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Output Power Leveling of Wind Turbine Generatorfor All Operating Regions by Pitch Angle ControlRyosei Sakamoto1, Tomonobu Senjyu1, Member, IEEE, Tatsuto Kinjo1Student Member, IEEE,Naomitsu Urasaki1, Member, IEEE, Toshihisa Funabashi2Senior Member, IEEE,Hideki Fujita3, and Hideomi Sekine1AbstractEffective utilization of renewable energies such aswind energy is expected instead of the fossil fuel. Wind energyis not constant and windmill output is proportional to thecube of wind speed, which cause the generated power of windturbine generators to fluctuate. In order to reduce fluctuatingcomponents, there is a method to control pitch angle of bladesof windmill. We have proposed the pitch angle control usingminimum variance control in a previous work. However, it is acontrolled output power for only rated wind speed region. Thispaper presents a control strategy based on average wind speedand standard deviation of wind speed, and pitch angle controlusing a generalized predictive control in all operating regions forwind turbine generator. The simulation results with using actualdetailed model for wind power system show effectiveness of theproposed method.Index TermsGeneralized predictive control, output powerfluctuation, pitch angle control, wind turbine generator.I. INTRODUCTIONIN recent years, there have been problems such as exhaus-tion of fossil fuels, e.g., coal and oil, and environmentalpollution resulting from consumption. An effective utilizationof renewable energies such as wind energy is expected insteadof the fossil fuel 1. However, wind energy is not constantand windmill output is proportional to the cube of wind speed,which cause the generated power of wind turbine generator(WTG) to fluctuate. If capacity ratio of power source forWTG is very small, power source does not fluctuate thefrequency by output fluctuation. However, if the ratio becomeslarge, fluctuation of frequency for power system will increase.Wind farm for many WTG has the tendency of levelingoutput power. However, synchronization phenomena of windturbines in wind farm are reported 2. Thus, if synchroniza-tion of output fluctuation from synchronization phenomenais generated, effect of leveling output power may be lost.Considering above, recently, provision using power storagesystem is proposed, but the cost increases. Also provisionsfor stand-alone WTG is proposed 3, 4, such as variable-speed (V-S) WTG 5. In V-S mode electronic converters areinserted between the generator and the grid, or a doubly-fedinduction generator (DFIG) controlled by the rotor circuit is(1) Ryosei Sakamoto, Tomonobu Senjyu, Tatsuto Kinjo, NaomitsuUrasaki,Hideomi Sekine are with the Department of Electrical and ElectronicsEngineering, Faculty of Engineering, University of the Ryukyus, Okinawa,Japan (e-mail: k048482eve.u-ryukyu.ac.jp, b985542tec.u-ryukyu.ac.jp,e985538eve.u-ryukyu.ac.jp ), (2) Toshihisa Funabashi is with the MeidenshaCorporation, Tokyo, Japan (e-mail: funabashi-thonsha.meidensha.co.jp), (3)Hideki Fujita is with the Chubu Electric Power Co., Inc., Aichi, Japan (e-mail:Fujita.hidekichuden.co.jp).used 6. The V-S WTG can change a speed of rotor with windspeed variation, and can absorb a part of output fluctuationas rotation energy, and V-S WTG is especially useful in thisoperating region since the electronic converter can maximizethe conversion efficiency by controlling the generator torque5, 6. However, the cost has been increased since V-S WTGhas some electronic converters and system is complication. Onthe other hand, in medium-size to large-size WTG, the controlof the pitch angle is a usual method for output power controlabove rated wind speed 58. Several control methods forcontrolling of pitch angle have been