TELKOMNIKA ISSN: 1693-6930
Fluctuations Mitigation of Variable Speed Wind Turbine through Optimized…Ali Mohammadi 709
α sinα
0.5v v
o mo
d dou
− =
α
cos
α
0.5v v
o mo
d dou
− =
, sinα
v v
i i
qi
= ,
cos
α
v v
i i
di
=
, sinα
v v
o o
qo
= ,
, cos
α
v v
o o
do
=
i
v ,
o
v amplitude of the input and output voltage sources, R
i
, L
i
input resistance and inductance, R
o
, L
o
output resistance and inductance, C, capacitor capacity of dc-link between two converters,
i
ω ,
o
ω input and output electrical rotational speeds,
i
α ,
o
α phase angle of the input and output voltages
,
mi
A
,
mi
α ,
mo
A
,
mo
α amplitude and phase
modulation indices of input and output converters. In this model, pulse width modulation PWM technique from transforming switching reference frame into dqo is converted to modulation
indices as converter inputs. Note that amplitude and phase modulations are definably on interval [0 1] and [-π, π], respectively.
2.7. Overall Model of WECS
To achieve the overall modelling, it is essential to integrate the shared-variable equations and eliminate equivalent variables and form the state space representation as
follows:
, v
ω a
Ψ X
ω L
ω a
Ψ D
X X
r L
ω D
X r
R ω
a Ψ
ω Ψ
D ω
X L
ω a
Ψ D
X r
R ω
D X
r L
ω a
Ψ
qou b
1,0 dr
M r
o b
1,0 qr
2 M
ss r
o 2
b M
s o
b 1,0
ds ds
rr o
b 1,0
qs rr
s o
b 2
M r
o 2
b 1,0
qs
2
+ +
− +
+
+
−
+
− =
D
, v
ω a
Ψ D
X X
r L
ω D
X r
R ω
a Ψ
X ω
L ω
a Ψ
D X
r R
ω D
X r
L ω
a Ψ
ω Ψ
D ω
X L
ω a
Ψ
dou b
1,0 dr
2 M
ss r
o 2
b M
s o
b 1,0
qr M
r o
b 1,0
ds rr
s o
b 2
M r
o 2
b 1,0
qs ds
rr o
b 1,0
ds
2
+
−
+ +
−
+
− +
+ =
D
,
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
− −
− =
,
dr ss
r qr
r ds
M r
b dr
ψ
D X
r
ω Ψ
ω ω
Ψ
D X
r
ω Ψ
− −
+ =
[ ]
,
qgn qg
dg i
i qg
i i
qg
v v
i ω
L i
R L
1 i
− +
− −
=
[ ]
,
dgn dg
qg i
i dg
i i
dg
v v
i ω
L i
R L
1 i
− +
+ −
=
, i
α sinosα
A a
i α
sinα A
a Ψ
α cosα
A D
X a
Ψ α
sinα A
D X
a Ψ
α cosα
A D
X a
Ψ α
sinα A
D X
a v
dg i
mi mi
qg i
mi mi
dr o
mo mo
M qr
o mo
mo M
ds o
mo mo
rr qs
oi mo
mo rr
d
− +
− +
− +
− +
− −
− −
=
, 7
, 7
, 7
, 7
, 7
, 7
, T
J 1
T nJ
1 ω
J D
ω
e g
s g
r t
t r
+ +
− =
, T
nJ D
T J
D T
J n
1 J
1 ω
J D
D ω
J D
D T
e g
s t
t s
s g
2 t
r g
g s
t t
t s
s
+ +
+ −
− −
− =
s s
s
D K
n K
1
.
β τ
1
β τ
1
β
ref
β β
+ −
=
22 where subscript g denotes grid variables replaced for input variable subscript i and
,
1 rr
o b
1,0
D X
L ω
1 a
−
+ =
. C
0.75 a
7,0
= To make sure of valid modelling, the simulated WECS is proposed to inject active and
, T
J 1
T J
1 ω
J D
ω
t t
s t
t t
t t
+ −
− =
ISSN: 1693-6930
TELKOMNIKA
Vol. 10, No. 4, December 2012 : 703 – 714 710
reactive power conveniently in an open loop manner.
2.8. Control Design
For the MIMO system under study, a centralised controller based on PID in cascaded scheme Figure 5 is employed, due to its easy implementation and common application in
industry. Variables to problem design are injected reactive and active power into the grid, q-axis current and dc-link voltage. Compensator dimension with respect to manipulated and controlled
variables is assigned as
4 4
×
. As WECS under study is extremely nonlinear, PID coefficients assignment is a challenging task to meet the best performance. In this study, there has been an
attempt to employ the approach including simple implementation using GA rather than methods based on control principle as pole placement. As a PID includes K
p
, P
i
, T
d
coefficients, totally, there are 16 optimal parameters. The aim to control is to have the most optimal performance in
reference tracking. Among different performance indices common in control principle, Integral Abs Error IAE is preferred to others due to involving reasonable view of error reduction. This
multi-objective problem is easily convertible into single objective through weighted-sum method [21] as follows:
∑
=
=
4 1
i i
i
IAE C
Fk min
23 where
i
C
,
i
IAE
are the weight and IAE asscociated to the i
th
controlled variable.
3. Results and Analysis
