## Wind Shear

Wind shear is the change in wind speed or direction over some distance (Figure 3.4). There can even be a vertical wind shear (Figure 3.5). The change in wind speed with height, a horizontal wind shear, is an important factor in estimating wind turbine energy production. The change in wind speed with height has been measured for different atmospheric conditions [3, chap. 4].

The general methods of estimating wind speeds at higher heights from known wind speed at lower heights are power law, logarithm with surface roughness, and logarithm with surface roughness that has zero wind velocity at ground level. The power law for wind shear is v = v„

where v0 = measured wind speed, H0 = height of known wind speed v0, and H = height.

The wind shear exponent a is around 1/7 (0.14) for a stable atmosphere (decrease in temperature with height); however, it will vary, depending on terrain and atmospheric conditions. From Equation 3.6 the change in wind speed with height can be estimated (Figure 3.6). Notice that for a = 0.14, the wind power at 50 m is double the value at 10 m, a convenient way to estimate power, so many wind maps give wind speed and power classes for 10 and 50 m heights. However, for wind farms, wind power potential is determined for heights from 50 m to hub heights.

The wind shear exponent values in continental areas will be closer to 0.20 for heights of 10-40 m and above, with large differences from low values during the day to high values at night.

FIGURE 3.4 Left: Wind shear caused by a difference in wind speed with height. Right: Wind shear caused by a difference in wind direction.
FIGURE 3.5 Example of vertical wind shear.

Measurements taken at heights of 10, 20, and 50 m for the northwest Texas region [3] for 12 h periods (6-18 h, day-night) showed a large difference between 10-20 m and 50 m levels. Data for sixteen sites in Texas and one site in New Mexico show the same results, a change in diurnal wind speed pattern at around 40 m [4]. Wind speeds were sampled at 1 Hz and averaging time was 1 h. The data were averaged by hour over a month, and then those were averaged over a year to obtain an annual average day (Figure 3.7). This same pattern is noted for data taken at heights above 50 m (Figure 3.8). The wind speed is still increasing with height, so the issue for wind farms is the tradeoff between increased output with wind turbine height and increased cost for taller towers. These results clearly show that wind speed data need to be taken at least at a height of 40 m or higher to find the shift in pattern between day and night wind speeds. Once there are data at 10 m and 40-50 m, the wind shear can be used to predict wind speeds at higher levels. The higher night wind speeds means there is more power; however, those hours are also when there is less demand, so if the wind farm is selling at the market price, that energy may be worth less.

The wind shear exponent changes from low values during the day to high values at night over a 2 h period (Figure 3.9). Time of day data were averaged over each month. So the low values occur for more hours in the summer. There are locations where there is little wind shear, primarily mountain passes (Figure 3.10). In this case taller towers for wind turbines would not be needed.

The world standard height is 10 m for meteorology measurements for weather; however, using 10 m data and the 0.14 wind shear exponent to estimate wind power potential for 50 m for many

Height Wind Speed, m/s m

50 40 30 20

12.6

12.2

11.7

FIGURE 3.6 Wind shear, change in wind speed with height. Calculations are for given wind speed of 10 m/s at 10 m, a = 1/7.

CD CD CP

aaaaa?o

10 12 14 16 18 20 22

FIGURE 3.7 Annual average wind speed by time of day at 10, 25, 40, and 50 m heights, Dalhart, Texas, April 1996-2000.

locations will vastly underestimate the wind power potential for wind farms. The other formulas for estimating wind speed with height are ln

 o oo°o O □□□ °Oo!880On 0°° O o □ VOOUnOo°nn o y a ^ 5 0 g^oo0.

FIGURE 3.8 Annual average wind speed by time of day at 50, 75, and 100 m heights, Washburn, Texas, September 2003-2006.

FIGURE 3.9 Wind shear exponent between 10 and 50 m for average month by time of day, Dalhart, Texas, April 1996-2000.

Hour 15

FIGURE 3.9 Wind shear exponent between 10 and 50 m for average month by time of day, Dalhart, Texas, April 1996-2000.

where z0 is the roughness parameter. Equation 3.8 allows a zero wind speed at the surface. The roughness parameter ranges from 0.01-0.03 m for flat open terrain with short grass to larger than 1 m for rough terrain (Table 3.4).

### EXAMPLE 3.3

A met tower is located close to the edge of town. If the wind speed is 8 m/s at 10 m height, what is the wind speed at 50 m? Use Equation 3.8 and select z0 = 1.2.

 „B888B.„ -sas_ go H go 3 n et

FIGURE 3.10 Annual average wind speed by time of day at 10, 25, and 40 m height, Guadalupe Pass, Texas, 1995-1999.

TABLE 3.4

Typical Values of the Roughness Parameter, z0

Terrain Description

Snow, flat ground Calm open sea Blown sea

Snow, cultivated farmland

Grass

Crops

Farmland and grassy plains Few trees

Many trees, hedges, few buildings

Forest and woodlands

Cities and large towns

Centers of cities with tall buildings

This compares to 10 m/s using the power law with a shear exponent = 0.14

## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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