windpowerlib.wind_speed.v_wind_hellman¶

windpowerlib.wind_speed.v_wind_hellman(v_wind, v_wind_height, hub_height, hellman_exp=None, z_0=None)[source]¶

Calculates the wind speed at hub height using the hellman equation.

It is assumed that the wind profile follows a power law. This fuction is carried out when the parameter wind_model of an instance of the Modelchain class is ‘hellman’.

Parameters:	v_wind (pandas.Series or array) – Wind speed time series. v_wind_height (float) – Height for which the parameter v_wind applies. hub_height (float) – Hub height of wind turbine. hellman_exp (float) – The Hellman exponent, which combines the increase in wind speed due to stability of atmospheric conditions and surface roughness into one constant. Default: 1/7. If roughness length is given hellman_exp = 1 / ln(h_hub/z_0). z_0 (float) – Roughness length. Default: None.
Returns:	Wind speed at hub height.
Return type:	pandas.Series or array

Notes

The following equation is used [1], [2], [3]:

$v_{wind,hub}=v_{wind,data}\cdot \left(\frac{h_{hub}}{h_{data}} \right)^\alpha$

with:: v: wind speed, h: height, $\alpha$ : Hellman exponent

$h_{data}$ is the height in which the wind speed $v_{wind,data}$ is measured and $h_{hub}$ is the hub height of the wind turbine.

For the Hellman exponent $\alpha$ many studies use a value of 1/7 for onshore and a value of 1/9 for offshore. The Hellman exponent can also be calulated by the following equation [2], [3]:

$\alpha = \frac{1}{ln\left(\frac{h_{hub}}{z_0} \right)}$

with:: $z_{0}$ : roughness length

References

[1]	Sharp, E.: “Spatiotemporal disaggregation of GB scenarios depicting increased wind capacity and electrified heat demand in dwellings”. UCL, Energy Institute, 2015, p. 83

[2]	(1, 2) Hau, E.: “Windkraftanlagen - Grundlagen, Technik, Einsatz, Wirtschaftlichkeit”. 4. Auflage, Springer-Verlag, 2008, p. 517

[3]	(1, 2) Quaschning V.: “Regenerative Energiesysteme”. München, Hanser Verlag, 2011, p. 279