Wind Projects - Site Selection - Rules of Thumb

Estimating annual wind energy output

The forecasting of annual energy generated by a single wind turbine or a wind park at a specific site is a very complex task requiring very much work in advance for wind measurement and the following site evaluation. However, some basic relationships like the increase of wind power with wind speed, the increase in wind speed with height, the dependency of wind power towards air density and general assumptions about the wind speed distribution can be used to create a rough estimation of the annual wind energy output.

The relationship of wind speed to wind power

The power $P$ of a wind stream with the speed $v$ is given by 

$P=1/2\cdot \rho \cdot A\cdot V^{3}(1)$

where $\rho$ is the density of air and A is the swept area by the rotor of the wind turbine. Using air density at sea level $\rho$=1,225 kg/m³ the relationship can be expressed as $P=0,6125AV^{3}$. The power in the wind stream is influenced by the wind speed with a cubic exponent. This means even a small increase in wind speed substantially raises the power in the wind and stresses the need for a good estimation of wind speeds choosing a new site for a turbine. The increase in power caused by a certain increase in wind speed can be easily estimated: Leaving the influence of air density and rotor area apart, assume a site with a wind speed $v_{1}$ of 10 m/s and another site with an average wind speed $v_{2}$ of 12 m/s. The difference in wind speed is only 20 % or $v_{2}/v_{1}=12/10=1.2$. Nevertheless this relatively small increase in wind speed results in bigger increase of wind power:

${\frac {P_{2}}{P_{1}}}=({\frac {V_{2}}{V_{1}}})^{3}$

$P_{2}=1,2^{3}\cdot P_{1}=1,73\cdot P_{1}$

The wind power at the site with an average wind speed of 12 m/s is almost 70 % higher than the wind power at the other site.

The increase in wind speed with height

Near the ground the wind speed is influenced by any obstacle, because the flow of the wind is disrupted and therefore slowed down. At sites with very rough terrain often a dramatically increase in wind speed with height can be observed. For that reason wind speed data for a specific site should always contain information about the height the wind speed was measured. If nothing is stated concerning the height of measurement, usually a height of 10 meters can be assumed. The standard height set in the German Renewable Energies Law within the definition of a reference site is 30 m above the ground.

A rough but conservative and easy method of wind speed estimation in higher altitudes is the power law method using the following simple equation

${\frac {V}{V_{0}}}=({\frac {H}{H_{0}}})^{\alpha }$

where $V_{0}$ is the wind speed at the measured height $H_{0}$, $V$ is the wind speed on the 'wanted' height $H$ and $\alpha$ is parameter characterizing the roughness of the terrain. The appropriate values for the exponent $\alpha$ have been set by experience and a couple of typical roughness exponents are shown in table 1.

Table 1: Typical roughness exponents

	Surface roughness exponent $\alpha$
Water or ice	0,1
Low Grass or Steppe	0,14
Rural with obstacles	0,2
Suburb and Woodlands	0,25

Thus an estimate of wind speed $V$ in the height $H$ can be generated by

$V=({\frac {H}{H_{0}}})^{\alpha }\cdot V_{0}$

As an example, a typical farmland in a rural area with a couple of obstacles is considered: According to Table 1 a value of 0,2 can be chosen for $\alpha$. If a wind speed of 5 m/s at a height of 2 meters is measured, how great will the wind speed be at a typical small wind turbine height of 30 m? The answer is given by

$V=({\frac {30m}{10m}})^{0,2}\cdot 5m/s\approx 6,22m/s$.

Thus in a rural area the wind speed increases about 25% between the height of 10 to 30 meters. At an altitude of 60 m the wind speed is approximately 43% higher than at 10 meters height.

The increase of wind power with height

Combining these first rules of thumb it can easily be understood why wind turbines are typically placed on high towers. Because of the cubic relation between wind speed and wind power the increase in wind speed with height has an very important impact on the increase of wind power with height. Using the previous example the wind speed increases by 25% between the heights of 10 m and 30 m. We compare the at the two wind speeds using the first rule of thumb:

$P=({\frac {6,38m/s}{5m/s}})^{3}\cdot P_{0}=2,08\cdot P_{0}\qquad$   

The power contained in the wind stream more than doubles with an increase in height of 20 m.

The dependency of wind power on air density

As the initially mentioned equation for wind power shows, the air density $\rho$ has an influence on the wind power. Air density changes with temperature, thus comparing two sites with equal average wind speeds, wind power will be higher at the site with lower temperatures. Generally wind turbines generate more power in the winter than in the summer months.

Air density decreases with elevation: The less dense air on a mountain top can cut power production by 10-20 % compared to sea level conditions. As a conclusion the higher the considered site is located above sea level and the higher are the average temperatures at the site, the smaller will be the energy which can be generated by a wind turbine installed at this site. Compared to the increases in wind speed with height, changes in air density have a relatively small impact on the wind energy generation.

The dependency of wind power generation on the swept rotor area

Until now only variables influencing the wind speed and the power contained in a wind stream have been described. The area $A$ swept by a wind turbine influences the wind power generation in a linear way. Doubling the swept rotor area means doubling the power available in the wind stream covered by the rotor. As the rotor area $A$ is given by $A=\pi R^{2}$ a small increase in the radius $R$ of the rotor has significant impact on the power which can be generated by the turbine. As an example increasing the length of the rotor blades from 10 to 12 meters results in an increase of the swept area by 44%:

$A_{2}=(12/10)^{2}\cdot A_{1}=1,44\cdot A_{1}$