A FUZZY WAVELET NEURAL NETWORK LOAD FREQUENCY CONTROLLER BASED ON GENETIC ALGORITHM

Transcription

1 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE) Publshed by Internatonal Organzaton of IOTPE ISSN IJTPE Journal June 22 Issue Volume 4 Number 2 Pages 89 A FUZZY WAVELET NEURAL NETWORK LOAD FREQUENCY CONTROLLER BASED ON GENETIC ALGORITHM M. Shahrar Kahesh F. Sheholeslam Electrcal Engneerng Department, Faculty of Engneerng, Isfahan Unversty of Technology, Isfahan, Iran m.shahryarahesh@ec.ut.ac.r, sheh@cc.ut.ac.r Abstract- In ths paper, a self tunng load frequency controller based on Fuzzy Wavelet Neural Networ (FWNN) and Genetc Algorthm (GA) s developed to quench the devatons n frequency and te lne power due to load dsturbances n an nterconnected power system. The error between desred system output and output of control object s employed to tune the networ parameters. Tunng rule s accomplshed based on GA approach by mnmzng a compound of control error. For the purpose of the proposed method s evaluaton, the proposed method s appled to a two area power system wth consderatons regardng governor saturaton and the results are compared to the one obtaned by a classc PI controller. Moreover, the robustness of the proposed method s tested aganst change of parameters. The smulaton studes show that the desgned controller by proposed method has a very desrable dynamc performance, better operaton and mproved system parameters such as settlng tme and step response rse tme even when the system parameters change. Keywords: Fuzzy Wavelet Neural Networ, Load Frequency Controller, Genetc Algorthm. I. INTRODUCTION Load Frequency Control (LFC) has been one of the major ssues n electrc power system desgn and operaton and s becomng much more sgnfcant recently n accordance wth ncreasng sze, changng structure and complexty of modern nterconnected power systems. The prmary objectve of the LFC n an nterconnected power system s to mantan reasonably unform frequency for dvdng the load between generators of each area and to eep the te-lne power nterchanges to permssble lmts n the presence of modelng uncertantes, system nonlneartes and area load dsturbances []. The conventonal proportonal-ntegral (PI) control s probably the most commonly used technque n load frequency control problem. The man dsadvantage of ths method s that the dynamc performance of the system s hghly dependent on the selecton of ts gan. Moreover, due to the nonlnearty of power systems, unpredctablty of load varatons and errors n the modelng, the operatng ponts of a power system may vares very remarably and randomly durng a daly cycle. As a result, a fxed controller based on classcal theory may no longer be sutable n all operatng condtons for LFC problem. Durng the past decades, several control approaches have been proposed and appled to the LFC desgn problem ncludng; optmal control, adaptve control, model predctve control, sldng mode control and robust control whch can be found n [2], respectvely. Each of these technques has ther own advantages and dsadvantages. More recently, there has been a growng concern n Artfcal Intellgence (AI) technques, such as fuzzy logc control (FLC) [7], Artfcal Neural Networ (ANN) [8] and Bologcally Inspred (BI) algorthms [9-3] to desgn of load frequency controller n a power system by the researches around the world. Recently, based on the combnaton of feed-forward neural networs and wavelet decompostons, wavelet neural networ (WNN) has receved a lot of attenton and has become a popular tool for functon learnng [4]. The man characterstc of WNN s that some nds of wavelet functon are used as the actvaton functon n the hdden layer of neural networ, so tme frequency property of wavelet s ncorporated nto the learnng ablty of neural networs. However, the man problem of WNN wth fxed wavelet bases s the selecton of wavelet frames because the dlaton and translaton parameters of wavelet bass are fxed and only the weghts are adjustable. Danel et al, [5] have proposed a FWNN based on the wavelet theory, fuzzy concepts and neural networ to mprove functon approxmaton accuracy. The FWNN has mult resoluton capablty, smple structure, hgh approxmaton accuracy and good generalzaton performance. The complexty and uncertanty of the system can be also reduced and handled by the concepts of fuzzy logc. Also, the local detals of non statonary sgnals can be analyzed n terms of the dlaton and translaton parameters of wavelets. Consderng these specfcatons, there are many papers that dscuss the synthess of a fuzzy wavelet neural nference system for functon approxmaton, dentfcaton and control of nonlnear systems [6]. 8

