SAPM (King 2004)

Method

The temperature of the back of the module rises above the air in proportion to the irradiance, by a factor that falls exponentially with the wind speed (1). The cells run warmer than the back by a difference that scales with the irradiance, ΔT at 1000 W/m² (2). The irradiance is the plane irradiance after near shading and soiling, before the glass-reflection step: the irradiance on which King fitted the coefficients. The wind is the weather file's wind speed, the 10 m wind the model was fitted on. The temperature follows the weather of each timestep with no lag. Where the coefficients come from: the Physics tab's a, b and ΔT when all three are given; otherwise King's table, chosen by the racking and the module: open rack for fixed tilt and trackers, glass/glass for a bifacial module and glass/polymer otherwise, and close roof mount on rooftop racking (Settings).

Settings

King's table row, used when a, b and ΔT are empty	a, b, ΔT
Open rack, glass/glass: fixed tilt or trackers, bifacial module	−3.47, −0.0594 s/m, 3 °C
Open rack, glass/polymer: fixed tilt or trackers, monofacial module	−3.56, −0.0750 s/m, 3 °C
Close roof mount, glass/glass: rooftop racking	−2.98, −0.0471 s/m, 1 °C

The math

1. Module back temperature
2. Cell temperature

$$T_{back} = E\,e^{a_{SAPM} + b_{SAPM}\,v} + T_{amb} \tag{1}$$ $$T = T_{back} + \frac{E}{1000}\,\Delta T \tag{2}$$

where

Symbol	Meaning	Unit
$T_{back}$	the temperature of the back of the module	°C
$E$	the plane irradiance before the glass-reflection step	W/m²
$a_{SAPM}$	the SAPM coefficient at no wind	—
$b_{SAPM}$	the SAPM wind coefficient	s/m
$v$	the wind speed	m/s
$T_{amb}$	the ambient temperature	°C
$T$	the cell temperature	°C
$\Delta T$	the difference between the cells and the module back at 1000 W/m²	°C

References

1. King, Boyson & Kratochvil 2004, Photovoltaic Array Performance Model, Sandia report SAND2004-3535
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 = sapm, thermal.sapm_a, thermal.sapm_b, thermal.sapm_delta_t

Symbols follow the symbol registry.