSO method to show the effectveness of the p roposed algorthms. Proposed algorthms been appled to IEEE- bus system observed APSO outperforms the CA a nd Conventonal PSO. RE FERENCES [ ] J. Kennedy R. Eberhart Partcle swarm optmzaton n P roc. IEEE Int. Conf. Neural Networs 99 vol. IV p p [ ] M. Dorgo Optmzaton learnng natural algorthms Ph.D. dssertaton Poltecnco de Mlano M lano Italy 99. [ 3] R.. Reynolds A. V. Sebald L. J. Fogel Eds. An ntroducton to cultural algorthms n Proc. 3rd Annu. Conf. volutonary Programmn g Rver Edge NJ 994 p p [ 4] C. A. Coello R. L. Becerra W. B. Langdon E. Cantú- Paz K. Mathas R. Roy D. Davs R. Pol K. Balarshnan V. Honavar. Rudolph J.Wegener L. Bull M. A. Potter A. C. Schultz J. F. Mller E. Bure a nd N. Jonosa Eds. Addng nowledge effcent data structures to evolutonary programmng: A cultural a lgorthm for constraned optmzaton n Proc. enetc w ww.jerm.com

6 C omparatve analyss of PSO varants for Voltage control mnmzaton E volutonary Computaton Conf. San Francsco CA Jul. 0 pp. 9. [ ] K. E. Parsopoulos D. K. Tasouls M. N. Vrahats Multobjectve optmzaton usng parallel vector e valuated partcle swarm optmzaton n Proc. IASTED I nt. Conf. Artfcal Intellgence Applcatons Innsbruc A ustra 04. [ 6] K. Y. Lee M. A. El-S haraw Ed s. Modern Heurstcs Optmzaton TechnquesWth Applcatons to Power S ystems. Pscataway NJ: IEEE Power Engneerng S ocety (0TP60) 0. [ 7] H. Yoshda K. Kawata Y. Fuuyama S. Taayama Y. N aansh A partcle swarm optmzaton for reactve power voltage control consderng voltage securty a ssessment I EEE Trans. Power Syst. vol. no. 4 pp Nov. 00. [ 8] S. Naa T. enj T. Yura Y. Fuuyama A hybrd partcle swarm optmzaton for dstrbuton state e stmaton I EEE Trans. Power Syst. vol. 8 no. pp Feb. 03. [ 9] A. A. A. Esmn. Lambert- Torres A. C. Z. de Souza A hybrd partcle swarm optmzaton appled to loss p ower mnmzaton I EEE Trans. Power Syst. vol. n o. pp May 0. [ ] J. - B. Par K. - S. Lee J. - R. Shn K. Y. Lee A partcle swarm optmzaton for economc dspatch wth n onsmooth cost functons I EEE Trans. Power Syst. vol. no. pp Feb. 0. [ ] Z. -L. ang Partcle swarm optmzaton to solvng the economc dspatch consderng the generator constrants IEEE Trans. Power Syst. vol. 8 no. 3 pp A ug. 03. [ ] T. Aruldoss A. Vctore A. E. Jeyaumar Hybrd PSO-SQP for economc dspatch wth valve- pont effect E lect. Power Syst. Res. vol. 7 no. pp [ 3] M. A. Abdo Optmal power flowusng partcle swarm o ptmzaton I nt. J. Elect. Power Energy Syst. vol. 4 n o. 7 pp [ 4] S. Kannan M. R. Slochanal P. Subbaraj N. P. P adhy Applcaton of partcle swarm optmzaton technque ts varants to generaton expanson p lannng problem E lect. Power Syst. Res. vol. 70 no. 3 p p [ ] X. - M. Yu X. - Y. Xong Y. -W. Wu A PSO- based a pproach to optmal capactor placement wth harmonc d storton consderaton E lect. Power Syst. Res. vol. 7 n o. pp [ 6] A. Mendonca N. Fonseca J. P. Lopes V. Mra Robust tunng of power system stablzers usng evolutonary PSO n P roc. ISAP Lemnos reece 03. [ 7] C. - M. Huang C. - J. Huang M. - L. Wang A partcle swarm optmzaton to dentfyng the ARMAX model for short- t erm load forecastng I EEE Trans. Power Syst. v ol. no. pp May 0. [ 8] I. N. Kassabalds M. A. El-S haraw R. J. Mars L. S. Mouln A. P. A. da Slva Dynamc securty border dentfcaton usng enhanced partcle swarm o ptmzaton I EEE Trans. Power Syst. vol. 7 no. 3 p p Aug. 0. [ 9] J. K. Parrsh W. M. Hammer Anmal roups n Three D mensons. Cambrdge U.K.: Cambrdge Unv. Press 997. [ ] The IEEE - Bus Test System. [Onlne]. Avalable: a bus.htm. I NDIA. nterest are R.Prade ep Sudha has receved Bachelor of Technology degree n Electrcal Electroncs Engneerng from odavar Insttute Of Engneerng And Technology In. Presently he s pursung M.Tech n Power System Control & Automaton f rom Sr Vasav Engneerng College Tadepallgudem Andhra Pradesh C H V S R opala Krshna Was receved B.Tech Electrcal & Electroncs Engneerng M.Tech degree from Sr Vasav Engneerng College Tadepallgudem JNTU Kanada. Currently worng as a A sst.prof n Sr Vasav Engneerng College Tadepallgudem. Hs areas of n Embedded systems Power Electroncs. C h.rambabu receved the Bachelor of Engneerng degree n Electrcal & Electroncs Engneerng from Madras U nversty n 00 Master s degree from JNTU Anantapur n 0. He s p ursung Ph.D. from JNTU Kanada. Currently he s a Professor at Sr Vasav Engneerng College. Hs areas of nterests are power system control O ptmzaton technques FACTS. 6 w ww.jerm.com