2 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun. 22 In ths paper, a new Load Frequency Controller based on fuzzy wavelet neural networ (FWNN-LFC) s proposed to desgn load frequency controller of a multarea power system wth system parametrc uncertantes. The FWNN s used to construct load frequency controllers. The archtecture of the control system s presented and the parameter update rules of the system are derved. Learnng rules are based on the Genetc Algorthm (GA). The orthogonal least square (OLS) algorthm s used to purfy the wavelets for each rule and determne the number of fuzzy rules and networ dmenson. Furthermore, n order to mprove the functon approxmaton accuracy and general capablty of the FWNN system, a self-tunng process that uses the GA s used to adjust the networ s nonlnear and lnear parameters such as translaton parameter of wavelets, membershp functon characterstc and weghts coeffcents of sub-wnn. The proposed approach s mplemented to a two-area nterconnected power system wth consderatons regardng governor saturaton. The results obtaned by proposed approach are compared wth those obtaned by classc PI controller reported n the lterature. Smulaton studes show that the dynamc performance of the proposed controller s consderably desrable. The paper s organzed as follows: to mae a proper bacground, the basc concepts of the FWNN and GA are brefly explaned n Secton II. The study system whch used n the smulatons studes s gven n secton III. In secton IV, the proposed FWNN-LFC scheme s descrbed. Smulaton results n the study system are provded n secton V and some conclusons are drawn n secton VI. II. AN OVERVIEW OF FWNN AND GA A. Fuzzy Wavelet Neural Networ Structure The FWNN s a mult-layer networ whch ntegrates fuzzy model wth wavelet neural networs. For a multnput-sngle-output (MISO) wth x = [ x,..., x q ] as nput and y as output of the system, a typcal fuzzy wavelet neural networ for approxmatng arbtrary nonlnear functon y can be descrbed by a set of fuzzy rules as follow [5]: R : f x s A and x s A and... and x s A, 2 2 q q T ( ) yˆ = wm ψ t, M x t, = q t q, and M, then ( ) () M z t R w R x R where R ( c) s the th fuzzy rule and x j s the jth nput varable of x. Also yˆ calculates the output of local model for rule R. M and T determne the dlaton parameters and total number of wavelets for the th rule, respectvely. t = [ t, t2,..., t q ], where t j denotes the translaton value of correspondng wavelet. j Fnally, A s the fuzzy set characterzed by the followng Gaussan type membershp functon and Aj ( x j ) s the grade of membershp of x j n A j, where: j pj 2 p j 2 ( x ) ( ) j( j) e, j, j2 A x = p p R (2) where p j represents the center of membershp functon and p j2 determne the wdth and the shape of membershp functon, respectvely. Moreover, wavelets ( ) ψ M, ( ) tx are expressed by the tensor product of -D wavelet functons: ψ M ( ) 2 ( ) M M, t ψ q M 2 ( ) M ψ xj j j= ( x) = 2 (2 x t ) = = 2 (2 t ) By applyng fuzzy nference mechansm and let y ˆ be the output of each sub-wnn, the whole output of FWNN for functon y( x ) s as follows: FWN = c yˆ ( x) = ˆ μ ( x) yˆ (4) where ˆ μ ( x) = μ ( x) and c μ ( x) = q x Aj xj j= (3) μ ( ) = ( ) are the frng strength of the th rule for current nput and satsfes ˆ, μ c = ˆ μ =. Also, ˆ μ determnes the contrbuton degree of the output of the wavelet based model wth resoluton level, M. A good ntalzaton of wavelet neural networs leads to fast convergence. Numbers of methods are mplemented for ntalzng wavelets, such as Orthogonal Least Square (OLS) procedure and clusterng method [9]. In ths paper the OLS algorthm s used to select mportant wavelets and to determne the number of fuzzy rules and networ dmenson. More detals about constructon of FWNN and networ parameter ntalzaton can be found n [9]. The structure of appled FWNN s shown n Fgure. Furthermore, t s mportant to adjust the requred networ parameters n the desgn of dynamc systems. In order to avod tral-and-error, a self-tunng process s used by employng the GA to determne sgnfcant parameters such as dlaton, translaton, weghts, and membershp functons. On the other word, durng the learnng process, these networ parameters are optmzed usng GA. To mae a proper bacground, the concept of GA s gven n the next subsecton. 82

