ISSN: 1693-6930
TELKOMNIKA
Vol. 10, No. 4, December 2012 : 703 – 714 706
6 5
2 m
m 2
v ω
L 1
v L
0.475σ ω
S
+
= .
7
Considering wind speed passing through the blades, high frequency damping and shadow effect are about to be modelled. High frequency damping can be approximately represented as
a low pass filter [15].
1 τs
1 Hs
+ =
8 Shadow effect results in periodic torque pulsation caused by passing any blade across
the tower. This phenomenon is modelled by adding a sinusoidal periodic torque at N times mechanical speed where N is blades number
[16]. Figure 2 demonstartes the wind speed in time domain, considering the effective model above. The Wind tunnel parameteres are available
in Appendix I.
2.4. Pitch Angle Model
To track desired pitch angle, a control system is needed. This task is accomplished via the hydraulic actuator. Pitch angle dynamic is represented as a first-order constrained by the
amplitude and derivative of the output pitch Figure 2. With the assumption to working in linear region, state space to pitch angle is yielded as Equation 9 where
ref
β denotes desired pitch
angle and
β
τ time constant. Practically, β ranges from −2
o
to 3
o
and varies at a maximum rate of ±10 os
[17] . β
β τ
1 β
ref β
− =
9
2.5. Generator Model
To consider the electromagnetic torque meaningfully, it is necessary to develop all dynamics associated to the generator. In this study, squirrel cage induction generator IG is
employed. Due to simplicity, machine equations are described at dqo reference frame.
Figure 2. Wind speed simulation Hence, it is essential to transform abc coordinates into synchronously rotating dqo reference
frame through Park transformation as follows [18]:
1 2
9.85 10.00
10.15
Duration [sec] W
in d
s p
e e
d [
m s
e c
] Effective wind speed
Mean wind speed
TELKOMNIKA ISSN: 1693-6930
Fluctuations Mitigation of Variable Speed Wind Turbine through Optimized…Ali Mohammadi 707
Figure 3. Pitch angle block digram
+ −
+ −
=
c b
a 3
2π 3
2π 3
2π 3
2π d
q
f f
f sinθ
sinθ sin
cosθ cosθ
cos f
f θ
θ
10
where,
∫
= ω
dt θ
,
ω
set to stator electrical speed at synchronously rotating reference frame. Further, IG state equations in terms of flux linkage is represented as
[18]:
qs b
qr M
s b
ds qs
rr s
b qs
v
ω ψ
D X
r
ω ωΨ
Ψ
D X
r
ω Ψ
+ +
− −
=
11
ds b
dr M
s b
qs rr
s b
qs ds
v
ω ψ
D X
r
ω Ψ
D X
r
ω ωΨ
Ψ
+ +
− =
12
dr r
qr ss
r b
qs M
r b
qr
ψ ω
ω Ψ
D X
r
ω Ψ
D X
r
ω Ψ
− −
− =
13
dr ss
r qr
r ds
M r
b dr
ψ
D X
r
ω Ψ
ω ω
Ψ
D X
r
ω Ψ
− −
+ =
14 where,
qs
ψ
,
qs
ψ
q-axis and d-axis stator flux linkages ,
qr
ψ
,
dr
ψ
q-axis and d-axis rotor flux linkages,
M ls
ss
X X
X +
=
,
M lr
rr
X X
X +
=
,
2 M
rr ss
X X
X D
− =
, r
s
, r
r
stator and rotor resistances, X
ls
, X
lr
stator and rotor leakage reactances and X
M
magnetization reactance, ω ,
r
ω ,
b
ω stator electrical angular speed, rotor electrical angular speed and base angular speed,
qs
v ,
ds
v
, q-axis and d-axis stator voltages. Finally, the developed electromagnetic torque is computed in terms of the flux linkages and poles number p as:
qr ds
dr qs
b M
e
Ψ Ψ
Ψ Ψ
D
ω
X 2
p 2
3 T
− =
15 Alternatively, IG currents are calculated in terms of flux linkages in the following matrix.
Ψ Ψ
Ψ Ψ
− −
− −
=
dr qr
ds qs
ss M
ss M
M rr
M rr
dr qr
ds qs
X X
X X
X X
X X
D i
i i
i 1
16
ref
β β
Controller Limiter
Integrator
ISSN: 1693-6930
TELKOMNIKA
Vol. 10, No. 4, December 2012 : 703 – 714 708
Figure 4. VSC-VSC topology
2.6. Converter Model
