Key-Words: - PSSs; Multimachine Power System; Particle Swarm Optimization; Bacteria Foraging.

Transcription

1 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm Optmal Power System Stablzers Desgn for Multmachne Power System Usng Hybrd BFOA-PSO Approach Al, E S a and Abd-Elazm, S M b a- Assstant Professor, Electrc Power and Machne Department, Faculty of Engneerng, Zagazg Unversty, Zagazg, Egypt, E-mal address: ehabsalmalsalama@yahoocom b- Assstant Professor, Electrc Power and Machne Department, Faculty of Engneerng, Zagazg Unversty, Zagazg, Egypt, E-mal address: sahareldeep@yahoocom Abstract- A novel hybrd approach nvolvng Partcle Swarm Optmzaton (PSO) and Bacteral Foragng Optmzaton Algorthm (BFOA) called Bacteral Swarm Optmzaton (BSO) s llustrated for desgnng Power System Stablzers (PSSs) n a multmachne power system In BSO, the search drectons of tumble behavour for each bacterum are orented by the ndvdual s best locaton and the global best locaton of PSO he proposed hybrd algorthm has been extensvely compared wth the orgnal BFOA algorthm and the PSO algorthm Smulatons results have shown the valdty of the proposed BSO n tunng PSSs compared wth BFOA and PSO Moreover, the results are presented to demonstrate the effectveness of the proposed controller to mprove the power system stablty over a wde range of loadng condtons Key-Words: - PSSs; Multmachne Power System; Partcle Swarm Optmzaton; Bactera Foragng Introducton Low frequency oscllatons are observed when large power systems are nterconnected by weak te lnes hese oscllatons may sustan and grow, causng system separaton f no adequate dampng s avalable Moreover, low frequency oscllatons present lmtatons on the power transfer capablty [] Power system stablzers (PSSs) are now routnely used n the ndustry to damp out oscllatons An approprate selecton of PSS parameters results n satsfactory performance durng system dsturbances [] he problem of PSS parameter tunng s a complex exercse A number of conventonal technques have been reported n the lterature pertanng to desgn problems of conventonal PSSs namely: the egenvalue assgnment, mathematcal programmng, gradent procedure for optmzaton and also the modern control theory [] Unfortunately, the conventonal technques are tme consumng as they are teratve and requre heavy computaton burden and slow convergence In addton, the search process s susceptble to be trapped n local mnma and the soluton obtaned may not be optmal [4] he power system stablty enhancement va PSS and a thyrstor controlled seres capactor (CSC) based stablzer when appled ndependently and also through coordnated applcaton s dscussed and nvestgated n [5] An augmented fuzzy logc PSS for stablty enhancement of power system s presented n [6] he desgn of robust PSS whch place the system poles n an acceptable regon n the complex plane for a gven set of operatng and system condtons s ntroduced n [7] A novel evolutonary algorthm based approach to optmal desgn of multmachne PSSs s developed n [8] hs approach employs a partcle swarm optmzaton (PSO) technque to search for optmal settngs of PSS parameters Optmal mult-objectve desgn of robust multmachne PSSs usng genetc algorthm (GA) s addressed n [9] PSSs desgn usng the rule based bactera foragng (RBBF) optmzaton technques s nvestgated n [] A comprehensve assessment of the effects of PSS based dampng controller s carred out n [] he desgn problem of the controller s transformed nto an optmzaton problem PSO based optmal tunng algorthm s used to optmally tune the parameters of the PSS Optmal locatons and desgn of robust multmachne PSSs usng GA s presented n [] he possblty of usng a lnearzed power system model to evaluate the stablty and estmate the attracton area of the system n a partcular operatng condton s nvestgated n [] Mult-objectve desgn of multmachne PSSs usng PSO s ntroduced n [4] A new robust control strategy to synthess of robust proportonal-ntegral-dervatve (PID) based PSS s addressed n [5] he desgn of a smple, yet robust controller for power system stablzaton, usng Khartonov s stablty theory s employed n [6] A novel algorthm for smultaneous coordnated desgnng of PSSs and CSC n a multmachne power system s dscussed n [7] GA has attracted the attenton n the feld of controller parameter optmzaton However, GA s very satsfactory n fndng global or near global optmal result of the problem; t needs a very long run tme that may be several mnutes or even several E-ISSN: 4-5X 85 Issue, Volume 8, Aprl