3 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun. 22 Fgure. Structure of FWNN [5] B. Genetc Algorthm A genetc algorthm s a probablstc and populaton search technque that computatonally smulates the process of bologcal evoluton. The GA starts wth a randomly selected ntal populaton of feasble solutons, and then recombnes them n a way to gude ther search to only the most promsng areas of the state space. The changes to the populaton occur through the processes of selecton based on ftness, and alteraton usng crossover and mutaton. The applcaton of selecton and alteraton leads to a populaton wth a hgher proporton of better solutons. The evolutonary cycle contnues untl an acceptable soluton s found n the current generaton of populaton, or some control parameter such as the number of generatons s exceeded. Each feasble soluton s encoded as a chromosome (strng) also called a genotype, and each chromosome s gven a measure of ftness va a ftness (evaluaton or objectve) functon. Durng each generaton, the structures n the current populaton are rated for ther effectveness as doman solutons, and on the bass of these evaluatons, a new populaton of canddate solutons s formed usng specfc genetc operators such as reproducton, crossover, and mutaton Crossover may be regarded as artfcal matng n whch chromosomes from two ndvduals are combned to create the chromosome for the next generaton. Ths s done by splcng two chromosomes from two dfferent solutons at a crossover pont and swappng the splced parts. The dea s that some genes wth good characterstcs from one chromosome may as a result combne wth some good genes n the other chromosome to create a better soluton represented by the new chromosome. Mutaton s a random adjustment n the genetc composton. It s useful for ntroducng new characterstcs n a populaton somethng not acheved through crossover alone. The mutaton operator changes the current value of a gene to a dfferent one. For bt strng chromosome ths change amounts to flppng a bt to a or vce versa. The steps n the typcal genetc algorthm for fndng a soluton to a problem are lsted:. Create an ntal soluton populaton of a certan sze randomly 2. Evaluate each soluton n the current generaton and assgn t a ftness value. 3. Select good solutons based on ftness value and dscard the rest. 4. If acceptable soluton(s) found n the current generaton or maxmum numbers of generatons s exceeded then stop. 5. Alter the soluton populaton usng crossover and mutaton to create a new generaton o solutons. 6. Go to step 2. III. POWER SYSTEM MODEL In actual power system operatons, the load s varyng randomly and contnuously throughout the day. As a result, both frequences n all areas and te-lne power flow between the areas are affected by these load changes at operatng pont. These changes create a msmatch between generatons and demand that result n exact forecast of real power demand cannot be assured. Therefore, for good and stable power system operaton, both the frequency and te-lne power flow should be ept constant aganst the sudden area load perturbatons, system parameter uncertantes and unnown external dsturbances. Therefore, to ensure the qualty of power 83

