Source code for windpowerlib.tools
"""
The ``tools`` module contains a collection of helper functions used in the
windpowerlib.
SPDX-FileCopyrightText: 2019 oemof developer group <contact@oemof.org>
SPDX-License-Identifier: MIT
"""
import numpy as np
class WindpowerlibUserWarning(UserWarning):
"""
The WindpowerlibUserWarning is used to warn users if they use the
windpowerlib in an untypical way. It is not necessarily wrong but could
lead to an unwanted behaviour if you do not know what you are doing.
If you know what you are doing you can easily switch the warnings off:
Examples
--------
>>> import warnings
>>> warnings.filterwarnings("ignore", category=WindpowerlibUserWarning)
"""
pass
[docs]
def linear_interpolation_extrapolation(df, target_height):
r"""
Linearly inter- or extrapolates between the values of a data frame.
This function can be used for the linear inter-/extrapolation of a
parameter (e.g wind speed) available at two or more different heights, to
approximate the value at hub height.
The function is carried out when the parameter `wind_speed_model`,
`density_model` or `temperature_model` of an instance of the
:class:`~.modelchain.ModelChain` class is 'interpolation_extrapolation'.
Parameters
----------
df : :pandas:`pandas.DataFrame<frame>`
DataFrame with time series for parameter that is to be interpolated or
extrapolated. The columns of the DataFrame are the different heights
for which the parameter is available. If more than two heights are
given, the two closest heights are used. See example below on how the
DataFrame should look like and how the function can be used.
target_height : float
Height for which the parameter is approximated (e.g. hub height).
Returns
-------
:pandas:`pandas.Series<series>`
Result of the inter-/extrapolation (e.g. wind speed at hub height).
Notes
-----
For the inter- and extrapolation the following equation is used:
.. math:: f(x)=\frac{(f(x_2) - f(x_1))}{(x_2 - x_1)} \cdot
(x - x_1) + f(x_1)
Examples
---------
>>> import numpy as np
>>> import pandas as pd
>>> wind_speed_10m=np.array([[3], [4]])
>>> wind_speed_80m=np.array([[6], [6]])
>>> weather_df=pd.DataFrame(np.hstack((wind_speed_10m,
... wind_speed_80m)),
... index=pd.date_range('1/1/2012',
... periods=2,
... freq='H'),
... columns=[np.array(['wind_speed',
... 'wind_speed']),
... np.array([10, 80])])
>>> value=linear_interpolation_extrapolation(
... weather_df['wind_speed'], 100)[0]
"""
# find closest heights
heights_sorted = df.columns[
sorted(
range(len(df.columns)),
key=lambda i: abs(df.columns[i] - target_height),
)
]
return (df[heights_sorted[1]] - df[heights_sorted[0]]) / (
heights_sorted[1] - heights_sorted[0]
) * (target_height - heights_sorted[0]) + df[heights_sorted[0]]
[docs]
def logarithmic_interpolation_extrapolation(df, target_height):
r"""
Logarithmic inter- or extrapolation between the values of a data frame.
This function can be used for the logarithmic inter-/extrapolation of the
wind speed if it is available at two or more different heights, to
approximate the value at hub height.
The function is carried out when the parameter `wind_speed_model`
:class:`~.modelchain.ModelChain` class is
'log_interpolation_extrapolation'.
Parameters
----------
df : :pandas:`pandas.DataFrame<frame>`
DataFrame with time series for parameter that is to be interpolated or
extrapolated. The columns of the DataFrame are the different heights
for which the parameter is available. If more than two heights are
given, the two closest heights are used. See example in
:py:func:`~.linear_interpolation_extrapolation` on how the
DataFrame should look like and how the function can be used.
target_height : float
Height for which the parameter is approximated (e.g. hub height).
Returns
-------
:pandas:`pandas.Series<series>`
Result of the inter-/extrapolation (e.g. wind speed at hub height).
Notes
-----
For the logarithmic inter- and extrapolation the following equation is
used [1]_:
.. math:: f(x)=\frac{\ln(x) \cdot (f(x_2) - f(x_1)) - f(x_2) \cdot
\ln(x_1) + f(x_1) \cdot \ln(x_2)}{\ln(x_2) - \ln(x_1)}
References
----------
.. [1] Knorr, K.: "Modellierung von raum-zeitlichen Eigenschaften der
Windenergieeinspeisung für wetterdatenbasierte
Windleistungssimulationen". Universität Kassel, Diss., 2016,
p. 83
"""
# find closest heights
heights_sorted = df.columns[
sorted(
range(len(df.columns)),
key=lambda i: abs(df.columns[i] - target_height),
)
]
return (
np.log(target_height) * (df[heights_sorted[1]] - df[heights_sorted[0]])
- df[heights_sorted[1]] * np.log(heights_sorted[0])
+ df[heights_sorted[0]] * np.log(heights_sorted[1])
) / (np.log(heights_sorted[1]) - np.log(heights_sorted[0]))
[docs]
def gauss_distribution(function_variable, standard_deviation, mean=0):
r"""
Gauss distribution.
The Gauss distribution is used in the function
:py:func:`~.power_curves.smooth_power_curve` for power curve smoothing.
Parameters
----------
function_variable : float
Variable of the gaussian distribution.
standard_deviation : float
Standard deviation of the Gauss distribution.
mean : float
Defines the offset of the Gauss distribution. Default: 0.
Returns
-------
:pandas:`pandas.Series<series>` or numpy.array
Wind speed at hub height. Data type depends on the type of
`wind_speed`.
Notes
-----
The following equation is used [1]_:
.. math:: f(x)=\frac{1}{\sigma \sqrt{2 \pi}} \exp
\left[-\frac{(x-\mu)^2}{2 \sigma^2}\right]
with:
:math:`\sigma`: standard deviation, :math:`\mu`: mean
References
----------
.. [1] Berendsen, H.: "A Student's Guide to Data and Error Analysis".
New York, Cambridge University Press, 2011, p. 37
"""
return (
1
/ (standard_deviation * np.sqrt(2 * np.pi))
* np.exp(
-((function_variable - mean) ** 2) / (2 * standard_deviation ** 2)
)
)
[docs]
def estimate_turbulence_intensity(height, roughness_length):
r"""
Estimate turbulence intensity by the roughness length.
Parameters
----------
height : float
Height above ground in m at which the turbulence intensity is
calculated.
roughness_length : pandas.Series or numpy.array or float
Roughness length.
Notes
-----
The following equation is used [1]_:
.. math:: TI=\frac{1}{\ln\left(\frac{h}{z_\text{0}}\right)}
with:
TI: turbulence intensity, h: height, :math:`z_{0}`: roughness length
References
----------
.. [1] Knorr, K.: "Modellierung von raum-zeitlichen Eigenschaften der
Windenergieeinspeisung für wetterdatenbasierte
Windleistungssimulationen". Universität Kassel, Diss., 2016,
p. 88
"""
return 1 / (np.log(height / roughness_length))