Wind Driven Induction Genertor Regultion Using Ant system Approch to Tkgi Sugeno Fuzzy PID Control A.H.Besheer 1 Electricl Engineering Deprtment, Fculty of Engineering University of Tbuk P.O. Box 7031, Unit No. 1, Tbuk 47315-3470 KSA besheer@ut.edu.s Abstrct: - This study introduces new tuning technique for the PID control scheme nd its ppliction to regulte the voltge mgnitude nd the frequency of wind energy conversion system (WECS). The developed technique is stem from blending the nt system optimiztion method with Tkgi Sugeno (T-S) fuzzy system pproch. The optimum reltionship between the PID controller gins nd the prmeters of T-S fuzzy modules is explored using Ant system lgorithm. A stedy-stte nlysis for self excited slip ring induction genertor is performed. The clculted nd the experimentl results on 1.1 KW lbortory mchine enbles the control chrcteristics to be deduced. Different simultion exmples re provided to illustrte the effectiveness of the proposed technique. Finlly, the response of closed loop control scheme for WECS using chopper controlled externl rotor resistnce nd fixed cpcitor with thyristor controlled rector shows tht the proposed control pproch exhibits superior performnce to tht of estblished trditionl control methods. Key-Words: - T-S fuzzy control, PID control, Ant system optimiztion, WECS 1 Introduction In the world of tody there is need for lterntives to the lrge col nd oil fired power plnts. Renewble energy is one wy to go, nd in prticulr wind turbines hve proven to be solution [1]. The rrivl of the new power devices technologies, new circuit topologies nd novel control strtegies re contributing to the success of the wind genertion technology. A WECS cn vry in size from few hundred kilowtts to severl megwtts. The size of the wind turbine lrgely determines the choice of the genertor nd converter system. Asynchronous genertors re more common with systems up to 2MW, beyond which directdriven permnent mgnet synchronous mchines re preferred [2][2]. In wind energy stndlone genertion systems, the frequency nd the terminl voltge of the Self Excited Induction genertors (SEIG) vry with lod even when the rotor speed is mintined constnt. The increse of the wind speed will led to increse in the rotor speed tht results in commensurte increse in frequency, voltge nd current. The use of slip-ring mchine driven by vrible-speed turbine permits rotor slip-power control nd when grid connection is llowble the slip-ring mchine my be operted s doubleoutput induction genertor (DOIG) using the slipenergy recovery technique. In the cse of SESRIG, the use of simple rotor resistnce controller leds to reduction of the system cost [3-4]. Since only 1 On leve from ESRI Minoufiy University cpcitor bnk needs to be connected to the sttor terminls, the SESRIG provides good qulity c source with little hrmonic distortion to the sttor lod. Moreover, independent control of the voltge nd frequency cn be chieved esily. the genertor frequency cn be mintined resonbly constnt - even with wide vrition in speed - by rotor resistnce control, while the voltge cn be controlled by vrying the excittion cpcitnce. PID controller is by fr the most widely used control lgorithm in the process industry, the performnce of PID controller, however, fully depends on the tuning of its prmeters. Fuzzy control nd tuning methodologies hve emerged in lst yers s promising wys to pproch nonliner control problems nd to del with difficulties of conventionl PID controllers [5][5]. The re of uto-tuning of PID controller using fuzzy systems hs ttrcted mny uthors [6-8]. However, common bottleneck encountered in fuzzy controller design is tht derivtion of fuzzy rules is often difficult nd time-consuming, nd relies on expert knowledge. To overcome this disdvntge, mny utomtic methods for fuzzy system design nd optimiztion lgorithms hve been proposed, such s neurl fuzzy systems [9][9][9] nd evolutionry fuzzy systems [10][10]. One of the widely used methods for optimizing fuzzy logic controller is to modify the rule bse using this self-orgnizing lgorithm utomticlly ISSN: 1991-8763 427 Issue 12, Volume 6, December 2011
ccording to previous responses until the desired control performnce is chieved. Mny works studied this problem such s [11], [10][12][12] nd [13]. In [11], trcking control problem is ssumed to develop self tuning PID control scheme with ppliction to Antilock Brking System vi combintions of fuzzy nd genetic lgorithms. While in [12], the pproximtion of nlyticl test function is performed using nt colony lgorithm to tune the prmeters of Tkgi Sugeno (T-S) fuzzy rule bse. The uthors simplified their work by ssuming constnt consequence prt insted of the ordinry liner function consequent prt of T-S fuzzy system. In [13], Incrementl fuzzy PID controller is used which is slightly different from the T-S fuzzy PID controller where, the scling fctors for input/output Mcvicr-Wheln bsed fuzzy system re ddressed in the nt colony optimiztion frmework. In T-S fuzzy systems design, one chllenging design tsk is the determintion of the prmeters of the consequent prt. Fuzzy PID is profusely pplied to wind genertion systems for the purpose of regultion nd/or for cpturing optimum power. In [14][14], Mmdni type