2 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm hours dependng on the sze of the system under study Moreover swarmng strateges n brd flockng and fsh schoolng are used n the PSO and ntroduced n [8] However, PSO suffers from the partal optmsm, whch causes the less exact at the regulaton of ts speed and the drecton Also, the algorthm cannot work out the problems of scatterng and optmzaton [9] In addton, the algorthm pans from slow convergence n refned search stage, weak local search ablty and algorthm may lead to possble entrapment n local mnmum solutons A relatvely newer evolutonary computaton algorthm, called Bactera Foragng (BF) scheme has been proposed by [4] he BF algorthm depends on random search drectons whch may lead to delay n reachng the global soluton A new algorthm BF orented by PSO s proposed that combne the above mentoned optmzaton algorthms [56] hs combnaton ams to make use of PSO ablty to exchange socal nformaton and BF ablty n fndng a new soluton by elmnaton and dspersal hs new hybrd algorthm called Bacteral Swarm Optmzaton (BSO) s adopted n ths paper to solve the above mentoned problems and drawbacks hs paper proposes a new optmzaton algorthm known as BSO for optmal desgnng of the PSSs controller n a multmachne power system he performance of BSO has been compared wth these of PSO and BFOA n tunng the PSSs controller parameters he desgn problem of the proposed controller s formulated as an optmzaton problem and BSO s employed to search for optmal controller parameters An egenvalue based objectve functon reflectng the combnaton of dampng factor and dampng rato s optmzed for dfferent operatng condtons Smulatons results assure the effectveness of the proposed controller n provdng good dampng characterstc to system oscllatons over a wde range of loadng condtons Also, these results valdate the superorty of the proposed method n tunng controller compared wth BFOA and PSO Bactera foragng optmzaton: A bref overvew he survval of speces n any natural evolutonary process depends upon ther ftness crtera, whch reles upon ther food searchng and motle behavour he law of evoluton supports those speces who have better food searchng ablty and ether elmnates or reshapes those wth poor search ablty he genes of those speces who are stronger gets propagated n the evoluton chan snce they possess ablty to reproduce even better speces n future generatons So a clear understandng and modellng of foragng behavour n any of the evolutonary speces, leads to ts applcaton n any nonlnear system optmzaton algorthm he foragng strategy of Eschercha col bactera present n human ntestne can be explaned by four processes, namely chemotaxs, swarmng, reproducton, and elmnaton dspersal [56] Chemotaxs he characterstcs of movement of bactera n search of food can be defned n two ways, e swmmng and tumblng together knows as chemotaxs A bacterum s sad to be swmmng f t moves n a predefned drecton, and tumblng f movng n an altogether dfferent drecton Mathematcally, tumble of any bacterum can be represented by a unt length of random drecton φ(j) multpled by step length of that bacterum C() In case of swmmng, ths random length s predefned Swarmng For the bactera to reach at the rchest food locaton (e for the algorthm to converge at the soluton pont), t s desred that the optmum bacterum tll a pont of tme n the search perod should try to attract other bactera so that together they converge at the desred locaton (soluton pont) more rapdly o acheve ths, a penalty functon based upon the relatve dstances of each bacterum from the fttest bacterum tll that search duraton, s added to the orgnal cost functon Fnally, when all the bactera have merged nto the soluton pont, ths penalty functon becomes zero he effect of swarmng s to make the