Adaptive Neuro-Fuzzy Approach for the Power System Stabilizer Model in Multi-machine Power System

Transcription

1 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: 02 6 Adaptve Neuro-Fuzzy Approach for the Poer System Stablzer Model n Mult-machne Poer System Agus Jamal and Ramadon Syahputra Abstract Ths paper proposes an adaptve neuro-fuzzy approach for desgnng robust poer system stablzers (PSS) n order to mprove the stablty of a mult-machne poer system under fault condtons. Smulatons ere carred out usng several fault tests at transmsson lne on a To-Area Mult-machne Poer System that conssts of four machne and ten buses. The system s smulated n Smulnk Softare hle the PSS s mplemented usng Fuzzy Logc Toolbox n Matlab. As a reference the PSS model, Delta PSS has been used for comparson th the PSS under consderaton. The result shos that poer transfer response usng the model s more robust than Delta PSS, especally for both sngle lne to ground fault and symmetrcal three phase fault. Index Terms Poer system stablzer, transent stablty, mult-machne poer system, neuro-fuzzy adaptve. P I. INTRODUCTION oer system oscllatons, especally lo frequency electromechancal oscllatons have been a major concern n poer system plannng and operaton. On the other hand, ncreasng operatng and mantenance costs as ell as contnuously ncreasng demand on electrcal energy has forced poer companes to call upon all of ther nstalled capactes despte rapdly fluctuatng operatng condtons. These reasons and the apparton of lo frequency local and nter area oscllatons hnderng poer flo have caused reneed nterest n robust PSS technques. Lo frequency oscllatons are detrmental to the goals of maxmum poer transfer and optmal poer system securty. A contemporary soluton to ths problem s the addton of poer system stablzers (PSS) to the automatc voltage regulators on the generators n the poer system. The dampng provded by ths addtonal stablzer provdes the means to reduce the nhbtng effects of the oscllatons. For large scale poer systems comprsng of many nterconnected machnes, the PSS parameter tunng s a complex exercse due to the presence of several poorly damped modes of oscllaton. The problem s further beng complcated by contnuous varaton n poer system operatng condtons. In the smultaneous tunng approach, exhaustve computatonal Manuscrpt receved n March 6, 2012, revsed n Aprl 2, Agus Jamal s th the Department of Electrcal Engneerng, Faculty of Engneerng, Unverstas Muhammadyah Yogyakarta, Yogyakarta. Indonesa. (phone: ; e-mal: ajamal_me@ yahoo.co.d). Ramadon Syahputra s th the Department of Electrcal Engneerng, Faculty of Engneerng, Unverstas Muhammadyah Yogyakarta, Yogyakarta. Indonesa. (phone: ; e-mal: ramadons@ ymal.com). tools are requred to obtan optmum parameter settngs for the PSS, hle n the case of sequental tunng, although the computatonal load s feer, evaluatng the tunng sequence s an addtonal requrement. There s a further problem of egenvalue drft. Among technques to enhance poer flo, poer system stablzers have been used th feld proven effcent for more than 80 years resultng n savngs of mllons of dollars [1]. PSS have been nstalled n many countres n the early 60s hch tnessed the expanson of system exctaton task by usng auxlary stablzng sgnals to control the feld voltage to damp system oscllatons n addton to the termnal voltage error sgnal. Ths part of exctaton control has been coned as PSS,.e. poer system stablzer [2]. Early PSS ere bascally statc phase lead compensators nserted ahead of the regulator excter to supply supplementary stablzng sgnals to compensate for the large phase lag ntroduced by the exctaton system. Yet rapdly fluctuatng loadng condtons requre a more ntellgent and more robust approach. Advances n so called ntellgent control [3] have thrusted forard ther applcatons n poer system control