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Method

The steady cell temperature of each timestep is Faiman's heat balance with the rated efficiency (1). The cell temperature is the mean of the steady temperatures of the timesteps in the 20 minutes before it, each weighted by an exponential of its lag (2, 3). The response rate of the weights grows with the wind and falls with the module's mass per unit area. The first timestep keeps its steady temperature. With timesteps of 20 minutes or more no earlier timestep lies in the window, and each timestep keeps its steady temperature.

The math

1. Steady cell temperature
2. Weighted average over the 20 minutes before
3. Response rate

$$T_{ss} = T_{amb} + \frac{a\,G\,(1 - \eta_{STC})}{U_c + U_v\,v} \tag{1}$$ $$T_k = \frac{\sum_{j=1}^{N_w} w_j\,T_{ss,k-j}}{\sum_{j=1}^{N_w} w_j},\qquad w_j = e^{-k_{th}\,j\,\Delta t},\qquad N_w = \left\lfloor \frac{20\ \text{min}}{\Delta t} \right\rfloor \tag{2}$$ $$k_{th} = 0.0046 + 0.00046\,v - 0.00023\,m_A - 0.000016\,v\,m_A \tag{3}$$

where

Symbol	Meaning	Unit
$T_{ss}$	the steady-state cell temperature of a timestep	°C
$T_{amb}$	the ambient temperature	°C
$a$	the absorptivity: the fraction of the light the module absorbs	—
$G$	the effective irradiance on the modules	W/m²
$\eta_{STC}$	the module efficiency at standard test conditions	—
$U_c$	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
$T_k$	the cell temperature of timestep k	°C
$T_{ss,k-j}$	the steady-state temperature j timesteps before	°C
$w_j$	the weight of the timestep $j$ steps before	—
$N_w$	the number of timesteps in the 20 minutes before	—
$\Delta t$	the length of one timestep	s
$k_{th}$	the module's thermal response rate	1/s
$m_A$	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

API

thermal.model = prilliman_published, thermal.transient = true

Symbols follow the symbol registry.