tessl/pypi-pvlib

A comprehensive toolbox for modeling and simulating photovoltaic energy systems.

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Temperature Models

Name: tessl/pypi-pvlib
Author: tessl

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.

Capabilities

SAPM Temperature Models

Sandia Array Performance Model temperature calculations for cells and modules.

def sapm_cell(poa_global, temp_air, wind_speed, a, b, deltaT, 
             irrad_ref=1000, temp_ref=25):
    """
    Calculate cell temperature using SAPM model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - a: numeric, SAPM module parameter (dimensionless)
    - b: numeric, SAMP module parameter (s/m)
    - deltaT: numeric, SAPM module parameter (C)
    - irrad_ref: numeric, reference irradiance (W/m^2)
    - temp_ref: numeric, reference temperature (C)
    
    Returns:
    numeric, cell temperature (C)
    """

def sapm_module(poa_global, temp_air, wind_speed, a, b):
    """
    Calculate module back-of-module temperature using SAPM model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - a: numeric, SAPM module parameter (dimensionless)
    - b: numeric, SAPM module parameter (s/m)
    
    Returns:
    numeric, module back-of-module temperature (C)
    """

def sapm_cell_from_module(module_temperature, poa_global, deltaT, 
                         irrad_ref=1000, temp_ref=25):
    """
    Calculate cell temperature from module temperature using SAMP model.
    
    Parameters:
    - module_temperature: numeric, module back-of-module temperature (C)
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - deltaT: numeric, SAPM module parameter (C)
    - irrad_ref: numeric, reference irradiance (W/m^2)
    - temp_ref: numeric, reference temperature (C)
    
    Returns:
    numeric, cell temperature (C)
    """

PVsyst Temperature Model

Temperature model used in PVsyst software.

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):
    """
    Calculate cell temperature using PVsyst model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - u_c: numeric, combined heat loss coefficient (W/m^2/C)
    - u_v: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
    - eta_m: numeric, module efficiency under STC
    - alpha_absorption: numeric, absorption coefficient
    
    Returns:
    numeric, cell temperature (C)
    """

Faiman Temperature Model

Simple temperature model based on energy balance.

def faiman(poa_global, temp_air, wind_speed=1.0, u0=25.0, u1=6.84):
    """
    Calculate cell temperature using Faiman model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - u0: numeric, combined heat loss coefficient (W/m^2/C)
    - u1: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
    
    Returns:
    numeric, cell temperature (C)
    """

def faiman_rad(poa_global, temp_air, wind_speed=1.0, ir_down=None, 
              u0=25.0, u1=6.84, emissivity=0.85, temp_sky=None):
    """
    Calculate cell temperature using Faiman model with radiative cooling.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - ir_down: numeric, downwelling longwave irradiance (W/m^2)
    - u0: numeric, combined heat loss coefficient (W/m^2/C)
    - u1: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
    - emissivity: numeric, module emissivity (0-1)
    - temp_sky: numeric, sky temperature (C)
    
    Returns:
    numeric, cell temperature (C)
    """

Ross Temperature Model

Simple temperature model based on NOCT (Nominal Operating Cell Temperature).

def ross(poa_global, temp_air, noct):
    """
    Calculate cell temperature using Ross model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - noct: numeric, nominal operating cell temperature (C)
    
    Returns:
    numeric, cell temperature (C)
    """

Fuentes Temperature Model

Temperature model accounting for module mounting configuration.

def fuentes(poa_global, temp_air, wind_speed, noct_installed, 
           module_height=5, wind_height=9.144):
    """
    Calculate cell temperature using Fuentes model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - noct_installed: numeric, NOCT for installed module configuration (C)
    - module_height: numeric, module mounting height (m)
    - wind_height: numeric, wind measurement height (m)
    
    Returns:
    numeric, cell temperature (C)
    """

NOCT Model from SAM

NOCT-based temperature model used in SAM software.

def noct_sam(poa_global, temp_air, wind_speed, noct, module_efficiency, 
            effective_irradiance):
    """
    Calculate cell temperature using SAM NOCT model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - noct: numeric, nominal operating cell temperature (C)
    - module_efficiency: numeric, module efficiency under STC
    - effective_irradiance: numeric, effective irradiance (W/m^2)
    
    Returns:
    numeric, cell temperature (C)
    """

Generic Linear Temperature Model

Configurable linear temperature model with custom coefficients.

def generic_linear(poa_global, temp_air, wind_speed, u_const, du_wind, 
                  eta_m, alpha_absorption):
    """
    Calculate cell temperature using generic linear model.
    