drven by progress n computng technology as ell as theoretcal advances methodologes based on hnan ntellgence emulatng algorthms such as fuzzy systems, artfcal neural netorks, genetc algorthms, etc. Ne trends ere set n PSS leadng to a profuson of papers amd hch Kothar et al. [4] ho developed a varable structure poer system stablzer th desred egenvalues n the sldug mode. Harr and Malk [5] combned fuzzy control th learnng proprety of neural netork to elaborate a PSS hch could lead the equlbrum state to be trapped nto local mnma. Hoang and Tomosovc [6] ntroduced an adaptve fuzzy PSS th 49 fuzzy rules. Abdo and Abdel-Magd [7] made use of an evolutonary programmng algorthm to calculate the optmal values of a classcal lead-lag PSS. Rashd et al. [8] n hch autbors proposed to adapt the gan of the dscontnuous component of the control sgnal used n the sldng mode controller usng a fuzzy nference system augmented by lnear state feedback appled to a sldng surface th an ntegral term. Elshafe et al. [9] proposed poer system stablzaton usng fuzzy logc and drect adaptve technque. Hossen-Zadeh and Kalam [10] developed an ndrect adaptve ndrect fuzzy. Elshafe et al. [11] extended the drect adaptve fuzzy approach to nclude stablzaton of mult-machne poer systems. An ntellgent robust PSS combnng advantages of fuzzy logc and sldng mode control callng upon a fuzzy supervsor to contnuously modulate ther respectve control IJECS-IJENS Aprl 2012 IJENS

2 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: 02 7 acton s proposed n ths study. Frst a fuzzy stablzer s developed as ell as a sldng mode PSS usng pole placement technque n the sldng mode [4] are elaborated to enhance oscllatons dampng n a sngle machne poer system connected to an nfnte bus through a double lne feeder. Contnuous acton of both separate stablzers s managed through a fuzzy supervsor that enforces SMC acton hen aay from the equlbrum pont and emphaszes FLC acton hen near the steady-state stuaton greatly reducng chatterng. Frale-Ardanuy and Zufra [12] proposed an adaptve poer system stablzer usng ANFIS and Genetc Algorthms. Genetc algorthms are used to tune a conventonal PSS and then, the relatonshp beteen these operatng ponts and the PSS parameters s learned by the ANFIS. The PSS has been tested on a synchronous machnenfnte bus model. In ths research, an adaptve neuro-fuzzy based for PSS desgn n order to mprove the stablty of poer system s presented. Smulatons ere carred out usng several fault tests at transmsson lne on a To-Area Mult-machne Poer System. The smulaton has been tested on a four machne ten bus poer system. Smulaton of a neuro-fuzzy PSS and a Delta PSS of a poer system, under normal load, s presented. A fuzzy supervsory controller s then added to modulate control acton of the prevous developed PSS. Dscusson of smulaton s then presented and results are compared to neuro-fuzzy PSS and to Delta PSS to assess chatterng reducton and performance enhancements folloed by ths study. A. Poer System Stablzer II. FUNDAMENTAL THEORY The basc functon of a poer system stablzer s to extend stablty lmts by modulatng generator exctaton to provde dampng to the oscllaton of synchronous machne rotors relatve to one another. The oscllatons of concern typcally occur n the frequency range of approxmately 0.2 to 3.0 Hz, and nsuffcent dampng of these oscllatons may lmt ablty to transmt poer. To provde dampng, the stablzer must produce a component of electrcal torque, hch s n phase th the speed changes. The mplementaton detals dffer, dependng upon the stablzer nput sgnal employed. Hoever, for any nput sgnal, the transfer functon of the stablzer must compensate for the gan and phase of exctaton system, the generator and the poer system, hch collectvely determnes the transfer functon from the stablzer output to the component of electrcal