TS-fuzzy controlled DFIG based Wind Energy Conversion Systems

Transcription

1 TS-fuzzy controlled DFIG baed Wind Energy Converion Sytem S. Mihra, Senior Member, IEEE, Y. Mihra, Student Member, IEEE, Fangxing Li, Senior Member IEEE, Z. Y. Dong, Senior Member, IEEE Abtract Thi paper focue on the implementation of the TS (Tagaki-Sugino) fuzzy controller for the active power and the DC capacitor voltage control of the Doubly Fed Induction Generator (DFIG) baed wind generator. DFIG ytem i repreented by a third-order model where electromagnetic tranient of the tator are neglected. The effectivene of the TS-fuzzy controller on the rotor peed ocillation and the DC capacitor voltage variation of the DFIG damping controller on converter rating of the DFIG ytem i alo invetigated. The reult of the time domain imulation tudie are preented to elucidate the effectivene of the TS-fuzzy controller compared with conventional PI controller in the DFIG ytem. The propoed TS-fuzzy controller can improve the fault ride through capability of DFIG compared to the conventional PI controller. Index Term Doubly Fed Induction Generator (DFIG), Wind Turbine (WT), dynamic ytem tability, TS fuzzy controller, damping controller. I. INTRODUCTION RECENTLY there ha been a growing amount of interet in wind energy converion ytem (WECS). Among variou other technique of wind power generation, the doubly fed induction generator (DFIG) ha been popular becaue of it higher energy tranfer capability, low invetment and flexible control [1]. DFIG i different from the conventional induction generator in a way that it employ a erie voltage-ource converter to feed the wound rotor. The feedback converter conit of Rotor ide converter (RSC) and Grid ide converter (GSC). The control capabilitie of thee converter give DFIG an additional advantage of flexible control and tability over other induction generator. The dynamic behavior of DFIG ha been invetigated by everal author in the pat. A third order model for tranient tability uing PSS/E ha been reported in []. Furthermore, the detailed model of the grid connected DFIG ha been preented in [3] wherea the modal analyi ha been dicued in [4]. The change in modal propertie for different operating condition and ytem parameter i dicued in [4]. However, the detailed S. Mihra i with the Department of Electrical Engineering at IIT Delhi, India. ( ukumar@ee.iitd.ac.in) Y. Mihra i with the School of ITEE, The Univerity of Queenland, Autralia and preently alo a viiting cholar at The Univerity of Tenneee, Knoxville, TN, USA. ( ymihra@itee.uq.edu.au; ymihra@utk.edu) Fangxing Li i with the Department of Electrical Engineering, The Univerity of Tenneee, Knoxville, TN, USA. ( fli6@utk.edu) Z. Y. Dong i with the Department of Electrical Engineering, Hong kong Polytechnic Univerity, Hong Kong ( zydong@ieee.org) model for the converter and the controller wa either neglected or overly implified. The performance of decoupled control of active and reactive power of DFIG i preented in [5]. The control method for DFIG to make it work like a ynchronou generator and the fault ride through behavior have been reported in [6] and [7] repectively. The DFIG control trategy i baed on conventional Proportional Integral (PI) technique which i well accepted in the indutry. The decoupled control of DFIG ha following controller namely P ref, V ref, V dcref and q cref. Thee controller are required to maintain maximum power tracking, tator terminal voltage, DC voltage level and reactive power level at GSC repectively. However, the intelligent controller like fuzzy and neural network controller, capturing the ytem operator experience, outperform the conventional PI controller and have been reported in the pat [8-16]. The TS-fuzzy logic control ha been uccefully applied for UPFC in [17] for a multi machine power ytem. The fuzzy logic approach provide the deign of a non-linear, model free controller and hence, can be ued for the coordinated control of RSC and GSC in the DFIG ytem. The Mamdani type fuzzy logic controller may not be able to provide uperior control over a wide range of operation [18]. Intead, a Takagi-Sugeno (TS) type fuzzy controller can provide a wide range of control gain variation by utilizing both linear and non-linear rule in the conequent expreion of the fuzzy rule bae [18]. A new method have been outlined for the deign of TS fuzzy controller, the purpoe of thi paper i to highlight the application of TS fuzzy controller to provide regulation of the active power output and DC capacitor voltage of the DFIG. The imulation reult preented highlight the effectivene of the TS-fuzzy controller in damping rotor peed ocillation and in controlling the DC voltage variation. According to the preent grid code, the wind farm hould be able to ride through any fault in the ytem. Hence fault ride through capability i required by the ytem operator a mentioned in [11]. Therefore, the contribution of thi paper are: (i) to tudy the effectivene of the TS-fuzzy controller on the variation of the DC voltage acro capacitor and rotor peed ocillation (ii) the efficacy of the TS-fuzzy controller in improving the fault ride through capability of the ytem. Thi paper i tructured a follow: Section II preent the modeling of the DFIG ytem. The detailed control methodology i dicued in Section III. Section IV decribe the TS-fuzzy controller and it application to the DFIG. Section V dicue imulation and reult followed by concluion in Section VI /9/$5. 9 IEEE Authorized licened ue limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 7, 9 at 16:57 from IEEE Xplore. Retriction apply.