    Parameters:
    - poa_global: numeric, plane-of-array global irradiance (W/m^2)
    - temp_air: numeric, ambient air temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - u_const: numeric, constant heat loss coefficient (W/m^2/C)
    - du_wind: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
    - eta_m: numeric, module efficiency under STC
    - alpha_absorption: numeric, solar absorption coefficient
    
    Returns:
    numeric, cell temperature (C)
    """

class GenericLinearModel:
    """
    Generic linear temperature model class.
    
    Parameters:
    - u_const: numeric, constant heat loss coefficient (W/m^2/C)
    - du_wind: numeric, wind-dependent heat loss coefficient (W*s/m^3/C)
    - eta_m: numeric, module efficiency under STC
    - alpha_absorption: numeric, solar absorption coefficient
    """
    
    def __init__(self, u_const, du_wind, eta_m, alpha_absorption):
        pass
    
    def __call__(self, poa_global, temp_air, wind_speed):
        """Calculate cell temperature."""
        pass

Prilliman Cooling Model

Model for cell temperature cooling due to wind effects.

def prilliman(temp_cell, wind_speed, unit_mass=11.1, coefficients=None):
    """
    Calculate cell temperature cooling using Prilliman model.
    
    Parameters:
    - temp_cell: numeric, initial cell temperature (C)
    - wind_speed: numeric, wind speed (m/s)
    - unit_mass: numeric, module mass per unit area (kg/m^2)
    - coefficients: array-like, model coefficients
    
    Returns:
    numeric, cooled cell temperature (C)
    """

Temperature Model Parameters

TEMPERATURE_MODEL_PARAMETERS = {
    'sapm': {
        'open_rack_glass_glass': {'a': -3.47, 'b': -0.0594, 'deltaT': 3},
        'close_mount_glass_glass': {'a': -2.98, 'b': -0.0471, 'deltaT': 1},
        'open_rack_glass_polymer': {'a': -3.56, 'b': -0.0750, 'deltaT': 3},
        'insulated_back_glass_polymer': {'a': -2.81, 'b': -0.0455, 'deltaT': 0}
    },
    'pvsyst': {
        'freestanding': {'u_c': 29.0, 'u_v': 0.0},
        'insulated': {'u_c': 15.0, 'u_v': 0.0}
    },
    'faiman': {
        'open_rack': {'u0': 25.0, 'u1': 6.84},
        'close_mount': {'u0': 15.0, 'u1': 2.3}
    }
}

Usage Examples

Comparing Temperature Models

import pvlib
from pvlib import temperature
import numpy as np
import pandas as pd

# Environmental conditions
poa_global = 800  # W/m^2
temp_air = 25     # °C
wind_speed = 3    # m/s

# SAPM model (open rack, glass-glass)
temp_sapm = temperature.sapm_cell(
    poa_global=poa_global,
    temp_air=temp_air,
    wind_speed=wind_speed,
    a=-3.47,
    b=-0.0594,
    deltaT=3
)

# PVsyst model (freestanding)
temp_pvsyst = temperature.pvsyst_cell(
    poa_global=poa_global,
    temp_air=temp_air,
    wind_speed=wind_speed,
    u_c=29.0,
    u_v=0.0
)

# Faiman model (open rack)
temp_faiman = temperature.faiman(
    poa_global=poa_global,
    temp_air=temp_air,
    wind_speed=wind_speed,
    u0=25.0,
    u1=6.84
)

# Ross model (using typical NOCT)
temp_ross = temperature.ross(
    poa_global=poa_global,
    temp_air=temp_air,
    noct=45
)

print("Temperature Model Comparison:")
print(f"Ambient air temperature: {temp_air}°C")
print(f"POA irradiance: {poa_global} W/m²")
print(f"Wind speed: {wind_speed} m/s")
print()
print(f"SAPM:   {temp_sapm:.1f}°C")
print(f"PVsyst: {temp_pvsyst:.1f}°C")
print(f"Faiman: {temp_faiman:.1f}°C")
print(f"Ross:   {temp_ross:.1f}°C")

Temperature vs. Irradiance

import pvlib
from pvlib import temperature
import numpy as np
import matplotlib.pyplot as plt

# Environmental conditions
temp_air = 25
wind_speed = 2
irradiance = np.linspace(0, 1200, 13)

# Calculate temperatures using different models
temps_sapm = temperature.sapm_cell(
    irradiance, temp_air, wind_speed, 
    a=-3.47, b=-0.0594, deltaT=3
)

temps_faiman = temperature.faiman(
    irradiance, temp_air, wind_speed,
    u0=25.0, u1=6.84
)

temps_ross = temperature.ross(
    irradiance, temp_air, noct=45
)

