Prilliman transient

Method

The cell temperature is the temperature at which the heat the module sheds to the air equals the heat it absorbs from the sunlight minus the electricity it produces. The balance is Faiman's, with the efficiency taken as the module's own efficiency at that temperature, found by iteration. The result is then blended with the previous timestep's value, so that the temperature lags the weather. The rate of the lag, which depends on the wind and on the module's mass, is that of Prilliman, Stein, Riley and Tamizhmani. Their model averages the past twenty minutes; the weight here is that exponential rate averaged over one whole timestep, (1 − e^(−x))/x, which reproduces the module temperature of PVsyst 8.1.5 to 0.0013 °C over a year.

The math

$$a\,G\,(1 - \eta) = (U_c + U_v\,v)\,(T_{ss} - T_{amb}) \tag{1}$$ $$T = w\,T_{ss,prev} + (1 - w)\,T_{ss},\qquad w = \frac{1 - e^{-x}}{x},\qquad x = 3600\,\Delta t\,(0.0046 + 0.00046\,v - 0.00023\,m - 0.000016\,v\,m) \tag{2}$$

where

Symbol	Meaning	Unit
$a$	the absorptivity: the fraction of the light the module absorbs	—
$G$	the effective irradiance on the modules	W/m²
$\eta$	the module efficiency at the operating point	—
$U_c$	the constant heat-loss factor	W/(m²·K)
$U_v$	the wind heat-loss factor	W/(m²·K) per m/s
$v$	the wind speed	m/s
$T_{ss}$	the steady-state cell temperature of the timestep	°C
$T_{amb}$	the ambient temperature	°C
$T$	the cell temperature	°C
$T_{ss,prev}$	the steady-state temperature of the previous timestep	°C
$w$	the weight of the previous timestep	—
$x$	the timestep length times the module's thermal response rate	—
$\Delta t$	the timestep length	h
$m$	the mass of the module per unit area	kg/m²

References

1. Faiman 2008, Assessing the outdoor operating temperature of photovoltaic modules, Progress in Photovoltaics 16(4) 307–315
2. Prilliman, Stein, Riley & Tamizhmani 2020, Transient weighted moving-average model of photovoltaic module back-surface temperature, IEEE Journal of Photovoltaics 10(4) 1053–1060
3. Analysis of PVsyst 8.1.5 outputs shows this convention in its results.

API

thermal.model = prilliman, thermal.transient = true

Symbols follow the symbol registry.