"""
The ``temperature`` module contains functions for modeling temperature of
PV modules and cells.
"""
import numpy as np
TEMPERATURE_MODEL_PARAMETERS = {
'sapm': {
'open_rack_glass_glass': {'a': -3.47, 'b': -.0594, 'deltaT': 3},
'close_mount_glass_glass': {'a': -2.98, 'b': -.0471, 'deltaT': 1},
'open_rack_glass_polymer': {'a': -3.56, 'b': -.0750, 'deltaT': 3},
'insulated_back_glass_polymer': {'a': -2.81, 'b': -.0455, 'deltaT': 0},
},
'pvsyst': {'freestanding': {'u_c': 29.0, 'u_v': 0},
'insulated': {'u_c': 15.0, 'u_v': 0}}
}
def _temperature_model_params(model, parameter_set):
try:
params = TEMPERATURE_MODEL_PARAMETERS[model]
return params[parameter_set]
except KeyError:
msg = ('{} is not a named set of parameters for the {} cell'
' temperature model.'
' See pvlib.temperature.TEMPERATURE_MODEL_PARAMETERS'
' for names'.format(parameter_set, model))
raise KeyError(msg)
[docs]def sapm_cell(poa_global, temp_air, wind_speed, a, b, deltaT,
irrad_ref=1000):
r'''
Calculate cell temperature per the Sandia Array Performance Model.
See [1]_ for details on the Sandia Array Performance Model.
Parameters
----------
poa_global : numeric
Total incident irradiance [W/m^2].
temp_air : numeric
Ambient dry bulb temperature [C].
wind_speed : numeric
Wind speed at a height of 10 meters [m/s].
a : float
Parameter :math:`a` in :eq:`sapm1`.
b : float
Parameter :math:`b` in :eq:`sapm1`.
deltaT : float
Parameter :math:`\Delta T` in :eq:`sapm2` [C].
irrad_ref : float, default 1000
Reference irradiance, parameter :math:`E_{0}` in
:eq:`sapm2` [W/m^2].
Returns
-------
numeric, values in degrees C.
Notes
-----
The model for cell temperature :math:`T_{C}` is given by a pair of
equations (Eq. 11 and 12 in [1]_).
.. math::
:label: sapm1
T_{m} = E \times \exp (a + b \times WS) + T_{a}
.. math::
:label: sapm2
T_{C} = T_{m} + \frac{E}{E_{0}} \Delta T
The module back surface temperature :math:`T_{m}` is implemented in
:py:func:`~pvlib.temperature.sapm_module`.
Inputs to the model are plane-of-array irradiance :math:`E` (W/m2) and
ambient air temperature :math:`T_{a}` (C). Model parameters depend both on
the module construction and its mounting. Parameter sets are provided in
[1]_ for representative modules and mounting, and are coded for convenience
in ``pvlib.temperature.TEMPERATURE_MODEL_PARAMETERS``.
+---------------+----------------+-------+---------+---------------------+
| Module | Mounting | a | b | :math:`\Delta T [C]`|
+===============+================+=======+=========+=====================+
| glass/glass | open rack | -3.47 | -0.0594 | 3 |
+---------------+----------------+-------+---------+---------------------+
| glass/glass | close roof | -2.98 | -0.0471 | 1 |
+---------------+----------------+-------+---------+---------------------+
| glass/polymer | open rack | -3.56 | -0.075 | 3 |
+---------------+----------------+-------+---------+---------------------+
| glass/polymer | insulated back | -2.81 | -0.0455 | 0 |
+---------------+----------------+-------+---------+---------------------+
References
----------
.. [1] King, D. et al, 2004, "Sandia Photovoltaic Array Performance
Model", SAND Report 3535, Sandia National Laboratories, Albuquerque,
NM.
See also
--------
sapm_cell_from_module
sapm_module
Examples
--------
>>> from pvlib.temperature import sapm_cell, TEMPERATURE_MODEL_PARAMETERS
>>> params = TEMPERATURE_MODEL_PARAMETERS['sapm']['open_rack_glass_glass']
>>> sapm_cell(1000, 10, 0, **params)
44.11703066106086
'''
module_temperature = sapm_module(poa_global, temp_air, wind_speed,
a, b)
return sapm_cell_from_module(module_temperature, poa_global, deltaT,
irrad_ref)
[docs]def sapm_module(poa_global, temp_air, wind_speed, a, b):
r'''
Calculate module back surface temperature per the Sandia Array
Performance Model.
See [1]_ for details on the Sandia Array Performance Model.
Parameters
----------
poa_global : numeric
Total incident irradiance [W/m^2].
temp_air : numeric
Ambient dry bulb temperature [C].
wind_speed : numeric
Wind speed at a height of 10 meters [m/s].
a : float
Parameter :math:`a` in :eq:`sapm1mod`.
b : float
Parameter :math:`b` in :eq:`sapm1mod`.
