Environmental Engineering Reference
In-Depth Information
Then the optimal value of
C
P
opt
=
C
P
(
l
opt
) is kept and by choosing
l
opt
=
l
R
,
AEP
Max in eqn (10). The second term of in the integral of the right side of eqn
(10) is determined by the wind speed probability function
f
(
V
).
→
5.2.4 In case of constant-speed WT
In case of fi xed-speed WT,
l
varies with
V
in proportion to 1/
V
. Therefore, an
optimal value of design tip-speed ratio
l
opt
may vary from
l
R
. It will be soon
understood if eqn (10) is rewritten as:
r
⎧
V
V
⎫
1
R
out
⎪
⎪
3
∫
3
∫
AEP
=
A
fVVCV V VCV
(
)
(
) d
+
(
)
fV V
(
) d
(13 )
⎨
⎬
P
R
P
R
2
⎪
⎪
⎩
⎭
V
V
in
R
Since
C
P
is a function of
V
,
AEP
is also a function of
V
, but depends on
C
P
(
V
)
and
f
(
V
). This means an optimal rated wind speed
V
R
and an optimal design wind
speed
V
D
will be obtained through making AEP
Max. taking into account the
characteristics of WT, i.e.
C
P
(
V
), and wind, i.e.
f
(
V
), which are independent of
each another.
An empirical formula is known as
→
V
≈−
(1.2
1.5)
V
(14 )
R
mean
where
V
mean
is the annual mean wind speed at the site and is statistically given as
follows when the wind characteristics follow Weibull distribution:
∞
1
⎛
⎞
[]
∫
( 15 )
V
=
E V
=
V
⋅
f V
()d
V
=
C
Γ
1
+
⎜
⎟
mean
⎝
⎠
k
0
where
Γ
denotes the Gamma function.
5.2.5 Multi-point optimal rotor design
A goal is to give AEP a maximum value of the integration in eqn (10). One of the
simplest methods is “Multi-points design method”, with which some desirable
power curve is delivered by combination of plural design points. Various original
designs are possible, but most important thing is to fi nd a solution that the operation
modes together with the power curve of a SWT will most fi t to the characteristics of
the wind at the site where to install the WT.
It is very often experienced that under low wind speed conditions just around
cut-in wind speed, a fi xed-pitch SWT will hard to start rotation or generation if it
stands still, however it will soon do if it is in idling state. Let assume that cut-in
and rated wind speed are 2.5 and 10 m/s, respectively. The ratio of the power out-
put is 1:64. Although the power output at cut-in wind speed is less than 2% of that
at rated wind speed, fast start-up performance will result in better availability in
time and higher energy production.
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