Environmental Engineering Reference
In-Depth Information
Table 14.1 Parameters for wind turbine model (see Fig.
14.12
and [
2
])
K
l
low-speed shaft torsional stiffness coefficient
(Nm/rad)
B
l
low-speed shaft torsional damping
coefficient (Nms/rad)
K
h
high-speed shaft torsional stiffness coefficient
(Nm/rad)
B
h
high-speed shaft torsional damping
coefficient (Nms/rad)
h
l
angular position of the gearbox low- speed
part (rad)
h
h
angular position of the gearbox high-
speed part (rad)
T
l
torque applied to the gearbox by the low-
speed shaft (Nm)
T
h
torque applied to the gearbox by the
high-speed shaft (Nm)
R
t
gear ratio (-)
I
w
equivalent moment of inertia of gearbox
elements, at h
l
(kg m2)
v
1
upstream wind speed (m/s)
N number of blades (-)
m
t
mass of the tower (kg)
m
n
mass of the nacelle (kg)
m
h
mass of the hub (kg)
m
b
mass of each blade (kg)
r
b
blade radius (m)
h tower height (m)
y
t
axial displacement nacelle (m)
c angular displacement blade (rad)
K
t
tower stiffness coefficient (N/m)
B
t
tower damping coefficient (Ns/m)
K
b
blade stiffness coefficient (N/m)
B
b
blade damping coefficient (Ns/m)
I
r
moment of inertia of elements at X
r
(rotor,
blades, hub, shaft, etc.) (Kg m
2
)
Ig moment of inertia of elements at X
g
(generator, shaft, etc.) (Kg m
2
)
h
r
rotor angular position (rad)
h
g
generator angular position (rad)
X
r
¼
h
r
rotor angular speed (rad/s)
X
g
¼
h
g
generator angular speed (rad/s)
T
r
aerodynamic torque applied by the
wind on the rotor (Nm)
Tg antagonistic electrical torque applied on
the shaft (Nm)
F
T
thrust force applied by the wind on the rotor (N)
r
p
distance from the center of the rotor to the center of pressure, or point where the equivalent
lumped force F
T
is applied. r
p
= (2/3) r
b
(m)
of the system. For each angle (pitch and yaw), at the end of the actuator drive-train
(end of the gearbox—see Figs.
14.5
and
14.6
), there is an encoder. These encoders
are the same as the glide wheel on the rotor (see Fig.
14.7
c and [
6
]). They are
configured to record the absolute angle of the nacelle and tower for the pitch and
yaw angles, respectively—see Fig.
14.2
, numbers (7) and (8).
For measuring the electrical properties of the wind turbine there is a current
sensor (CurrentMeter for NXT) and a voltage sensor (VoltMeter for NXT) on each
wind turbine—see Figs.
14.7
d and e respectively, and Fig.
14.2
, numbers (9) and
(10). The current sensor has a resolution of 1 mA and can measure currents up to
12.5 A. The voltage sensor has a resolution of 1 mv and can measure voltages up
to 26 v. These sensors are very reliable and the inherent offset errors are easily
accounted for in software. Although they are not made by LEGO, they are built
specifically to work with LEGO NXT Intelligent Brick firmware and are shaped to
work the LEGO blocks [
6
]. Each sensor is directly connected to the NXT
microcontroller.
