16 out power leveling of wind turbine generator for all operating regions by pitch angle control

8/13/2019 16 Out Power Leveling of Wind Turbine Generator for All Operating Regions by Pitch Angle Control

1/8

Output Power Leveling of Wind Turbine Generator

for All Operating Regions by Pitch Angle Control

Ryosei Sakamoto1, Tomonobu Senjyu1, Member, IEEE, Tatsuto Kinjo1 Student Member, IEEE,

Naomitsu Urasaki1, Member, IEEE, Toshihisa Funabashi2 Senior Member, IEEE,

Hideki Fujita3, and Hideomi Sekine1

Abstract Effective 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. This

paper presents a control strategy based on average wind speed

and 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 Terms Generalized predictive control, output powerfluctuation, pitch angle control, wind turbine generator.

I. INTRODUCTION

IN 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 utilization

of renewable energies such as wind energy is expected instead

of 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 for

WTG is very small, power source does not fluctuate the

frequency by output fluctuation. However, if the ratio becomes

large, fluctuation of frequency for power system will increase.

Wind farm for many WTG has the tendency of leveling

output power. However, synchronization phenomena of wind

turbines in wind farm are reported [2]. Thus, if synchroniza-

tion of output fluctuation from synchronization phenomena

is generated, effect of leveling output power may be lost.

Considering above, recently, provision using power storage

system is proposed, but the cost increases. Also provisions

for stand-alone WTG is proposed [3], [4], such as variable-

speed (V-S) WTG [5]. In V-S mode electronic converters are

inserted between the generator and the grid, or a doubly-fed

induction 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: [email protected], [email protected],[email protected] ), (2) Toshihisa Funabashi is with the MeidenshaCorporation, Tokyo, Japan (e-mail: [email protected]), (3)Hideki Fujita is with the Chubu Electric Power Co., Inc., Aichi, Japan (e-mail:[email protected]).

used [6]. The V-S WTG can change a speed of rotor with wind

speed variation, and can absorb a part of output fluctuation

as rotation energy, and V-S WTG is especially useful in this

operating region since the electronic converter can maximize

the conversion efficiency by controlling the generator torque

[5], [6]. However, the cost has been increased since V-S WTG

has some electronic converters and system is complication. On

the other hand, in medium-size to large-size WTG, the control

of the pitch angle is a usual method for output power controlabove rated wind speed [5][8]. Several control methods forcontrolling of pitch angle have been reported so far, such as the

backstepping method, feed-forward method [1], [8]. However,

those methods have not considered the variation in parameters

and effect of wind shear [9] for windmill. Hence, considering

above, we proposed the pitch angle control using minimum

variance control [10][12] and generalized predictive control(GPC) [13], [14] in our previous work. However, the methods

mentioned above have fixed pitch angle at 10 degree in below

rated wind speed and an actual wind speed distribution has

more below rated wind speed. Thus, if many WTGs using

squirrel-cage induction generators are interconnected to power

system, output power fluctuation is supplied to power system.The V-S WTG occurs similar situations because the V-S

WTG in below rated wind speed is based on the maximum

energy capture strategy that is corresponding to wind speed

variation. But the leveling of output power has a problem

which is reduction of output power in below rated wind speed.

However, a large-scaled wind farm could be increased in

near future. Thus, in all operating regions, the output power

fluctuation 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 proposed

method presents a control strategy based on average wind

speed and standard deviation of wind speed, and pitch angle

control using GPC in all operating regions for WTG. Outputpower command is determined by approximate equation for

windmill output using average wind speed and, standard

deviation of wind speed is corrected by using fuzzy reasoning

[15]. Output power of WTG for all operating regions are

leveled by GPC, which is based on output power command.

In addition, standard deviation of wind speed is corrected

by using fuzzy reasoning, which corresponds to rapid change

in wind speed. That means WTG using proposed method is

possible to provide stability operation for rapid change of

operating point. Thus, proposed method is possible to level

output power of WTG for all operating regions by pitch


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Vw

PgPgoe Pitch angle

control system

Windmill and generator

Hydraulicservo system

CMD

Fig. 1. Wind generating system.

angle control. Moreover, the proposed pitch angle control

is able to apply regardless of the kind of the generators

such as permanent magnet synchronous generator (PMSG),

synchronous generator (SG), and DFIG. The simulation results

using actual detailed model for wind power system show

effectiveness of the proposed method.

