@@ -178,6 +178,7 @@ def power_curve_density_correction(
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Calculates the turbine power output using a density corrected power curve.
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This function is carried out when the parameter `density_correction` of an
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instance of the :class:`~.modelchain.ModelChain` class is True.
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Parameters
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----------
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wind_speed : :pandas:`pandas.Series<series>` or numpy.array
@@ -190,25 +191,29 @@ def power_curve_density_correction(
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`power_curve_wind_speeds`.
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density : :pandas:`pandas.Series<series>` or numpy.array
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Density of air at hub height in kg/m³.
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Returns
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-------
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:pandas:`pandas.Series<series>` or numpy.array
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Electrical power output of the wind turbine in W.
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Data type depends on type of `wind_speed`.
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Notes
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-----
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The following equation is used for the site specific power curve wind
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speeds [1]_ [2]_ [3]_:
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- .. math:: v_{site}=v_{std}\cdot\left(\frac{\rho_0}
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- {\rho_{site}}\right)^{p(v)}
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+
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+ .. math:: v_{site}=v_{std}\cdot\left(\frac{\rho_0} {\rho_{site}}\right)^{p(v)}
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with:
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.. math:: p=\begin{cases}
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\frac{1}{3} & v_{std} \leq 7.5\text{ m/s}\\
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\frac{1}{15}\cdot v_{std}-\frac{1}{6} & 7.5
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\text{ m/s}<v_{std}<12.5\text{ m/s}\\
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\frac{2}{3} & \geq 12.5 \text{ m/s}
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\end{cases},
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v: wind speed [m/s], :math:`\rho`: density [kg/m³]
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:math:`v_{std}` is the standard wind speed in the power curve
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(:math:`v_{std}`, :math:`P_{std}`),
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:math:`v_{site}` is the density corrected wind speed for the power curve
@@ -217,17 +222,19 @@ def power_curve_density_correction(
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and :math:`\rho_{site}` the density at site conditions (and hub height).
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It is assumed that the power output for wind speeds above the maximum
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and below the minimum wind speed given in the power curve is zero.
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References
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----------
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.. [1] Svenningsen, L.: "Power Curve Air Density Correction And Other
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- Power Curve Options in WindPRO". 1st edition, Aalborg,
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- EMD International A/S , 2010, p. 4
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+ Power Curve Options in WindPRO". 1st edition, Aalborg,
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+ EMD International A/S , 2010, p. 4
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.. [2] Svenningsen, L.: "Proposal of an Improved Power Curve Correction".
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- EMD International A/S , 2010
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+ EMD International A/S , 2010
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.. [3] Biank, M.: "Methodology, Implementation and Validation of a
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- Variable Scale Simulation Model for Windpower based on the
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- Georeferenced Installation Register of Germany". Master's Thesis
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- at Reiner Lemoine Institute, 2014, p. 13
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+ Variable Scale Simulation Model for Windpower based on the
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+ Georeferenced Installation Register of Germany". Master's Thesis
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+ at Reiner Lemoine Institute, 2014, p. 13
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+
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"""
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if density is None :
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raise TypeError (
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