torque hch can be modulated va exctaton system [13]. Implementaton of a poer system stablzer mples adjustment of ts frequency characterstc and gan to produce the desred dampng of the system oscllatons n the frequency range of 0.2 to 3.0 Hz. The transfer functon of a generc poer system stablzer may be expressed as Tω s(1 + st1 )(1 + st3 ) GP ( s) = K G ( s) (1) s f (1 + T s)(1 + st )(1 + st ) ω here Ks represents stablzer gan and Gf (s) represents combned transfer functon of torsonal flter (f requred) and nput sgnal transducer. The stablzer frequency characterstc s adjusted by varyng the tme constant T, T 1, 2 4 T 2, T 3 and T 4. A torsonal flter may not be necessary th sgnals lke poer or delta-p-omega sgnal [14]. A poer system stablzer can be most effectvely appled f t s tuned th an understandng of the assocated poer characterstcs and the functon to be performed by the stablzer. Knoledge of the modes of poer system oscllaton to hch the stablzer s to provde dampng establshes the range of frequences over hch the stablzer must operate. Smple analytcal models, such as that of a sngle machne nfnte bus (SMIB) system, can be useful n determnng the frequences of local mode oscllatons durng the plannng stage of a ne plant. It s also desrable to establsh the eak poer system condtons and assocated loadng for hch stable operaton s expected, as the adequacy of the poer system stablzer applcaton ll be determned under these performance condtons. Snce the lmtng gan of the some stablzers, vz., those havng nput sgnal from speed or poer, occurs th a strong transmsson system, t s necessary to establsh the strongest credble system as the tunng condton for these stablzers. Experence suggest that desgnng a stablzer for satsfactory operaton th an external system reactance rangng from 20% to 80% on the unt ratng ll ensure robust performance [15]. B. Adaptve Neuro-Fuzzy Method Adaptve neuro-fuzzy method (or Adaptve neuro-fuzzy nference system, ANFIS) has been became a popular method n control area. In ths secton, e gve a bref descrpton of the prncples of Adaptve neuro-fuzzy nference system (ANFIS) hch are refered to [16]. The basc structure of the type of fuzzy nference system could be seen as a model that maps nput characterstcs to nput membershp functons. Then t maps nput membershp functon to rules and rules to a set of output characterstcs. Fnally t maps output characterstcs to output membershp functons, and the output membershp functon to a snglevalued output or a decson assocated th the output. It has been consdered only fxed membershp functons that ere chosen arbtrarly. Fuzzy nference s only appled to only modelng systems hose rule structure s essentally predetermned by the user's nterpretaton of the characterstcs of the varables n the model. Hoever, n some modelng stuatons, t cannot be dstngush hat the membershp functons should look lke smply from lookng at data. Rather than choosng the parameters assocated th a gven membershp functon arbtrarly, these parameters could be chosen so as to talor the membershp functons to the nput/output data n order to account for these types of varatons n the data values. In such case the necessty of the adaptve neuro fuzzy nference system becomes obvous. The neuro-adaptve learnng method orks smlarly to that of neural netorks. Neuro-adaptve learnng technques provde a method for the fuzzy modelng procedure to learn nformaton about a data set. It computes the membershp functon parameters that best allo the assocated fuzzy nference system to track the gven nput/output data. A netork-type structure smlar to that of a neural netork can be used to nterpret the nput/output map so t maps nputs through nput membershp functons and assocated parameters, and then through output membershp functons and assocated parameters to outputs,. The parameters IJECS-IJENS Aprl 2012 IJENS

