windpowerlib.power_output.p_curve_density_corr¶

windpowerlib.power_output.p_curve_density_corr(v_wind, rho_hub, p_values)[source]¶

Calculates the turbine power output using a density corrected power curve.

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

Parameters:	v_wind (pandas.Series or array) – Wind speed time series at hub height in m/s. rho_hub (pandas.Series or array) – Density of air at hub height in kg/m³. p_values (pandas.DataFrame) – Power curve of the wind turbine. The indices are the corresponding wind speeds of the power curve, the power values containing column is called ‘P’.
Returns:	power_output – Electrical power output of the wind turbine in W.
Return type:	pandas.Series

Notes

The following equation is used for the wind speed at site [1], [2], [3]:

$v_{site}=v_{std}\cdot\left(\frac{\rho_0} {\rho_{site}}\right)^{p(v)}$

with:: $p=\begin{cases} \frac{1}{3} & v_{std} \leq 7.5\text{ m/s}\\ \frac{1}{15}\cdot v_{std}-\frac{1}{6} & 7.5 \text{ m/s}<v_{std}<12.5\text{ m/s}\\ \frac{2}{3} & \geq 12.5 \text{ m/s} \end{cases},$

v: wind speed [m/s], $\rho$ : density [kg/m³]

$v_{std}$ is the standard wind speed in the power curve ( $v_{std}$ , $P_{std}$ ). $v_{site}$ is the density corrected wind speed for the power curve ( $v_{site}$ , $P_{std}$ ).

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

References

[1]	Svenningsen, L.: “Power Curve Air Density Correction And Other Power Curve Options in WindPRO”. 1st edition, Aalborg, EMD International A/S , 2010, p. 4

[2]	Svenningsen, L.: “Proposal of an Improved Power Curve Correction”. EMD International A/S , 2010

[3]	Biank, M.: “Methodology, Implementation and Validation of a Variable Scale Simulation Model for Windpower based on the Georeferenced Installation Register of Germany”. Master’s Thesis at Reiner Lemoine Institute, 2014, p. 13