Hello all, i have wind speeds at 10 m height, and using the power law application i have wind speeds at 30 metres. I also have the count of occurrence's out of 8760 in which the wind speeds ranging from 0- 20 m/s occur at those speeds throughout the year at 10m. For example, 5m/s has a count of 330 meaning that for 330 hours of the year the wind speed is at 5m/s . am i able to apply the power law to this? so 5(30/10) 0.21 (power law exponent) = 6.3. Therefore 330 hours of the year the wind speed is at 6.3 m/s at 30 m height? im using this to determine the annual energy production of a selected wind turbine. so for example if the power curve shows that the approximate power output at 6.3 m/s is 15.5kW, then 5115 kWh output for the wind turbine for the year? i would do this for every value within the cut in speed and cut out speed which in this case is 3-25 and then add it all together, i do not have the Cp of these wind turbines so i am considering this alternative method.
The power output of a wind turbine depends on the wind speed and the specific characteristics of the turbine itself. The power law is a widely used model for estimating the wind speed at different heights, which can then be used to estimate the power output of a wind turbine at that height.
The power law model assumes that the wind speed at any height above ground level can be described as a function of the wind speed at a reference height and a power law exponent:
V(z) = V_ref * (z / z_ref) ^ alpha
where V(z) is the wind speed at height z, V_ref is the wind speed at a reference height z_ref, and alpha is the power law exponent.
To estimate the power output of a wind turbine, we need to know the wind speed at the height of the turbine rotor. Assuming the rotor diameter D and the hub height h above ground level, the wind speed at the hub height can be estimated as:
V(h) = V_ref * (h / z_ref) ^ alpha
The power output of a wind turbine can be estimated as:
P = 0.5 * rho * A * Cp * V(h) ^ 3
where rho is the air density, A is the rotor swept area, and Cp is the power coefficient, which depends on the specific characteristics of the turbine.
To apply the power law model, we need to determine the values of the reference height z_ref and the power law exponent alpha. These values can be determined empirically from wind speed measurements at different heights.
One common approach is to use the logarithmic wind profile, which assumes that the wind speed varies logarithmically with height. In this case, the power law exponent can be estimated as:
alpha = ln(V_2 / V_1) / ln(z_2 / z_1)
where V_1 and V_2 are the wind speeds at heights z_1 and z_2, respectively.
The reference height z_ref can be chosen based on the characteristics of the specific turbine and the site conditions. Common choices for z_ref are 10 meters or 50 meters above ground level.
Once we have estimated the wind speed at the hub height of the turbine, we can use the power equation to estimate the power output of the turbine. However, note that this is a simplified model and actual power output may vary due to a variety of factors such as turbulence, wind shear, and wake effects.
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