3 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: 02 8 assocated th the membershp functons changes through the learnng process. The computaton of these parameters (or ther adjustment) s facltated by a gradent vector. Ths gradent vector provdes a measure of ho ell the fuzzy nference system s modelng the nput/output data for a gven set of parameters. When the gradent vector s obtaned, any of several optmzaton routnes can be appled n order to adjust the parameters to reduce some error measure (performance ndex). Ths error measure s usually defned by the sum of the squared dfference beteen actual and desred outputs. ANFIS uses a combnaton of least squares estmaton and back propagaton for membershp functon parameter estmaton. The suggested ANFIS has several propertes: 1. The output s zero th order Sugeno-type system. 2. It has a sngle output, obtaned usng eghted average defuzzfcaton. All output membershp functons are constant. 3. It has no rule sharng. Dfferent rules do not share the same output membershp functon, namely the number of output membershp functons must be equal to the number of rules. 4. It has unty eght for each rule. Fg. 1 shos Sugeno s fuzzy logc model. Fg. 2 shos the archtecture of the ANFIS, comprsng by nput, fuzzfcaton, nference and defuzzfcaton layers. The netork can be vsualzed as consstng of nputs, th N neurons n the nput layer and F nput membershp functons for each nput, th F*N neurons n the fuzzfcaton layer. There are F N rules th F N neurons n the nference and defuzzfcaton layers and one neuron n the output layer. For smplcty, t s assumed that the fuzzy nference system under consderaton has to nputs x and y and one output z as shon n Fg. 2. For a zero-order Sugeno fuzzy model, a common rule set th to fuzzy f-then rules s the follong: Rule 1: If x s A 1 and y s B 1, Then f 1 = r 1 (2) Rule 2: If x s A 2 and y s B 2, Then f 2 = r 2 (3) µ µ A 1 B 1 1 f 1 = p 1 x + q 1 y + r 1 x y µ µ A 2 B 2 2 f 2 = p 2 x + q 2 y + r 2 x y Fg. 1. Sugeno s fuzzy logc model f = Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 x y A 1 A 2 B 1 B N N 1 2 x y x y f Fg. 2. The archtecture of the ANFIS IJECS-IJENS Aprl 2012 IJENS

4 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: 02 9 Here the output of the th node n layer n s denoted as O n, : Layer 1. Every node n ths layer s a square node th a node Ofuncton: 1 = µa (x), for = 1, 2, (4) or, O 1 = µb -2 (y), for = 3, 4 (5) here x s the nput to node-, and A s the lngustc label (small, large, etc.) O1 assocated th ths node functon. In other ords, s the membershp functon of A and t specfes the degree to hch the gven x satsfes the quantfer A. Usually µa(x) s chosen to be bell-shaped th maxmum equal to 1 and mnmum equal to 0, such as the generalzed bell functon: 1 µ A (x) = (6) 2b x c 1 + a Parameters n ths layer are referred to as premse parameters. Layer 2. Every node n ths layer s a crcle node labeled Π hch multples the ncomng sgnals and sends the product out. OFor nstance, 2 = = µa(x) x µb(y), = 1, 2. (7) Each node output represents the frng strength of a rule. (In fact, other T-norm operators that performs generalzed AND can be used as the node functon n ths layer.) Layer 3. Every node n ths layer s a crcle node labeled N. The -th node calculates the rato of the -th rule s frng strength to the sum of all rules frng strengths: O 3 = =, = 1, 2. (8) For convenence, outputs of ths layer ll be called called normalzed frng strengths. Layer 4. Every node n ths layer s a square node th a node functon: 4 O = f = (p x + q y + r ) (9) here s the output of layer 3, and {p, q, r } s the parameter set. Parameters n ths layer ll be referred to as consequent parameters. Layer 5. The sngle node n ths layer s a crcle node labeled Σ that computes the overall output as the summaton of all ncomng sgnals,.e., 5 O f (10) = III. METHODOLOGY The procedure of ths research s shon n Fg. 3. The smulaton envronment based on MATLAB softare package s selected. It s used as the man engneerng tool for performng modelng and smulaton of mult-machne poer systems, as ell as for nterfacng the user and approprate smulaton programs. MATLAB has been chosen due to avalablty of the poerful set of programmng tools, sgnal processng, numercal functons, and convenent user-frendly nterface. In ths specally developed smulaton envronment, the evaluaton procedures can be easly performed. We have used Fuzzy logc Toolbox of MATLAB to develop the ANFIS model th 4 nputs and sngle output as gven n Fg. 6. Start Lterature study Create the multmachne poer system model Create the Neuro-Fuzzy Based PSS Examne the Neuro-Fuzzy Based PSS Examne the short crcut fault on the multmachne thout PSS Examne the short crcut fault on the multmachne th PSS Examne other PSS? Fg. 3. Procedure of the research. IV. EXPERIMENTAL RESULTS A. Mult-machne Poer System The mult-machne poer system s shon n Fg. 4 that conssts of to fully symmetrcal areas lnked together by to 230 kv lnes of 220 km length. Each area s equpped th to dentcal round rotor synchronous acts as thermal plant generators rated 20kV/900MVA connected to transformer (T 1, T 2, T 3, and T 4 ). The synchronous machnes (M 1, M 2, M 3, and M 4 ) n all area have dentcal parameters, except for nerta hch s H = 6.5s for all generators n Area No Analyze performance of the PSS Concluson Fnsh Yes IJECS-IJENS Aprl 2012 IJENS

5 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: and H = 6.175s for all generators n Area 2. Thermal generatng plants havng dentcal speed regulators and fast statc excters th a 200 gan at all locatons. Each generator produces 700 MW. The loads are assumed everyhere as constant mpedance load. The Area 1 and Area 2 loads are 967 MW (L 1 ) and 1767 MW (L 2 ) respectvely. The load voltage profle as mproved by nstallng 187 MVAr capactors (C 1 and C 2 ) n each area to make closer to unty. Area 1 s exportng to Area 2 through to te-lnes and a sngle te-lne th poer transfer level 413 MW and 353 MW, respectvely. Varous ANFIS are desgned for PSS to extend stablty lmts by modulatng generator exctaton to provde dampng to the oscllaton of synchronous machne rotors relatve to one another. Membershp functon of nputs varable for PSS s shon n Fg. 5, hle the structure of Sugeno type ANFIS for PSS s shon n Fg Tranng the ANFIS. Varous netork confguratons ere traned n order to establsh an approprate netork th satsfactory performances. The ANFIS s are traned to detect presence of fault, classfy fault and fnally hen the stablty system s acheved. Fg. 4. Multmachne poer system. B. Adaptve Neuro-Fuzzy PSS The desgn process of the Adaptve Neuro-Fuzzy (ANFIS) for PSS go through the follong steps: 1. Generaton a sutable tranng data. In order to use the ANFIS technque for poer system stablty usng PSS, the nput parameters lmt should be determned precsely. The nput parameters are obtaned from recordng devces sparsely located at sendng end n a poer system netork. Due to lmted avalable amount of practcal fault data of transmsson lnes, t s necessary to generate tranng/testng data usng smulaton. To generate data for the typcal transmsson system, a computer program have been desgned to generate tranng data for dfferent faults. 2. Selecton of a sutable ANFIS structure for a gven applcaton. Fg. 5. Membershp functon of Inputs Varable for PSS Fg. 6. Structure of Sugeno type ANFIS for PSS. Fg. 7. Poer transfer from Area1 to Area IJECS-IJENS Aprl 2012 IJENS