fuzzy logic control is used to tune the integrl gin (K i ) of PI controller to supervisory voltge/frequency control of self-excited induction genertor while in [15] n dptive fuzzy proportionl integrl derivtive control strtegy to cpture optiml power is presented. However, despite of the good results provided by ll the forementioned works, ll hve some common drwbcks tht cn be summrized in the following points: The behviour of FLC depends on shpe of membership functions nd the rule bse. The design of the FLC ws done ccording to the tril-nd-error method rther thn guided pproch. The presence of n expert knowledge is compulsory; conversely, in the bsence of such knowledge, their design is usully slow nd not optimized Recently, the socil inspired optimiztion lgorithms become successful lterntive for the conventionl tuning method to dpt the PID controllers. Using these new methods, the globl optiml or suboptiml solutions of the optimized control scheme re found. These lgorithms re dopted by mny reserchers for tuning PID controller in its clssicl nd intelligent forms. One such pproch is Ant System Optimiztion (ASO) which is founded on the forging behvior of nts nd their indirect communiction bsed on pheromones; see for instnce [16]. ASO hs been pplied to severl combintoril problems such s job scheduling, routing optimiztion in dt communiction networks nd telephone networks [17]. In this pper, ASO is employed to design the consequent prt of Tkgi Sugeno fuzzy PI controller. The pper presents design procedures for model free T-S fuzzy PI controller. Two independent T-S fuzzy systems re combined to tune different gins of PI controller. The optimum reltionship between the PI controller prmeters nd the prmeters of T-S fuzzy modules is explored. Using Ant system lgorithm, the prmeters of ech T-S fuzzy system re optimlly determined. The ide is to strt with tuned, conventionl PI controller, replce it with n equivlent Tkgi-Sugeno fuzzy PI controller nd eventully fine-tune the T-S fuzzy tuner. This is relevnt whenever PI controller is possible or lredy implemented. In the proposed T-S Fuzzy Ant System PI, structure of T-S fuzzy system is well dpted vi defining the optimum prmeters of its consequence prt. Once new rules re generted, the PI controller prmeters re clculted from the defuzzifiction process. The developed technique extends our previous work in [16] to the cse of WECS tht presents interesting control demnds nd exhibits intrinsic non liner chrcteristics. The key dvntges for this pper re threefold: Developing systemtic pproch to generte fuzzy rules from given input output dt set by proposing T-S fuzzy module s full optimizer for the PID controller insted of Mmdni fuzzy system [14] or simplified T-S fuzzy module [12]. Fine tune the consequent prt of the ordinry T-S fuzzy system tht is reported s chllenging design tsk [11][11-12]. Explore the optimum reltionship between the PID gins nd the consequent prt prmeters of T-S fuzzy optimizer in highly nonliner ppliction without depend on prior knowledge bse of the chrcteristics nd response for the wind turbine system [14-15]. This pper hs two min contributions. Firstly, PI controller hs been designed for WECS using blending tuning mechnism nmely Tkgi Sugeno fuzzy Ant system lgorithm. Secondly, stisfctory closed loop performnce is chieved with respect to the conventionl ZN frequency response tuning method. The objective of Ant System Optimiztion in this pper is to improve both the design efficiency of Tkgi Sugeno fuzzy systems nd its performnce to get optiml PI prmeters. In this pper the voltge nd frequency control of three phse SESRIG is investigted by vrying the externl rotor resistnce nd the ISSN: 1991-8763 428 Issue 12, Volume 6, December 2011
excittion cpcitnce using the proposed Ant Tkgi Sugeno Fuzzy PI controller. This pper is orgnized s follows: section II demonstrtes stedy stte model nlysis of SESRIG tht is considered s min prt of the proposed WECS. The control chrcteristic is deduced in section III by compring the Experimentl results to the clculted results with lod nd no lod conditions. Specificlly, the stndlone WECS terminl output voltge nd frequency control re shown in section IV. Tkgi Sugeno fuzzy tuner for PI controller is presented in section V. Section VI introduces optiml prmeter determintion for Tkgi Sugeno fuzzy systems using nt system optimiztion lgorithm. Some simultion exmples re provided to illustrte the effectiveness of the proposed technique in section VII. The proposed control strtegy is pplied to WECS in section VIII. Finlly, conclusion is set in section IX. Dt X t 1 X 2 = zero (4) 2 2 R X X m R t + t 2 2 2 ( ) + X 2 b Where RL 2 X C 2 Dt = ( ) + ( X L ) (5) 2 2 RL X C R1 RL 2 X C 2 Rt = + [( ) + ( X ) ] 5 L (6) 2 2 2 2 R X X X X X X ( L C L C L C t = + ) 4 2 (7) R 2 X 2 X1[( L ) + ( X C L ) ] 2 2 Anlysis of SESRIG stedy stte model In this section, the stedy stte model nlysis of SESRIG tht used in the proposed WECS control problem here is illustrted. Normlized equivlent circuit of SESRIG cn be proposed s seen in Fig. 1 where the rotor resistnce R 2 is the sum of the rotor winding resistnce nd the externl rotor resistnce R x, both referred to the sttor side. The excittion cpcitnce is required