Fitted to the power coefficient

Method

The band gap in the saturation-current law (1) is the cell technology's, from the table below. The temperature coefficient of the ideality factor (2) 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 fit runs on the curve with that band gap. A coefficient given with the module is not read. A cadmium telluride module rated −0.32 %/°C runs with +0.000457 1/°C. A crystalline silicon module rated −0.352 %/°C runs with −0.000509 1/°C.

Settings

Cell technology	Band gap $E_g$
Cadmium telluride	1.5 eV
Copper indium gallium selenide	1.03 eV
Amorphous silicon	1.7 eV
Crystalline silicon, or no technology given	1.12 eV

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
2. PVsyst 8 help, Standard one-diode model
3. Analysis of PVsyst 8.1.5 outputs shows this convention in its results.

API

options.module_temperature_fit = mu_pmp

Symbols follow the symbol registry.