reported so far, such as thebackstepping method, feed-forward method 1, 8. However,those methods have not considered the variation in parametersand effect of wind shear 9 for windmill. Hence, consideringabove, we proposed the pitch angle control using minimumvariance control 1012 and generalized predictive control(GPC) 13, 14 in our previous work. However, the methodsmentioned above have fixed pitch angle at 10 degree in belowrated wind speed and an actual wind speed distribution hasmore below rated wind speed. Thus, if many WTGs usingsquirrel-cage induction generators are interconnected to powersystem, output power fluctuation is supplied to power system.The V-S WTG occurs similar situations because the V-SWTG in below rated wind speed is based on the maximumenergy capture strategy that is corresponding to wind speedvariation. But the leveling of output power has a problemwhich is reduction of output power in below rated wind speed.However, a large-scaled wind farm could be increased innear future. Thus, in all operating regions, the output powerfluctuation control of stand-alone WTG becomes important.In this paper, output power leveling of WTG for all operat-ing regions by pitch angle control is proposed. The proposedmethod presents a control strategy based on average windspeed and standard deviation of wind speed, and pitch anglecontrol using GPC in all operating regions for WTG. Outputpower command is determined by approximate equation forwindmill output using average wind speed and, standarddeviation of wind speed is corrected by using fuzzy reasoning15. Output power of WTG for all operating regions areleveled by GPC, which is based on output power command.In addition, standard deviation of wind speed is correctedby using fuzzy reasoning, which corresponds to rapid changein wind speed. That means WTG using proposed method ispossible to provide stability operation for rapid change ofoperating point. Thus, proposed method is possible to leveloutput power of WTG for all operating regions by pitchVwPgPgoePitch angle control systemWindmill and generatorHydraulicservo systemCMDFig. 1. Wind generating system.angle control. Moreover, the proposed pitch angle controlis able to apply regardless of the kind of the generatorssuch as permanent magnet synchronous generator (PMSG),synchronous generator (SG), and DFIG. The simulation resultsusing actual detailed model for wind power system showeffectiveness of the proposed method.The paper is organized as follows. Section II provides a con-figuration of WTG system and equations. Section III describesthe control method of pitch angle control using GPC. SectionIV provides the pitch angle control law for all operatingregions. In Section V, an effectiveness of the proposed methodis demonstrated by simulation results. Conclusions are drawnin Section VI.II. WIND TURBINE GENERATOR SYSTEMThe block diagram of WTG is shown in Fig. 1. Subtractingoutput power command Pgofrom output power Pggivesoutput power error e that evaluates pitch angle commandCMDvia pitch angle control system. Output power Pgissmoothed by hydraulic servo system that is driving blade.A. Windmill and generatorWindmill output, Pwis given by the following equationPw=Cp(1,)V3wA2(1)where Vwis wind speed, is air density, A is cross-sectionof rotor for windmill, and Cpis power coefficient. Powercoefficient Cpis approximated by the following equationCp(1,) = c1()21+ c2()31+ c3()41(2)c1() = c10+ c11 + c122+ c133+ c144c2() = c20+ c21 + c222+ c233+ c244c3() = c30+ c31 + c322+ c333+ c344(3)where c10to c34represent by performance characteristic ofwindmill are constants, is pitch angle, 1is tip speed ratiothat is given by1=RVw(4)where is angular speed of rotor for windmill, R is radiusof windmill. Angular speed of rotor for windmill given by2=?2J(Pw Pg)dt(5)sqrtIG(slip)C (1, )p P (V )ww 2sJ1(,V )wslip( ) V wPgFig. 