The paper is organized as follows. Section II provides a con-

figuration of WTG system and equations. Section III describes

the control method of pitch angle control using GPC. Section

IV provides the pitch angle control law for all operatingregions. In Section V, an effectiveness of the proposed method

is demonstrated by simulation results. Conclusions are drawn

in Section VI.

II. WIND TURBINE GENERATOR SYSTEM

The block diagram of WTG is shown in Fig. 1. Subtracting

output power command Pgo from output power Pg gives

output power error e that evaluates pitch angle commandCM D via pitch angle control system. Output power Pg is

smoothed by hydraulic servo system that is driving blade.

A. Windmill and generator

Windmill output, Pw is given by the following equation

Pw= Cp(1, ) V

3w A

2 (1)

where Vw is wind speed, is air density, A is cross-section

of rotor for windmill, and Cp is power coefficient. Power

coefficient Cpis approximated by the following equation

Cp(1, ) =c1() 21+ c2()

31+ c3()

41 (2)

c1() =c10+ c11+c122 + c13

3 + c144

c2() =c20+ c21+c222

+ c233

+ c244

c3() =c30+ c31+c322 + c33

3 + c344 (3)

where c10 to c34 represent by performance characteristic of

windmill are constants, is pitch angle, 1 is tip speed ratio

that is given by

1= R

Vw(4)

where is angular speed of rotor for windmill, R is radius

of windmill. Angular speed of rotor for windmill given by

2 =

2

J(PwPg) dt (5)

sqrt IG(slip)C (1, )p P (V )ww2sJ

1(,V )w

slip( )

Vw

Pg

Fig. 2. System configuration of windmill and generator.

0

0.02

0.04

0.06

0.08

0.10

0.12

0 5 10 15 20 25 30 35

Vw15 [m/s]17.5[m/s]20 [m/s]22.5[m/s]24 [m/s]

12.5[m/s]

[ deg ]

Wind speed

Pitch angle

Controlquantityofpitchangle

G(

)

Fig. 3. Control quantity of pitch angle.

whereJis moment of inertia for windmill. Slip sis expressed

with the following equation by angular speed of rotor for

windmill

s= o

o(6)

whereois synchronous angular speed of rotor for generator.

If angular speed of rotor for windmill is greater than or

equal to synchronous angular speed of rotor for generator,electric power is generated by induction generator. WTG is

used as squirrel-cage induction generator. Output power Pgcan be expressed by

Pg = 3V2s (1 +s) R2

(R2 sR1)2 + s2 (X1+ X2)2 (7)

where V is phase voltage, s is slip, R1 is stator resistance,

R2 is rotor resistance, X1 is stator reactance, X2 is rotor

reactance. If energy loss is disregarded, Pw = Pg and Pwcan be approximated by

Pw = d1() +d2() V2

w (8)

d1() =11+12+ 132 + 14

3

d2() =21+22+ 232 + 24

3

where 11 to 24 are constants. The above equations are

applied to windmill and generator as shown in Fig. 2. Tip

speed ratio 1 in (4) is calculated by wind speed Vw and

angular speed of rotor for windmill in Fig. 2. Power

coefficient Cpof (2) and windmill output Pwof (1) and output

power Pg are calculated by 1 and pitch angle in Fig. 2.

Angular speed of rotor for windmill in Fig. 2 is calculated

by Pw and Pg. Slip s in Fig. 2 is calculated by using (6).

Finally,Pgis calculated by (7).


3/8

0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25 30

(a) (b) (c) (d)

[m/s]

[p.u.]

Vw

Pw

W

indmilloutput

Wind speed

cut-in

rated cut-out

=90deg. =90deg.=10deg. =10~90deg.

Fig. 4. Windmill output power curve.

e

Vw

G( ) CMD

Pitch angle selector

90deg

10deg

1+T sa

1+T sb P

Table2D

Fig. 5. Pitch angle control system.

B. Pitch angle control system

Control quantity of pitch angle G()is given by

G () =

P =

1

A1+A2Vw2 (9)

A1 = 12+ 213+ 3142

A2 = 22+ 223+ 3242

where P and are small-signal state variable of outputpowerPg, and pitch angle , respectively.

