Environmental Engineering Reference
In-Depth Information
theoretical power can be extracted, no matter how well designed the turbine is. In
reality, after all the losses and friction are accounted for, only about 40-50 % is
actually extracted. C
T
has a similar explanation, but dealing with thrust force. Both
expressions depend on the TSR k and the blade pitch angle b.
Typical wind turbines are built up by five major components; tower, nacelle,
rotor, generator, and drive train. The nacelle is on top of the tower and houses the
drive train and the generator. The drive train is divided into two parts, the low-
speed shaft and the high-speed shaft. The rotor is attached to the low-speed shaft
and is driven by the wind. The velocity of the low-speed shaft is geared up
typically about hundred times. The low-speed shaft drives the induction generator
and electrical power is produced. Although lately, drive trains without gearboxes
are being developed. These are called direct drive solutions, where the wind
directly drives a permanent magnet synchronous generator. Recently, a novel
mathematical modeling and parameter tuning of the OC3-Hywind spar-type
floating wind turbine with a tuned mass damper (TMD) installed in nacelle is
proposed in [
21
].
A variety of control techniques are often solved by formulating the problem in
terms of Linear Matrix Inequalities
ðLMI
s
Þ
[
9
]. Formulating the problem in such
a way gives an opportunity to impose a special structure on the
LMI
variables.
This comes in very handy when it comes to constrained information systems. This
means that it is possible to design a controller which can handle the fact that not all
the information in the feedback loop is used. There can be several reasons for this,
i.e., some of the information is simply not needed, some of the sensors are
especially prone to failure, switching between controllers and they do not need the
same information, etc. State-feedback is widely used in control applications, but in
practice full state measurement is usually not possible. A more practical approach
is output-feedback. However, the output gain matrix is not computed as easily as in
the state-feedback case, where a simple change of variables converts a nonconvex
problem into a convex problem. In the output-feedback case, the gain matrix is not
directly isolated from the other
LMI
variables. In [
25
-
27
], they proposed an
explicit solution to calculate the gain matrix. In [
20
], an even simpler solution is
found. With the solution found in [
20
], it is possible to impose zero-nonzero
constraints on the
LMI
variables. An application of these developed methods to
wind turbines has been investigated in [
4
,
5
,
7
]. Other solutions to make the system
more tolerant to failures have been suggested in [
23
] and [
15
]. Faults in the grid
can also cause the turbine to behave in a nonsatisfactory manner, this is discussed
and dealt with in [
28
].
Nowadays, modern wind turbines are getting bigger and bigger and are often
located in harsh environments. This leads to larger loads on critical parts and the
possibility of sensor failure is always present. This chapter tries to alleviate these
two issues. A traditional controller might force the turbine to shut down completely,
if a sensor in the feedback loop should fail. With the controller designed in this
chapter, the turbine is able to stay in operation, although the failed sensor should of
course be fixed as soon as possible. This is not managed without consequences, as
will be discussed later in the chapter. The main contributions of this chapter are
