Environmental Engineering Reference
In-Depth Information
8
<
dI
rd
d/
sd
dt
dt
¼
rL
r
V
rd
R
r
I
rd
þ
sx
s
rL
r
I
rq
L
s
dI
rq
ð
2
:
6
Þ
dt
¼
rL
r
V
rq
R
r
I
rq
sx
s
rL
r
I
rd
sx
s
M
L
s
/
sd
:
T
em
¼
p
L
s
/
sd
I
rq
where r is the leakage coefficient (r = 1 - M
2
/L
s
L
r
).
2.3 Control of the DFIG-Based Wind Turbine
2.3.1 Problem Formulation
Wind turbines are designed to produce electrical energy as cheaply as possible.
Therefore, they are generally designed so that they yield maximum output at wind
speeds around 15 m/sec. In case of stronger winds, it is necessary to waste part of
the excess energy of the wind in order to avoid damaging the wind turbine. All
wind turbines are therefore designed with some sort of power control. This stan-
dard control law keeps the turbine operating at the peak of its C
p
curve.
T
ref
¼
kx
2
;
with k
¼
1
2
pqR
5
C
pmax
ð
2
:
7
Þ
k
opt
There is a significant problem with this standard control. Indeed, wind speed
fluctuations force the turbine to operate off the peak of its C
p
curve much of the
time. Tight tracking C
pmax
would lead to high mechanical stress and transfer
aerodynamic fluctuations into the power system. This, however, will result in less
energy capture.
To effectively extract wind power while at the same time maintaining safe
operation, the wind turbine should be driven according to the following three
fundamental operating regions associated with wind speed, maximum allowable
rotor speed, and rated power. The three distinct regions are shown by Fig.
2.4
,
where v
rmax
is the wind speed at which the maximum allowable rotor speed is
reached, while v
cut-off
is the furling wind speed at which the turbine needs to be
shut down for protection. In practice, there are three possible regions of turbine
operation, namely, the high-, constant- and low-speed regions. High speed oper-
ation (III) is frequently bounded by the power limit of the machine while speed
constraints apply in the constant-speed region. Conversely, regulation in the low-
speed region (I) is usually not restricted by speed constraints. However, the system
has nonlinear non-minimum phase dynamics in this region. This adverse behavior
is an obstacle to perform the regulation task [
9
].
A common practice in addressing DFIG control problem is to use a linearization
approach [
10
-
12
]. However, due to the stochastic operating conditions and the
inevitable uncertainties inherent in DFIG-based wind turbines, much of these control