Equation (9) depends on wind speed Vw so that feature of

G()in Fig. 3 is varying for cut-off wind speed 24 m/s fromrated wind speed 12.5 m/s. Controlling of pitch angle control

is according to windmill output power curve in Fig. 4. For

example, wind speed range (a) in Fig. 4 is Pw = 0pu sothat pitch angle is fixed at = 90degree 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= 10degree because energy of windmill is the largest at 10

degree. 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 = 90degree for safety reasons. Fig. 5 shows thepitch angle control system that resolves pitch angle command

CM D , where output power error eis used as input into PD

controller. Pitch angle variable is multiplied by outputpower signal Pof PD controller and G() of (9), and byaddingand , pitch angle command CM D is obtained asshown in Fig. 5. Where Table2D in Fig. 5 is feature in Fig. 3.

As can be seen in Fig. 3, ifVw = 15m/s, and= 20 degree,the control quantity of pitch angle G()will be 0.05. SoG()

1+Tsc

1CMD

10 deg

90 deg

Fig. 6. Hydraulic servo system.

Vw

PgPgoe Pitch angle

control system

Windmill and

generator

Hydraulic

servo system

CMD

Identifier

GPC u2

u1

STR

Fig. 7. Pitch angle control system using GPC.

is determined by wind speed and pitch angle as shown in

Fig. 5.

C. Hydraulic servo system

Hydraulic servo system is shown in Fig. 6. Originally,

hydraulic servo system has nonlinear characteristics, but it

is able to make first-order lag system [7], [8]. Pitch angle

commandCM Dis limited by limiter at the range of10degreeto90 degree.

III. CONTROL SYSTEM

In this paper, the proposed pitch angle control system using

GPC 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 by

A(q1)e(k) =qkmB(q1)u2(k) +(k)

(10)

A = 1 + a1q1 + + anqn

B = b0+b1q1 + +bmqm

where km is dead time, q1 is backward shift operator, (k)is white noise that is equal to average value of zero and

decentralization 2, is differencing operator 1 q1, nandm are model order. For (10), GPC law is derived from by

minimizing performance index J1 [13], [14], which is given

by

J=E

N

j=1

{e(k+j)}2 +NUj=1

2(j){u(k+j1)}2(11)

where E= []is expected value (interval average), 2(j)is aweighting function. For (11), first term of right-hand side is


4/8

summing output power error e(k+j)for predictive intervalN,and second term is summing difference of control input ufor control interval N U, which is multiplied by weighting

function 2(j). In consequence, difference of control inputu(k +j1)for control intervalN Uis possible to minimizeoutput power error e(k+j)for interval j . Moreover, controlinput u2 for GPC is limited by 2(j) so as to preventdivergence. In order to set up GPC law, Ej(q

1)and Fj(q1)

are calculated by

1 = A(q1)Ej(q1) + qj Fj(q

1) (12)

where Ej(q1)and Fj(q

1)are expressed by

Ej(q1) = 1 + e1q

1 + +ej1q(j1)Fj(q

1) =f0+ f1q1 + +fnqn.

Moreover, Rj(q1)and Sj (q

1)are calculated by

Ej(q1)B(q1) =Rj(q

1) + qj Sj (q1) (13)

where Rj(q1)and Sj (q

1)are expressed by

Rj(q1) =r0+r1q1 +

+ rj1q

(j1)

Sj (q

1) =s0+ s1q

1 + +sm1q(m1)At this time GPC law is set up by

Fp(q1)e(k) + Gp(q

1)u(k) = 0 (14)

where polynomials are expressed by

Fp(q1) =p1F1(q1) + +pNFN

Sp(q1) = p1S1(q

1) + +pNSNGp(q

1) = 1 +q1Sp(q1)

[p1, p2, , pN] = [1, 0, , 0

N1

](RTR+2)1

RT

2 = diag

{2(j)

}

R=

r0 0 0r1 r0

. . ....

.... . . 0

rNU1 rNU2 r0...

...

rN1 rN2 rNNU

(15)

IV. ALL OPERATING REGIONS L AW

Conventional method for pitch angle law is fixed at more

than cut-in wind speed and less than rated wind speed so that

output power for wind turbine generator is proportional to thefluctuation of wind speed at more than cut-in wind speed and

less than rated wind speed. Thus, in order to achieve output

power leveling of WTG for all operating regions by pitch angle

control, pitch angle control law have been extended as shown

in Fig. 8 while fixed rated output power command have been

converted to variable output power command. The decision of

output power command is described below.

