Environmental Engineering Reference
In-Depth Information
power needs to be limited. Although there are both mechanical and electrical con-
straints, the more severe ones are commonly on the generator and the converter. Hence,
regulation of the power produced by the generator is usually intended, and this is the
main objective of this chapter for a DFIG (Doubly-Fed Induction Generator)-based
WT (Wind Turbine) using a second order sliding mode controller [
3
]. In particular,
three control aspects will be presented: (1) A high-gain observer to estimate the
aerodynamic torque [
4
]; (2) A high-order sliding mode speed observer [
5
]; (3) Fault-
ride trough performance using high-order sliding mode control [
6
].
Simulations using the NREL FAST code will be shown for validation purposes.
2.2 The Wind Turbine Modeling
The global scheme for a grid-connected wind turbine is given in Fig.
2.1
.
2.2.1 Turbine Model
The turbine modeling is inspired from [
7
]. In this case, the aerodynamic power P
a
captured by the wind turbine is given by
P
a
¼
1
2
pqR
2
C
p
ðÞ
v
3
ð
2
:
1
Þ
where the tip speed ratio is given by
k
¼
Rx
mr
v
ð
2
:
2
Þ
and where x
mr
is the wind turbine rotor speed, q is the air density, R is the rotor
radius, C
p
is the power coefficient, and v is the wind speed.
The C
p
- k characteristics, for different values of the pitch angle b, are illus-
trated in Fig.
2.2
. This figure indicates that there is one specific k at which the
turbine is most efficient. Normally, a variable speed wind turbine follows the C
pmax
to capture the maximum power up to the rated speed by varying the rotor speed to
keep the system at k
opt
. Then it operates at the rated power with power regulation
during high wind periods by active control of the blade pitch angle or passive
regulation based on aerodynamic stall.
The rotor power (aerodynamic power) is also defined by
P
a
¼
x
mr
T
a
ð
2
:
3
Þ
where T
a
is the aerodynamic torque.
