11"""
22The ``power_curves`` module contains functions for applying alterations like
3- power curve smoohting or reducing power values by an efficiency to the power
3+ power curve smoothing or reducing power values by an efficiency to the power
44curve of a wind turbine, wind farm or wind turbine cluster.
55
66"""
@@ -18,7 +18,7 @@ def smooth_power_curve(power_curve_wind_speeds, power_curve_values,
1818 standard_deviation_method = 'turbulence_intensity' ,
1919 mean_gauss = 0 , ** kwargs ):
2020 r"""
21- Smoothes the input power curve values by using a Gauss distribution.
21+ Smooths the input power curve values by using a Gauss distribution.
2222
2323 Parameters
2424 ----------
@@ -29,8 +29,8 @@ def smooth_power_curve(power_curve_wind_speeds, power_curve_values,
2929 Power curve values corresponding to wind speeds in
3030 `power_curve_wind_speeds`.
3131 block_width : float
32- Width between the wind speeds in the sum of the equation shown below in
33- Notes. Default: 0.5.
32+ Width between the wind speeds in the sum of equation :eq:`power`.
33+ Default: 0.5.
3434 wind_speed_range : float
3535 The sum in the equation below is taken for this wind speed range below
3636 and above the power curve wind speed. Default: 15.0.
@@ -39,7 +39,7 @@ def smooth_power_curve(power_curve_wind_speeds, power_curve_values,
3939 distribution. Options: 'turbulence_intensity', 'Staffell_Pfenninger'.
4040 Default: 'turbulence_intensity'.
4141 mean_gauss : float
42- Mean of the Gaus distribution in
42+ Mean of the Gauss distribution in
4343 :py:func:`~.tools.gauss_distribution`. Default: 0.
4444
4545 Other Parameters
@@ -58,18 +58,20 @@ def smooth_power_curve(power_curve_wind_speeds, power_curve_values,
5858 -----
5959 The following equation is used to calculated the power curves values of the
6060 smoothed power curve [1]_:
61+
6162 .. math:: P_{smoothed}(v_{std}) = \sum\limits_{v_i} \Delta v_i \cdot P(v_i)
6263 \cdot \frac{1}{\sigma \sqrt{2 \pi}}
6364 \exp \left[-\frac{(v_{std} - v_i -\mu)^2}{2 \sigma^2} \right]
65+ :label: power
6466
6567 with:
6668 P: power [W], v: wind speed [m/s],
67- :math:`\sigma`: standard deviation (Gauss), :math: `\mu`: mean (Gauss)
69+ :math:`\sigma`: standard deviation (Gauss), :math:`\mu`: mean (Gauss)
6870
6971 :math:`P_{smoothed}` is the smoothed power curve value,
7072 :math:`v_{std}` is the standard wind speed in the power curve,
7173 :math: `\Delta v_i` is the interval length between
72- :math: `$ v_\text{i}$ ` and :math: `$ v_\text{i+1}$ `
74+ :math: `v_\text{i}` and :math: `v_\text{i+1}`
7375
7476 Power curve smoothing is applied to take account for the spatial
7577 distribution of wind speed. This way of smoothing power curves is also used
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