2. System configuration of windmill and generator.00.020.040.060.080.100.1205101520253035Vw15m/s17.5m/s20m/s22.5m/s24m/s12.5m/s deg Wind speedPitch angleControl quantity of pitch angle G( ) Fig. 3. Control quantity of pitch angle.where J is moment of inertia for windmill. Slip s is expressedwith the following equation by angular speed of rotor forwindmills =o o(6)where ois synchronous angular speed of rotor for generator.If angular speed of rotor for windmill is greater than orequal to synchronous angular speed of rotor for generator,electric power is generated by induction generator. WTG isused as squirrel-cage induction generator. Output power Pgcan be expressed byPg=3V2s(1 + s)R2(R2 sR1)2+ s2(X1+ X2)2(7)where V is phase voltage, s is slip, R1is stator resistance,R2is rotor resistance, X1is stator reactance, X2is rotorreactance. If energy loss is disregarded, Pw= Pgand Pwcan be approximated byPw= d1() + d2()V2w(8)d1() = 11+ 12 + 132+ 143d2() = 21+ 22 + 232+ 243where 11to 24are constants. The above equations areapplied to windmill and generator as shown in Fig. 2. Tipspeed ratio 1in (4) is calculated by wind speed Vwandangular speed of rotor for windmill in Fig. 2. Powercoefficient Cpof (2) and windmill output Pwof (1) and outputpower Pgare calculated by 1and pitch angle in Fig. 2.Angular speed of rotor for windmill in Fig. 2 is calculatedby Pwand Pg. Slip s in Fig. 2 is calculated by using (6).Finally, Pgis calculated by (7).00.20.40.60.81.01.2051015202530(a)(b)(c)(d) m/sp.u.VwPwWindmill outputWind speedcut-inratedcut-out=90deg. =90deg. =10deg.=1090deg.Fig. 4. Windmill output power curve.eVwG( )CMDPitch angle selector90deg10deg1+T sa1+T sbPTable2DFig. 5. Pitch angle control system.B. Pitch angle control systemControl quantity of pitch angle G() is given byG() =P=1A1+ A2Vw2(9)A1= 12+ 213 + 3142A2= 22+ 223 + 3242where P and are small-signal state variable of outputpower Pg, and pitch angle , respectively.Equation (9) depends on wind speed Vwso that feature ofG() in Fig. 3 is varying for cut-off wind speed 24 m/s fromrated wind speed 12.5 m/s. Controlling of pitch angle controlis according to windmill output power curve in Fig. 4. Forexample, wind speed range (a) in Fig. 4 is Pw= 0pu sothat pitch angle is fixed at = 90 degree because energy ofwindmill is the smallest at 90 degree. Wind speed range (b)is Pw= 0pu to Pw= 1pu so that pitch angle is fixed at = 10 degree because energy of windmill is the largest at 10degree. Wind speed range (c) is Pw= 1pu so that pitch angle is selected to keep windmill output Pw= 1pu. Finally,wind speed range (d) is Pw= 0pu so that pitch angle isfixed at = 90 degree for safety reasons. Fig. 5 shows thepitch angle control system that resolves pitch angle commandCMD, where output power error e is used as input into PDcontroller. Pitch angle variable is multiplied by outputpower signal P of PD controller and G() of (9), and byadding and , pitch angle command CMDis obtained asshown in Fig. 5. Where Table2D in Fig. 5 is feature in Fig. 3.As can be seen in Fig. 3, if Vw= 15 m/s, and = 20 degree,the control quantity of pitch angle G() will be 0.05. So G()1+T sc1CMD10 deg90 degFig. 6. Hydraulic servo system.VwPgPgoePitch angle control systemWindmill and generatorHydraulicservo systemCMDIdentifierGPCu2u1STRFig. 7. Pitch angle control system using GPC.is determined by wind speed and pitch angle as shown inFig. 