for inititing voltge buildup nd mintining the output voltge. The circuit hs been normlized to the bse (rted) frequency through the introduction of the per-unit frequency nd the per-unit speed b [18][18][18]. The solution of the SEIG equivlent circuit hve been developed using vrious methods. Among them, the nodl dmittnce method [19], is considered very simple nd esy to follow, hence the following reltionship my be estblished for successful voltge build-up: E 1 (Y t + Y m + Y 2 ) = 0 (1) For successful build-up ir gp voltge E 1 cn't be zero then: Y t + Y m + Y 2 = 0 (2) With some mthemticl mnipultions nd by equting the rel nd imginry prts to zero, respectively, the following two equtions in rel numbers re obtined: R2 Dt Rt + b 2 2 R X R t + t 2 2 2 ( ) + X 2 b nd = zero (3) Fig. 1 Normlized equivlent circuit of Self Excited Slip Ring Induction Genertor Where is per unit frequency (ctul frequency/bse frequency), b per-unit speed (rotor speed/synchronous speed) corresponding to bse frequency, C excittion cpcitnce per phse, E 1 ir-gp voltge per phse referred to bse frequency, R 1 & R 2 sttor nd rotor winding resistnces per phse. R L sttor lod resistnce per phse. V 1 Lod voltge per phse, X 1 & X 2 Sttor nd rotor lekge rectnce per phse, X c Excittion cpcitive rectnce per phse nd X L Lod rectnce per phse. nd consequently X m cn be determined by itertively solving (3) nd (4). The mgnetiztion curve (plot of E 1 versus X m ), enbles E 1 to be determined nd the equivlent circuit is completely solved [20]. For detils on the prmeters of the mchine used see the Appendix. 3 Computed nd Experimentl Results The min feture of the control chrcteristic for SESRIG used in stndlone WECS is deduced in this section. For convenience, ll of the mchine prmeters, except the excittion cpcitnce, re expressed in per unit. The effect of chnging the externl rotor resistnce with constnt excittion cpcitnce nd vice vers on the output terminl voltge nd frequency t lod nd no-lod condition is presented. By the end of this section, the fesibility of the control method is confirmed by performing lbortory experiments on 1.1 KW ISSN: 1991-8763 429 Issue 12, Volume 6, December 2011
mchine described in the Appendix. Fig. 2 shows the vrition of the terminl voltge (V 1 ) ginst the rotor speed (b) t different vlues of excittion cpcitnce with zero externl rotor resistnce. At the sme rotor speed, the voltge increses s the cpcitnce increses. Fig. 3 shows the vrition of the output frequency () ginst the rotor speed (b) t different vlues of excittion cpcitnce with zero externl rotor resistnce. At the sme rotor speed, chnging the excittion cpcitnce hs no effect on the frequency. Fig. 4 shows the vrition of the terminl voltge (V 1 ) ginst the rotor speed (b) t different vlues of externl rotor resistnce nd t excittion cpcitnce of 24 µf. At the sme rotor speed, the voltge decreses s the rotor resistnce increses. Fig. 5 shows the vrition of the output frequency () ginst the rotor speed (b) t different vlues of externl rotor resistnce nd t externl cpcitnce of 24 µf. At the sme rotor speed, the frequency decreses s the rotor resistnce increses. Figs. (6-9) show the effect of chnging the excittion cpcitnce with constnt externl rotor resistnce nd vice vers t loding conditions (R L = 8 p.u) on the SESRIG output terminl voltge nd frequency. Remrk 1: (1) It is obvious from Fig. 3 tht, t no-lod, the rted frequency (i.e. 1 p.u.) is lmost occurred t the rted rotor speed. (2) Compring (Fig. 6-7) to (Fig. 2-3) shows tht loding cuses voltge nd frequency drop from the no-lod vlues. (3) Compring (Fig.8-9) to (Fig.4-5) shows tht the chnge cused by vrying the externl resistnce in the loding cse is much greter thn the no-lod cse. (4) It is shown from (Fig. 2-5) tht chnging the excittion cpcitnce ffects the voltge only, but chnging the externl resistnce simultneously chnges the voltge nd frequency. Fig. 3 Output Frequency () versus Rotor Speed (b) t different excittion cpcitnces t no lod (R x =0) Fig. 4 Terminl Voltge (V 1 ) versus Rotor Speed (b) t different externl resistnce (R x ) t no lod Fig. 5 Output Frequency () versus Rotor Speed (b) t different externl resistnce (R x ) t no lod Fig. 2 Terminl Voltge (V 1 ) versus Rotor Speed (b) t different excittion cpcitnces t no lod (R x =0) Fig. 6 Terminl Voltge (V 1 ) versus Rotor Speed (b) t different excittion cpcitnces t R L = 8 p.u. (R x =0) ISSN: 1991-8763 430 Issue 12, Volume 6, December 2011
Fig. 7 Output Frequency () versus Rotor Speed (b) t different excittion cpcitnces t R L = 8 p.u. (R x =0) Fig. 8 Terminl Voltge (V 1 ) versus Rotor Speed (b) t different externl resistnce (R x ) t R L = 8 p.u 4 SESRIG Voltge nd Frequency Control From the previous chrcteristics, obtining constnt voltge nd constnt frequency output from the SESRIG used in stndlone WECS is chievble by mens of chnging the excittion cpcitor nd the externl rotor resistnces simultneously, s the rotor speed nd the lod vry. Fig. 10 shows tht s the rotor speed (b) increse the externl rotor resistnce (R x ) required to mintin the frequency constnt t 1 p.u. increses. It is noted tht unity per-unit frequency is only chievble t rotor speeds bove 1 p.u. Fig. 11 shows the corresponding terminl voltge. The terminl