CEC 6-parameter › Published

Method

The circuit and its temperature laws are those of the CEC six-parameter option with this module's own parameters (1 to 4). They are the one-diode model of De Soto, Klein and Beckman with Dobos's adjustment of the temperature coefficient of the short-circuit current. The parameters are this module's CEC database entry, used as the database gives them. Boltzmann's constant takes its CODATA value. The module delivers power at any irradiance above zero. Where the parameters come from: the module record's CEC block, which every module of the CEC library carries.

Settings

Setting	Value
Reference temperature $T_{ref}$	298.15 K (25 °C)
Boltzmann constant $k_B$	8.617333262 × 10⁻⁵ eV/K

The math

1. Light current
2. Saturation current
3. Ideality and shunt resistance
4. Circuit

$$I_L = \frac{G}{1000}\left[I_{L,ref} + \alpha_{sc}\left(1 - \frac{\text{Adj}}{100}\right)(T - T_{ref})\right] \tag{1}$$ $$I_0 = I_{0,ref}\left(\frac{T}{T_{ref}}\right)^3 \exp\!\left[\frac{1}{k_B}\left(\frac{1.12}{T_{ref}} - \frac{E_g}{T}\right)\right],\qquad E_g = 1.12\,\big(1 - 0.0002677\,(T - T_{ref})\big) \tag{2}$$ $$a_T = a_{ref}\,\frac{T}{T_{ref}},\qquad R_{sh} = R_{sh,ref}\,\frac{1000}{G} \tag{3}$$ $$I_m = I_L - I_0\left[\exp\!\left(\frac{V_m + I_m R_s}{a_T}\right) - 1\right] - \frac{V_m + I_m R_s}{R_{sh}} \tag{4}$$

where

Symbol	Meaning	Unit
$I_L$	the light current	A
$G$	the effective irradiance on the modules	W/m²
$I_{L,ref}$	the light current at reference conditions	A
$\alpha_{sc}$	the temperature coefficient of the short-circuit current	A/°C
$\text{Adj}$	the adjustment of that coefficient	%
$T$	the cell temperature	K
$T_{ref}$	the cell temperature of standard test conditions, 25 °C	K
$I_0$	the diode saturation current	A
$I_{0,ref}$	the saturation current at reference conditions	A
$k_B$	Boltzmann's constant	eV/K
$E_g$	the band gap. 1.12 eV at 25 °C, the silicon value, used for both representative modules	eV
$a_T$	the modified ideality factor	V
$a_{ref}$	the modified ideality factor at reference conditions	V
$R_{sh}$	the shunt resistance	Ω
$R_{sh,ref}$	the shunt resistance at reference conditions	Ω
$I_m$	the module current	A
$V_m$	the module voltage	V
$R_s$	the series resistance	Ω

References

1. De Soto, Klein & Beckman 2006, Improvement and validation of a model for photovoltaic array performance, Solar Energy 80(1) 78–88
2. Dobos 2012, An improved coefficient calculator for the California Energy Commission 6 parameter photovoltaic module model, Journal of Solar Energy Engineering 134(2) 021011
3. California Energy Commission, Solar Equipment Lists: PV modules, with the six-parameter model fitted by NREL as distributed in the System Advisor Model library (CEC Modules.csv)

API

options.module_model = cec_published (module.model = cec_published), module.cec

Symbols follow the symbol registry.