Environmental Engineering Reference
In-Depth Information
with,
K
a
¼
0
:
5 q Ar
b
C
pmax
.
k
opt
ð
14
:
45
Þ
and
where
C
pmax
is
the
maximum
power
coefficient,
obtained
at k
opt
—see
Fig.
14.11
a.
Equation (
14.44
) shows a very simple and useful expression to set up the torque
in Regions 1 and 2 (below rated, Fig.
14.10
). The expression is based on the rotor
speed sensor X
r
and the C
p
/k curves provided by the blade manufacturer
(Fig.
14.11
). These curves usually give only a first approach for steady state and
laminar flow conditions. For a more complete approach, some improvement can be
done by slightly changing Eqs. (
14.44
) and (
14.45
), taking into account drive-train
losses and some additional dynamic conditions. Due to the erosion and dirtiness of
the blades and the variation of the air density at different weather conditions, the
aerodynamic power coefficient C
p
also becomes time variant. Then, for a more
advanced approach, a reduction of the constant K
a
, or the application of adaptive
techniques to estimate it, will be appropriate to optimize the energy capture
(Maximum Power Point Tracking, MPPT).
14.6 Research and Education Experiments
14.6.1 Effect of Number of Blades, Aerodynamic
and Generator Efficiency
As we saw in Sect.
14.2.1.3
, the generator torque T
g
, and as a result the generator
power P
g
and efficiency g
g
, varies with the rotor speed X
r
according to
Eqs. (
14.1
)-(
14.3
)—see also Fig.
14.20
a. At the same time, the number of blades
of the rotor affects the rotor speed and then the aerodynamic power coefficient C
p
,
as it was described in Sect.
14.3.2
and Eqs. (
14.7
)(
14.8
) and (
14.10
).
The rotor radius of each wind turbine is r
b
= 0.13 m, and the rotor effective
surface A
r
= p r
2
= 0.0531 m
2
. Knowing the normal air density q = 1.225 kg/m
3
,
and putting a wind turbine under the effect of an average wind speed of
v
1
= 4.24 m/s, a constant pitch angle b = 0, a constant yaw angle a = 0 and a
constant demanded electrical torque T
gd
, the results of the experiments for a rotor
with 2,3,4, and 6 blades are shown in Table
14.2
and Fig.
14.19
.
The last row shows the experimental results found for the aerodynamic power
coefficient C
p
for a rotor with 2, 3, 4 and 6 blades—see also Fig.
14.20
b.
The results are consistent with the typical aerodynamic power coefficient in
classical drag-machines. Additionally, the profile of the C
p
/N curve found is
similar to the experimental expression (
14.10
).