voltge (V 1 ) is constnt s the rotor speed increses. At the sme rotor speed, incresing the excittion cpcitnce increses the voltge. At certin vlue of excittion cpcitnce, unity per-unit voltge cn be obtined. For exmple, t rotor speed b = 1.1 p.u. nd lod resistnce R L = 8 p.u., the externl rotor resistnce required to chieve = 1 p.u. is 0.66 p.u. To keep the voltge t 1 p.u. t the sme time, the externl cpcitnce is djusted to 16.11 µf. Fig. 12-13, show the externl resistnce nd excittion cpcitnce needed to mintin nominl voltge nd frequency t constnt rotor speeds (b) of 1.1 p.u. nd 1.2 p.u. s the lod current increses. For exmple, when rotor speed (b) is 1.1 nd lod current (I L ) is 0.25 p.u., the vlues of the externl resistnce nd excittion cpcitnce which re needed to mintin the frequency nd voltge t 1 p.u. re 0.7 p.u. nd 16.55 µf respectively. Fig. 9 Output Frequency () versus Rotor Speed (b) t different externl resistnce (Rx) t RL= 8 p.u. Fig. 10 Externl Rotor Resistnce (Rx) required to mintin rted frequency s the rotor speed vries t different excittion cpcitnce (RL=8) Fig. 11 Terminl voltge (V 1 ) t rted frequency s the rotor speed vries t different excittion cpcitnce (R L =8) ISSN: 1991-8763 431 Issue 12, Volume 6, December 2011
delivered to the lod) should ccompny with decresing the externl rotor resistnce nd incresing the excittion cpcitnce). Fig. 12 Vrition of externl resistnce (R x ) to operte t rted voltge nd frequency s the lod current increses Fig. 13 Vrition of excittion cpcitnce (C) to operte t rted voltge nd frequency s the lod current increses Remrk 2: From the bove figures nd discussions in the lst two sections, the following points cn be concluded: (1) Comprison between the computed nd experimentl results reflects their close mtching tht reflects the dequteness of the circuit model nd the solution method proposed in [20] nd [21]. (2) At constnt lod conditions, chnging the externl rotor resistnce will ffect the stndlone WECS terminl output voltge nd frequency while the excittion cpcitnce remins unchnged (i.e. incresing rotor speed (i.e. wind speed) should ccompny with incresing the externl rotor resistnce while the excittion remins nerly constnt) (3) At vrible lod conditions, simultneous chnge in the externl rotor resistnce nd the excittion cpcitnce is required in order to keep the stndlone WECS working t the rted voltge nd frequency (i.e. incresing the loding condition (the output power required from the stndlone WECS) to be 5 T S fuzzy Tuner for PID Controller Mny PID controllers were presented in literture, the expression of PID control lw for continuous time system is given s follows: (8) where e(t) is the error between the input nd the output of the system; u(t) is the control ction generted by the PID controller; K p is the proportionl gin; T i is the integrl time constnt; nd T d is the derivtive time constnt. In this section, three independent T-S fuzzy systems re used to tune different gins of PID controller. Ech fuzzy module is ssigned to obtin ech PID gins. The typicl T-S fuzzy systems studied in this pper hve two inputs nd one output. The input vribles re error nd rte of chnge of the error. We denote e(t), nd y(t) s error, rte of chnge of error nd system output, respectively. A fuzzy set for e(t) (or ) is denoted s M (or L) nd the corresponding membership is designted s or. Throughout this work, Gussins membership functions for the two inputs of the premise prt of T-S fuzzy system re used. The error e(t) nd the rte of chnge of the error re normlized using three Gussin membership functions; negtive N, zero Z, nd positive P, so tht nine rules constitute the rule bse for ech module. For simplicity, the consequent prt hs been chosen to be first order function of e(t) nd. The rule bses hve the following form: Rule j: If e(t) is M nd is L then k i = ij e(t)+b ij de(t)/dt Where k i = f (e(t), de(t)/dt) is the gin to be tuned, i.e. K p, K i or K d. ij nd b ij re the constnts, nd j=1, 2, 9 is the rule number. In this pper, the weighted verge technique is utilized to get the overll fuzzy output s follows: Given pir of e(t), ), the finl output of the fuzzy system is inferred s follows [22]:, /,, (9),, ISSN: 1991-8763 432 Issue 12, Volume 6, December 2011
WSEAS TRANSACTIONS on SYSTEMS nd CONTROL,, Where, is the grde of membership of, in M nd L. In this pper we ssume tht, w j (e(t), de(t)/dt) 0 for j=1,2,,r, 0 for ll t. Therefore we obtin, 0 for j=1,2,,r nd, 1 Remrk 3: Our pproch is different from those of [11], [12] nd [13] in the following wys. (1) A Tkgi Sugeno type of the fuzzy PID control system is ssumed insted of incrementl fuzzy PID control system. (2) The input membership functions of T-S fuzzy tuner re ssumed to be constnt (i.e. the membership function s center c nd its spred σ re constnt over ech rules nd fuzzy system). (3) The totl no. of free prmeters to be tuned in is 117 prmeters while in our proposed design procedures re 54 prmeters (i.e. smller computtionl burden). 