2 II. MODELLING OF DFIG The grid connected ingle machine infinite bu ytem i a hown in Fig. 1. The tator and rotor voltage of the doubly excited DFIG are upplied by the grid and the power converter repectively. Simulation of the realitic repone of the DFIG ytem require the modeling of the controller in addition to the main electrical and mechanical component. The component conidered include, (i) turbine, (ii) drive train, (iii) generator and (iv) the converter ytem. Fig. 1. DFIG ytem. A. Turbine The turbine in DFIG ytem i the combination of blade and hub. It function i to convert the kinetic energy of the wind into the mechanical energy, which i available for the generator. In general the detailed model of the turbine are ued for the purpoe of deign and mechanical teting only. The tability tudie done in thi paper do not require detailed modeling of the wind turbine blade and hence it i neglected in thi paper. Input to the wind turbine are the wind peed, pitch angle and the rotor peed and the output from the wind turbine i the mechanical torque. B. Drive train In tability tudie, when the repone of a ytem ubjected to any diturbance i analyzed, the drive train ytem hould be modeled a a erie of rigid dik connected via ma-le haft. The two-ma drive train model i conidered for the tability tudie of DFIG ytem and the dynamic can be expreed by the differential equation below [4], dω t Ht = Tm T (1) h dω r Hg = Th T () e dθtw = ( ωt ωr) ω (3) B dθtw = θ + (4) H and t Th K tw D H [] are the turbine and generator inertia, g ω t where and ω r [p.u] are the turbine and DFIG rotor peed, and T h i the haft torque, Tm i the mechanical torque and T e i the electrical torque. θ tw [rad] i the haft twit angle, K[p.u./rad] the haft tiffne, and D[p.u. /rad] the damping coefficient. C. Generator The mot common way of repreenting DFIG for the purpoe of imulation and control i in term of direct and quadrature axe (dq axe) quantitie, which form a reference frame that rotate ynchronouly with the tator flux vector [3]. deq Lm = ω Ed + ω vdr dx L (5) rr 1 [ Eq ( X X ) iq ] T de dx d L = ω E ω v m q qr Lrr 1 [ E d ( X X ) iq ] + T Wherea, the parameter are defined a: X = ωl = x + X, m Lm X = ω( L ) and Lrr T =. The algebraic equation can be Lrr Rr expreed a P = Edid Eqi (7) q Q = Ediq Eqi (8) d Ed = ri d + Xiq + v (9) d Eq = ri q Xid + v (1) q where i the rotor lip; P i the output active power of the tator of the DFIG; L i the tator elf-inductance; Lrr i the rotor elf-inductance; L i the mutual inductance; ω m i the ynchronou angle peed; X i the tator reactance; x i the tator leakage reactance; x r i the rotor leakage reactance; X i the tator tranient reactance; E d and Eq are the d and q axi voltage behind the tranient reactance, repectively; T i the rotor circuit time contant; i d and i q are the d and q axi tator current, repectively; v d and v q are the d and q axi tator terminal voltage, repectively; vdr andv qr are the d and q axi rotor voltage, repectively; Q i the reactive power of the tator of the DFIG. The voltage equation and the flux linkage equation of the DFIG are baed on the motor convention. D. Converter model The converter model in DFIG ytem comprie of two pule wih modulation invertor connected back to back via a dc link. The rotor ide converter (RSC) i a controlled voltage ource a ince it inject an AC voltage at lip frequency to the rotor. The grid ide converter (GSC) act a a controlled voltage ource and maintain the dc link voltage contant. The power balance equation for the converter model can be written a: Pr = Pgc + Pdc (11) where P r, P, P dc are the active power at RSC, GSC and DC gc (6) Authorized licened ue limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 7, 9 at 16:57 from IEEE Xplore. Retriction apply.