5.C. Hydraulic servo systemHydraulic servo system is shown in Fig. 6. Originally,hydraulic servo system has nonlinear characteristics, but itis able to make first-order lag system 7, 8. Pitch anglecommand CMDis limited by limiter at the range of 10 degreeto 90 degree.III. CONTROL SYSTEMIn this paper, the proposed pitch angle control system usingGPC is shown in Fig. 7, where Pgo(k) is output powercommand, Pg(k) is output power, e(k) is output power errorof generator, u2(k) is control input of STR, k is number ofsampling. The error equation can by expressed byA(q1)e(k) = qkmB(q1)u2(k) +(k)(10)A=1 + a1q1+ + anqnB=b0+ b1q1+ + bmqmwhere kmis dead time, q1is backward shift operator, (k)is white noise that is equal to average value of zero anddecentralization 2, is differencing operator 1 q1, nand m are model order. For (10), GPC law is derived from byminimizing performance index J113, 14, which is givenbyJ = EN?j=1e(k + j)2+NU?j=12(j)u(k + j 1)2(11)where E = is expected value (interval average), 2(j) is aweighting function. For (11), first term of right-hand side issumming output power error e(k+j) for predictive interval N,and second term is summing difference of control input ufor control interval NU, which is multiplied by weightingfunction 2(j). In consequence, difference of control inputu(k+j1) for control interval NU is possible to minimizeoutput power error e(k + j) for interval j. Moreover, controlinput u2for GPC is limited by 2(j) so as to preventdivergence. In order to set up GPC law, Ej(q1) and Fj(q1)are calculated by1 = A(q1)Ej(q1) + qjFj(q1)(12)where Ej(q1) and Fj(q1) are expressed byEj(q1)= 1 + e1q1+ + ej1q(j1)Fj(q1)= f0+ f1q1+ + fnqn.Moreover, Rj(q1) and Sj(q1) are calculated byEj(q1)B(q1) = Rj(q1) + qjSj(q1)(13)where Rj(q1) and Sj(q1) are expressed byRj(q1)= r0+ r1q1+ + rj1q(j1)Sj(q1)= s0+ s1q1+ + sm1q(m1)At this time GPC law is set up byFp(q1)e(k) + Gp(q1)u(k) = 0(14)where polynomials are expressed byFp(q1) = p1F1(q1) + + pNFNSp(q1) = p1S1(q1) + + pNSNGp(q1) = 1 + q1Sp(q1)p1,p2,pN = 1,0,0? ? ?N1(RTR + 2)1RT2= diag2(j)R =r000r1r0.0rNU1rNU2r0.rN1rN2rNNU(15)IV. ALL OPERATING REGIONS LAWConventional method for pitch angle law is fixed at morethan cut-in wind speed and less than rated wind speed so thatoutput power for wind turbine generator is proportional to thefluctuation of wind speed at more than cut-in wind speed andless than rated wind speed. Thus, in order to achieve outputpower leveling of WTG for all operating regions by pitch anglecontrol, pitch angle control law have been extended as shownin Fig. 8 while fixed rated output power command have beenconverted to variable output power command. The decision ofoutput power command is described below.A. Output power commandIn (8), d1and d2are expressed as a function of pitch angle. When pitch angle is at 10 degree, captured energy of00.20.40.60.81.01.2051015202530 m/sp.u.VwPwWindmill outputWind speedcut-inratedcut-out=90deg. =90deg. =1090deg.Fig. 8. Pitch angle control system for all operating regions.windmill is maximized. Eq.(8) is replaced by output powercommand Pgoas a function of pitch angle at fixed pitchangle 10 degree. Thus, new output power command Pgoareexpressed byPgo(Vw) = d1+ d2V2w.(16)If wind speed information Vwis given as input to (16),generally outputpower command Pgois fluctuated by variationof wind speed. In order to smooth output power command,average wind speed and standard deviation of wind speed aredefined asVw=?t0Vw(t)dtt(0 t 600)(17)V=?t0?VwVw?2dtt(0 t 600).(18)Average wind speed of (17) is smoother information thaninstant wind speed. On the contrary, standard deviation ofwind speed for (18) is an index of error, which is expressedas dimension of distance to average wind speed from instantwind speed. Generally, statistic wind speed is the average of10 minutes so that time t of (17) and (18) are reset to 0 atevery 10 minutes, where instant wind speed of (16) is replacedby average wind speed of (17). Pgois expressed byPgo(Vw) = d1+ d2V2w.(19)Moreover, average wind speed of (19) is represented bydifference for average wind speed and standard deviation ofwind speed. Pgois expressed byPgo(Vw V) = d1+ d2(Vw V)2.