One-Diode Model

Given the 1-diode model parameters for the module, this routine computes the module’s current-voltage characteristics. Figure 35 shows the equivalent circuit of a PV cell. The following algorithm includes the recombination current, Irec, a refinement in the model that can be set to zero if the parameters required to determine the current (μ, τeff, di, Vbi) are not provided in the module definition input file.

Module Curve Figure 17
 

Figure 35. One-Diode Equivalent Electric Circuit Model of a PV Module

 

 

Inputs

Module Curve Inputs

Outputs

Module Curve Outputs

Algorithm

1.) Solve the following transcendental equation that relates the module’s output current i and output voltage υ to the photocurrent Iph, and the 1-diode parameters corrected for the temperature and irradiance level (I0, Rsh, Rs, γ).

Module Curve Algo90
 

Module Curve Algo91
 

Module Curve Algo92
 

Module Curve Algo93

The parameter b, given in the module parameter definition, combines the following terms:

Module Curve Algo93-1

Expanded, the transcendental function for the output current becomes:

Module Curve Algo94
 

Module Curve Algo95
 

2.) The current should be solved for diode voltages in the interval [0, νoc,g], where νoc,g is the guess for the open-circuit voltage, and can be found by setting the I to zero in the above equation (neglecting Irec):

Module Curve Algo96
3.) The limits of the I(V) curve in the first quadrant are defined by the open-circuit voltage and short-circuit current, which can be found by setting i and ν to 0, respectively.

 

4.) Find the maximum power point diode voltage using the Newton-Raphson method by iteratively solving the following equation until the difference between Vd,n+1 and νd,n is arbitrarily small.

Module Curve Algo97
5.) Find the maximum power point current by solving the 1-diode equation.

Module Curve Algo98
6.) Find the maximum power point voltage at the output terminal of the equivalent circuit by subtracting the voltage drop across the series resistance.

Module Curve Algo99
 

Reference

Mermoud, A., Conception et dimensionnement de systèmes photovoltaïques : Introduction des modules PV en couches minces dans le Logiciel PVsyst. Université de Genève, 2005.