Returns
-------
numeric, values in degrees C.
Notes
-----
The model for module temperature :math:`T_{m}` is given by Eq. 11 in [1]_.
.. math::
:label: sapm1mod
T_{m} = E \times \exp (a + b \times WS) + T_{a}
Inputs to the model are plane-of-array irradiance :math:`E` (W/m2) and
ambient air temperature :math:`T_{a}` (C). Model outputs are surface
temperature at the back of the module :math:`T_{m}` and cell temperature
:math:`T_{C}`. Model parameters depend both on the module construction and
its mounting. Parameter sets are provided in [1]_ for representative
modules and mounting, and are coded for convenience in
``temperature.TEMPERATURE_MODEL_PARAMETERS``.
+---------------+----------------+-------+---------+---------------------+
| Module | Mounting | a | b | :math:`\Delta T [C]`|
+===============+================+=======+=========+=====================+
| glass/glass | open rack | -3.47 | -0.0594 | 3 |
+---------------+----------------+-------+---------+---------------------+
| glass/glass | close roof | -2.98 | -0.0471 | 1 |
+---------------+----------------+-------+---------+---------------------+
| glass/polymer | open rack | -3.56 | -0.075 | 3 |
+---------------+----------------+-------+---------+---------------------+
| glass/polymer | insulated back | -2.81 | -0.0455 | 0 |
+---------------+----------------+-------+---------+---------------------+
References
----------
.. [1] King, D. et al, 2004, "Sandia Photovoltaic Array Performance
Model", SAND Report 3535, Sandia National Laboratories, Albuquerque,
NM.
See also
--------
sapm_cell
sapm_cell_from_module
'''
return poa_global * np.exp(a + b * wind_speed) + temp_air
[docs]def sapm_cell_from_module(module_temperature, poa_global, deltaT,
irrad_ref=1000):
r'''
Calculate cell temperature from module temperature using the Sandia Array
Performance Model.
See [1]_ for details on the Sandia Array Performance Model.
Parameters
----------
module_temperature : numeric
Temperature of back of module surface [C].
poa_global : numeric
Total incident irradiance [W/m^2].
deltaT : float
Parameter :math:`\Delta T` in :eq:`sapm2` [C].
irrad_ref : float, default 1000
Reference irradiance, parameter :math:`E_{0}` in
:eq:`sapm2` [W/m^2].
Returns
-------
numeric, values in degrees C.
Notes
-----
The model for cell temperature :math:`T_{C}` is given by Eq. 12 in [1]_.
.. math::
:label: sapm2
T_{C} = T_{m} + \frac{E}{E_{0}} \Delta T
The module back surface temperature :math:`T_{m}` is implemented in
:py:func:`~pvlib.temperature.sapm_module`.
Model parameters depend both on the module construction and its mounting.
Parameter sets are provided in [1]_ for representative modules and
mounting, and are coded for convenience in
``pvlib.temperature.TEMPERATURE_MODEL_PARAMETERS``.
+---------------+----------------+-------+---------+---------------------+
| Module | Mounting | a | b | :math:`\Delta T [C]`|
+===============+================+=======+=========+=====================+
| glass/glass | open rack | -3.47 | -0.0594 | 3 |
+---------------+----------------+-------+---------+---------------------+
| glass/glass | close roof | -2.98 | -0.0471 | 1 |
+---------------+----------------+-------+---------+---------------------+
| glass/polymer | open rack | -3.56 | -0.075 | 3 |
+---------------+----------------+-------+---------+---------------------+
| glass/polymer | insulated back | -2.81 | -0.0455 | 0 |
+---------------+----------------+-------+---------+---------------------+
References
----------
.. [1] King, D. et al, 2004, "Sandia Photovoltaic Array Performance
Model", SAND Report 3535, Sandia National Laboratories, Albuquerque,
NM.
See also
--------
sapm_cell
sapm_module
'''
return module_temperature + (poa_global / irrad_ref) * deltaT
[docs]def pvsyst_cell(poa_global, temp_air, wind_speed=1.0, u_c=29.0, u_v=0.0,
eta_m=0.1, alpha_absorption=0.9):
r"""
Calculate cell temperature using an empirical heat loss factor model
as implemented in PVsyst.
Parameters
----------
poa_global : numeric
Total incident irradiance [W/m^2].
temp_air : numeric
Ambient dry bulb temperature [C].
wind_speed : numeric, default 1.0
Wind speed in m/s measured at the same height for which the wind loss
factor was determined. The default value 1.0 m/2 is the wind
speed at module height used to determine NOCT. [m/s]
u_c : float, default 29.0
Combined heat loss factor coefficient. The default value is
representative of freestanding modules with the rear surfaces exposed
to open air (e.g., rack mounted). Parameter :math:`U_{c}` in
:eq:`pvsyst` [W/(m^2 C)].
u_v : float, default 0.0
Combined heat loss factor influenced by wind. Parameter :math:`U_{v}`
in :eq:`pvsyst` [(W/m^2 C)(m/s)].
eta_m : numeric, default 0.1
Module external efficiency as a fraction, i.e., DC power / poa_global.
