"""
The ``wind_speed`` module contains functions to calculate the wind speed at
hub height 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
[docs]
def logarithmic_profile(
wind_speed,
wind_speed_height,
hub_height,
roughness_length,
obstacle_height=0.0,
):
r"""
Calculates the wind speed at hub height using a logarithmic wind profile.
The logarithmic height equation is used. There is the possibility of
including the height of the surrounding obstacles in the calculation. This
function is carried out when the parameter `wind_speed_model` of an
instance of the :class:`~.modelchain.ModelChain` class is 'logarithmic'.
Parameters
----------
wind_speed : :pandas:`pandas.Series<series>` or numpy.array
Wind speed time series.
wind_speed_height : float
Height for which the parameter `wind_speed` applies.
hub_height : float
Hub height of wind turbine.
roughness_length : :pandas:`pandas.Series<series>` or numpy.array or float
Roughness length.
obstacle_height : float
Height of obstacles in the surrounding area of the wind turbine. Set
`obstacle_height` to zero for widespread obstacles. Default: 0.
Returns
-------
:pandas:`pandas.Series<series>` or numpy.array
Wind speed at hub height. Data type depends on type of `wind_speed`.
Notes
-----
The following equation is used [1]_ [2]_ [3]_:
.. math:: v_{wind,hub}=v_{wind,data}\cdot
\frac{\ln\left(\frac{h_{hub}-d}{z_{0}}\right)}{\ln\left(
\frac{h_{data}-d}{z_{0}}\right)}
with:
v: wind speed, h: height, :math:`z_{0}`: roughness length,
d: boundary layer offset (estimated by d=0.7 * `obstacle_height`)
For d=0 it results in the following equation [2]_ [3]_:
.. math:: v_{wind,hub}=v_{wind,data}\cdot\frac{\ln\left(\frac{h_{hub}}
{z_{0}}\right)}{\ln\left(\frac{h_{data}}{z_{0}}\right)}
:math:`h_{data}` is the height at which the wind speed
:math:`v_{wind,data}` is measured and :math:`v_{wind,hub}` is the wind
speed at hub height :math:`h_{hub}` of the wind turbine.
Parameters `wind_speed_height`, `roughness_length`, `hub_height` and
`obstacle_height` have to be of the same unit.
References
----------
.. [1] Quaschning V.: "Regenerative Energiesysteme". München, Hanser
Verlag, 2011, p. 278
.. [2] Gasch, R., Twele, J.: "Windkraftanlagen". 6. Auflage, Wiesbaden,
Vieweg + Teubner, 2010, p. 129
.. [3] Hau, E.: "Windkraftanlagen - Grundlagen, Technik, Einsatz,
Wirtschaftlichkeit". 4. Auflage, Springer-Verlag, 2008, p. 515
"""
if 0.7 * obstacle_height > wind_speed_height:
raise ValueError(
"To take an obstacle height of {0} m ".format(obstacle_height)
+ "into consideration, wind "
+ "speed data of a greater height is needed."
)
# Return np.array if wind_speed is np.array
if isinstance(wind_speed, np.ndarray) and isinstance(
roughness_length, pd.Series
):
roughness_length = np.array(roughness_length)
return (
wind_speed
* np.log((hub_height - 0.7 * obstacle_height) / roughness_length)
/ np.log(
(wind_speed_height - 0.7 * obstacle_height) / roughness_length
)
)
[docs]
def hellman(
wind_speed,
wind_speed_height,
hub_height,
roughness_length=None,
hellman_exponent=None,
):
r"""
Calculates the wind speed at hub height using the hellman equation.
It is assumed that the wind profile follows a power law. This function is
carried out when the parameter `wind_speed_model` of an instance of
the :class:`~.modelchain.ModelChain` class is 'hellman'.
Parameters
----------
wind_speed : :pandas:`pandas.Series<series>` or numpy.array
Wind speed time series.
wind_speed_height : float
Height for which the parameter `wind_speed` applies.
hub_height : float
Hub height of wind turbine.
roughness_length : :pandas:`pandas.Series<series>` or numpy.array or float
Roughness length. If given and `hellman_exponent` is None:
`hellman_exponent` = 1 / ln(hub_height/roughness_length),
otherwise `hellman_exponent` = 1/7. Default: None.
hellman_exponent : None or float
The Hellman exponent, which combines the increase in wind speed due to
stability of atmospheric conditions and surface roughness into one
constant. If None and roughness length is given
`hellman_exponent` = 1 / ln(hub_height/roughness_length),
otherwise `hellman_exponent` = 1/7. Default: None.
Returns
-------
:pandas:`pandas.Series<series>` or numpy.array
Wind speed at hub height. Data type depends on type of `wind_speed`.
Notes
-----
The following equation is used [1]_ [2]_ [3]_:
.. math:: v_{wind,hub}=v_{wind,data}\cdot \left(\frac{h_{hub}}{h_{data}}
\right)^\alpha
with:
v: wind speed, h: height, :math:`\alpha`: Hellman exponent
:math:`h_{data}` is the height in which the wind speed
:math:`v_{wind,data}` is measured and :math:`v_{wind,hub}` is the wind
speed at hub height :math:`h_{hub}` of the wind turbine.
For the Hellman exponent :math:`\alpha` many studies use a value of 1/7 for
onshore and a value of 1/9 for offshore. The Hellman exponent can also
be calculated by the following equation [2]_ [3]_:
.. math:: \alpha=\frac{1}{\ln\left(\frac{h_{hub}}{z_0} \right)}
with:
:math:`z_{0}`: roughness length
Parameters `wind_speed_height`, `roughness_length`, `hub_height` and
`obstacle_height` have to be of the same unit.
References
----------
.. [1] Sharp, E.: "Spatiotemporal disaggregation of GB scenarios depicting
increased wind capacity and electrified heat demand in dwellings".
UCL, Energy Institute, 2015, p. 83
.. [2] Hau, E.: "Windkraftanlagen - Grundlagen, Technik, Einsatz,
Wirtschaftlichkeit". 4. Auflage, Springer-Verlag, 2008, p. 517
.. [3] Quaschning V.: "Regenerative Energiesysteme". München, Hanser
Verlag, 2011, p. 279
"""
if hellman_exponent is None:
if roughness_length is not None:
# Return np.array if wind_speed is np.array
if isinstance(wind_speed, np.ndarray) and isinstance(
roughness_length, pd.Series
):
roughness_length = np.array(roughness_length)
hellman_exponent = 1 / np.log(hub_height / roughness_length)
else:
hellman_exponent = 1 / 7
return wind_speed * (hub_height / wind_speed_height) ** hellman_exponent