bactera congregate nto groups and move as concentrc patterns wth hgh bacteral densty Reproducton he orgnal set of bactera, after gettng evolved through several chemotactc stages reaches the reproducton stage Here, best set of bactera (chosen out of all the chemotactc stages) gets dvded nto two groups he healther half replaces wth the other half of bactera, whch gets elmnated, owng to ther poorer foragng abltes hs makes the populaton of bactera constant n the evoluton process 4 Elmnaton and dspersal In the evoluton process, a sudden unforeseen event can occur, whch may drastcally alter the smooth process of evoluton and cause the elmnaton of the set of bactera and/or dsperse E-ISSN: 4-5X 86 Issue, Volume 8, Aprl

3 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm them to a new envronment Most roncally, nstead of dsturbng the usual chemotactc growth of the set of bactera, ths unknown event may place a newer set of bactera nearer to the food locaton From a broad perspectve, elmnaton, and dspersal are parts of the populaton level long dstance motle behavour In ts applcaton to optmzaton, t helps n reducng the behavour of stagnaton (e beng trapped n a premature soluton pont or local optma) often seen n such parallel search algorthms he detaled mathematcal dervatons as well as theoretcal aspect of ths new concept are presented n [67] Problem Statement Power System Model A power system can be modelled by a set of nonlnear dfferental equatons are: X f ( X, U) () Where X s the vector of the state varables and U s the vector of nput varables In ths study X [,, E, E, V ] and U s the PSS q fd f output sgnal Here, and are the rotor angle and speed, respectvely Also, E, E and V are q fd f the nternal, the feld, and exctaton voltages respectvely In the desgn of PSS, the lnearzed ncremental models around an equlbrum pont are usually employed herefore, the state equaton of a power system wth n machnes and m PSSs can be wrtten as: X AX Bu () Where A s a 5n 5n matrx and equals f / X whle B s a 5 n m matrx and equals f / U Both A and B are evaluated at a certan operatng pont X s a 5n state vector and U s a m nput vector Structure of PSS he operatng functon of a PSS s to produce a proper torque on the rotor of the machne nvolved n such a way that the phase lag between the excter nput and the machne electrcal torque s compensated he supplementary stablzng sgnal consdered s one proportonal to speed A wdely speed based used conventonal PSS s consdered throughout the study [] he transfer functon of the th PSS s gven by: S ( S ) W (S ) U K Δω () (S ) ( S ) ( S ) W 4 Where s the devaton n speed from the synchronous speed hs type of stablzer conssts of a washout flter, a dynamc compensator he output sgnal s fed as a supplementary nput sgnal, U to the regulator of the exctaton system he washout flter, whch essentally s a hgh pass flter, s used to reset the steady state offset n the output of the PSS he value of the tme constant s usually not crtcal and t can range from 5 W to second he dynamc compensator s made up to two lead lag crcuts, lmters and an addtonal gan he adjustable PSS parameters are the gan of the PSS, K and the tme constants, he 4 lead lag block present n the system provdes phase lead compensaton for the phase lag that s ntroduced n the crcut between the excter nput and the electrcal torque System under Study Fg shows the sngle lne dagram of the test system used Detals of system data are gven n [7] he partcpaton matrx can be used n mode dentfcaton able () shows the egenvalues, and frequences assocated wth the rotor oscllaton modes of the system Examnng able () ndcates that the 7 Hz mode s the nterarea mode wth G swngng aganst G and G he 955 Hz mode s the ntermachne oscllaton local to G Also, the 849 Hz mode s the ntermachne mode local to G he postve real part of egenvalue of G ndcates system nstablty he system and generator loadng levels are gven n able () reated wth the ral Edton of SmartDraw ~ ~ 5 7 load A Local load 8 ~ load C load B Fg System under study E-ISSN: 4-5X 87 Issue, Volume 8, Aprl