Parameter :math:`\eta_{m}` in :eq:`pvsyst`.
alpha_absorption : numeric, default 0.9
Absorption coefficient. Parameter :math:`\alpha` in :eq:`pvsyst`.
Returns
-------
numeric, values in degrees Celsius
Notes
-----
The Pvsyst model for cell temperature :math:`T_{C}` is given by
.. math::
:label: pvsyst
T_{C} = T_{a} + \frac{\alpha E (1 - \eta_{m})}{U_{c} + U_{v} \times WS}
Inputs to the model are plane-of-array irradiance :math:`E` (W/m2), ambient
air temperature :math:`T_{a}` (C) and wind speed :math:`WS` (m/s). Model
output is cell temperature :math:`T_{C}`. Model parameters depend both on
the module construction and its mounting. Parameters are provided in
[1]_ for open (freestanding) and close (insulated) mounting configurations,
, and are coded for convenience in
``temperature.TEMPERATURE_MODEL_PARAMETERS``. The heat loss factors
provided represent the combined effect of convection, radiation and
conduction, and their values are experimentally determined.
+--------------+---------------+---------------+
| Mounting | :math:`U_{c}` | :math:`U_{v}` |
+==============+===============+===============+
| freestanding | 29.0 | 0.0 |
+--------------+---------------+---------------+
| insulated | 15.0 | 0.0 |
+--------------+---------------+---------------+
References
----------
.. [1] "PVsyst 6 Help", Files.pvsyst.com, 2018. [Online]. Available:
http://files.pvsyst.com/help/index.html. [Accessed: 10- Dec- 2018].
.. [2] Faiman, D. (2008). "Assessing the outdoor operating temperature of
photovoltaic modules." Progress in Photovoltaics 16(4): 307-315.
Examples
--------
>>> from pvlib.temperature import pvsyst_cell, TEMPERATURE_MODEL_PARAMETERS
>>> params = TEMPERATURE_MODEL_PARAMETERS['pvsyst']['freestanding']
>>> pvsyst_cell(1000, 10, **params)
37.93103448275862
"""
total_loss_factor = u_c + u_v * wind_speed
heat_input = poa_global * alpha_absorption * (1 - eta_m)
temp_difference = heat_input / total_loss_factor
return temp_air + temp_difference
[docs]def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84):
'''
Calculate cell or module temperature using the Faiman model. The Faiman
model uses an empirical heat loss factor model [1]_ and is adopted in the
IEC 61853 standards [2]_ and [3]_.
Usage of this model in the IEC 61853 standard does not distinguish
between cell and module temperature.
Parameters
----------
poa_global : numeric
Total incident irradiance [W/m^2].
temp_air : numeric
Ambient dry bulb temperature [C].
wind_speed : numeric, default 1.0
Wind speed in m/s measured at the same height for which the wind loss
factor was determined. The default value 1.0 m/s is the wind
speed at module height used to determine NOCT. [m/s]
u0 : numeric, default 25.0
Combined heat loss factor coefficient. The default value is one
determined by Faiman for 7 silicon modules. [W/(m^2 C)].
u1 : numeric, default 6.84
Combined heat loss factor influenced by wind. The default value is one
determined by Faiman for 7 silicon modules. [(W/m^2 C)(m/s)].
Returns
-------
numeric, values in degrees Celsius
Notes
-----
All arguments may be scalars or vectors. If multiple arguments
are vectors they must be the same length.
References
----------
.. [1] Faiman, D. (2008). "Assessing the outdoor operating temperature of
photovoltaic modules." Progress in Photovoltaics 16(4): 307-315.
.. [2] "IEC 61853-2 Photovoltaic (PV) module performance testing and energy
rating - Part 2: Spectral responsivity, incidence angle and module
operating temperature measurements". IEC, Geneva, 2018.
.. [3] "IEC 61853-3 Photovoltaic (PV) module performance testing and energy
rating - Part 3: Energy rating of PV modules". IEC, Geneva, 2018.
'''
# Contributed by Anton Driesse (@adriesse), PV Performance Labs. Dec., 2019
# The following lines may seem odd since u0 & u1 are probably scalar,
# but it serves an indirect and easy way of allowing lists and
# tuples for the other function arguments.
u0 = np.asanyarray(u0)
u1 = np.asanyarray(u1)
total_loss_factor = u0 + u1 * wind_speed
heat_input = poa_global
temp_difference = heat_input / total_loss_factor
return temp_air + temp_difference