(20)Three different calculations have been run. Fig. 9 shows thesimulation results with wind speed and output power commandPgofor (16), (19), and (20). In Fig. 9, a possibility that outputpower command Pgoof (20) exceeds captured maximum windenergy (by calculated (16) is the lowest of the three equations.This is very important and explanation is mentioned later.Moreover, output power leveling is achieved by using (20).B. Compensating value using fuzzy reasoningIf output power error e for difference of captured maximumwind energy and output power command Pgois too big, by51015200204060801001201401601802000100200300400500600T i m e s Eq.(16)Eq.(19)Eq.(20)Output power command Pgo kW Wind speed Vwm/sFig. 9. Simulation results with output power command.feedback of its value, control system has possibility to beunstable. Because GPC law heavily depends on output powererror e. In consequently, output power command Pgohas to besmaller than maximum wind energy. However, if wind speedis rapid change wind speed, WTG system has possibility thatoutput power command Pgoof (20) could not correspond.Authors present new method using fuzzy reasoning so thatabove-mentioned problems are solved. Fuzzy reasoning isdescribed by a set of “If-then” rules that is based on fuzzyrules so that it does not always have to need determinativeof model 15. Moreover, when mathematical expressions aredifficult by included complex or non-linear, it is considered tobe availableness. Thus, wind speed for standard deviation of(18) is changed asV= (k)?t0?VwVw?2dtt(0 t 600).(21)Compensating value (k) of (21) is determined by fuzzyreasoning so that above-mentioned problems are solved. (21)is the product of wind speed for standard deviation of (18)and compensating value (k). In consequence, output powercommand Pgois possible to correspond to variation of windspeed by adjusting (k). Proposed output power commandsystem is shown in Fig. 10. There are two input of fuzzyreasoning. One is difference of Vw(k) and Vw(k 1), where(k) is number of sampling. On the other hand, when comparedwith transient wind speed Vwand average wind speedVw,smaller Vnew(k) of its value is used as input of fuzzy rea-soning. Thus, one is represented as rapid change wind speed,the other is represented as state of wind speed at the moment.Output power command Pgois determined by (20) that uses(17) and (27). Compensating value (k) is adjusted by fuzzyrules and membership function are shown Fig. 11 as presentedin Table I. Generally, frequency distribution of wind speed hasleft-right asymmetry. In fact, frequency distribution is biasedtoward to left side that means weak wind side. In fact, even ifwind speed is high wind, wind speed has possibility that is ona rapid decline at short times. In consequence, setup of fuzzyrules and parameters of membership functions are determinedby prioritizing to prevent in rapid reduction for output powercommand Pgo. The ith of fuzzy rules is expressed asRule i : if Vnew(k) is Lkand Vw(k) is Mkthen (k) is Zl(22)k = 1,2,7, l = 1,2,49where Lk, Mkand Zlare membership functions respectively.Final fuzzy reasoning (k)is calculated by(k) =49?i=1wiZl?49?i=1wi(23)where goodness of fit wifor“Rule i” is expressed bywi= wVnewiwVwi(24)where wVnewiand wVwiare goodness of fit of membershipfunction for (22) respectively.V. SIMULATION RESULTSIn this paper, the effectiveness of the output power com-mand using proposed method is examined by simulationusing system model and parameters for mentioned in (3).Constant output power command using pitch angle control ofconventional system is compared with the proposed system.Simulation is allowed for influence of wind shear. Simulationparameters of windmill, induction