4 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm able () he egenvalues, and frequences of the rotor oscllaton modes of the system Generator Egenvalues Frequences Dampng rato G G G +5 49j -5 84j -67 6j j j j Generator G G G 4 Objectve Functon o mantan stablty and provde greater dampng, the parameters of the PSSs may be selected to mnmze the followng objectve functon: np np J ( ) ( ) (4) t j j j j j j hs wll place the system closed loop egenvalues n the D-shape sector characterzed by and as shown n Fg j able () Loadng of the system (n pu) Lght Normal case Heavy P Q P Q P Q Load P Q P Q P Q A B C at G Where, np s the number of operatng ponts consdered n the desgn process, and are the real part and the dampng rato of the egenvalue of the operatng pont In ths study, and are chosen to be -5 and respectvely [9] o reduce the computatonal burden n ths study, the value of the wash out tme constant W s fxed to second, the values of and 4 are kept constant at a reasonable value of 5 second and tunng of and are undertaken to acheve the net phase lead requred by the system ypcal ranges of the optmzed parameters are [- ] for K and [6- ] for and Based on the objectve functon J optmzaton problem can be stated as: Mnmze t J subjected to: t K mn K K max mn max mn max (5) j Fg A D-shape sector n the s-plane 5 he Bacteral Swarm Optmzaton Algorthm PSO s a stochastc optmzaton technque that draws nspraton from the behavour of a flock of brds or the collectve ntellgence of a group of socal nsects wth lmted ndvdual capabltes In PSO a populaton of partcles s ntalzed wth random postons X and veloctes V, and a ftness functon usng the partcle s postonal coordnates as nput values Postons and veloctes are adjusted, and the functon s evaluated wth the new coordnates at each tme step he velocty and poston update equatons for the d-th dmenson of the -th partcle n the swarm may be gven as follows: V ( t) V ( t) C ( V X ( t)) C ( P X ( t)) d d ld d gd d (6) X ( t ) X ( t) V ( t ) d d d (7) On the other hand, the BF s based upon search and optmal foragng decson makng capabltes of the Eschercha col bactera [5] he coordnates of a bacterum here represent an ndvdual soluton of the optmzaton problem Such a set of tral solutons converges towards the optmal soluton followng the foragng group dynamcs of the bactera populaton Chemotactc movement s contnued untl a bacterum goes n the drecton of postve nutrent gradent After a certan number of complete swms the best half of the populaton undergoes reproducton, elmnatng the rest of the populaton In order to escape local optma, an elmnaton dsperson event s carred out where, some bactera are lqudated at random wth a very small probablty and the new replacements are ntalzed at random locatons of the search space A detaled descrpton of the complete algorthm can be traced n [56] [Step ] Intalze parameters n, S N, N, N, P, C re ed ed C( )(,,, N ), E-ISSN: 4-5X 88 Issue, Volume 8, Aprl

5 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm Where, n : Dmenson of the search space, S : he number of bactera n populaton, N : he number of chemotactc steps, C N : he number of reproducton steps, re N ed : he number of elmnaton-dspersal events to be mposed over the bactera, P : he probablty wth whch the ed elmnaton and dspersal wll contnue, C () : he sze of the step taken n the random drecton specfed by the tumble, : he nerta weght, C : he swarm confdence, (, : Poston vector of the -th bacterum, n j-th chemotactc step and k-th reproducton, V : Velocty vector of the -th bacterum [Step ] Update the followng J (, : Cost or ftness value of the -th bacterum n the jth chemotaxs, and the k-th reproducton loop g _ best : Poston vector of the best poston found by all bactera J (, : Ftness value of the best poston best found so far [Step ] Reproducton loop: k k [Step 4] Chemotaxs loop: j j [Sub step a] For =,,, S, take a chemotaxs step for bacterum as follows [Sub step b] Compute ftness functon, J (, [Sub step c] Let J J (, to save ths last value snce one may fnd a better cost va a run [Sub step d] umble: generate a random vector ( ) R n wth each element ( ), m,,, p, a random number m on [, ] [Sub step e] Move: ( ) Let (, j, (, C( ) ( ) ( ) [Sub step f] Compute J (, j, [Sub step g] Swm: one consders only the -th bacterum s swmmng whle the others are not movng then ) Let m (counter for swm length) ) Whle m N (have not clmbed down too S long) Let m m If J (, j, J (f dong better), last Let J J (, j, and let last ( ) (, j, (, C( ) ( ) ( ) and use ths (, j, to compute the new J (, j, as shown n new [sub step f] Else, let m N S the whle statement [Step 5] Mutaton wth PSO operator For =,,,S hs s the end of Update the g _ best and J (, best Update the poston and velocty of the d-th coordnate of the -th bacterum accordng to the followng rule: V new V new C old (, d d g_ best d d new (, j, old (, j, V new d d d [Step 6] Let S _ r S / he S _ r bactera wth hghest cost functon (J ) values de and other half bactera populaton wth the best values splt (and the copes that are made are placed at the same locaton as ther parent) [Step 7] If k N, go to [step ] One has not re reached the number of specfed reproducton steps, so one starts the next generaton n the chemotaxs loop he detaled mathematcal dervatons as well as theoretcal aspect of ths new concept are presented n [56] 6 Results and Smulatons In ths secton, the superorty of the proposed BSO algorthm n desgnng PSS () n compare to optmzed PSS wth BFOA () and optmzed PSS controller based on PSO () s llustrated Fg shows the varatons of objectve functon wth varous optmzaton technques he objectve functons decrease monotoncally over generatons of BFOA, PSO and BSO he fnal value of the objectve functon s J = for all algorthms, ndcatng that all modes t have been shfted to the specfed D-shape sector n E-ISSN: 4-5X 89 Issue, Volume 8, Aprl

6 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm the S-plane and the proposed objectve functon s satsfed Moreover, BSO converges at a faster rate (5 generatons) compared to that for PSO (64 generatons) and BFOA (8 generatons) able (), shows the system egenvalues, and dampng rato of mechancal mode wth three dfferent loadng condtons It s clear that the shft substantally the electromechancal mode egenvalues to the left of the S-plane and the values of the dampng factors wth the proposed are sgnfcantly mproved to be ( =- 95,-94,-5) for lght, normal, and heavy loadng respectvely Also, the dampng ratos correspondng to controllers are almost greater than that correspondng to and Hence, compared to and, greatly enhances the system stablty and mproves the dampng characterstcs of electromechancal modes Results of PSSs parameters set values based on the proposed objectve functon usng BFOA, PSO and BSO are gven n able (4) Objectv e functon BSO PSO BFOA able (4) Parameters of PSSs for dfferent technques BFOA PSO BSO PSS K=6696 =65 =495 K=66544 =4684 =748 K=86585 =45 =6455 PSS K=788 =4986 =9 K=487 =98 =49 K=645 =776 =984 PSS K=5 =5 =789 K=97 =456 =955 K=7 =7 =96 6 Response for lght load condton: he effectveness of the performance due to step ncrease n reference voltage of generator s verfed Fgs 4-6, show the response of,, and due to ths dsturbance for lght loadng condton From these fgures, t can be seen that the usng the proposed objectve functon acheves good robust performance, and provdes superor dampng n comparson wth the other controllers Moreover, the requred mean tme to suppress these oscllatons s approxmately second wth, 5 second for, and 8 second wth so the desgned controller s capable of provdng suffcent dampng to the system oscllatory modes 4 5 x Generatons able () Mechancal modes and under dfferent loadng condtons and controllers Lght load Normal load Heavy load Fg Varatons of objectve functon C h a n g e n w (ra d /s e c o n d ) me n second Fg 4 Change n for lght load E-ISSN: 4-5X 9 Issue, Volume 8, Aprl