A. Output power command

In (8), d1and d2are expressed as a function of pitch angle

. When pitch angle is at 10 degree, captured energy of

0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25 30

[m/s]

[p.u.]

Vw

Pw

Windmilloutput

Wind speed

cut-in

rated cut-out

=90deg. =90deg.=10~90deg.

Fig. 8. Pitch angle control system for all operating regions.

windmill is maximized. Eq.(8) is replaced by output power

command Pgo as a function of pitch angle at fixed pitch

angle 10 degree. Thus, new output power command Pgo are

expressed by

Pgo(Vw) = d1+d2V2w . (16)

If wind speed information Vw

is given as input to (16),

generally output power commandPgois fluctuated by variation

of wind speed. In order to smooth output power command,

average wind speed and standard deviation of wind speed are

defined as

Vw =

t0

Vw (t)dt

t (0< t600) (17)

V =

t0

VwVw

2dt

t (0< t600). (18)

Average wind speed of (17) is smoother information than

instant wind speed. On the contrary, standard deviation of

wind speed for (18) is an index of error, which is expressedas dimension of distance to average wind speed from instant

wind speed. Generally, statistic wind speed is the average of

10 minutes so that time t of (17) and (18) are reset to 0 at

every 10 minutes, where instant wind speed of (16) is replaced

by average wind speed of (17). Pgo is expressed by

Pgo(Vw) = d1+d2V2w . (19)

Moreover, average wind speed of (19) is represented by

difference for average wind speed and standard deviation of

wind speed. Pgo is expressed by

Pgo(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 command

Pgofor (16), (19), and (20). In Fig. 9, a possibility that output

power commandPgoof (20) exceeds captured maximum wind

energy (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 reasoning

If output power error efor difference of captured maximum

wind energy and output power command Pgo is too big, by


5/8

5

10

15

20

0 20 40 60 80 100 120 140 160 180 2000

100

200

300

400500

600

T i m e [ s ]

Eq.(16)Eq.(19)

Eq.(20)

OutputpowercommandPg

o[kW]

WindspeedVw[m/s]

Fig. 9. Simulation results with output power command.

feedback of its value, control system has possibility to be

unstable. Because GPC law heavily depends on output power

errore. In consequently, output power command Pgohas to besmaller than maximum wind energy. However, if wind speed

is rapid change wind speed, WTG system has possibility that

output power command Pgo of (20) could not correspond.

Authors present new method using fuzzy reasoning so that

above-mentioned problems are solved. Fuzzy reasoning is

described by a set of If-then rules that is based on fuzzy

rules so that it does not always have to need determinative

of model [15]. Moreover, when mathematical expressions are

difficult by included complex or non-linear, it is considered to

be availableness. Thus, wind speed for standard deviation of

(18) is changed as

V =(k)t

0VwVw2 dt

t (0< t600). (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 Pgo is possible to correspond to variation of wind

speed by adjusting (k). Proposed output power commandsystem is shown in Fig. 10. There are two input of fuzzy

reasoning. One is difference ofVw(k)and Vw(k1), where(k)is number of sampling. On the other hand, when comparedwith transient wind speed Vw and average wind speed Vw,

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 Pgo is determined by (20) that uses

(17) and (27). Compensating value (k)is adjusted by fuzzyrules and membership function are shown Fig. 11 as presented

in Table I. Generally, frequency distribution of wind speed has

left-right asymmetry. In fact, frequency distribution is biased

toward to left side that means weak wind side. In fact, even if

wind speed is high wind, wind speed has possibility that is on

a rapid decline at short times. In consequence, setup of fuzzy

rules and parameters of membership functions are determined

by prioritizing to prevent in rapid reduction for output power

commandPgo. The ith of fuzzy rules is expressed as

Rule i: if Vnew(k) is Lk and Vw(k) is Mk

then (k) is Zl (22)

k= 1, 2, , 7, l= 1, 2, , 49

where Lk, Mk and Zlare membership functions respectively.Final fuzzy reasoning (k)is calculated by

(k) =49

i=1

wiZl

49i=1

wi (23)

where goodness of fit wiforRule i is expressed by

wi= wVnewiwVwi (24)

where wVnewi and wVwi are goodness of fit of membershipfunction for (22) respectively.

V. SIMULATION RESULTS

In this paper, the effectiveness of the output power com-mand using proposed method is examined by simulation

using system model and parameters for mentioned in (3).

Constant output power command using pitch angle control of

conventional system is compared with the proposed system.