# Print results
print("Irradiance vs Cell Temperature:")
print("Irr(W/m²)  SAPM(°C)  Faiman(°C)  Ross(°C)")
for i, irr in enumerate(irradiance):
    print(f"{irr:8.0f}  {temps_sapm[i]:7.1f}  {temps_faiman[i]:9.1f}  {temps_ross[i]:7.1f}")

Wind Speed Effects

import pvlib
from pvlib import temperature
import numpy as np

# Fixed conditions
poa_global = 800
temp_air = 30
wind_speeds = np.array([0, 1, 2, 3, 5, 8, 10])

# Calculate temperatures for different wind speeds
temps_sapm = temperature.sapm_cell(
    poa_global, temp_air, wind_speeds,
    a=-3.47, b=-0.0594, deltaT=3
)

temps_faiman = temperature.faiman(
    poa_global, temp_air, wind_speeds,
    u0=25.0, u1=6.84
)

# PVsyst model (wind-independent by default)
temps_pvsyst = temperature.pvsyst_cell(
    poa_global, temp_air, wind_speeds
)

print("Wind Speed Effects on Cell Temperature:")
print("Wind(m/s)  SAPM(°C)  Faiman(°C)  PVsyst(°C)")
for i, ws in enumerate(wind_speeds):
    print(f"{ws:8.1f}  {temps_sapm[i]:7.1f}  {temps_faiman[i]:9.1f}  {temps_pvsyst[i]:9.1f}")

Module Mounting Effects

import pvlib
from pvlib import temperature

# Fixed conditions
poa_global = 800
temp_air = 25
wind_speed = 3

# Different mounting configurations using SAPM parameters
mounting_configs = {
    'open_rack_glass_glass': {'a': -3.47, 'b': -0.0594, 'deltaT': 3},
    'close_mount_glass_glass': {'a': -2.98, 'b': -0.0471, 'deltaT': 1},
    'open_rack_glass_polymer': {'a': -3.56, 'b': -0.0750, 'deltaT': 3},
    'insulated_back_glass_polymer': {'a': -2.81, 'b': -0.0455, 'deltaT': 0}
}

print("Module Mounting Configuration Effects:")
print("Configuration                     Cell Temp(°C)")
for config_name, params in mounting_configs.items():
    temp_cell = temperature.sapm_cell(
        poa_global, temp_air, wind_speed, **params
    )
    print(f"{config_name:<30} {temp_cell:11.1f}")

Daily Temperature Profile

import pvlib
from pvlib import temperature, solarposition, clearsky, atmosphere
import pandas as pd

# Location and date
lat, lon = 40.0583, -74.4057  # Princeton, NJ
date = '2023-07-15'  # Summer day
times = pd.date_range(f'{date} 00:00', f'{date} 23:00', 
                     freq='H', tz='US/Eastern')

# Solar position
solar_pos = solarposition.get_solarposition(times, lat, lon)

# Clear sky irradiance
airmass = atmosphere.get_relative_airmass(solar_pos['zenith'])
airmass_abs = atmosphere.get_absolute_airmass(airmass)
clear_sky = clearsky.ineichen(
    solar_pos['apparent_zenith'], airmass_abs, linke_turbidity=3.0
)

# Environmental conditions (simplified daily patterns)
temp_air = 20 + 10 * np.sin(np.pi * (times.hour - 6) / 12)  # Daily temp cycle
temp_air = np.maximum(temp_air, 15)  # Minimum 15°C
wind_speed = 2 + np.random.normal(0, 0.5, len(times))  # Variable wind
wind_speed = np.maximum(wind_speed, 0.5)  # Minimum wind

# Calculate cell temperatures
temp_cell = temperature.sapm_cell(
    poa_global=clear_sky['ghi'],
    temp_air=temp_air,
    wind_speed=wind_speed,
    a=-3.47, b=-0.0594, deltaT=3
)

# Show results for daylight hours
print("Daily Temperature Profile:")
print("Time   Air(°C)  GHI(W/m²)  Wind(m/s)  Cell(°C)")
for i in range(6, 19):  # 6 AM to 6 PM
    time_str = times[i].strftime('%H:%M')
    air_temp = temp_air[i]
    ghi = clear_sky['ghi'].iloc[i]
    wind = wind_speed[i]
    cell = temp_cell[i]
    print(f"{time_str}   {air_temp:5.1f}   {ghi:7.0f}    {wind:5.1f}    {cell:5.1f}")

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