generator, controller areshown in Table II. Sampling interval of controller is Ts= 1ms,and parameter 2of GPC, value of order m and n, andmaximum costing horizon N, and control horizon NU arebased on simulation results in achieved good performance.Output power error parameters of (10) are unknown. Thus,unknown parameters are determined by least square methodso that it is possible to identify the parameters online. If theparameter is not converged in the worst case, pitch angle con-trol system have possibility to be unstable. Proposed methodadds compensation u2to u1of conventional system as shownin Fig. 7. If we observe u2as unstable, u2is removed from thesystem. Moreover, application of system as shown in Fig. 7is simplicity. Hence, it is applied in existence of wind turbinesystem with comparative ease.A. Performance function of output powerPerformance of output power Pgleveling is represented asmaximum energy function Pmaxand leveling function Plevelwhich are expressed asPmax=?t0Pg(t)dt(25)Plevel=?t0?dPg(t)dt?dt.(26)If Pmaxof (25) is large, wind energy efficiency is goodperformance. On the other hand, Plevelof (26) is integralof the absolute value for the differentiation value of outputpower Pg. Thus, if Plevelis small, output power fluctuation issmall so that leveling of output power is good performance.In cut-in wind speed region to rated wind speed region, whenTABLE IFUZZYRULESVw(k)NBNMNSZOPSPMPBNBNBNBNBNBNMNSZONMNBNBNBNMNSZOPSNSNBNBNMNSZOPSPMVnew(k)ZONBNMNSZOPSPMPBPSNMNSZOPSPMPBPBPMNSZOPSPMPBPBPBPBZOPSPMPBPBPBPBNB=Negative BigNM=Negative MediumNS=Negative SmallPB=Positive BigPM=Positive MediumPS=Positive SmallZO=ZeroqVw(k)VwEq.(17) Fuzzy reasoning Vnew(k)minimum selectorEq.(21)Eq.(20)Pgo(k)VVw-1Fig. 10. Output power command system.01Vnew(k)NBL1NMNSZOPMPBPSl2m/sL2L3L4L5L6L7l3l4l1l5l6l7l8l9l1=5l2=5.375l3=6.5l4=7.625l5=8.75l6=9.875l7=11l8=12.125l9=12.5(a) Membership functions for Vnew(k).01Vw(k)NBM1NMNSZOPMPBPSm1m/sM2M3M4M5M6M7m2m3m4m5m6m7m1=-4.5m2=-3m3=-1.5m4=0m5=1.5m6=3m7=4.5(b) Membership functions for Vw(k).NBNSPS01NMZO(k)PMPBZ1Z2Z3Z4Z5Z6Z7z7z6z5z4z3z2z1z1=1.4z2=1.2z3=1.1z4=1z5=0.95z6=0.9z7=0.85(c) Membership functions for (k)Fig. 11. Membership functions.TABLE I ISIMULATIONPARAMETERSParameters of Windmillblade radius R14 minertia coefficient J62993 kgm2air density 1.225 kg/m3Parameters of Induction generatorrated output Pg275 kWphase voltage V4003 Vstator resistance R10.00397 stator reactance X10.0376 rotor resistance R20.00443 rotor reactance X20.0534 Control parameters for GPCweighting factor 2diag50(j)dead time order d1model order n3model order m3maximum costing horizon N5control horizon NU1pitch angle is fixed at 10degree, Pmaxis maximum. However,if pitch angel is fixed, input torque can not be controlled andresults with increasing Plevelin consequence, Pmaxand Plevelare related to trade-off.B. Simulation results with nominal parametersSimulation results with wind speed variation is shown inFig. 12. Here, amount of statistics for wind speed is definedas gust factorGu=Vw maxVw(27)where Vw maxis maximum transientwind speed of 10 minutesmean,Vwis average wind speed of 10 minutes mean. In periodbetween from March 1997 to March 1998, average of Guis 1.20 at 30m observation point on Miyako island in Japanand standard deviation of Guis 0.18. From Fig. 12(a), Guis 1.35. Thus, as can be seen in Fig. 12(a) wind speed ishigh wind. Output power Pgusing conventional method isshown in Fig. 12(b). In rated wind speed region, pitch anglecontrol using GPC constrains output power fluctuation andmaintain to rated output power 275kW. However, in belowrated wind speed region, output power fluctuation is same aswind speed. On the other hand, as can be seen in Fig. 12(c)the output power fluctuations are levelled by the applicationby