Environmental Engineering Reference
In-Depth Information
Based on the IEC procedure, the AEP can be derived by integrating the mea-
sured power curve to a reference distribution of wind speed for the test site, assum-
ing a given availability of the wind turbine [3]. The AEP is a central feature for
economical considerations.
The standard procedure defi ned by the IEC offers some interesting insights. It is
a great advance as it sets a common ground for wind power performance. As the
wind industry develops, common standards help building a general understanding
between manufacturers, scientists and end-users. The IEC procedure serves this
purpose as the most widely used method to estimate power performance.
A detailed analysis of this standard is of great importance for anyone who
wishes to test power performance. The procedure defi nes a set of important param-
eters, such as the wind direction, terrain corrections and requirements for wind
speed measurements. These parameters are relevant for performance measure-
ments, regardless of the fi nal method used to handle data. The main strength of the
method lies in the defi nition of these important parameters.
Unfortunately, the standard procedure presents important limits. In contrast to a
good defi nition of the requirements above, the way the measured data is analyzed
suffers mathematical imperfections. In order to deal with the complexity of the
conversion process, the data is systematically averaged. A statistical averaging is
indeed necessary to extract the main features of the complex process, and the cen-
tral question is how to perform this averaging. The IEC method applies the averag-
ing over 10-min intervals, which lack physical meaning. The wind fl uctuates on various
time scales, down to seconds (and less). A systematic averaging over such time scales
as 10 min neglects all high frequency fl uctuations present in the wind dynamics, but
also in the dynamics of the extraction process. In combination with the fundamental
non-linearity characteristics of the power curve, i.e.
P
(
u
)
u
3
, the resulting power
curve is spoiled by mathematical errors, as derived below [see eqn (7)].
One can split the wind speed
u
(
t
) into its mean value and the fl uctuations around
this mean value:
∝
ut
()
=
ut
()
+
vt
()
=
V
+
vt
().
( 5)
where
represents the average (arithmetic mean) value of
u
(
t
). Applying a
Taylor expansion to
P
(
u
) gives [ 10 ]:
〈
u
(
t
)
〉
2
3
∂
PV
()
1
∂
PV
()
1
∂
PV
()
2
3
4
(6 )
Pu
()
=
PV
( )
+
v
+
v
+
v
+
ov
( )
2
3
∂
u
2
∂
u
6
∂
u
(
)
Pu
()
≠
PV
( )
=
P u
( 7)
It appears that the average of the power is not the power of the average, due to the
non-linear relation
P
(
u
)
u
3
and the high frequency turbulent fl uctuations. The
IEC procedure gives
P
(
V
) exactly
P
(
∝
bin
), which neglects the high-order
terms in the Taylor expansion. The resulting IEC power curve should be corrected
by the second- and third-order terms.
As a consequence of this mathematical over-simplifi cation, the result depends
on the turbulence intensity
I
=
s
/
V
(where
s
² =
〈〈
u
(
t
)
〉
10min
〉
〈
u
²(
t
)
〉
) and on the wind condition
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