Environmental Engineering Reference
In-Depth Information
briefly in Chapter 10, and the equation is reproduced here:
v
1
h
2
h
1
a
v
2
=
(11.1)
As written here,
h
1
and
h
2
refer to the top anemometer height and hub height, respec-
tively, and the equation has been rearranged so that the known parameters are all on
the right. Surprisingly, the power law equation has no basis in meteorological theory,
but it has proved highly useful in practice because it fits many wind speed profiles
quite well, is simple, and requires just one parameter, the shear exponent,
α
. An alter-
native approach more firmly rooted in theory is based on a logarithmic equation. It is
discussed later in this chapter.
The key question when applying the power law is what to assume for the shear
exponent. It might seem reasonable to use the exponent that was calculated between
the first (top) and second heights on the tower, or if the ratio of those two heights is
not large enough to obtain an accurate shear value, between the first and third heights.
This is in fact a reasonable starting point, but it is not the end of the analysis.
The challenge is to determine whether the shear exponent changes with height
above the mast top. In fairly open and flat terrain, it usually does not change very
much. But the assumption of constant shear exponent may not hold in other situations,
such as where there is dense forest or strong topographic enhancement or blocking
of the wind flow, or when the most energetic wind is confined to a relatively shallow
layer near the surface, as occurs in thermally driven drainage (katabatic) wind flows.
In such situations, adjustments to the mean shear exponent may be warranted.
The following sections discuss several strategies that can be followed to determine
what shear adjustment, if any, is warranted.
11.1.1 Direct Measurement
The ideal is to measure the wind speed up to (and even beyond) the turbine hub
height. This can be done with either a hub-height mast or a ground-based sodar or
lidar system. Strictly speaking, such measurements apply only to the locations at which
they were taken. Why not then simply measure the profile to hub height at every mast?
Desirable though that would be, there are two reasons why it is not always practical.
First, hub-height towers are expensive and difficult to install in some sites. Second,
it is often not possible to deploy sodars or lidars right next to an existing mast. This
may not matter very much if the site is relatively uniform—open land cover with
few trees and little steep terrain—so that the shear is more or less constant across the
project area. Then the shear to hub height observed at one location may be applied
with some confidence to other locations.
At more complex wind sites, however, the remotely sensed wind profile may not
match the profile observed at the site's primary meteorological towers very closely. In
that case, one is left to decide how to modify the observed shear at each of the towers
to account for the information provided by the hub-height mast or remote sensing
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