windpowerlib.power_output.cp_curve

windpowerlib.power_output.cp_curve(v_wind, rho_hub, d_rotor, cp_values)[source]

Calculates the turbine power output using a cp curve.

This function is carried out when the parameter power_output_model of an instance of the Modelchain class is ‘cp_values’ and the parameter density_corr is False.

Parameters:
  • v_wind (pandas.Series or array) – Wind speed at hub height in m/s.
  • rho_hub (pandas.Series or array) – Density of air at hub height in kg/m³.
  • d_rotor (float) – Diameter of rotor in m.
  • cp_values (pandas.DataFrame) – Power coefficient curve of the wind turbine. Indices are the wind speeds of the power coefficient curve in m/s, the corresponding power coefficient values are in the column ‘cp’.
Returns:

Electrical power output of the wind turbine in W.

Return type:

pandas.Series

Notes

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

P=\frac{1}{8}\cdot\rho_{hub}\cdot d_{rotor}^{2}
\cdot\pi\cdot v_{wind}^{3}\cdot cp\left(v_{wind}\right)

with:
P: power [W], \rho: density [kg/m³], d: diameter [m], v: wind speed [m/s], cp: power coefficient

It is assumed that the power output for wind speeds above the maximum wind speed given in the power coefficient curve is zero.

References

[1]Gasch, R., Twele, J.: “Windkraftanlagen”. 6. Auflage, Wiesbaden, Vieweg + Teubner, 2010, pages 35ff, 208
[2]Hau, E.: “Windkraftanlagen - Grundlagen, Technik, Einsatz, Wirtschaftlichkeit”. 4. Auflage, Springer-Verlag, 2008, p. 542