4 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun. 22 supply, a load frequency controller s needed to restorng the system frequency and the net nterchanges to ther desred values for each control area, stll reman. The area frequency devaton ( Δ f ) and te-lne power devaton ( ΔP te ) are two mportant parameters of nterest. The lnear combnatons of them are nown as area control error (ACE). The measurements of all the generaton and all load n the system for computaton of the msmatch between the generaton and oblgaton n one area s so hard. The msmatch s measured at the area control center by usng ACE. The ACE for the th area s defned as: act s act s ACE = Pte P ( ) te B f f = (5) =ΔPte B Δf act s where P te and P te are the actual and scheduled (manually set) nterchange of th area wth neghborng act areas, respectvely. Also, f and f s are the area s actual and scheduled frequency, n th area, and B s the frequency bas coeffcent of th area that s a negatve number measured n MW per.hz. However, the ACE sgnal often s calculated usng the area frequency response characterstc β nstead of B as follows: ACE =Δ P β Δ f (6) te β = D (7) R In whch D s the dampng rato or the frequency senstvty of the th area s load and R s the regulaton due to governor acton n the th area, or droop characterstc. Also, β s frequency bas constant and should be hgh enough such that each area adequately contrbutes to frequency control [2]. The frequency and nterchanged power are ept at ther desred values by means of feedbac of area control error contanng devaton n frequency and error n telne power, and controllng the prme movers of generators. The man objectve of control system s to damp these varatons to zero as fast and smooth as possble and followng a change n load demand values. A two-area nterconnected power system wth consderng governor lmters s nvestgated n ths study. Each area conssts of three major components, whch are turbne, governor, and generator. The detaled transfer functon bloc dagram of uncontrolled two-area system s shown n Fgure 2 where Δf and Δ f 2 are the frequency devatons n area and area 2 respectvely n Hz. Also Δ P L and Δ P L 2 are the load demand changes n areas and 2 respectvely n per unt. Moreover, T g, T t and M are speed governor tme constant (s), turbne tme constant (s), and power system tme constant (s) of th area, respectvely. The detaled transfer functon models of the speed governors and turbnes are dscussed n []. Typcal data for the system parameters and governor lmters, for nomnal operaton condton, are presented n Table. β β 2 u ACE ACE 2 u R R2 Fgure 2. Two-area nterconnected power system Table. Two Area Interconnected Power System Parameters Area Area Area 2 X X X X T g S T g2 S X X Parameters M=, D =.8, T g =.2, T t =.5, R =.5, X =.4, X =.5, X =.2 X =.4, T 2 =2 M=8, D 2 =.9, T g =.3, T t =.6, R 2 =.625, X =.4, X =.5, X =.2, X X T t S M S D T t 2 S ΔP L ΔP L2 X =.4, T 2 =2 M 2S D2 IV. DESIGN OF FUZZY WAVELET NEURAL NETWORK LOAD FREQUENCY CONTROLLER USING GENETIC ALGORITHM The detaled bloc dagram for the proposed FWNN load frequency controller s gven n Fgure 3. Accordng to ths fgure, the proposed FWNN-LFC mplements two nput sgnals for each area. The two sgnals used for area number one s the area control error (ACE) for area number one and t s rate of change. The two nput sgnals used for the FWNN load frequency controller of area number two s the area control error (ACE) for the area number two, and t s rate of change. The objectve of the control problem s to trac the frequency devaton to zero n the case of a load dsturbance. To acheve ths control means, the neural control system synthess s performed n the d-loop control system and the lnear combnatons of frequency devaton and te-lne power devaton,.e. area control error (ACE) s taen as tracng error for tunng FWNN load frequency controller parameters to provde approprate control nput. By mnmzng a quadratc measure of the tracng error, the desgn problem can be characterzed by the GA formulaton. On the other hand, the GA s used to correct the networ parameters for adjustng of FWNN load frequency controller. By usng above control strategy, the desgnng FWNN load frequency controller s equvalent to determnaton of the FWNN parameters. T 2 S Δf Δf 2 84