6 ASO lgorithm bsed T-S fuzzy optiml prmeter determintion 6.1 Ant System Optimiztion The Ant System is the first member of clss of lgorithms clled Ant Colony Optimiztion (ACO) tht ws initilly proposed by Colorni, Dorigo nd Mniezzo[23]. This technique is dopted in this pper due to its simplicity. The min underlying ide, loosely inspired by the behvior of rel nts, is tht of prllel serch over severl constructive computtionl threds bsed on locl problem dt nd on dynmic memory structure contining informtion on the qulity of previously obtined result. In this lgorithm, computtionl resources re llocted to set of rtificil nts tht exploit form of indirect communiction medited by the environment to find the shortest pth from the nt nest to set trget. Ant lgorithms hve been proved to be quick globl optiml solution finder when compred to other heuristic methods such s simulted nneling nd genetic lgorithms. It lso sttes tht the nt lgorithms hve the qulity to find new optiml solution without reinititing the computtions from scrtch. 6.2 T-S Fuzzy PID optimiztion problem Usully, the optimiztion process consists of finding the controller prmeters such s to minimize or mximize given cost function of the closed loop system consisting of fuzzy PID controller nd n unknown plnt. The optimiztion of step response of the system under control by minimizing suitble performnce criterion is the im of this work. Ech T-S fuzzy module consists of constnt premise prmeters (tht is needn t to be optimized) nd 18 free consequence prmeters (tht will be optimized). The totl number of free prmeters to be optimized for the overll fuzzy system is 54. The AS lgorithm is pplied to optimize two different prmeter mtrices (A & B). These prmeters mtrices re driven by the consequence prts of fuzzy rule bse. The dimension of both prmeter mtrices is 3x9. The effectiveness of the proposed T-S Fuzzy controller is quntified by the following performnce criteri tht re evluted t the end of step response experiment. It includes the overshoot, settling time t s nd stedy stte error e ss of the system unit step response. The performnce criterion of the system F is designed s follows: F = λ ζ f 1 +λ ts f 2 +λ ess f 3 (10) Where λ ζ, λ ts nd λ ess re three weighting coefficients nd f 1, f 2 & f 3 re defined s follows: f 1 = ζ/ζ o,f 2 =t s /t so nd 0 0 0 (11) Where ζ o, t so nd e sso re the performnce vlues obtined from ZN tuning formul. The prmeters mtrices for the problem of tuning T-S fuzzy PID controller re defined s: & (12) Now, the control problem in this pper cn be formulted s follows: Given plnt G(s) to be controlled (Fig.14), determine the optimum vlues of the prmeters in (9) using nt system lgorithm, hence, find the optiml PID prmeters K p, T i nd T d so tht the control system hs the minimum vlue of given performnce criterion F (10). Fig. 14 depicts the closed loop control system used in this pper. ISSN: 1991-8763 433 Issue 12, Volume 6, December 2011
e Tkgi Sugeno Fuzzy Tuner T-S Fuzzy Sys 1 T-S Fuzzy Sys 2 Ant Sys. Fine Tuner SP + e T-S Fuzzy Sys 3 Fig. 14 The Proposed Closed loop Control System We ssume tht the vlue of ech prmeter inside the mtrices A & B hs two digits; one digit before deciml point nd the other fter the deciml point. Using nt system optimiztion frme work plnr structure of 10 rows nd 108 lines is dopted. 10 rows men the number of 0~9; 108 lines men 108 bits of 54 prmeters ij nd b ij. The nodes of lines~1~2~is the 1st~2nd bit of 11 ; line~3~4~is the 1st~2nd bit of b 11 ; line~5~6~is the 1st~2nd bit of 12; line ~7~8~is the 1st~2nd bit of b 12 nd so on till 39 & b 39. So, in the PID control AS, there re totlly 1080 nodes. n ij is used to denote the node j on line L i. The y coordinte of the node n ij is denoted by j. Let n nt deprt from the origin O. In its ech step forwrd, it chooses node from the next line L i (i=1, 2,, 108) nd then moves to this node long the stright line. When it moves to node on line L 108, it completes one tour. Its moving pth cn be expressed s Pth={O, n 1j, n 2j,, n 108j }. Obviously, the elements of A & B mtrices represented by this pth cn be computed by the following for loop Mtlb code: k=1; for i=1:3 for j=1:9 (i,j)=pth(1,k,m)+pth(1,k+1,m)*1e-1; b(i,j)=pth(1,k+2,m)+pth(1,k+3,m)*1e-1; k=k+4; end end (13) where k is dummy prmeter nd m is the totl no. of nts. 6.3 Proposed Algorithm Using the sme technique used in [24][24] or the nt system optimiztion, we cn modify the design lgorithm presented in [13] to tke into ccount the presence of T-S fuzzy system. The proposed AS Algorithm bsed T-S Fuzzy optiml PID prmeter determintion cn be summrized s follows: Step 1: Determine K po, K io nd K do using the clssicl Ziegler-Nichols tuning formul for given Kd Kp Ki PID Controller + + + G(S) y(t control system with PID controller nd compute the system's performnce indexes ζ o, t so nd e sso. Step 2: Specify the initiliztion prmeters of our proposed problem tht contin the following: Vlues of α, β, ρ, τ o nd m. The mximum number of itertions t mx. A one-dimensionl rry Pth k with 108 elements. Arry Pth k cn be used to denote the moving pth of nt k. Step 3: Set the itertion counter t=1 nd then plce ll of the m nts t the origin O. Step 4: Set i=1. Step 5: Set k=1. Step 6: Compute the trnsition probbility of ech node on line L i using the following formul,,,,,,,,,, Where η(i,j,t) is the visibility of the node (i,j) nd defined s η(i,j,t) = 10 j j* / 10 Where the vlues of j* re set in the following wy: In the first itertion of the AS lgorithm, the