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# Temperature Models
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Calculate PV cell and module temperatures using various models including SAPM, Faiman, Ross, Fuentes, and PVsyst approaches. Accurate temperature modeling is essential for realistic PV system performance predictions.
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## Capabilities
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### SAPM Temperature Models
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Sandia Array Performance Model temperature calculations for cells and modules.
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```python { .api }
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def sapm_cell(poa_global, temp_air, wind_speed, a, b, deltaT, 
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             irrad_ref=1000, temp_ref=25):
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    """
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    Calculate cell temperature using SAPM model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - a: numeric, SAPM module parameter (dimensionless)
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    - b: numeric, SAMP module parameter (s/m)
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    - deltaT: numeric, SAPM module parameter (C)
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    - irrad_ref: numeric, reference irradiance (W/m^2)
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    - temp_ref: numeric, reference temperature (C)
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    Returns:
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    numeric, cell temperature (C)
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    """
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def sapm_module(poa_global, temp_air, wind_speed, a, b):
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    """
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    Calculate module back-of-module temperature using SAPM model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - a: numeric, SAPM module parameter (dimensionless)
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    - b: numeric, SAPM module parameter (s/m)
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    Returns:
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    numeric, module back-of-module temperature (C)
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    """
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def sapm_cell_from_module(module_temperature, poa_global, deltaT, 
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                         irrad_ref=1000, temp_ref=25):
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    """
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    Calculate cell temperature from module temperature using SAMP model.
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    Parameters:
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    - module_temperature: numeric, module back-of-module temperature (C)
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - deltaT: numeric, SAPM module parameter (C)
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    - irrad_ref: numeric, reference irradiance (W/m^2)
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    - temp_ref: numeric, reference temperature (C)
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    Returns:
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    numeric, cell temperature (C)
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    """
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```
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### PVsyst Temperature Model
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Temperature model used in PVsyst software.
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```python { .api }
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def pvsyst_cell(poa_global, temp_air, wind_speed=1.0, u_c=29.0, u_v=0.0, 
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               eta_m=0.1, alpha_absorption=0.9):
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    """
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    Calculate cell temperature using PVsyst model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - u_c: numeric, combined heat loss coefficient (W/m^2/C)
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    - u_v: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
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    - eta_m: numeric, module efficiency under STC
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    - alpha_absorption: numeric, absorption coefficient
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    Returns:
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    numeric, cell temperature (C)
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    """
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```
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### Faiman Temperature Model
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Simple temperature model based on energy balance.
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```python { .api }
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def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84):
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    """
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    Calculate cell temperature using Faiman model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - u0: numeric, combined heat loss coefficient (W/m^2/C)
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    - u1: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
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    Returns:
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    numeric, cell temperature (C)
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    """
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def faiman_rad(poa_global, temp_air, wind_speed=1.0, ir_down=None, 
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              u0=25.0, u1=6.84, emissivity=0.85, temp_sky=None):
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    """
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    Calculate cell temperature using Faiman model with radiative cooling.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - ir_down: numeric, downwelling longwave irradiance (W/m^2)
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    - u0: numeric, combined heat loss coefficient (W/m^2/C)
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    - u1: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
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    - emissivity: numeric, module emissivity (0-1)
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    - temp_sky: numeric, sky temperature (C)
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    Returns:
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    numeric, cell temperature (C)
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    """
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```
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### Ross Temperature Model
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Simple temperature model based on NOCT (Nominal Operating Cell Temperature).
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```python { .api }
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def ross(poa_global, temp_air, noct):
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    """
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    Calculate cell temperature using Ross model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - noct: numeric, nominal operating cell temperature (C)
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    Returns:
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    numeric, cell temperature (C)
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    """
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```
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### Fuentes Temperature Model
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Temperature model accounting for module mounting configuration.
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```python { .api }
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def fuentes(poa_global, temp_air, wind_speed, noct_installed, 
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           module_height=5, wind_height=9.144):
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    """
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    Calculate cell temperature using Fuentes model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - noct_installed: numeric, NOCT for installed module configuration (C)
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    - module_height: numeric, module mounting height (m)
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    - wind_height: numeric, wind measurement height (m)
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    Returns:
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    numeric, cell temperature (C)
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    """
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```
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### NOCT Model from SAM
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NOCT-based temperature model used in SAM software.
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```python { .api }
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def noct_sam(poa_global, temp_air, wind_speed, noct, module_efficiency, 
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            effective_irradiance):
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    """
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    Calculate cell temperature using SAM NOCT model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - noct: numeric, nominal operating cell temperature (C)
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    - module_efficiency: numeric, module efficiency under STC
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    - effective_irradiance: numeric, effective irradiance (W/m^2)
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    Returns:
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    numeric, cell temperature (C)
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    """
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```
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### Generic Linear Temperature Model
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Configurable linear temperature model with custom coefficients.
