windpowerlib.wind_speed.hellman¶

windpowerlib.wind_speed.hellman(wind_speed, wind_speed_height, hub_height, roughness_length=None, hellman_exponent=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 function is carried out when the parameter wind_speed_model of an instance of the ModelChain class is ‘hellman’.

Parameters:	wind_speed (pandas.Series or numpy.array) – Wind speed time series. wind_speed_height (float) – Height for which the parameter wind_speed applies. hub_height (float) – Hub height of wind turbine. roughness_length (pandas.Series or numpy.array or float) – Roughness length. If given and hellman_exponent is None: `hellman_exponent`=1 / ln(hub_height/roughness_length), otherwise `hellman_exponent`=1/7. Default: None. hellman_exponent (None or float) – The Hellman exponent, which combines the increase in wind speed due to stability of atmospheric conditions and surface roughness into one constant. If None and roughness length is given `hellman_exponent`=1 / ln(hub_height/roughness_length), otherwise `hellman_exponent`=1/7. Default: None.
Returns:	Wind speed at hub height. Data type depends on type of wind_speed.
Return type:	pandas.Series or numpy.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 $v_{wind,hub}$ is the wind speed at hub height $h_{hub}$ 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

Parameters wind_speed_height, roughness_length, hub_height and obstacle_height have to be of the same unit.

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