/
power_output.py
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/
power_output.py
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"""
The ``power_output`` module contains functions to calculate the power output
of a wind turbine.
SPDX-FileCopyrightText: 2019 oemof developer group <contact@oemof.org>
SPDX-License-Identifier: MIT
"""
import numpy as np
import pandas as pd
def power_coefficient_curve(
wind_speed,
power_coefficient_curve_wind_speeds,
power_coefficient_curve_values,
rotor_diameter,
density,
):
r"""
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 :class:`~.modelchain.ModelChain` class is
'power_coefficient_curve'.
Parameters
----------
wind_speed : :pandas:`pandas.Series<series>` or numpy.array
Wind speed at hub height in m/s.
power_coefficient_curve_wind_speeds : :pandas:`pandas.Series<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:`pandas.Series<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:`pandas.Series<series>` or numpy.array
Density of air at hub height in kg/m³.
Returns
-------
:pandas:`pandas.Series<series>` or numpy.array
Electrical power output of the wind turbine in W.
Data type depends on type of `wind_speed`.
Notes
-----
The following equation is used [1]_ [2]_:
.. math:: P=\frac{1}{8}\cdot\rho_{hub}\cdot d_{rotor}^{2}
\cdot\pi\cdot v_{wind}^{3}\cdot cp\left(v_{wind}\right)
with:
P: power [W], :math:`\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.
References
----------
.. [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
"""
power_coefficient_time_series = np.interp(
wind_speed,
power_coefficient_curve_wind_speeds,
power_coefficient_curve_values,
left=0,
right=0,
)
power_output = (
1
/ 8
* density
* rotor_diameter ** 2
* np.pi
* np.power(wind_speed, 3)
* power_coefficient_time_series
)
# Power_output as pd.Series if wind_speed is pd.Series (else: np.array)
if isinstance(wind_speed, pd.Series):
power_output = pd.Series(
data=power_output,
index=wind_speed.index,
name="feedin_power_plant",
)
else:
power_output = np.array(power_output)
return power_output
def power_curve(
wind_speed,
power_curve_wind_speeds,
power_curve_values,
density=None,
density_correction=False,
):
r"""
Calculates the turbine power output using a power curve.
This function is carried out when the parameter `power_output_model` of an
instance of the :class:`~.modelchain.ModelChain` class is 'power_curve'. If
the parameter `density_correction` is True the density corrected power
curve (see :py:func:`~.power_curve_density_correction`) is used.
Parameters
----------
wind_speed : :pandas:`pandas.Series<series>` or numpy.array
Wind speed at hub height in m/s.
power_curve_wind_speeds : :pandas:`pandas.Series<series>` or numpy.array
Wind speeds in m/s for which the power curve values are provided in
`power_curve_values`.
power_curve_values : pandas.Series or numpy.array
Power curve values corresponding to wind speeds in
`power_curve_wind_speeds`.
density : :pandas:`pandas.Series<series>` or numpy.array
Density of air at hub height in kg/m³. This parameter is needed
if `density_correction` is True. Default: None.
density_correction : bool
If the parameter is True the density corrected power curve (see
:py:func:`~.power_curve_density_correction`) is used for the
calculation of the turbine power output. In this case `density`
cannot be None. Default: False.
Returns
-------
:pandas:`pandas.Series<series>` or numpy.array
Electrical power output of the wind turbine in W.
Data type depends on type of `wind_speed`.
Notes
-------
It is assumed that the power output for wind speeds above the maximum
and below the minimum wind speed given in the power curve is zero.
"""
if density_correction is False:
power_output = np.interp(
wind_speed,
power_curve_wind_speeds,
power_curve_values,
left=0,
right=0,
)
# Power_output as pd.Series if wind_speed is pd.Series (else: np.array)
if isinstance(wind_speed, pd.Series):
power_output = pd.Series(
data=power_output,
index=wind_speed.index,
name="feedin_power_plant",
)
else:
power_output = np.array(power_output)
elif density_correction is True:
power_output = power_curve_density_correction(
wind_speed, power_curve_wind_speeds, power_curve_values, density
)
else:
raise TypeError(
"'{0}' is an invalid type. ".format(type(density_correction))
+ "`density_correction` must "
+ "be Boolean (True or False)."
)
return power_output
def power_curve_density_correction(
wind_speed, power_curve_wind_speeds, power_curve_values, density
):
r"""
Calculates the turbine power output using a density corrected power curve.
This function is carried out when the parameter `density_correction` of an
instance of the :class:`~.modelchain.ModelChain` class is True.
Parameters
----------
wind_speed : :pandas:`pandas.Series<series>` or numpy.array
Wind speed at hub height in m/s.
power_curve_wind_speeds : :pandas:`pandas.Series<series>` or numpy.array
Wind speeds in m/s for which the power curve values are provided in
`power_curve_values`.
power_curve_values : :pandas:`pandas.Series<series>` or numpy.array
Power curve values corresponding to wind speeds in
`power_curve_wind_speeds`.
density : :pandas:`pandas.Series<series>` or numpy.array
Density of air at hub height in kg/m³.
Returns
-------
:pandas:`pandas.Series<series>` or numpy.array
Electrical power output of the wind turbine in W.
Data type depends on type of `wind_speed`.
Notes
-----
The following equation is used for the site specific power curve wind
speeds [1]_ [2]_ [3]_:
.. math:: v_{site}=v_{std}\cdot\left(\frac{\rho_0}
{\rho_{site}}\right)^{p(v)}
with:
.. math:: 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], :math:`\rho`: density [kg/m³]
:math:`v_{std}` is the standard wind speed in the power curve
(:math:`v_{std}`, :math:`P_{std}`),
:math:`v_{site}` is the density corrected wind speed for the power curve
(:math:`v_{site}`, :math:`P_{std}`),
:math:`\rho_0` is the ambient density (1.225 kg/m³)
and :math:`\rho_{site}` the density at site conditions (and hub height).
It is assumed that the power output for wind speeds above the maximum
and below the minimum 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
"""
if density is None:
raise TypeError(
"`density` is None. For the calculation with a "
+ "density corrected power curve density at hub "
+ "height is needed."
)
# Convert pandas.Series to a numpy array to speed up the interpolation below.
if isinstance(wind_speed, pd.Series):
# save the indexes for later conversion to pd.Series
wind_speed_indexes = wind_speed.index
# change the wind speed Series to numpy array
wind_speed = wind_speed.values
# Set the panda series flag True
panda_series = True
else:
panda_series = False
power_output = [
(
np.interp(
wind_speed[i],
power_curve_wind_speeds
* (1.225 / density[i])
** (
np.interp(
power_curve_wind_speeds, [7.5, 12.5], [1 / 3, 2 / 3]
)
),
power_curve_values,
left=0,
right=0,
)
)
for i in range(len(wind_speed))
]
# Power_output as pd.Series if wind_speed is pd.Series (else: np.array)
if (
panda_series
): # use the flag to check if the data should be converted back to pandas.Series
power_output = pd.Series(
data=power_output,
index=wind_speed_indexes, # Use previously saved wind speed indexes
name="feedin_power_plant",
)
else:
power_output = np.array(power_output)
return power_output