3 link repectively, which can be expreed a, Pr = vdr idr + vqr iqr Pgc = vdgc idgc + vqgc iqgc Pdc = vdc idc = Cvdc dvdc (1) (13) long a the reactive current tay within the maximum current value (-Imax, Imax) impoed by the converter rating, the voltage i regulated at the reference voltage Vref. (14) III. CONTROLLERS FOR DFIG Thi ection decribe the controller ued for the DFIG ytem. A mentioned above, there are two back to back converter hence we need to control thee two converter ide. Primarily, thee controller are known a RSC and GSC controller. For controlling the aerodynamic power beyond certain point, pitch angle controller i ued. Thi ection alo introduce a new auxiliary control ignal which i added to the active power control loop to enhance the damping. Thi i known a the damping controller. A. Rotor ide converter (RSC) controller The RSC i ued to control the wind turbine output power and the voltage meaured at the grid terminal. The power i controlled uch that it follow a pre-defined power-peed characteritic, named tracking characteritic. Thi characteritic i illutrated by the ABCD curve in Fig. uperimpoed to the mechanical power characteritic of the turbine obtained at different wind peed. The peed of the turbine ωr i meaured and the correponding mechanical power of the tracking characteritic i ued a the reference power for the power control loop. The tracking characteritic i defined by four point: A, B, C and D. From zero peed to peed of point A the reference power i zero. Between point A and point B the tracking characteritic i a traight line. Between point B and point C the tracking characteritic i the locu of the maximum power of the turbine (maxima of the turbine power veru turbine peed curve). The tracking characteritic i a traight line from point C and point D. The power at point D i one per unit (1 p.u.). Beyond point D the reference power i a contant equal to 1 p.u. The power control loop i illutrated in Fig. 3. For RSC, the d-axi of the rotating reference frame ued for d-q tranformation i aligned with air-gap flux. The actual electrical output power, meaured at the grid terminal of the wind turbine, i added to the total power loe (mechanical and electrical) and i compared with the reference power obtained from the tracking characteritic. A Proportional-Integral (PI) regulator i ued to reduce the power error to zero. The output of thi regulator i the reference rotor current Iqr_ref, that mut be injected in the rotor by the RSC. Thi i the current component that produce the electromagnetic torque Tem. The actual Iqr component i compared to Iqr_ref and the error i reduced to zero by a current regulator (PI). The output of thi current controller i the voltage Vqr generated by the RSC. The voltage at grid terminal i controlled by the reactive power generated or aborbed by the RSC. The reactive power i exchanged with the grid, through the generator. In the exchange proce, generator aborb reactive power to upply it mutual and leakage reactance. The exce of reactive power i ent to the grid or to RSC. The control loop i hown in Fig. 4. The wind turbine control implement the V-I characteritic illutrated in Fig. 5. A Fig.. Turbine characteritic and tracking characteritic. Fi g. 3.RSC active power controller Fig. 4. RSC grid voltage controller. B. Grid ide converter (GSC) controller The GSC i ued to regulate the voltage of the DC capacitor. The control chematic i illutrated in Fig. 5. The d-axi of the rotating reference frame ued for d-q tranformation i aligned with the poitive equence of grid voltage. Thi controller conit of: (i) a meaurement ytem meauring the d and q component of AC current to be controlled a well a the DC voltage ( Vdc ); (ii) an outer regulation loop coniting of a DC voltage regulator. The output of the DC voltage regulator i the reference current Idgc_ref for the current regulator (Idgc i the current in phae with grid voltage which control active powerflow); (iii) an inner current regulation loop coniting of a current regulator. The current regulator control the magnitude and phae of the voltage generated by converter (Vgc) a hown in Fig. 6. Authorized licened ue limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 7, 9 at 16:57 from IEEE Xplore. Retriction apply.