Simulation is allowed for influence of wind shear. Simulation

parameters of windmill, induction generator, controller are

shown in Table II. Sampling interval of controller is Ts = 1ms,and parameter 2 of GPC, value of order m and n, andmaximum costing horizon N, and control horizon N U are

based on simulation results in achieved good performance.

Output power error parameters of (10) are unknown. Thus,

unknown parameters are determined by least square method

so 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 method

adds compensation u2to u1of conventional system as shown

in Fig. 7. If we observe u2as unstable, u2is removed from the

system. Moreover, application of system as shown in Fig. 7

is simplicity. Hence, it is applied in existence of wind turbine

system with comparative ease.

A. Performance function of output power

Performance of output power Pgleveling is represented as

maximum energy function Pmaxand leveling function Plevel

which are expressed as

Pmax =

t0

Pg(t)dt (25)

Plevel =

t0

dPg(t)dt dt. (26)

If Pmax of (25) is large, wind energy efficiency is good

performance. On the other hand, Plevel of (26) is integral

of the absolute value for the differentiation value of output

power Pg. Thus, ifPlevelis small, output power fluctuation is

small so that leveling of output power is good performance.

In cut-in wind speed region to rated wind speed region, when


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TABLE IFUZZYRULES

Vw(k)NB NM NS ZO PS PM PB

NB NB NB NB NB NM NS ZONM NB NB NB NM NS ZO PSNS NB NB NM NS ZO PS PM

Vnew(k) ZO NB NM NS ZO PS PM PBPS NM NS ZO PS PM PB PBPM NS ZO PS PM PB PB PBPB ZO PS PM PB PB PB PB

NB=Negative Big NM=Negative Medium NS=Negative SmallPB=Positive Big PM=Positive Medium PS=Positive Small

ZO=Zero

q

Vw(k)

Vw

Eq.(17)

Fuzzy

reasoning

Vnew(k)

minimum selector

Eq.(21) Eq.(20)Pgo

(k)

V

Vw

-1

Fig. 10. Output power command system.

0

1

Vnew(k)

NB

L1

NM NS ZO PM PBPS

l2 [m/s]

L2 L3 L4 L5 L6 L7

l3 l4l1 l5 l6 l7 l8 l9

l1=5 l2=5.375 l3=6.5 l4=7.625 l5=8.75

l6=9.875 l7=11 l8=12.125 l9=12.5

(a) Membership functions for Vnew(k).

0

1

Vw(k)

NB

M1

NM NS ZO PM PBPS

m1 [m/s]

M2 M3 M4 M5 M6 M7

m2 m3 m4 m5 m6 m7

m1=-4.5 m2=-3 m3=-1.5 m4=0m5=1.5 m6=3 m7=4.5

(b) Membership functions for Vw(k).

NBNSPS

0

1NMZO

(k)

PMPBZ1Z2Z3Z4Z5Z6Z7

z7 z6 z5 z4 z3 z2 z1

z1=1.4 z2=1.2 z3=1.1 z4=1z5=0.95 z6=0.9 z7=0.85

(c) Membership functions for (k)

Fig. 11. Membership functions.

TABLE IISIMULATIONPARAMETERS

Parameters of Windmill

blade radius R 14 m

inertia coefficient J 62993 kgm2air density 1.225 kg/m3

Parameters of Induction generator

rated output Pg 275 kW

phase voltage V 4003Vstator resistance R1 0.00397stator reactance X1 0.0376 rotor resistance R2 0.00443rotor reactance X2 0.0534

Control parameters for GPC

weighting factor 2 diag{50(j)}dead time order d 1

model order n 3

model order m 3

maximum costing horizon N 5

control horizon N U 1

pitch angle is fixed at 10degree, Pmaxis maximum. However,

if pitch angel is fixed, input torque can not be controlled and

results with increasingPlevelin consequence, PmaxandPlevelare related to trade-off.

B. Simulation results with nominal parameters

Simulation results with wind speed variation is shown in

Fig. 12. Here, amount of statistics for wind speed is defined

as gust factor

Gu= Vw max

Vw (27)

whereVw maxis maximum transient wind speed of 10 minutes

mean, 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 Japan

and standard deviation of Gu is 0.18. From Fig. 12(a), Guis 1.35. Thus, as can be seen in Fig. 12(a) wind speed is

high wind. Output power Pg using conventional method is

shown in Fig. 12(b). In rated wind speed region, pitch angle

control using GPC constrains output power fluctuation and

maintain to rated output power 275kW. However, in below

rated wind speed region, output power fluctuation is same as

wind speed. On the other hand, as can be seen in Fig. 12(c)the output power fluctuations are levelled by the application

by the proposed method using GPC. Moreover, output power

command does not exceed captured maximum wind energy.