7 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm x -5 5 x -4 C h a n g e n w (ra d /s e c o n d ) - - C h a n g e n w (ra d /s e c o n d ) me n second me n second Fg 5 Change n for lght load Fg 7 Change n for normal load 5 x -4 x -5 C h a n g e n w (ra d /s e c o n d ) -5 - Change n w (rad/sec ond) me n second Fg 6 Change n for lght load 6 Response for normal load condton: Fgs 7-9, show the response of the system to the same dsturbance for normal loadng condton hese fgures ndcate the capablty of the n reducng the settlng tme and dampng power system oscllatons Moreover, the mean settlng tme of these oscllatons s =, 9, and s second for,, and respectvely In addton, the proposed outperforms and outlasts and controller n dampng oscllatons effectvely and reducng settlng tme Hence, controller greatly enhances the system stablty and mproves the dampng characterstcs of power system C h a n g e n w (ra d /s e c o n d ) me n second x -5 Fg 8 Change n for normal load me n second Fg 9 Change n for normal load E-ISSN: 4-5X 9 Issue, Volume 8, Aprl

8 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm 6 Response for heavy load condton: Fgs, show the system response at heavy loadng condton wth fxng the controller parameters From these fgures, t can be seen that the response wth the proposed shows good dampng characterstcs to low frequency oscllatons and the system s more quckly stablzed than and he mean settlng tme of oscllaton s =, 4, and 96 s second for,, and respectvely Hence, the proposed extend the power system stablty lmt C hange n w (rad/s ec ond) x me n second Fg Change n for heavy load C hange n w (rad/s ec ond) - x me n second Fg Change n for heavy load 64 Response for severe dsturbance: he effectveness of the proposed s verfed by applyng a three phase fault of 6 cycle duraton at second near bus 7 Fgs -4, show the response of and due to severe dsturbance for normal loadng condton From these fgures, t s can be seen that the BSO based PSSs usng the proposed objectve functon acheves good robust performance and provdes superor dampng n comparson wth the other methods 5 x -5 5 x - C hange n w (rad/s ec ond) C hange n w (rad/s ec ond) me n second Fg Change for heavy load Fg Change n me n second for severe dsturbance E-ISSN: 4-5X 9 Issue, Volume 8, Aprl

9 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm C hange n w (rad/s ec ond) x me n second 65 Robustness and performance ndex: o demonstrate the robustness of the proposed controller, a performance ndex: the Integral of the me multpled Absolute value of the Error (IAE) s beng used as: IAE = t w w w dt (8) It s worth mentonng that the lower the value of ths ndex s, the better the system response n terms of tme doman characterstcs Numercal results of performance robustness for all cases are lsted n able (5) It can be seen that the values of these system performance wth the are smaller compared to that of and hs demonstrates that the overshoot, undershoot, settlng tme and speed devatons of all unts are greatly reduced by applyng the proposed BSO based tuned PSSs able (5) Values of performance ndex IAE * -4 Lght load Normal load Heavy load Fg 4 Change n for severe dsturbance 7 Conclusons hs paper proposes a new optmzaton algorthm known as BSO, whch synergstcally couples the BFOA wth the PSO for optmal desgnng of PSSs controller he desgn problem of the proposed controller s formulated as an optmzaton problem and BSO s employed to search for optmal controller parameters An egenvalue based objectve functon reflectng the combnaton of dampng factor and dampng rato s optmzed for dfferent operatng condtons Smulatons results assure the effectveness of the proposed controller n provdng good dampng characterstc to system oscllatons over a wde range of loadng condtons Also, these results valdate the superorty of the proposed method n tunng controller compared wth PSO and BFOA over wde range of operatng condtons 8 References [] P Kundur, Power System Stablty and Control, McGraw-Hll, 994 [] P Kundur, M Klen, G J Rogers, and M S Zywno, Applcaton of Power System Stablzers for Enhancement of Overall System Stablty, IEEE ransactons on Power System, Vol 4, No, 989, pp [] M A Abdo, Pole Placement echnque for PSS and CSC based Stablzer Desgn Usng Smulated Annealng, Electrcal Power and Energy Systems, Vol, No 8,, pp [4] YL Abdel Magd, and MA Abdo, Coordnated Desgn of a PSS and a SVC Based Controller to Enhance Power System Stablty, Int J of Electrcal Power and Energy System, Vol 5, No 9,, pp [5] YL Abdel