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8/13/2019 16 Out Power Leveling of Wind Turbine Generator for All Operating Regions by Pitch Angle Control
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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).
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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
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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
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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
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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
Conventional methodProposed method
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]
Conventional methodProposed method
(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
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8/13/2019 16 Out Power Leveling of Wind Turbine Generator for All Operating Regions by Pitch Angle Control
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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.
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