vlues of j* (i=1-108, j=0-9) re ssigned from the different vlues of the one dimensionl rry Pth k-initil. In ech of the following itertions, j* re determined from the clculted one dimensionl rry Pth k (it contins different entities of mtrices A & B) tht is corresponding to optiml trveling pth generted in the previous itertion by the nt α,β represent respectively the reltive importnce of the pheromone concentrtion nd visibility in trnsition probbility Step 7: Bsed on the clculted trnsition probbility in the previous step nd using Roulette wheel selection method, select node on line L i for nt k nd move nt k to this node, then sve the y coordinte of the node into the i th element of Pth k. Step 8: Set k k+1. If k m, go to Step 6; Otherwise, continue. Step 9: Set i i+1. If i 108, go to Step 5; Otherwise, continue. Step 10: For ech nt k (k=1, 2,, m): ccording to Pth k, compute different entities vlues of mtrices A & B using formul (12). Step 11: For ech nt k (k=1, 2,, m): evlute the PID gin vlues from the T-S fuzzy system ccording to formul (9). Step 12: For ech nt k (k=1, 2,, m): perform simultion experiment using the clculted mtrices A & B nd compute the system's performnce ISSN: 1991-8763 434 Issue 12, Volume 6, December 2011
WSEAS TRANSACTIONS on SYSTEMS nd CONTROL indexes, then compute the performnce criterion F k using formul (10). Step 13: Compre ll of the obtined F k vlues nd find the optiml nt pth of this itertion (Pth k- optiml), tht hs minimum vlue of the performnce criterion (i.e. F k, k=1,2,,m). Sve the Pth k- optiml nd the corresponding optiml PID gins. Step 14: Set ech element of Pth k to zero, k=1, 2,, m. Step 15: Updte the pheromone concentrtion of ech node on the moving nt pth using the following updting rule: τi,j,t ρτi,j,t Δτi,j Δ,, Where 0 < ρ < 1 is the pheromone decy prmeter τ k (i,j) is the mount of pheromone lid t n ij by nt k in the itertion just completed nd computed by the following formul: Δ,. 0 Where F k is the vlue of performnce criterion of nt k in the itertion just completed nd computed by the formul (10); Q is positive constnt. Step 16: Set t t +1. If t< t mx nd ll of the m nts do not mke the sme tour, plce ll the nts t the origin O nd go to Step 4; if t< t mx but ll of the m nts mke the sme tour or t = t mx, ; stop. 7 Simultion Exmple 7.1. Vlidtion simultion exmples Cse 1 (High-Order System) 1 1 1 0.011 0.051 0.2 controller (TSFASPID) re shown in Fig. 15-17 for ll the cses. The control performnce in these figures reflects the bility of the proposed control scheme in controlling different system. Hence, in the following section, it will be pplied to the WECS which presents interesting control demnds nd exhibits intrinsic non liner chrcteristics. Fig. 15 The unit step response of the control system using ASTSFPID controller cse (1) Unit Step Response 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 10 20 30 40 50 60 70 80 90 100 Time (sec.) Fig. 16 The unit step response of the control system using ASTSFPID controller cse (2) Cse 2 (Second Order System) 1 1.6 1 Cse 3 (Time dely System), 0.1, 1.0, 5.0 1 A unit step experiment is performed on closed loop control system tht is consisted of G(s) nd T-S fuzzy PID controller for ech cse. This controller is tuned vi Ant System lgorithm. The prmeters setting of the proposed lgorithm re: t mx =100, ρ=0.5, m=10, α =3 nd β = 2. The unit step responses of the control system with the proposed Tkgi Sugeno fuzzy nt system PID Fig. 17 The unit step response of the control system using ASTSFPID controller cse (3) ISSN: 1991-8763 435 Issue 12, Volume 6, December 2011
7.2. Stndlone WECS Simultion Using the Proposed Technique In this section, the proposed technique is pplied to the stndlone WECS configured in Fig. 18 to utomticlly control the terminl output voltge nd frequency of SESRIG when either the sttor lod impednce or the rotor speed chnges. The gol is to keep the voltge nd frequency t the vlue of 1 p.u. This is chieved by simultneously chnging the excittion cpcitor nd the dded rotor resistnce. 7.2.1. Chopper-controlled rotor externl resistnce A chopper-controlled externl resistnce my be employed, s illustrted in Fig. 18. Rotor voltge is firstly rectified using n uncontrolled diode bridge rectifier. A chopper controlled resistnce is connected on the dc output of the rectifier. Assuming tht the diodes in the rotor bridge rectifier re idel nd the choke is lossless, the effective externl resistnce per phse in the rotor circuit, referred to the sttor winding, is given by [25]: R x = 0.5n m 2 (1-D)R DC (14) As it cn be inferred from (14), chnging the duty cycle (D) of the chopper will result in chnging the effective rotor resistnce mens tht vrible externl resistnce is obtined in the rotor circuit. 