CEC six-parameter, representative module

Method

The circuit is the one-diode model of De Soto, Klein and Beckman with the adjustment of the temperature coefficient of the short-circuit current that Dobos added for the California Energy Commission's six-parameter model. The six parameters at reference conditions are the light current, the diode saturation current, the modified ideality factor, the series resistance, the shunt resistance and that adjustment. The parameters are those of a published module chosen by the cell technology on the Module tab: a 320 W monocrystalline silicon module for crystalline silicon and for an empty technology, and a 435 W cadmium telluride module for cadmium telluride, copper indium gallium selenide and amorphous silicon. At every timestep the parameters are translated to the effective irradiance and the cell temperature, and the maximum-power point is found exactly on the curve. Below 1 W/m² of effective irradiance the module produces nothing. The power is scaled by this module's nameplate over the representative module's $V_{mp}\,I_{mp}$, and the voltage by this module's maximum-power voltage over the representative one's, so the strings keep the voltage of the modules entered on the Module tab. This module's own circuit values are not used. The option reads only the nameplate. Without the maximum-power voltage the voltage keeps the representative module's. Without a width and a height the module area is the nameplate over the efficiency at 1000 W/m², with an efficiency of 19 %, or 18 % for cadmium telluride, copper indium gallium selenide and amorphous silicon, when none is given.

Settings

Setting	Value
Crystalline silicon: Canadian Solar CS1H-320MS	$a_{ref}$ 1.65916 V, $I_{L,ref}$ 9.51393 A, $I_{0,ref}$ 4.37813 × 10⁻¹¹ A, $R_s$ 0.269953 Ω, $R_{sh,ref}$ 654.059 Ω, Adj 5.79586 %, $\alpha_{sc}$ 0.004755 A/°C, $V_{mp}$ 35.8 V, $I_{mp}$ 9.01 A
Thin film: First Solar FS-6435A	$a_{ref}$ 7.97293 V, $I_{L,ref}$ 2.55475 A, $I_{0,ref}$ 2.69243 × 10⁻¹² A, $R_s$ 4.60991 Ω, $R_{sh,ref}$ 2476.95 Ω, Adj −2.49865 %, $\alpha_{sc}$ 0.00102 A/°C, $V_{mp}$ 183.6 V, $I_{mp}$ 2.37 A
Reference temperature $T_{ref}$	298.15 K (25 °C)
Boltzmann constant $k_B$	8.618 × 10⁻⁵ eV/K
Irradiance below which the power is zero	1 W/m²

The math

1. Light current
2. Saturation current
3. Ideality and shunt resistance
4. Circuit
5. Scaling to this module

$$I_L = \frac{G}{1000}\left[I_{L,ref} + \alpha_{sc}\left(1 - \frac{\text{Adj}}{100}\right)(T - T_{ref})\right] \tag{1}$$ $$I_0 = I_{0,ref}\left(\frac{T}{T_{ref}}\right)^3 \exp\!\left[\frac{1}{k_B}\left(\frac{1.12}{T_{ref}} - \frac{E_g}{T}\right)\right],\qquad E_g = 1.12\,\big(1 - 0.0002677\,(T - T_{ref})\big) \tag{2}$$ $$a_T = a_{ref}\,\frac{T}{T_{ref}},\qquad R_{sh} = R_{sh,ref}\,\frac{1000}{G} \tag{3}$$ $$I_m = I_L - I_0\left[\exp\!\left(\frac{V_m + I_m R_s}{a_T}\right) - 1\right] - \frac{V_m + I_m R_s}{R_{sh}} \tag{4}$$ $$P_{m,mpp} = P_{rep}\,\frac{P_{nom}}{V_{mp}\,I_{mp}},\qquad V_{m,mpp} = V_{rep}\,\frac{V_{mp,mod}}{V_{mp}} \tag{5}$$

where

Symbol	Meaning	Unit
$I_L$	the light current	A
$G$	the effective irradiance	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 reference temperature	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 bandgap: 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
$P_{m,mpp}, V_{m,mpp}$	the power and voltage of this module at its maximum-power point	W and V
$P_{rep}, V_{rep}$	the power and voltage of the representative module at its maximum-power point	W and V
$P_{nom}$	this module's nameplate power	W
$V_{mp}, I_{mp}$	the representative module's maximum-power voltage and current at standard test conditions	V and A
$V_{mp,mod}$	this module's maximum-power voltage at standard test conditions	V

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. Gilman, DiOrio, Freeman, Janzou, Dobos & Ryberg 2018, SAM Photovoltaic Model Technical Reference Update, NREL/TP-6A20-67399
4. NREL SAM Simulation Core (SSC) source code, release 2026.7.3, github.com/NatLabRockies/ssc: shared/lib_cec6par.cpp, cec6par_module_t; ssc/cmod_pvwattsv8.cpp, the module parameters of each module type

API

module.model = desoto, or options.module_model = desoto

Symbols follow the symbol registry.