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```python { .api }
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def generic_linear(poa_global, temp_air, wind_speed, u_const, du_wind, 
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                  eta_m, alpha_absorption):
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    """
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    Calculate cell temperature using generic linear model.
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    Parameters:
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    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
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    - temp_air: numeric, ambient air temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - u_const: numeric, constant heat loss coefficient (W/m^2/C)
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    - du_wind: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
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    - eta_m: numeric, module efficiency under STC
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    - alpha_absorption: numeric, solar absorption coefficient
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    Returns:
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    numeric, cell temperature (C)
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    """
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class GenericLinearModel:
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    """
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    Generic linear temperature model class.
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    Parameters:
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    - u_const: numeric, constant heat loss coefficient (W/m^2/C)
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    - du_wind: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
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    - eta_m: numeric, module efficiency under STC
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    - alpha_absorption: numeric, solar absorption coefficient
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    """
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    def __init__(self, u_const, du_wind, eta_m, alpha_absorption):
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        pass
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    def __call__(self, poa_global, temp_air, wind_speed):
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        """Calculate cell temperature."""
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        pass
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```
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### Prilliman Cooling Model
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Model for cell temperature cooling due to wind effects.
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```python { .api }
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def prilliman(temp_cell, wind_speed, unit_mass=11.1, coefficients=None):
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    """
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    Calculate cell temperature cooling using Prilliman model.
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    Parameters:
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    - temp_cell: numeric, initial cell temperature (C)
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    - wind_speed: numeric, wind speed (m/s)
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    - unit_mass: numeric, module mass per unit area (kg/m^2)
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    - coefficients: array-like, model coefficients
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    Returns:
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    numeric, cooled cell temperature (C)
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    """
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```
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## Temperature Model Parameters
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```python { .api }
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TEMPERATURE_MODEL_PARAMETERS = {
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    'sapm': {
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        'open_rack_glass_glass': {'a': -3.47, 'b': -0.0594, 'deltaT': 3},
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        'close_mount_glass_glass': {'a': -2.98, 'b': -0.0471, 'deltaT': 1},
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        'open_rack_glass_polymer': {'a': -3.56, 'b': -0.0750, 'deltaT': 3},
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        'insulated_back_glass_polymer': {'a': -2.81, 'b': -0.0455, 'deltaT': 0}
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    },
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    'pvsyst': {
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        'freestanding': {'u_c': 29.0, 'u_v': 0.0},
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        'insulated': {'u_c': 15.0, 'u_v': 0.0}
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    },
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    'faiman': {
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        'open_rack': {'u0': 25.0, 'u1': 6.84},
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        'close_mount': {'u0': 15.0, 'u1': 2.3}
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    }
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}
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```
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## Usage Examples
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### Comparing Temperature Models
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```python
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import pvlib
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from pvlib import temperature
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import numpy as np
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import pandas as pd
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# Environmental conditions
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poa_global = 800  # W/m^2
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temp_air = 25     # °C
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wind_speed = 3    # m/s
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# SAPM model (open rack, glass-glass)
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temp_sapm = temperature.sapm_cell(
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    poa_global=poa_global,
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    temp_air=temp_air,
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    wind_speed=wind_speed,
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    a=-3.47,
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    b=-0.0594,
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    deltaT=3
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)
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# PVsyst model (freestanding)
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temp_pvsyst = temperature.pvsyst_cell(
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    poa_global=poa_global,
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    temp_air=temp_air,
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    wind_speed=wind_speed,
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    u_c=29.0,
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    u_v=0.0
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)
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# Faiman model (open rack)
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temp_faiman = temperature.faiman(
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    poa_global=poa_global,
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    temp_air=temp_air,
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    wind_speed=wind_speed,
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    u0=25.0,
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    u1=6.84
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)
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# Ross model (using typical NOCT)
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temp_ross = temperature.ross(
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    poa_global=poa_global,
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    temp_air=temp_air,
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    noct=45
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)
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print("Temperature Model Comparison:")
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print(f"Ambient air temperature: {temp_air}°C")
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print(f"POA irradiance: {poa_global} W/m²")
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print(f"Wind speed: {wind_speed} m/s")
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print()
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print(f"SAPM:   {temp_sapm:.1f}°C")
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print(f"PVsyst: {temp_pvsyst:.1f}°C")
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print(f"Faiman: {temp_faiman:.1f}°C")
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print(f"Ross:   {temp_ross:.1f}°C")
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```
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### Temperature vs. Irradiance
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```python
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import pvlib
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from pvlib import temperature
