Environmental Engineering Reference
In-Depth Information
Generator effi ciency
h
gen
- It is related to all electrical and mechanical losses
in a wind generator, such as copper, iron, load, windage, friction, and other
miscellaneous losses.
Electric effi ciency
h
ele
- It encompasses all combined electric power losses in
the converter, switches, controls, and cables.
Therefore, the total power conversion effi ciency from wind to electricity
h
t
is
the production of these parameters, i.e.:
h
=
C
h
h
h
(17)
t
p
gear
gen
ele
The effective power output from a wind turbine to feed into a grid becomes
3
(18)
PC
=
hhh
P P
=
h
=
1
2
(
hr
u
)
eff
p
gear
gen
ele
w
t
w
t
5.3.3 Lanchester-Betz limit
The theoretical maximum effi ciency of an ideal wind turbomachine was derived
by Lanchester [43] in 1915 and Betz [44] in 1920. It was revealed that no wind tur-
bomachines could convert more than 16/27 (59.26%) of the kinetic energy of wind
into mechanical energy. This is known as Lanchester-Betz limit (or Lanchester-
Betz law) today.
As shown in Fig. 8,
-
1
and
-
4
are mean velocities far upstream and downstream
from the wind turbine;
-
2
and
-
3
are mean velocities just in front and back of the
wind rotating blades, respectively. By assuming that there is no change in the air
velocity right across the wind blades (i.e.
-
2
=
-
3
) and the pressures far upstream
and downstream from the wind turbine are equal to the static pressure of the undis-
turbed airfl ow (i.e.
p
1
=
p
4
=
p
), it can be derived that
2
2
(19)
pp
−=
1
r
(
uu
−
)
1
4
2
2
3
and
(20)
uu
==
1
2
(
uu
+
)
2
3
1
4
u
4
Streamtube boundary
u
1
u
3
u
2
p
3
u
4
u
1
p
2
p
4
p
1
Figure 8: Airfl ow through a wind turbine.
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