4 active power deviation and DC voltage deviation repectively a hown in Fig. 8 and Fig. 9 repectively. Fig. 5. Grid ide converter control (DC capacitor voltage control). Fig. 8. Rotor ide controller. Fig. 6. Grid ide converter control (Reactive power control). C. Pitch angle controller The pitch angle i kept contant at zero degree until the peed reache point D peed of the tracking characteritic. Beyond point D the pitch angle i proportional to the peed deviation from point D peed. The contruction of the pitch angle controller i hown in Fig. 7. Fig. 9. Grid ide converter DC voltage controller. The active power and DC voltage deviation are fuzzified uing two input fuzzy et P (poitive) and N (negative). The memberhip function ued for the poitive et i defined by (15) and can be repreented a hown in Fig. 1. Fig. 7. Pitch angle controller. IV. DESIGN OF TS FUZZY CONTROLLER FOR DFIG The fuzzy controller are conventional non-linear controller and can produce atifactory reult when contructed properly uing the experience of the ytem operator. The deign of fuzzy logic controller conit of (i) determining the input, (ii) etting up the rule and (iii) the deign method for converting the rule into a crip output ignal, known a defuzzification. Firt of all, the input ignal, in thi cae i the error and rate of change of error ignal, i meaured and depending on the crip value of the ignal, it can be expreed in term of the degree of memberhip of the fuzzy et. The hape of the fuzzy et can be determined by the expert knowledge of the ytem. The next tep i to contruct the fuzzy rule, again baed on the expert knowledge of the control problem, to accommodate all the poible combination of memberhip. The TS-fuzzy controller differ from the Mamdani-fuzzy in it rule conequent. The linguitic rule conequent i made variable by mean of it parameter. A the rule conequent i variable, the TS fuzzy control cheme can produce an infinite number of gain variation characteritic. In eence, the TS fuzzy controller i capable of offering more and better olution to a wide variety of non-linear control problem. The quadrature-current component of the RSC, iqr ref, and the direct-current component of the GSC, idgc ref, are controlled by (15) Where, xi ( k ) denote the input to the fuzzy controller at the k th ampling intant given by x1( k) = e( k) = Pref P or VDC ref V (16) DC x ( k) = e( k) (17) The memberhip function for x 1 and x i hown in Fig.11. The value of L 1 and L are choen on the bai of the maximum value of real power or DC voltage error and the integral of the error. The maximum value of error and it integral i determined oberving thee variation by running the program once with the PI controller. Fig. 1. Memberhip function. Authorized licened ue limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 7, 9 at 16:57 from IEEE Xplore. Retriction apply.

5 Fig. 1. SMIB ytem. Fig. 11. TS Fuzzy control cheme with error and integral of error. The TS fuzzy controller ue the four implified rule a Rule 1: If x ( k ) i P and x () 1 k i P then u ( k) = K ( ax( k) + a x ( k)) (18) Rule : If x ( k) 1 i P and x ( k ) i N then u( k) = K( u1( k)) (19) Rule 3: If x ( k) 1 i N and x ( k ) i P then u3( k) = K3( u1( k)) () A. Effect of TS fuzzy controller at wind peed 1m/ The damping of the wind turbine with DFIG uing TS Fuzzy controller and PI controller in it power control loop and DC voltage control loop i compared under 3-phae bu fault at Bu B1, which i cleared after 1 m. The wind peed i kept contant 1 m/. The improvement in the dynamic repone of rotor peed ocillation with TS fuzzy compared to the PI controller i hown in Fig. 13. The change in the repone of the real power with the implementation of the TS-fuzzy controller i hardly noticed a in Fig 14. Rule 4: If x ( k) 1 i N and x ( k ) i N then u4( k) = K4( u1( k)) (1) In the above rule bae u 1, u, u 3, and u 4 repreent the conequent of the TS fuzzy controller. The output of the TS fuzzy controller i defined a follow: uk ( ) = 4 μ j j= 1 4 j= 1 u ( k) V. SIMULATION RESULTS AND DISCUSSION j μ j () The TS fuzzy controller wa implemented in DFIG power control and DC voltage control, in MATLAB/SimPower Sytem environment, while the parameter of the wind turbine (WT) with DFIG are given in the Appendix. The parameter of all the other controller are taken from the MATLAB DFIG ytem model and are modified to improve the repone of rotor peed and DC ocillation. Uing hit and trial method, the parameter of active power and DC voltage control loop are adjuted to achieve the lowet poible peak for rotor and DC voltage ocillation. Then, the tuned TS-fuzzy controller are compared with thee PI parameter of the DFIG model. The Single Machine Infinite Bu (SMIB) ytem hown in Fig.1 i taken for the cae tudy and the imulation are performed to verify the effectivene of the TS fuzzy and the damping controller in improving the tranient tability, the ytem damping and the fault ride-through capability of the WT with DFIG. Fig. 13. Variation of rotor peed following a fault. Real power(pu) with PI controller Time(ec) Fig. 14. Variation in electrical power output at 1 m/ for 1m fault. The ocillation in the DC link capacitor voltage are alo compared. The poitive peak value of DC link voltage with the PI controller i 16 V, wherea thi i reduced to only 14 V in the cae of TS-fuzzy controller a hown in the Fig. 15. The improvement i beneficial for the operation of converter, ince thi reduce the tre on the RSC and GSC converter. Moreover, the ocillation/peak in the DC link capacitor voltage beyond the protection limit would trip the convertor. With the implementation of TS-fuzzy controller, the ytem will not reach the threhold and hence can utain the fault for longer duration, thereby enhancing the ytem tability margin. Authorized licened ue limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 7, 9 at 16:57 from IEEE Xplore. Retriction apply.