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import numpy as np
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import matplotlib.pyplot as plt
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# Environmental conditions
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temp_air = 25
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wind_speed = 2
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irradiance = np.linspace(0, 1200, 13)
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# Calculate temperatures using different models
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temps_sapm = temperature.sapm_cell(
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    irradiance, temp_air, wind_speed, 
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    a=-3.47, b=-0.0594, deltaT=3
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)
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temps_faiman = temperature.faiman(
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    irradiance, temp_air, wind_speed,
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    u0=25.0, u1=6.84
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)
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temps_ross = temperature.ross(
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    irradiance, temp_air, noct=45
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)
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# Print results
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print("Irradiance vs Cell Temperature:")
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print("Irr(W/m²)  SAPM(°C)  Faiman(°C)  Ross(°C)")
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for i, irr in enumerate(irradiance):
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    print(f"{irr:8.0f}  {temps_sapm[i]:7.1f}  {temps_faiman[i]:9.1f}  {temps_ross[i]:7.1f}")
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```
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### Wind Speed Effects
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```python
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import pvlib
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from pvlib import temperature
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import numpy as np
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# Fixed conditions
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poa_global = 800
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temp_air = 30
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wind_speeds = np.array([0, 1, 2, 3, 5, 8, 10])
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# Calculate temperatures for different wind speeds
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temps_sapm = temperature.sapm_cell(
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    poa_global, temp_air, wind_speeds,
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    a=-3.47, b=-0.0594, deltaT=3
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)
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temps_faiman = temperature.faiman(
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    poa_global, temp_air, wind_speeds,
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    u0=25.0, u1=6.84
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)
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# PVsyst model (wind-independent by default)
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temps_pvsyst = temperature.pvsyst_cell(
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    poa_global, temp_air, wind_speeds
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)
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print("Wind Speed Effects on Cell Temperature:")
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print("Wind(m/s)  SAPM(°C)  Faiman(°C)  PVsyst(°C)")
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for i, ws in enumerate(wind_speeds):
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    print(f"{ws:8.1f}  {temps_sapm[i]:7.1f}  {temps_faiman[i]:9.1f}  {temps_pvsyst[i]:9.1f}")
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```
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### Module Mounting Effects
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```python
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import pvlib
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from pvlib import temperature
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# Fixed conditions
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poa_global = 800
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temp_air = 25
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wind_speed = 3
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# Different mounting configurations using SAPM parameters
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mounting_configs = {
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    'open_rack_glass_glass': {'a': -3.47, 'b': -0.0594, 'deltaT': 3},
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    'close_mount_glass_glass': {'a': -2.98, 'b': -0.0471, 'deltaT': 1},
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    'open_rack_glass_polymer': {'a': -3.56, 'b': -0.0750, 'deltaT': 3},
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    'insulated_back_glass_polymer': {'a': -2.81, 'b': -0.0455, 'deltaT': 0}
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}
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print("Module Mounting Configuration Effects:")
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print("Configuration                     Cell Temp(°C)")
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for config_name, params in mounting_configs.items():
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    temp_cell = temperature.sapm_cell(
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        poa_global, temp_air, wind_speed, **params
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    )
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    print(f"{config_name:<30} {temp_cell:11.1f}")
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```
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### Daily Temperature Profile
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```python
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import pvlib
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from pvlib import temperature, solarposition, clearsky, atmosphere
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import pandas as pd
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# Location and date
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lat, lon = 40.0583, -74.4057  # Princeton, NJ
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date = '2023-07-15'  # Summer day
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times = pd.date_range(f'{date} 00:00', f'{date} 23:00', 
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                     freq='H', tz='US/Eastern')
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# Solar position
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solar_pos = solarposition.get_solarposition(times, lat, lon)
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# Clear sky irradiance
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airmass = atmosphere.get_relative_airmass(solar_pos['zenith'])
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airmass_abs = atmosphere.get_absolute_airmass(airmass)
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clear_sky = clearsky.ineichen(
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    solar_pos['apparent_zenith'], airmass_abs, linke_turbidity=3.0
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)
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# Environmental conditions (simplified daily patterns)
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temp_air = 20 + 10 * np.sin(np.pi * (times.hour - 6) / 12)  # Daily temp cycle
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temp_air = np.maximum(temp_air, 15)  # Minimum 15°C
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wind_speed = 2 + np.random.normal(0, 0.5, len(times))  # Variable wind
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wind_speed = np.maximum(wind_speed, 0.5)  # Minimum wind
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# Calculate cell temperatures
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temp_cell = temperature.sapm_cell(
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    poa_global=clear_sky['ghi'],
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    temp_air=temp_air,
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    wind_speed=wind_speed,
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    a=-3.47, b=-0.0594, deltaT=3
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)
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# Show results for daylight hours
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print("Daily Temperature Profile:")
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print("Time   Air(°C)  GHI(W/m²)  Wind(m/s)  Cell(°C)")
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for i in range(6, 19):  # 6 AM to 6 PM
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    time_str = times[i].strftime('%H:%M')
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    air_temp = temp_air[i]
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    ghi = clear_sky['ghi'].iloc[i]
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    wind = wind_speed[i]
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    cell = temp_cell[i]
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    print(f"{time_str}   {air_temp:5.1f}   {ghi:7.0f}    {wind:5.1f}    {cell:5.1f}")
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```