Fuentes › Published

Method

The heat balance is the one of the Fuentes option above, with the same equations and settings, as the code in the appendix of Fuentes's report runs it. The balance runs at every timestep, dark ones included, so the module cools below the air temperature at night by its radiation to the sky. The module starts at 20 °C before the first timestep. The installed nominal operating cell temperature is an input. The irradiance is the plane irradiance after shading and soiling, before the glass reflection.

Settings

Setting	Value
Installed nominal operating cell temperature	thermal.noct_installed_c; 45 °C, or 49 °C on rooftop racking, when not given
Module temperature before the first step	20 °C

The math

1. Wind at module height
2. Sky temperature
3. Module temperature over the timestep

$$v_m = v\left(\frac{5}{9.144}\right)^{0.2} + 0.0001 \tag{1}$$ $$T_{sky} = 0.68 \cdot 0.0552\,T_a^{1.5} + 0.32\,T_a \tag{2}$$ $$T_m = T_{m,prev}\,e^{\Lambda} + \frac{(1 - e^{\Lambda})\left(h_c T_a + h_s T_{sky} + h_g T_g + G_{abs,prev} + \frac{G_{abs} - G_{abs,prev}}{\Lambda}\right) + G_{abs} - G_{abs,prev}}{h_c + h_s + h_g},\qquad \Lambda = -\frac{(h_c + h_s + h_g)\,3600\,\Delta t}{C_{th}} \tag{3}$$

where

Symbol	Meaning	Unit
$v_m$	the wind speed at the module	m/s
$v$	the wind speed	m/s
$T_{sky}$	the sky temperature	K
$T_a$	the ambient temperature	K
$T_m$	the module temperature at the end of the timestep	K
$T_{m,prev}$	the module temperature of the previous timestep	K
$h_c$	the convection coefficient, free and forced	W/(m²·K)
$h_s$	the radiation coefficient to the sky	W/(m²·K)
$h_g$	the radiation coefficient to the ground	W/(m²·K)
$T_g$	the ground temperature, between the ambient and the module temperature	K
$G_{abs}$	the absorbed irradiance, 0.83 times the plane irradiance	W/m²
$G_{abs,prev}$	the absorbed irradiance of the previous timestep	W/m²
$\Delta t$	the length of one timestep	h
$C_{th}$	the module's heat capacity per unit area	J/(m²·K)

References

1. Fuentes 1987, A Simplified Thermal Model for Flat-Plate Photovoltaic Arrays, Sandia report SAND85-0330
2. pvlib-python 0.16.1 source code (github.com/pvlib/pvlib-python), reference implementation: pvlib/temperature.py, sapm_cell() and fuentes()

API

thermal.model = fuentes_published, thermal.noct_installed_c

Symbols follow the symbol registry.