The use of wind-powered generators to produce electricity is a matter of great interest as people become more sensitive to potential environmental consequences of nuclear power and the use of fossil fuels. If wind energy is to be considered as a potential source of electricity in a region, it is necessary to evaluate whether and where there is sufficient wind to justify electricity generation from wind. It is important to estimate the amount of power in the wind at a potential site. If we know (or can estimate) the wind speed at the height where the blades of a windmill are located and the air density at that height, we can estimate the amount of available power in the wind.
The study area consists of most of the state of Massachusetts in the U.S. We start by estimating the air density at the height of the windmill blades (assumed to be 50 meters). We will derive the air density by using a digital elevation model of the study area.
Air density is given by the following equation:
D = 01.226 - (1.194 * 10-4)z
where D is the air density in kg/cubic meter, z equals the elevation in meters and 1.226 kg/m3 corresponds to the standard air density at sea level (z = 0) at a temperature of 15 degrees C (Nelson, et al, 1994).
As a scalar map algebra step, we add 50 meters to the elevations in our digital elevation model. This produces the following image:
This elevation surface is used as "z" in the air density equation above. The equation can be evaluated in one step using Idrisi's Image Calculator, which allows us to type in the equation directly. Or if necessary or desired, the equation can be evaluated in two steps:
First step:
0.0001194 * (50-meter surface) = (intermediate result)
where * indicates multiplication and parentheses indicate that data layers are used as variables.
Second step:
(density at 50 meters) = 1.226 - (intermediate result)
This density image is the result:
We also have a wind speed surface for a 50-meter height above ground for the study area. It is beyond the scope of this example to discuss the derivation of the wind surface in detail. Essentially, long-term wind measurements at many known locations were analyzed and interpolated to derive a wind surface near the ground, where the measurements were taken. Empirically calibrated formulae allow the extrapolation of near-surface winds to elevated locations. Further information can be found in the materials referenced below. This is the 50-meter wind surface, which depicts the average wind speed at an elevation of 50 meters:
Now that we know the density of air at 50 meters above ground level and the average wind speed at 50 meters above ground level, we can use the following equation (from Nelson, et al, 1994) to estimate the power per cross-sectional area in the wind:
P/A = 0.5D(v exp 3)
where
P is power in watts
A is cross sectional area (through which wind is passing) in square meters
D = density of air in kilograms/cubic meter
v = wind speed in meters/second
v exp 3 = the cube of v
This can be evaluated using map algebra techniques as:
(answer, in watts per square meter) = (0.5 * (density50m) * ( (wind50) exp 3))
or:
(answer, in watts per square meter) = (0.5 * (density50m) * (wind50) * (wind50) * (wind50))
In Idrisi this can be performed in one step using Image Calculator. Depending on which GIS software is used, it might be necessary to evaluate the equation as a series of substeps. In any case the result we obtain is this:
Rohatgi and Nelson (1994) suggest that generation of electrical power
may be viable in areas where 50-meter wind power values exceed approximately
300 watts/sq m. Based on our analysis, it appears that large areas of the
State of Massachusetts could be considered for wind power development.
The wind power map above suggests parts of the state (e.g., the southeastern
corner of the state and along the southern border in the western half of
the state) where pilot tests might be conducted.