Magd and M A Abdo, Robust Coordnated Desgn of Exctaton and CSC Based Stablzers Usng Genetc Algorthms, Int J of Electrcal Power and Energy Systems, Vol 69, No -, 4, pp 9-4 [6] H A olyat, J Sadeh, and R Ghaz, Desgn of Augmented Fuzzy Logc Power System Stablzers to Enhance Power Systems Stablty, IEEE ransactons on Energy converson, Vol, No, March 996, pp 97- [7] P Shrkant, and I Sen, Robust Pole Placement Stablzer Desgn Usng Lnear Matrx Inequaltes, IEEE ransactons on Power System, Vol 5, No, February, pp - 9 [8] M A Abdo, Optmal Desgn of Power System Stablzers Usng Partcle Swarm Optmzaton, IEEE ransactons on Energy Converson, Vol 7, No, September, pp 46-4 [9] Y L Abdel-Magd and M A Abdo, Optmal Mult-Objectve Desgn of Robust Power System Stablzers Usng Genetc Algorthms, IEEE ransactons on Power Systems, Vol 8, No, August, pp 5 E-ISSN: 4-5X 9 Issue, Volume 8, Aprl

10 WSEAS RANSACIONS on POWER SYSEMS E S Al, S M Abd-Elazm [] S Mshra, M rpathy, and J Nanda, "Multmachne Power System Stablzer Desgn by Rule Based Bactera Foragng", Int J of Electrc Power Systems Research, Vol 77, No, October 7, pp [] S Panda, and N P Padhy, Robust Power System Stablzer Desgn usng Partcle Swarm Optmzaton echnque, Int J of Electrcal and Electroncs Engneerng, Vol, No, 8, pp -8 [] K Sebaa, and M Boudour, Optmal Locatons and unng of Robust Power System Stablzer Usng Genetc Algorthms, Int J of Electrc Power Systems Research, Vol 79, No, February 9, pp [] R A Ramos, Stablty Analyss of Power Systems Consderng AVR and PSS Output Lmters, Int J of Electrcal Power and Energy Systems Vol, No 4, May 9, pp 5-59 [4] H Shayegh, H A Shayanfar, A Safar, and R Aghmasheh, A Robust PSSs Desgn Usng PSO n a Multmachne Envronment, Int J of Energy Converson and Management, Vol 5, No 4,, pp [5] H Bevran, Hyama, and H Bevran, Robust PID Based Power System Stablzer: Desgn and Real-me Implementaton, Int J of Electrcal Power and Energy Systems, Vol, No, February, pp [6] G Rgatos, and P Sano, Desgn of Robust Electrc Power System Stablzers Usng Khartonov s heorem, Int J of Mathematcs and Computers n Smulaton, Vol 8, No, September, pp 8-9 [7] E S Al, and S M Abd-Elazm, Coordnated Desgn of PSSs and CSC va Bacteral Swarm Optmzaton Algorthm n a Multmachne Power System", Int J of Electrcal Power and Energy Systems, Vol 6, No, March, pp 84-9 [8] J Kennedy and R Eberhart, Partcle Swarm Optmzaton, Proceedngs of IEEE Int Conference on Neural Networks, 995, pp [9] D P Rn, S M Shamsuddn, and S S Yuhanz, Partcle Swarm Optmzaton: echnque, System and Challenges, Int J of Computer Applcatons, Vol 4, No, January, pp 97 [] V Selv, and R Umaran, Comparatve Analyss of Ant Colony and Partcle Swarm Optmzaton echnques, Int J of Computer Applcatons, Vol 5, No 4, August, pp - 6 [] K M Passno, Bommcry of Bacteral Foragng for Dstrbuted Optmzaton and Control, IEEE Control System Magazne, Vol, No, June, pp 5-67 [] S Mshra, A Hybrd Least Square Fuzzy Bactera Foragng Sstrategy for Harmonc Estmaton, IEEE ransactons Evolutonary Computer, Vol 9, No, February 5, pp 6-7 [] D B Fogel, Evolutonary Computaton towards a New Phlosophy of Machne Intellgence, IEEE, New York, 995 [4] E S Al, and S M Abd-Elazm, Bactera Foragng Optmzaton Algorthm Based Load Frequency Controller for Interconnected Power System, Int J of Electrcal Power and Energy Systems, Vol, No, March, pp 6-68 [5] A Bswas, S Dasgupta, S Das, and A Abraham, Synergy of PSO and Bacteral Foragng Optmzaton: A Comparatve Study on Numercal Benchmarks, Innovatons n Hybrd Intellgent Systems, ASC 44, 7, pp 556 [6] W Koran, Bacteral Foragng Orented by Partcle Swarm Optmzaton Strategy for PID unng, GECCO 8, July -6, 8, Atlanta, Georga, USA, pp 8-86 [7] P M Anderson and A A Fouad, Power System Control and Stablty, Iowa State Unversty Press, Iowa, 977 Appendx he system data are as shown below: a) Exctaton system: K 4; A 5 second; A K f 5; f second b) Bactera parameters: Number of bactera =; number of chemotatc steps =; number of elmnaton and dspersal events = ; number of reproducton steps = 4; probablty of elmnaton and dspersal = 5 c) PSO parameters: C = C =, =9 E-ISSN: 4-5X 94 Issue, Volume 8, Aprl