6 Rotorpeed(pu) D C -Link Voltage(v) with PI controller Time(ec) Fig.15. DC Voltage variation at 1m/ for 1 m fault. DC capacitor voltage Time(ec) with only PI controller Time(ec) with PI controller Fig. 16. DC Voltage variation at 1m/ for 18 m fault. When the fault duration i increaed to 18 m, the DC Link capacitor voltage of DFIG with PI controller i going toward negative (- V) which will initiate the trip circuit to trip the DFIG from the grid. Wherea, the TS-fuzzy controller keep the DC voltage poitive thereby prevent the tripping of protection relay. Thi i hown in Fig. 16. Hence, with the help of TS fuzzy controller in DFIG fault ride through capability i improved. B. Effect of TS fuzzy controller at wind peed 14m/ The performance of the TS-fuzzy controller i invetigated at the change wind peed. Fig. 17 how the comparion of the PI and the TS-fuzzy controller with the wind peed of 14 m/. TS-fuzzy i ha better repone by bringing rotor peed to the teady tate value quickly. Fig. 17. Rotor peed ocillation followed by a 3 phae fault at 1kv bu. VI. CONCLUSION A TS-fuzzy controller i developed for controlling the active power and DC capacitor voltage of the DFIG baed WT ytem. It i oberved that the damping of the rotor ocillation are improved with the implementation of TS-fuzzy controller compared to it counterpart PI controller. The poitive and negative peak ocillation in DC capacitor voltage, following a 3 phae fault, i reduced to only 14V and 5V in the cae of TS-fuzzy controller. Intead, thee peak are 16V and -V for the conventional PI controller. Thi reduction in the peak rie in the DC link voltage would not only help in reducing the tre on RSC and GSC convertor but would alo help in deigning the appropriate protection ytem for the reliable/ecure operation of the DFIG ytem. =Thi would, in turn improve the fault ride through capability of DFIG a the ytem can utain the fault for longer duration of time compared to PI controller. Fuzzy controller, in contrat to the conventional PI controller, can take care of the non-linearity in the control law and hence are known to have better performance than PI under variable operating condition. Moreover, the TS-fuzzy i better than the mamdani type fuzzy controller in term of the number of fuzzy et for the input fuzzification, number of rule ued and the number of coefficient to be optimized. Therefore, in thi paper, the TS-fuzzy baed controller i propoed for the active power and DC voltage control loop of the DFIG ytem. Furthermore, the application of thee controller for the multimachine DFIG ytem would be teted and hence would be the next part of our reearch. VII. APPENDIX - PARAMETERS OF WIND TURBINE SYSTEM (a) Turbine data Nominal wind turbine mechanical output power in MW =9 Pitch angle controller gain =5 Maximum rate of change of pitch angle (deg/ec) = Inertia contant of turbine in econd = (b) Generator data Nominal power in MVA = 1 Nominal voltage (L-L) in volt = 575 Stator reitance in p.u. =.76 Stator inductance in p.u. =.171 Rotor reitance in p.u. =.5 Rotor inductance in p.u. =.156 Magnetizing inductance =.9 Inertia contant in econd =.4 Friction factor or damping factor in p.u. =.1 Pair of pole (P) =3 (c)converter data Converter maximum power in p.u. =.5 Grid ide coupling inductor inductance and reitance in p.u =.15 and.15, repectively. Nominal DC voltage in volt =1 DC capacitor value in mf = 6 (d)controller data Grid voltage regulator gain K P =1.5 and K I =3 Authorized licened ue limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 7, 9 at 16:57 from IEEE Xplore. Retriction apply.

