Given coefficient

Method

The band gap in the saturation-current law (1) is 1.121 eV for every cell technology. The temperature coefficient of the ideality factor (2) is the value given with the module. When the module gives none, or gives 0, the coefficient is fitted so that the curve's maximum power at 1000 W/m² falls from 25 °C to 45 °C by the module's power temperature coefficient (3).

The math

1. Saturation current
2. Ideality factor
3. The fitted coefficient

$$I_0 = \max\!\left(2.07 \times 10^{-14}\ \text{A},\ I_{0,ref}\left(\frac{T}{T_{ref}}\right)^3 \exp\!\left[\frac{E_g}{\gamma_d\,k_B}\left(\frac{1}{T_{ref}} - \frac{1}{T}\right)\right]\right) \tag{1}$$ $$\gamma_d = \gamma_{d,ref} + \mu_{\gamma}\,(T - T_{ref}) \tag{2}$$ $$P_{mp}(G_{ref}, T_{45}) = P_{mp}(G_{ref}, T_{ref})\left[1 + \mu_{P}\,(T_{45} - T_{ref})\right] \tag{3}$$

where

Symbol	Meaning	Unit
$I_0$	the diode saturation current	A
$I_{0,ref}$	the saturation current at reference conditions	A
$T$	the cell temperature	K
$T_{ref}$	the cell temperature of standard test conditions, 25 °C	K
$E_g$	the band gap	J
$k_B$	Boltzmann's constant. 1.380649 × 10⁻²³ J/K	J/K
$\gamma_d$	the diode ideality factor	—
$\gamma_{d,ref}$	the ideality factor at standard conditions	—
$\mu_{\gamma}$	the temperature coefficient of the ideality factor	1/K
$P_{mp}(G, T)$	the maximum power of the module curve at irradiance $G$ and cell temperature $T$	W
$G_{ref}$	the irradiance of standard test conditions, 1000 W/m²	W/m²
$T_{45}$	45 °C	K
$\mu_{P}$	the module's power temperature coefficient	1/K

References

1. Mermoud & Lejeune 2010, Performance assessment of a simulation model for PV modules of any available technology, 25th European Photovoltaic Solar Energy Conference

API

options.module_temperature_fit = mu_gamma

Symbols follow the symbol registry.