@@ -178,6 +178,7 @@ def power_curve_density_correction(
178178 Calculates the turbine power output using a density corrected power curve.
179179 This function is carried out when the parameter `density_correction` of an
180180 instance of the :class:`~.modelchain.ModelChain` class is True.
181+
181182 Parameters
182183 ----------
183184 wind_speed : :pandas:`pandas.Series<series>` or numpy.array
@@ -190,25 +191,29 @@ def power_curve_density_correction(
190191 `power_curve_wind_speeds`.
191192 density : :pandas:`pandas.Series<series>` or numpy.array
192193 Density of air at hub height in kg/m³.
194+
193195 Returns
194196 -------
195197 :pandas:`pandas.Series<series>` or numpy.array
196198 Electrical power output of the wind turbine in W.
197199 Data type depends on type of `wind_speed`.
200+
198201 Notes
199202 -----
200203 The following equation is used for the site specific power curve wind
201204 speeds [1]_ [2]_ [3]_:
202- .. math:: v_{site}=v_{std}\cdot\left(\frac{\rho_0}
203- {\rho_{site}}\right)^{p(v)}
205+
206+ .. math:: v_{site}=v_{std}\cdot\left(\frac{\rho_0} {\rho_{site}}\right)^{p(v)}
204207 with:
205208 .. math:: p=\begin{cases}
206209 \frac{1}{3} & v_{std} \leq 7.5\text{ m/s}\\
207210 \frac{1}{15}\cdot v_{std}-\frac{1}{6} & 7.5
208211 \text{ m/s}<v_{std}<12.5\text{ m/s}\\
209212 \frac{2}{3} & \geq 12.5 \text{ m/s}
210213 \end{cases},
214+
211215 v: wind speed [m/s], :math:`\rho`: density [kg/m³]
216+
212217 :math:`v_{std}` is the standard wind speed in the power curve
213218 (:math:`v_{std}`, :math:`P_{std}`),
214219 :math:`v_{site}` is the density corrected wind speed for the power curve
@@ -217,17 +222,19 @@ def power_curve_density_correction(
217222 and :math:`\rho_{site}` the density at site conditions (and hub height).
218223 It is assumed that the power output for wind speeds above the maximum
219224 and below the minimum wind speed given in the power curve is zero.
225+
220226 References
221227 ----------
222228 .. [1] Svenningsen, L.: "Power Curve Air Density Correction And Other
223- Power Curve Options in WindPRO". 1st edition, Aalborg,
224- EMD International A/S , 2010, p. 4
229+ Power Curve Options in WindPRO". 1st edition, Aalborg,
230+ EMD International A/S , 2010, p. 4
225231 .. [2] Svenningsen, L.: "Proposal of an Improved Power Curve Correction".
226- EMD International A/S , 2010
232+ EMD International A/S , 2010
227233 .. [3] Biank, M.: "Methodology, Implementation and Validation of a
228- Variable Scale Simulation Model for Windpower based on the
229- Georeferenced Installation Register of Germany". Master's Thesis
230- at Reiner Lemoine Institute, 2014, p. 13
234+ Variable Scale Simulation Model for Windpower based on the
235+ Georeferenced Installation Register of Germany". Master's Thesis
236+ at Reiner Lemoine Institute, 2014, p. 13
237+
231238 """
232239 if density is None :
233240 raise TypeError (
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