7.2.2. Fixed cpcitor-thyristor controlled rector FC-TCR The scheme shown in Fig.18 comprises fixed excittion cpcitor (FC) in prllel with thyristor controlled rector (TCR). The vrition of the firing ngle of the thyristor results in vrible leding VARs. The effective susceptnce (B) per phse of such configurtion is given by [26]: (15) 7.2.3. Closed loop control The sttor terminl voltge nd the output frequency re chosen s the feedbck vrible since ny chnge in speed nd sttor lod impednce will result in corresponding chnge in the terminl voltge nd output frequency. The sttor terminl voltge signl is compred with the voltge reference signl. The voltge error signl is fed to proportionl-plus-integrl (PI) controller tht outputs signl for the firing ngle of the thyristor controlled inductor (TCR). The output frequency signl is compred with the frequency reference signl. The frequency error signl is fed to nother PI controller tht outputs signl for the duty cycle of the chopper controlled resistnce. Approprite tuning of the PI controller is mndtory in order to give stisfctory dynmic performnce of the proposed stndlone WECS. Ziegler-Nichols (ZN) technique hs been widely used mong different trditionl tuning methods. For this purpose, the SESRIG my be pproximted s firstorder system with the following trnsfer function [21][21]: Gs= ke-st o Ts+1 where K system gin T time constnt of the system t o time dely of the system (16) Fig. 18 Schemtic Digrm for the system configurtion In our Mtlb code expressing the proposed nt system bsed Tkgi Seguno Fuzzy PI lgorithm tht introduced in section VI, the bove trnsfer function nd the gins of PI controller tht concluded from ZN technique in [21][21] re used. The ide is to strt the proposed lgorithm with ZN PI gins then enhnce the dynmic response of the closed loop system ccording to the performnce index in (10) vi the steps of the lgorithm. Finlly, the lgorithm will rech to the optiml prmeters of the PI controller tht cn be used in controlling the voltge nd the frequency of the stndlone WECS. 7.2.4. Closed Loop Control Simultion Results This section contins the results of three simultion experiments using MATLAB/SIMULINK environment to study the dynmic response of SESRIG bsed stndlone WECS with Tkgi Seguno Fuzzy bsed Ant System PI closed loop control. For the sck of comprison, the results with ZN-PI controller designed in [21][21] re lso presented. Firstly the response for chnging the rotor speed (b) while the sttor lod resistnce kept constnt is presented. Secondly the response for chnging the sttor lod resistnce (R L ) while the rotor speed (b) kept constnt is studied. Thirdly the response for chnging the rotor speed (b) followed with chnge in the sttor lod resistnce (R L ) is introduced. Figs 19-24 show the dynmic response (output voltge nd frequency) of the stndlone WECS subjected to the proposed nd trditionl control method. The proposed PI controllers (ASTSFPI) fter short trnsient time restored both the output terminl voltge nd frequency to the reference vlue (i.e. 1 p.u.) with resonble overshoot nd zero stedy stte error irrespective of chnging the rotor speed nd the sttor lod resistnce. As seen from the following figures, the ISSN: 1991-8763 436 Issue 12, Volume 6, December 2011
proposed control method outperforms the trditionl control method Fig. 19 Voltge Dynmic Response s b increses from 1.2 to 1.3 p.u t R L = 4 p.u. Fig.22 Frequency Dynmic Response s the lod increses from 4 to 4.3 p.u t b = 1.2 p.u. with the proposed nd the trditionl control Fig. 20 Frequency Dynmic Response s b increses from 1.2 to 1.3 p.u t R L = 4 p.u. Fig. 23 Voltge Dynmic response s b & R L chnge from b = 1.15 to 1.3 p.u nd from R L = 4.5 to 4.3 p.u. with the proposed nd the trditionl control Fig. 21. voltge Dynmic Response s the lod increses from 4 to 4.3 p.u t b= 1.2 p.u. with the proposed nd the trditionl control Fig. 24 Frequency Dynmic response s b & R L chnge from b = 1.15 to 1.3 p.u nd from R L = 4.5 to 4.3 p.u. with the proposed nd the trditionl control ISSN: 1991-8763 437 Issue 12, Volume 6, December 2011
Remrks 4: The proposed Ant colony tuning lgorithm for the fuzzy PID scheme extends nd develops the norml nt colony lgorithm in [13&24] used to tune the PID controller scheme. The globl optiml solution using the proposed lgorithm is reched in less thn 10 itertions offering fst convergence speed. The CPU time needed for obtining the globl optiml solution is pproximtely 5 seconds reflecting high computtionl efficiency. 8 Conclusion In this pper, n optiml Tkgi Seguno fuzzy PI controller is determined using nt system lgorithm. The proposed controller is used to control the output voltge nd frequency for stndlone WECS t the sending end of self-excited slip-ring induction genertor. The nt system lgorithm serch for the optiml prmeters of the consequent prt of the Tkgi Seguno fuzzy system tht is in turn produces the optiml PID gins. Stedy-stte performnce nd the control chrcteristics of the SESRIG hve been obtined from n equivlent circuit nlysis. It is shown tht with vrying rotor speed nd lod impednce both the frequency nd the output voltge of the SESRIG cn be mintined constnt by rotor resistnce control nd excittion cpcitnce control over wide rnge of speeds without exceeding the sttor current limit. The proposed lgorithm is esily implemented, hs good convergence property nd hs n efficient serching bility for the optiml PID controller. Computer simultion of closed-loop control for the WECS hs lso been described. It is shown tht the proposed technique is very effective nd useful for mking the self excited induction genertor fesible for remote windy res. Appendix Performnce nlysis nd experiments were conducted on three-phse, two-pole, 