Thus, GPC is stable so that output power Pg is following

output power command Pgo by using pitch angle with GPC.

Because standard deviation of wind speed V is corrected

appropriately 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 reduction

for output power command. It smoothes reduction for Pgo .

In addition, if state of wind speed at the moment is high


7/8

0 20 40 60 80 100 120 140 160 180 2005

10

15

20

T i m e [ s ]

WindspeedVw[m/s]

(a) Wind speedVw.

0 20 40 60 80 100 120 140 160 180 2000

100

200

300

400

500

T i m e [ s ]

GeneratedpowerPg[kW]

Rated output 275kW

(b) Generated power Pg(conventional method).

0 20 40 60 80 100 120 140 160 180 2000

100

200

300

400

500

T i m e [ s ]

Generated power Pg

Output power command Pgo

GeneratedpowerPg[kW

]

(c) Output power commandPgo (proposed method)and generated power Pg .

0 20 40 60 80 100 120 140 160 180 2000.8

0.9

1.01.1

1.2

1.3

1.4

1.5

Compensatingrate

T i m e [ s ]

(d) Compensating rate (k).

0 20 40 60 80 100 120 140 160 180 20010

15

20

25

30

35

T i m e [ s ]

Pitchangle[deg]

Conventional methodProposed method

(e) Pitch angle.

0 20 40 60 80 100 120 140 160 180 2000

10

20

30

40

50


T i m e [ s ]MaximumenergyfunctionPmax[MJ]

(f) Maximum energy functionPmax .

0 20 40 60 80 100 120 140 160 180 2000

2

4

6

8

10

12

T i m e [ s ]LevelingfunctionP

level[MW]


(g) Leveling functionPlevel.

-0.14-0.12-0.1

-0.08-0.06-0.04-0.02

0

0 20 40 60 80 100 120 140 160 180 200

-0.5-0.4

-0.3-0.2-0.1

00.1

T i m e [ s ]

Identifiedparameters

an

Identifie

dparameters

bm

b0

b1 b2

b3

a1

a2 a3

(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 angle

of Fig. 12(e) with variations are generated by wind shear.

Output power Pg is a lot fluctuated by difference of a littlepitch angle in large-size and medium-size windmill. Proposed

method with GPC is smoothed output, no effect of wind shear

by opposite control input u 2. Fig. 12(f) and Fig. 12(g) are

shown in order to show the validity of the proposal method

numerically. As compared with the conventional method, max-

imum energy function Pmaxfor Fig. 12(f) of proposed method

drops to about 2/3. Because pitch angle is fixed at 10 degree

in below rated wind speed. However, as compared with the

conventional method, leveling function Plevel for Fig. 12(g)

of proposed method drops to about 1/3. Since slope ofPlevelfor proposed method is small compared with the conventional

method, if WTG is interconnected power system of small

capacity such as small island, in particular proposed methodis validated for frequency fluctuation. Moreover, when output

power 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) parameters

identification confirmed instantaneously convergence. Thus,

output power Pgis following output power command Pgo by

using pitch angle with GPC. Since the proposed method is

using wind speed information without predictive method, it

has to permit a certain amount of output power fluctuation.

However, it does not have to assume the large prediction error

which poses a problem by the predictive method and output


8/8

power leveling is achieved by proposed method.

VI. CONCLUSION

This paper presented output power leveling of WTG for

all operating regions by pitch angle control. Proposed method

presents a control strategy based on average wind speed and

standard deviation of wind speed, and pitch angle control

using GPC in all operating regions for WTG. Output powercommand is determined by approximate equation for windmill

output using average wind speed and standard deviation of

wind speed is corrected by using fuzzy reasoning. Thus, WTG

using proposed method is possible to stability operation for

rapid change of operating point. In the simulations, despite

rapid change of wind speed in below rated wind speed and

wind shear, output power leveling for all operating region is

achieved by proposed method.

REFERENCES

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16 out power leveling of wind turbine generator for all operating regions by pitch angle control

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