5 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun. 22 Genetc Algorthm Optmzer β β 2 ACE ACE 2 -Z - -Z - FWNN Controller FWNN Controller R u u 2 R2 Governor Governor Turbn Turbn ΔP L ΔP L2 Load and Machne T 2 S Load and Machne Δf Δf 2 Fgure 3. Fuzzy wavelet neural networ load frequency controller scheme The outputs of two FWNN-LFCs, U and U 2, are defned so that tracng error s mnmzed. To calculate the desred control sgnals, the FWNN parameters ncludng dlaton, translaton, weghts, and membershp functons should be set so that the ACE s mnmzed. In ths wor, to obtan the FWNN parameters the GA s used. In ths case, fndng the FWNN parameters s consdered as an optmzaton problem and the quadratc measure of ACE s consdered as the objectve functon. Here we used a ftness functon that usng the ACE of each area, as follow: L l= 2 2 ( 2 ) Ftness = ACE ACE (8) where L s number of networ tranng data. Accordng to Fgure 3, the ACE of each area s measured n each teraton and wll be gven to the GA optmzer. Then the soluton vector s obtaned by GA by mnmzng the ftness functon whch gves the FWNN-LFC parameters. By usng the obtaned parameters, the networ s outputs are calculated and appled to the system followed by calculatng the new ACEs. The procedure contnues untl a termnaton crteron s met. The termnaton crteron could be the number of teratons, or when a soluton of mnmal ftness s found. Equatons (2)-(4) show that the free parameters to be traned n FWNN b are p j, p j2, t and ω M where, =,..., c, j =,..., q. Our tas s to desgn the FWNN bass functon expanson such that the objectve functon (8) mnmzed. Therefore GA s appled for tunng parameters of FWNN by optmzng the followng objectve or cost functon. L 2 2 F = ACE, ACE2, (9) l= ( ) where F s the ftness of th chromosome. In the GA, each populaton s a soluton to the problem whch determnes the parameters of FWNN,.e. N N N N [ pj, pj2, t, w M ]. So th chromosome s represented as: T C = [ pj, pj2, t, wm ] () In Equaton (), the superscrpt T denotes the vector transpose operaton. Thus, all free desgn parameters that to be updated by GA n FWNN load frequency controller are as follows: c c p = [ p... p... pq... pq ] j c c p = [ p p2... pq2... pq2 ] j () S S t = [ t... t... tq... tq ] wm = [ w... ] M w Mc By applyng the GA, the best chromosome (soluton) correspondng to the smallest ftness value can be obtaned. In GA, durng each generaton, the chromosomes are evaluated wth some measure of ftness, whch s calculated from the objectve functon defned n (9). Then the best soluton s chosen. In the current problem, the best soluton s the one that has mnmum ftness. V. SIMULATION RESULTS In ths secton, a two-control area power system, shown n Fgure 2 s consdered as a test system. The typcal data for the system parameters and governor lmters for nomnal operaton condton can be gven as Table. To ndcate the effectveness of the proposed FWNN load frequency controller for the studed two area power system that s subjected to two dfferent load 85

6 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun. 22 dsturbances, the studed power system frequency devatons and te lne power are obtaned. Comparsons between the power system response usng the proposed wavelet neural networ controller, and that usng the conventonal proportonal plus ntegral (PI) controller are performed, and the results are dscussed At frst, ntalzng of the networ s performed and each FWNN-LFC was traned usng a set of 3 nputoutput. By applyng OLS algorthm, three fuzzy rules wth three selected wavelets are represented for constructng the FWNN based controller. Three fuzzy rules are used n FWNN structure and consequently 27 parameters have to be updated. The ntal values of the parameters of FWNNs are generated randomly n the nterval [, ] and a GA based approach s used to reach the optmal values. The tranng of FWNN system s performed for 3 data ponts. The ftness value s calculated as (9). The number of chromosomes n the populaton s set to be 2. One pont crossover s appled wth the crossover probablty p c =.9 and the mutaton probablty s selected to be p m =.. Also, the number of teratons s consdered to be 5. In order to show the ablty and effectveness of the proposed method, a conventonal PI controller by usng the approach adopted from [] s appled for comparson, too. It was found that KI = KI2 =.3 were the best selectons for havng the best performance. The desgned FWNN load frequency controller and those obtaned by PI controller are placed n the case study (Fgure 3). To show the effectveness of the desgned controllers, a tme doman analyss s performed for the case