50-Hz, 380-V, 2.2-A, 1.1-kW, str/str connected slipring induction mchine whose per-unit equivlent circuit constnts re R 1 =0.0511, X 1 =0.0452, R 2 =0.0413, X 2 =0.0452. The mgnetiztion curve ws represented by the following set of describing equtions: E 1 = 2.5 0.7625 X m X m < 2.1824 E 1 = 3.805 1.3769 X m 2.1824 X m < 2.3608 E 1 = 13.1 5.3219 X m 2.3608 X m < 2.3941 E 1 = 7.36 2.9242 X m 2.3941 X m < 2.486 E 1 = 0 X m 2.486 References: [1] J.F.Mnwell, J.G. McGown, A.L. Rogers, Wind Energy Explined Theory, Design nd Appliction, John Wiley & sons LTD, Englnd, 2002. [2] Rjib Dtt nd V. T. Rngnthn, Vrible- Speed Wind Power Genertion Using Doubly Fed Wound Rotor Induction Mchine A Comprison With Alterntive Schemes, IEEE Trnsctions on Energy Conversion, Vol.17, No. 3, September 2002, pp. 414 421. [3] A. A. Shltout nd A. F. El-Rmhi, " Mximum power trcking for wind driven induction genertor connected to utility network", Applied Energy, Vol. 52, Issues 2-3, 1995, pp. 243-253. [4] Bdrul H. Chowdhury nd Srinivs Chellpill, "Double-fed induction genertor control for vrible speed wind power genertion", Electric Power Systems Reserch, Vol. 76, Issues 9-10, June 2006, pp. 786-800. [5] S.R.Vishnv nd Z.J.Khn, "Design nd Performnce of PID nd Fuzzy Logic Controller with Smller Rule Set for Higher Order System", Proceedings of the World Congress on Engineering nd Computer Science 2007, Sn Frncisco, USA, October 24-26, 2007. [6] Constntin Volosencu, Control of Electricl Drives Bsed on Fuzzy Logic, WSEAS Trnsctions on Systems nd Control Volume 3, Issue 9,September 2008, ISSN: 1991-8763. [7] SHIUH-JER HUANG nd YI-HO LO, Metl Chmber Temperture control by Using Fuzzy PID Gin Auto-tuning strtegy, WSEAS Trnsctions on Systems nd Control,Vol. 4, Issue 1, Jnury 2009, ISSN: 1991-8763 [8] Constntin Volosencu, Stbiliztion of Fuzzy Control Systems, WSEAS Trnsctions on Systems nd Control, Vol. 3, Issue 10, October 2008. [9] Lin, C.T. nd Lee, C.S.G., Neurl Fuzzy Systems: A Neurl-Fuzzy Synergism to Intelligent Systems, Englewood Cliffs: Prentice Hll, 1996. [10] Cordon, O., Herrer, F., Hoffmnn, F. nd Mgdlen, L., Genetic Fuzzy Systems: Evolutionry Tuning nd Lerning of Fuzzy Knowledge Bses (Singpore: World Scientific), 2001. [11] Abdel Bdie Shrkwy, "Genetic fuzzy self tuning PID controllers for ntilock brking ISSN: 1991-8763 438 Issue 12, Volume 6, December 2011
systems", Alexndri Engineering Journl, Vol. 45, No. 6, 2006, pp. 657-673. [12] Hdi Nobhri, Seid H. Pourtkdoust, "Optimiztion of fuzzy rule bses using continuous nt colony system", Proceeding of the first Interntionl Conference on Modeling, Simultion nd Applied optimiztion, Shrjh, U.A.E, Februry 1-3, 2005. [13] Tn Gun-zheng nd Dou Hong-qun, ACS lgorithm-bsed dptive fuzzy PID controller nd its ppliction to CIP-I intelligent leg, J.Cent. South Univ. Technol. (2007)04-0528- 09, Springer,DOI:10.1007/s11771-007-0103-3. [14] Hussein F. Solimn, Abdel-Ftth Atti, S. M. Mokhymr, M. A. L. Bdr, Fuzzy Algorithm for Supervisory Voltge/Frequency Control of Self Excited Induction Genertor, Act Polytechnic Vol. 46 No. 6, 2006. [15] Kong Yigng nd Wng Zhixin, Optiml Power Cpturing of Multi-MW Wind Genertion System, WSEAS Trnsctions on Systems Issue 3, Volume 7, Mrch 2008. [16] A.H.Besheer, Tuning Method for PID Control Scheme:A blended Ant System Optimiztion Technique with Tkgi Sugeno Fuzzy System, ICFC 2010 - Interntionl Conference on Fuzzy Computtion, Vlenci, Spin 24-26 October 2010. [17] Krl O. Jones, André Bouffet COMPARISON OF ANT COLONY OPTIMISATION AND DIFFERENTIAL EVOLUTION, Interntionl Conference on Computer Systems nd Technologies - CompSysTech 07, 2007. [18] M. G. Sy, Alternting Current Mchines, 5th ed. London, U.K.: Pitmn Publishers (ELBS), 1983. [19] T.F.Chn, Anlysis of self excited induction genertors using n itertive method, IEEE Trnsction on Energy Conversion, Vol. 10, No. 3, September 1995. [20] T. F. Chn, " Stedy Stte Anlysis of Self Excited Induction genertors", IEEE Trnsctions on Energy Conversion, Vol. 9. No. 2, June 1994. [21] T. F. Chn, K. A. Nigim, nd L. L. Li, Voltge nd Frequency Control of Self- Excited Slip-Ring Induction Genertors, IEEE Trnsctions on Energy Conversion, vol. 19, No. 1, Mrch 2004. [22] A.H.Besheer nd H.R.Emr Relxed LMI Bsed designs for Tkgi Sugeno Fuzzy Regultors nd Observers; Poly-Qudrtic Lypunov Function pproch, Proceedings of the 2009 IEEE Interntionl Conference on Systems, Mn, nd Cybernetics, Sn Antonio, TX, USA - October 2009. [23] DORIGO M, V. Mniezzo nd A. Colorni, Ant system:noptimiztion by colony of cooperting gents, IEEE Trnsction on Systems Mn nd cybernetics prt B, 26 (1), 1996, pp. 29-41. [24] Gunzheng Tn, Qingdong Zeng, Shengjun He nd Gungcho, Adptive nd robust design for PID controller bsed on nt system lgorithm,advnces in Nturl Computtion, Lecture Notes in Computer Science,Vol 3612/2005, 2005, 915-24, DOI:10.1007/11539902_113 [25] Muhmmd H. Rshid, Power Electronics: Circuits, Devices nd Applictions, Newyork, USA: Prentice Hll PTR, 2003. [26] Cludio A. Cnizres, "Power Flow nd Trnsient Stbility Models of FACTS Controllers for Voltge nd Angle Stbility Studies", IEEE Power Engineering Society Winter Meeting, Vol. 2, Issue, 2000, pp. 1447 1454. ISSN: 1991-8763 439 Issue 12, Volume 6, December 2011