Environmental Engineering Reference
In-Depth Information
twofold: First, an
H
1
controller is designed to minimize the effect of disturbance
on the controlled output, practically this means it is possible to dampen unwanted
oscillations on critical parts due to turbulent wind; and second, the controller is
designed as a priori to reduce effects of sensor failures that might occur.
This chapter is organized as follows. Section
6.2
describes the model under
consideration and how the wind turbine model and blade pitch actuators are
interconnected. Section
6.3
goes into the control design and how it is possible to
calculate the constrained gain matrix. Simulation results for both the linear model
and the nonlinear model are presented in Sect.
6.6
. Finally, concluding remarks
and suggestions to future work are discussed in Sect.
6.5
.
Notation. Throughout this chapter, the notations
R
n
and
R
n
m
denote,
respectively, the n dimensional Euclidean space and the set of all n
m real
matrices. Superscript ''
T
'' denotes matrix transposition and I and 0 are the identity
matrix and the zero matrix with compatible dimensions, respectively. The symbol
denotes Kronecker product. The notation P [ 0 means that P is real symmetric
and positive definite and the symbol * denotes the transpose elements in the
symmetric positions. diag
fg
represents a block diagonal matrix and the operator
sym
ðÞ
represents A
þ
A
T
. All
LMI
variables are written with boldface font.
6.2 Model Description
A wind turbine system can be divided into several interconnected subsystems, see
Fig.
6.3
. The complexity of the subsystems are often related to the control strategy.
A model for control purpose should not be overly complicated, but it should still
describe the most important dynamics. Which dynamics that are important or not,
will differ depending on the control objective. The model under consideration is
obtained from FAST (Fatigue, Aerodynamics, Structures, and Turbulence) [
13
],
which is a fully nonlinear wind turbine simulation software developed at the
National Renewable Energy Laboratory (NREL) in Denver, USA. The code
models the wind turbine as a combination of both rigid and flexible bodies. These
bodies are then connected with several degrees of freedoms (DOFs). The code
provides with a nonlinear model with up to 24 DOFs. The turbine model is floating
and is rated for 5 MW, the main specifications are summarized in Table
6.1
. More
detailed information about the specifications can be found in [
14
]. Figure
6.4
shows the floating wind turbine. The platform DOFs are also indicated on the
figure, they include; translational heave, sway and surge motion and rotational
yaw, pitch and roll motion. Heave movement is defined along the z-axis, sway is
along the y-axis, and surge is along the x-axis. Yaw motion is defined about z-axis,
pitch is about the y-axis and roll is about the x-axis. This gives six DOFs.
Four more DOFs are related to the tower, two for longitudinal direction and two
for lateral direction. Yaw motion of the nacelle provides one DOF. Variable
generator- and rotor speeds gives another two DOFs, this also includes drive train