study. To test the proposed method, a sudden small load perturbaton whch contnuously dsturbs the normal operaton of the power system s appled to the system. Here we use a step load change of. p.u., (.e. Δ PL =Δ PL2 =. ). The frequency devaton of both areas and te-lne power varaton n nomnal condton of the d loop system are obtaned and shown n Fgures.4, 5 and 6, respectvely. delta F 3 x Tme(s) Fgure 4. Frequency devaton of area Convetonal PI controller delta F 2 (p.u) Te-lne power devaton (p.u) - 2 x -5 Convetonal PI controller Tme (s) - 2 x Fgure 5. Frequency devaton of area 2 Convetonal PI controller Tme (s) Fgure 6. Te-lne power devaton From the comparng curves t can be seen, usng the proposed method, the frequency devaton and te-lne power varaton of two areas followng the load changes and are qucly drven bac to zero. It should be mentoned that although the overshoot of frequency response of classcal PI controller shown n Fgure 4 s better than the proposed approach, but the settlng tme of the latter s better than the former. Generally, by loong at Fgures 4 t can be concluded that the proposed method gves a better performance than the classcal LFC. To show the robustness of the proposed approach and to nvestgate the effect of changng the system parameters on system performance, two system parameters are consdered as 2% ncrease for all system parameters (upper bound) and 2% decrease for all system parameters (lower bound). The dynamc behavor of the system was evaluated for 3 s. Fgures 7 show response system for upper bound and lower bound of parameters condton ncludng frequency devaton of areas and 2, and also, te-lne power devaton. 86

7 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun x 2 Convetonal PI controller x 2 Conventonal PI controller - delta F - -3 delta F Tme (s) Fgure 7. Frequency devaton of area for upper bound of parameters x Tme (sec) Fgure. Frequency devaton of area for lower bound of parameters x -5 delta F delta F Convetonal PI controller Tme (s) Fgure 8. Frequency devaton of area 2 for upper bound of parameters x Tme (sec) Fgure. Frequency devaton of area 2 for lower bound of parameters x Conventonal PI controller Te-lne power devaton (p.u) Convetonal PI controller Tme (s) Fgure 9. Te-lne power devaton for upper bound of parameters Te-lne power devaton - Conventonal PI controller Tme (sec) Fgure 2. Te-lne power devaton for lower bound of parameters 87

8 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun. 22 Fgures 7 show the dynamc performance of the studed two area power system wth the conventonal PI controller and wth the proposed fuzzy wavelet neural networ controller. The superorty of the proposed FWNN controller over the conventonal PI controller s evdent n dampng the system frequency oscllatons very fast. Also, there s less undershoot for area number one and area number two, and the dampng o the te lne power oscllatons s very fast wth the proposed FWNN controller. VI. CONCLUSIONS In ths paper a new load frequency controller based on fuzzy wavelet neural networ and genetc algorthm (FWNN-LFC) s developed to quench the devatons n frequency and te lne power due to load dsturbances n an nterconnected power system. The FWNN s traned to tune the parameters of FWNN-LFC based on real-tme measurements of area control error n each area. Also, an effcent genetc algorthm s proposed for the learnng of FWNN and to fnd optmal values of the parameters of FWNN-LFC. The performance of desgned FWNN-LFC s tested on a two area nterconnected power system wth consderng governor lmters and the results obtaned are compared wth the classcal PI controller. The robustness and effectveness of the proposed FWNN-LFC s verfed under dfferent dsturbances. Smulaton results show that the superorty of the proposed FWNN controller over the conventonal PI controller s evdent n dampng the system frequency oscllatons very fast. Also, there s less undershoot for area number one and area number two, and the dampng o the te lne power oscllatons s very fast wth the proposed FWNN load frequency controller. REFERENCES [] P. Kundur, Power System Stablty and Control, New Yor, Mc Graw Hll, 994. [2] N.N. Bengamn, W.C. Chan, Varable Structure