windpowerlib.power_output.power_coefficient_curve(wind_speed, power_coefficient_curve_wind_speeds, power_coefficient_curve_values, rotor_diameter, density)[source]

Calculates the turbine power output using a power coefficient curve.

This function is carried out when the parameter power_output_model of an instance of the ModelChain class is ‘power_coefficient_curve’.

  • wind_speed (pandas.Series or numpy.array) – Wind speed at hub height in m/s.
  • power_coefficient_curve_wind_speeds (pandas.Series or numpy.array) – Wind speeds in m/s for which the power coefficients are provided in power_coefficient_curve_values.
  • power_coefficient_curve_values (pandas.Series or numpy.array) – Power coefficients corresponding to wind speeds in power_coefficient_curve_wind_speeds.
  • rotor_diameter (float) – Rotor diameter in m.
  • density (pandas.Series or numpy.array) – Density of air at hub height in kg/m³.

Electrical power output of the wind turbine in W. Data type depends on type of wind_speed.

Return type:

pandas.Series or numpy.array


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)

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 and below the minimum wind speed given in the power coefficient curve is zero.


[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