7 Droop X in p.u. =. Power regulator gain K P = and K I =1 DC bu voltage regulator gain K P =. and K I =.5 Grid ide converter current regulator gain K P =1 and K I =1 Rotor ide converter current regulator gain K P =.3 and K I = 8 Damping controller proportional gain K P =1 [19] F. M. Hughe, O. A. Lara, N. Jenkin, and G. Strbac, A power ytem tabilizer for dfig-baed wind generation, IEEE Tranaction on Power Sytem, vol. 1, no., pp , May 6. (e)ts fuzzy controller coefficient Power controller K 1 =.5, K =.1, K 3 =1., and K 4 =.5 DC voltage controller K 1 =1., K =.5, K 3 =5., and K 4 =5. VIII. REFERENCES [1] P. B. Eriken, T. Ackermann, H. Abildgaard, P. Smith, W. Winter, and J. M. Rodriguez Garcia, Sytem operation with high wind penetration, IEEE Power Energy Mag, vol. 3, no. 6, pp , 5. [] Y. Lei, A. Mullane, G. Lightbody, and R. Yacamini, Modeling of the wind turbine with a doubly fed induction generator for grid integration tudie, IEEE Tranaction on Energy Converion, vol. 1, no. 1, pp , Mar. 6. [3] F. Mei and B. C. Pal, Modeling nd mall ignal analyi of a grid connected doubly fed induction generator, Proc. of IEEE PES General Meeting, San Francico, pp , 5. [4], Modal analyi of grid connected doubly fed induction generator, IEEE Tranaction on Energy Converion, vol., no. 3, pp , Sept. 7. [5] M. Yamamoto and O. Motoyohi, Active and reactive power control for doubly-fed wound rotor induction generator, IEEE Tranaction on Power Electronic, vol. 6, no. 4, pp , [6] F. M. Hughe, O. Anaya-Lara, N. Jenkin, and G. Strbac, Control ofdfig-baed wind generation for power network upport, IEEE Tranaction on Power Sytem, vol., no. 4, pp , Nov. 5. [7] J. Morren and S. W. H. de Haan, Ride through of wind turbine with doubly-fed induction generator during a voltage dip, IEEE Tranaction on Energy Converion, vol., no., pp , Jun. 5. [8] R.C. Banal, Bibliography on fuzzy ett theory application to power ytem (1994-1), IEEE Tran. Power Syt., vol. 18, no. 4, pp , Nov. 3. [9] K. Tomovic, and M.Y. Chow (editor), Tutorial on Fuzzy Logic Application in Power Sytem, IEEE PES Winter Meeting, Singapore, January. [1] Y.H. Song (editor), Modern Optimization Technique in Power Sytem, Kluwer Academic Publiher, Netherland, [11] Y.H. Song and A.T. John, Application of Fuzzy Logic in Power Sytem: Part. Comparion and Integration with Expert Sytem, Neural Network and Genetic Algorithm, IEE Power Engineering Journal, Vol. 1, No. 4, 1998, pp [1] Y.H. Song and A.T. John, Application of Fuzzy Logic in Power Sytem: Part 3. Example Application, IEE Power Engineering Journal, Vol. 13, No., April 1999, pp [13] Y. H. Song and R. Dunn, Fuzzy Logic and Hybrid Sytem, in Artificial Intelligence Technique in Power Sytem, in K. Wardwick, A. Ekwue, and R. Aggarwal, Artificial Intelligence Technique in Power Sytem, IEE Power Engineering Serie, London, UK, 1997, pp [14] Y.H. Song and A.T. John, Application of Fuzzy Logic in Power Sytem: Part 1. General Introduction to Fuzzy Logic, IEE Power Engineering Journal, Vol. 11, No.5, 1997, pp [15] S. Madan and K.E. Bollinger, Application of Artificial Intelligence in Power Sytem, Electric Power Sytem Reearch, Vol. 41, No., 1997, pp [16] M.A. Laughton, Artificial Intelligence Technique in Power Sytem, in K. Wardwick, A. Ekwue, and R. Aggarwal, Artificial Intelligence Technique in Power Sytem, IEE Power Engineering Serie, London, UK, 1997, pp [17] S. Mihra, P. K. Dah and G. Panda TS-fuzzy controller for UPFC in a multi machine power ytem, IEE proceeding on generation, tranmiion and ditribution, vol. 147, no 1, January, pp [18] H. Ying, Contructing non-linear variable gain controller via the Takagi-Sugeno fuzzy control, IEEE Tran. Fuzzy Syt., 1998, 6, (), pp Authorized licened ue limited to: UNIVERSITY OF TENNESSEE. Downloaded on October 7, 9 at 16:57 from IEEE Xplore. Retriction apply.