Renewable Energy Technology Assessments - Kauai Island Utility ...

Kaua’i Island Utility Cooperative
Renewable Energy Technology Assessments 9.0 Wind
where ρ is the air density, A is the rotor area intercepting the wind, and V is the upstream
wind velocity. Of these, wind velocity is most important. The cubic dependence of wind
power on wind speed implies that energy output, and consequently the economics of a
wind turbine installation, is highly sensitive to wind speed. A 10 percent change in
velocity results in about 30 percent change in available energy; thus wind speed is one of
the most critical factors in determining wind energy generation. Wind power density is
expressed in Watts per meter squared (W/m 2 ) and incorporates the combined effects of
the time variant wind speed and the dependence of wind power on both air density and
cube of wind speed. The figures in this report show wind power density categorized by
wind power class from 0-7, as discussed in Section 3.8 previously.
Average wind speeds vary significantly geographically. Local factors such as
high altitude, unobstructed terrain, lofty airflow height, and natural wind tunneling
features cause some areas to have inherently higher wind speeds than others. Wind speed
is affected by the height above ground level (AGL). Ideally, wind resources assessments
are performed at the hub height of the candidate wind turbine (40 to 80 m); however, if
measurements at the actual hub height (Z) are not available, wind speed (v) can be
extrapolated from other measurement heights. The most common method is the
following relation, known as the one-seventh power law:
v
v
2
1
⎛ Z
= ⎜
⎝ Z
2
1
⎞
⎟
⎠
1/
7
or
P2
⎛ Z 2 ⎞
= ⎜
⎟
P1
⎝ Z1
⎠
For example, based on the one-seventh power law, wind speed and wind power
(P) at 30 m above the ground are respectively 17 and 60 percent greater than at 10 m.
Although a convenient approximation, the one-seventh power law has no theoretical
basis. A custom power law can be applied to a specific site data by measuring wind
speed at two or more different heights on the same tower and determining the wind sheer
factor (s) for a specific site. Once a sheer factor is known for a site wind speed can be
scaled using the following equation:
Z
v v
Z ⎟ ⎛ 2 ⎞
⎜
2 = 1 *
⎝ 1 ⎠
The site-specific nature of the wind energy resource underscores the need for well
planned assessments. The one-seventh power law may be inadequate because it is only
an approximation and the amount of wind energy available is strongly affected by the
local terrain. If the wind sheer factor for a specific site is known, a more accurate power
estimate can be made from non hub height data. A thorough study of the wind at a
21 March 2005 9-2 Black & Veatch
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