the proposed method using GPC. Moreover, output powercommand does not exceed captured maximum wind energy.Thus, GPC is stable so that output power Pgis followingoutput power command Pgoby using pitch angle with GPC.Because standard deviation of wind speed Vis correctedappropriately by using compensating value (k) of Fig. 12(d).If wind speed is rapid decline (Vnew(k) of Big), (k) isbeforehand made up larger than 1. That is smoothed reductionfor output power command. It smoothes reduction for Pgo.In addition, if state of wind speed at the moment is high0204060801001201401601802005101520T i m e s Wind speed Vwm/s(a) Wind speed Vw.0204060801001201401601802000100200300400500T i m e s Generated power PgkWRated output 275kW(b) Generated power Pg(conventional method).0204060801001201401601802000100200300400500T i m e s Generated power PgOutput power command PgoGenerated power PgkW(c) Output power command Pgo(proposed method)and generated power Pg.0204060801001201401601802000.80.91.01.11.21.31.41.5Compensating rate T i m e s (d) Compensating rate (k).020406080100120140160180200101520253035T i m e s Pitch angle degConventional methodProposed method(e) Pitch angle .02040608010012014016018020001020304050Conventional methodProposed methodT i m e s Maximum energy function Pmax MJ(f) Maximum energy function Pmax.020406080100120140160180200024681012T i m e s Leveling function Plevel MWConventional methodProposed method(g) Leveling function Plevel.-0.14-0.12-0.1-0.08-0.06-0.04-0.020020406080100120140160180200-0.5-0.4-0.3-0.2-0.100.1T i m e s Identified parameters anIdentified parameters bmb0b1b2b3a1a2a3(h) Identified parameters.Fig. 12. Simulation results with wind speed variation.wind speed (Vnew(k) of Big), (k) is beforehand made upsmaller than 1. That is increasing energy efficiency. Pitch angleof Fig. 12(e) with variations are generated by wind shear.Output power Pgis a lot fluctuated by difference of a littlepitch angle in large-size and medium-size windmill. Proposedmethod with GPC is smoothed output, no effect of wind shearby opposite control input u2. Fig. 12(f) and Fig. 12(g) areshown in order to show the validity of the proposal methodnumerically. As compared with the conventional method, max-imum energy function Pmaxfor Fig. 12(f) of proposed methoddrops to about 2/3. Because pitch angle is fixed at 10 degreein below rated wind speed. However, as compared with theconventional method, leveling function Plevelfor Fig. 12(g)of proposed method drops to about 1/3. Since slope of Plevelfor proposed method is small compared with the conventionalmethod, if WTG is interconnected power system of smallcapacity such as small island, in particular proposed methodis validated for frequency fluctuation. Moreover, when outputpower fluctuation is compensated by power storage system,capacity of power storage system can be made small by apply-ing the proposed method. As shown in Fig. 12(h) parametersidentification confirmed instantaneously convergence. Thus,output power Pgis following output power command Pgobyusing pitch angle with GPC. Since the proposed method isusing wind speed information without predictive method, ithas to permit a certain amount of output power fluctuation.However, it does not have to assume the large prediction errorwhich poses a problem by the predictive method and outputpower leveling is achieved by proposed method.VI. CONCLUSIONThis paper presented output power leveling of WTG forall operating regions by pitch angle control. Proposed methodpresents a control strategy based on average wind speed andstandard deviation of wind speed, and pitch angle controlusing GPC in all operating regions for WTG. Output powercommand is determined by approximate equation for windmilloutput using average wind speed and standard dev