6 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: Fg. 8. Performace of Delta PSS for angle speed of machne (ω), actve poer of machne (P a ), and termnal voltage of machne hen sngle lne to ground fault occurs n transmsson lne. Fg. 9. Performace of Neuro-Fuzzy based PSS for angle speed of machne (ω), actve poer of machne (P a ), and termnal voltage of machne hen sngle lne to ground fault occurs n transmsson lne. Fg. 10. Performace of Delta PSS for angle speed of machne (ω), actve poer of machne (P a ), and termnal voltage of machne hen symmetrcal three phase fault occurs n transmsson lne IJECS-IJENS Aprl 2012 IJENS

7 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: Fg. 11. Performace of Neuro-Fuzzy based PSS for angle speed of machne (ω), actve poer of machne (P a ), and termnal voltage of machne hen symmetrcal three phase fault occurs n transmsson lne. 4. Evaluaton of the traned ANFIS usng test patterns untl ts performance s satsfactory. When Netork s traned, ANFIS s should be gven an acceptable output for unseen data. When output of test pattern and netork s error reached an acceptable range then, fuzzy system s adjusted n the best stuaton hch means the membershp functons and fuzzy rules are ell adjusted. All of these steps above are done off-lne and hen the structure and parameters of ANFIS are adjusted, t can be used as an on-lne the PSS. In ths smulaton, mult-machne poer system s demonstrated under a sngle lne to ground fault smulaton and then cleared th openng breaker on lne hch fault occurred. Dsconnectng one of to te-lne transmsson lnes can change the area poer transfer level nto snglelne poer transfer level. System ll oscllate to ts ne stable pont, durng that tme system parameters ll devate. Poer transfer from Area1 to Area2, voltage devaton response at M 1, and poer armature devaton response at M 1 are observed and shon n Fg. 7. Fg. 8 shos the performance of Delta PSS for angle speed of machne (ω), actve poer of machne (P a ), and termnal voltage of machne hen sngle lne to ground fault occurs n transmsson lne. The mult-machne poer system has achevng the stablty state n 5s, although the system has oscllatng n 3s. The Delta PSS need to mprove n order to stable the mult-machne poer system more robust. The poerful of Neuro-Fuzzy based PSS s shon n Fg. 9. In Fg. 9, the PSS has successfully created the stablty of mult-machne poer system n 3s, although the system has oscllatng n 2s. The tme for stablty s faster than Delta PSS. Therefore, Neuro-Fuzzy based PSS more robust than Delta PSS n order to acheve the stablty of mult-machne poer system. Fg. 10 shos the performance of Delta PSS for angle speed of machne (ω), actve poer of machne (P a ), and termnal voltage of machne hen symmetrcal three phase fault occurs n transmsson lne. The mult-machne poer system has achevng the stablty state n 7s, although the system has oscllatng n 4s. The Delta PSS need to mprove n order to stable the mult-machne poer system more robust. The poerful of Neuro-Fuzzy based PSS s shon n Fg. 9. In Fg. 11, the PSS has successfully created the stablty of mult-machne poer system n 4s, although the system has oscllatng n 3s. The tme for stablty s faster than Delta PSS. Therefore, Neuro-Fuzzy based PSS more robust than Delta PSS n order to acheve the stablty of mult-machne poer system. V. CONCLUSIONS In ths study, e present an adaptve neuro-fuzzy approach for the desgn of poer system stablzer (PSS). The PSS has been tested on a to-area mult-machne poer system that conssts of four machnes and ten buses under several fault condtons. Smulaton for to dfferent fault condtons seems to ndcate that the approach puts to good use the advantages of the PSS model. Smulaton test shoed the effectveness of the robustness of the proposed adaptve neuro-fuzzy based PSS, especally for both sngle lne to ground fault and symmetrcal three phase fault. ACKNOWLEDGMENTS The author s gratefully acknoledge the contrbutons of the Drectorate General of Hgher Educaton (DIKTI), Mnstry of Educaton and Culture, Republc of Indonesa, for fundng n ths research under