Control of Electrc Power Generaton, IEEE Trans. Power App. Syst., Vol. PAS-, pp , 982. [3] C.T. Pan, C.M. Law, An Adaptve Controller for Power System Load-Frequency Control, IEEE Trans. Power Syst., Vol. 4, pp. 228, February 989. [4] A.M. Kassem, Neural Predctve Controller of a Two-Area Load Frequency Control for Interconnected Power System, An Shams Engneerng Journal, Vol., pp , 2. [5] K. Vrdolja, N. Perc, I. Petrovc, Sldng Mode Based Load-Frequency Control n Power Systems, Electrc Power Systems Research, Vol. 8, pp , 2. [6] H. Shayegh, A Robust Decentralzed Power System Load Frequency Control, Journal of Electrcal Engneerng, Vol. 59, pp. 2893, 28. [7] H. Mohamed, L. Hassan, M. Moghavvem, S. Yang, Load Frequency Controller Desgn for Iraq Natonal Super Grd System Usng Fuzzy Logc Controller, SICE Annual Conference, pp , August 28. [8] D.K. Chaturved, P.S. Satsang, P.K. Kalra, Load Frequency Control: A Generalzed Neural Networ Approach, Internatonal Journal of Electrcal Power and Energy Systems, Vol. 2, pp. 455, 999. [9] H. Shayegh, A. Jall, H.A. Shayanfar, Robust Modfed GA Based Mult-Stage Fuzzy LFC, Energy Converson and Management, Vol. 48, pp. 6567, 27. [] Y.L. Abdel-Magd, M.M. Dawoud, Genetc Algorthms Applcatons n Load Frequency Control, Genetc Algorthms n Eng. Sys. Innovatons and Applcatons, Vol., September 995. [] E Bjam, R. Abshar, J. Asar, S.M. Saghaannejad, Load Frequency Control of Interconnected Power System Usng Bran Emotonal Learnng Based Intellgent Controller, Proc. 9th Iranan Conference n Electrcal Engneerng, 2. [2] H. Shayegh, H.A. Shayanfar, Applcaton of PSO for Fuzzy Load Frequency Desgn wth Consderng Superconductng Magnetc Energy Storage, Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Issue 2, Vol. 2, No., pp , 2. [3] H.A. Shayanfar, M. Ghazal, M. Karam, Load Frequency Control Usng Multvarable Characterstc Loc Method n Power Systems, Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Issue, Vol., No., pp. 5-, 29. [4] Q. Zhang, A. Benvenste, Wavelet Networs, IEEE Transactons on Neural Networs, Vol. 3, pp , 992. [5] D.W. C. Ho, P.A. Zhang, J. Xu, Fuzzy Wavelet Networs for Functon Learnng, IEEE Trans. Fuzzy Systems, Vol. 9, No., pp. 2, 2. [6] S.T. Tzeng, Desgn of Fuzzy Wavelet Neural Networs Usng the GA Approach for Functon Approxmaton and System Identfcaton, Fuzzy Sets and Systems, Vol. 6, pp , 2. [7] R.H. Abyev, O. Kayna, Fuzzy Wavelet Neural Networs for Identfcaton and Control of Dynamc Plants - A Novel Structure and a Comparatve Study, IEEE Transactons on Industral Electroncs, Vol. 55, pp , 28. [8] M. Shahrar Kahesh, E. Bjam, F. Sheholeslam, M. Zer, M.M. Farsang, Power System Stablzer Desgn for Dampng Power System Low Frequency Oscllaton Based on Fuzzy Wavelet Neural Networ, Intellgence Systems n Electrcal Engneerng, Vol., No., pp. 2, 2. [9] T. Kugarajah, Q. Zhang, Multdmensonal Wavelet Frames, IEEE Transacton on Neural Networs, Vol. 6, pp , 995. [2] A. Khodabahshan, M. Edrs, A New Robust PID Load Frequency Controller, Control Engneerng Practce, Vol. 6, pp. 69,

9 Internatonal Journal on Techncal and Physcal Problems of Engneerng (IJTPE), Iss., Vol. 4, No. 2, Jun. 22 BIOGRAPHIES Maryam Shahrar Kahesh receved her B.Sc. degree n Bomedcal Engneerng from Isfahan Unversty, Isfahan, Iran n 28. She also receved her M.Sc. degree n Electrcal Engneerng from Isfahan Unversty of Technology, Isfahan, Iran n 2. She s currently pursung the Ph.D. degree n Electrcal Engneerng at Isfahan Unversty of Technology, Isfahan, Iran. Her nterests nclude fuzzy wavelet neural networ, fuzzy logc, neuro fuzzy, ntellgent control, nonlnear control systems and soft computng. Fard Sheholesalm receved the B.Sc. degree n Electroncs from Sharf Unversty of Technology, Tehran, Iran n 99. He also receved hs M.Sc. degree n Communcatons and a Ph.D. n Electrcal Engneerng from Isfahan Unversty of Technology, Isfahan, Iran n 994 and 998, respectvely. Snce 999, he has been wth the Department of Electrcal and Computer Engneerng at Isfahan Unversty of Technology, Isfahan, Iran where he s currently an Assocate Professor of Electrcal Engneerng. Hs research nterests are control algorthms, stablty analyss, nonlnear systems, ntellgent control and robotcs. 89