Environmental Engineering Reference
In-Depth Information
The generator efficiency—Fig.
14.20
a is modeled as a second order polyno-
mial, as shown in Eq.(
14.46
), where the rotor speed X
r
is in rpm and the generator
efficiency g
g
in per unit.
g
g
¼
6
:
8654
10
7
Þ
2
þ
0
:
6131
ð
X
r
945
ð
14
:
46
Þ
14.6.2 Rotor Speed Control with Pitch System
This section applies the control algorithm designed in Sect.
14.5.1
—Eq. (
14.42
)-
to regulate the rotor speed X
r
(t) of the wind turbine with the pitch angle actuator
b
d
(t) in Region 3 (above rated, Fig.
14.10
). The main objective of the pitch control
system is to regulate the rotor speed at the rated (nominal) value X
r
= X
r-ref
,
rejecting the wind disturbances v
1
, and avoiding over-speed situations that can be
dangerous for the turbine.
Figures
14.14
and
14.16
show the control system configuration and Figs.
14.21
,
14.22
,
14.23
the results of this experiment. The wind speed is set as a periodic
function v
1
= v
1m
+ v
1a
sin(2pft+ h) m/s, with v
1a
= 0.125 m/s, f = 0.2 Hz,
h = 58, and v
1m
= 3.66 m/s at 0 B t \ 25 s and t [ 31 s, and v
1m
= 4.3 m/s at
25 B t B 31 s—see Fig.
14.21
a. The rotor speed control system is set at a set
point rotor speed X
r
= X
r-ref
= 320 rpm.
Using the control algorithm calculated in Eq. (14.42), the wind turbine changes
the controller output (the demanded pitch angle or motor input b
di
) as shown in
Fig.
14.21
b, and then the nacelle pitch angle b, also shown in Fig.
14.21
b, to keep
the rotor speed X
r
at the nominal value X
r-ref
= 320 rpm, as shown in Fig.
14.22
a.
The experimental mechanical power at the rotor shaft P
a
given by the wind
speed v
1
, and the electrical power at the generator output P
g
are both shown in
Fig.
14.22
b. Finally Fig.
14.23
shows experimental results for (a) the wind speed
v
1
and blade tip speed X
r
r
b
; (b) the tip-speed ratio k; (c) the aerodynamic power
coefficient C
p
; and (d) the C
p
versus k plot.
14.6.3 Maximum Power Point Tracking for Individual Wind
Turbine
For Maximum Power Point Tracking (MPPT), Fig.
14.24
shows an experiment of
a 6-blade wind turbine working with a constant pitch angle b = 0, a constant yaw
angle a = 0, and under a wind speed profile v
1
= v
1m
+ v
1a
sin(2pft+ h), with
v
1m
= 4.75 m/s, v
1a
= 0.125 m/s and f = 0.2 Hz, h = 58. At time t = 20 s the
antagonistic electrical torque T
gd
(generator torque command) varies from 5.45 to
4.5 mNm—see Fig.
14.24
a. As a result the rotor speed X
r
speeds up from 560 rpm
(58.64 rad/s) to 625 rpm (65.45 rad/s)—see Fig.
14.24
c. This implies a change in