Compettve Research Grant (Program Peneltan Hbah Bersang), Number of Contract: 111/SP2H/PL/Dt.Ltabmas/IV/2011. REFERENCES [1] Berube, G.R., L. Hajagos and R. Beauleu, Practcal Utlty Experence th Applcaton of Poer System Stablzers. IEEE PES Workng Group Panel Presentaton on Poer System Stablzers. [2] Kundur. P Poer System Stablty and Control, McGra-Hll. [3] Saadat, H Poer System Analyss, McGra-Hll, Sngapore. [4] Kothar. M.L.. J. Nanda and K. Bhattacharya Desgn of varable structure poer system stablzers th desred egenvalues n the sldng mode. IEEE. Froc. Generaton Trans. Dstrbut., 140: [5] Harr. A and O.P. Malk Adaptve-Netork-Based Fuzzy Logc Poer System Stablzer. IEEE Wescanex 95. Proceedngs Wescanex. pp: IJECS-IJENS Aprl 2012 IJENS

8 Internatonal Journal of Electrcal & Computer Scences IJECS-IJENS Vol: 12 No: [6] Hoang, P. and K. Tomosovc, Desgn and Analyss of an Adaptve Fuzzy Poer System Stablzer. IEEE Transacton Energy Converson, Vol. 11. [7] Abdo. M.A. and y.l. Abdel-Magd Desgn of poer system stablzers usng evolutonary programmng. IEEE Transacton on Energy Converson, Vol. 17. [8] Rashd. F., M. Rashd and H. Amr An adaptve fuzzy sldng mode control for poer system stablzer. Industral E1ectroncs Socety. IECON. The 29th Ann. Conf. IEEE. 1: [9] E1shafe. AL.. K. E1-Metal1y andaa Sha1tout A varable structure adaptve fuzzy logc stablzer for sngle and mult-machne poer systems. Control Engneerng Practce, Elsever, 13: [10] Hossen-Zadeh. N. and A Ka1am An ndrect adaptve fuzzylogc poer system stablzer, Elsever. Elec. Poer and Energy Sys., 24: [11] E1shafe. AL.. K. E1-Metal1y andaa Sha1tout A varable structure adaptve fzzy logc stablzer for sngle and mult-machne poer systems. Control Engneerng Practce, Elsever, 13: [12] Frale-Ardanuy, J. and P.J.Zufra Adaptve Poer System Stablzer Usng ANFIS and Genetc Algorthms, Proceedngs of the 44th IEEE Conference on Decson and Control, and the European Control Conference 2005 Sevlle, Span, December 12-15, 2005, pp [13] Jyothsna, T.R., & Vasakh, K Mult-objectve Evolutonary Programmng Based Desgn of PSS, SVC, and TCSC for Transent Stablty Improvement, Proceedngs of World Academy of Scence: Engneerng & Technology; 39, [14] Mahabuba, A., & Khan, M.A Optmal Locaton of Poer System Stablzers n a Multmachne Poer System Usng Relatve Gan Array (RGA) and Genetc Algorthm (GA). Internatonal Journal of Electrcal and Poer Engneerng, 2(1), [15] Henche, A., Kama, I., & Grondn, R Torsonal-mode dentfcaton for turbogenerators th applcaton to PSS tunng, Proceedng os Internatonal Conference on Poer Systems Transents, Montreal, Paper No. IPST [16] Jang, J.S.R., 1993, "ANFIS: Adaptve-Netork-based Fuzzy Inference System", IEEE Trans. Syst., Man, Cybern., 23, , June. Authors Agus Jamal as born n Bumayu, Central Java, Indonesa, on August 29, He receved both B.Sc. degree and M.Eng. degree from Department of Electrcal Engneerng, Unverstas Gadjah Mada, Yogyakarta, Indonesa, n 1994 and 2010, respectvely. He s a Lecturer n the Department of Electrcal Engneerng, Faculty of Engneerng, Unverstas Muhammadyah Yogyakarta (UMY), Indonesa. Hs research nterests are n poer system operaton, poer system stablty, poer system control, electrcal machne analyss, and reneable energy. Ramadon Syahputra as born n Del Serdang, North Sumatera, Indonesa, on October 10, He receved B.Sc. degree from Department of Electrcal Engneerng, Insttut Teknolog Medan and M.Eng. degree from Department of Electrcal Engneerng, Unverstas Gadjah Mada, Yogyakarta, Indonesa n He s a Lecturer n the Department of Electrcal Engneerng, Faculty of Engneerng, Unverstas Muhammadyah Yogyakarta (UMY), Indonesa. Hs research nterests are n poer system operaton, computatonal of poer system, artfcal ntellgence n poer system, poer system control, poer qualty, dstrbuted generaton, and reneable energy IJECS-IJENS Aprl 2012 IJENS