*2.1. Double Diode Model (DDM)*

The DDM uses dual diodes and dual resistors coupled in a series and shunted to the diode; this configuration is designed to compensate for the losses. The DDM of a solar cell is shown in Figure 1; with this concept, a second diode is added to reduce the transmission losses caused by the depletion layer carrier recombination and surface recombination, as specified by *Id*<sup>2</sup> [29,66]. The component of the current is represented by the current of the first diode *Id*1.

The DDM can be formulated as follows:

$$I\_{PV} = I\_{ph} - I\_{d1} - I\_{d2} - I\_{sh} \tag{1}$$

$$I\_{PV} = I\_{ph} - I\_{d1} \left[ \exp\left[\frac{q[V\_{PV} + R\_s I\_{PV}]}{A\_1 KT}\right] - 1\right] - I\_{d2} \left[ \exp\left[\frac{q[V\_{PV} + R\_s I\_{PV}]}{A\_2 KT}\right] - 1\right] - \left[\frac{V\_{PV} + R\_s I\_{PV}}{R\_{sl}}\right] \tag{2}$$

This model has seven parameters to be computed; they are provided as a vector, as given in Equation (3).

$$\mathbf{x} = \begin{bmatrix} A\_1 A\_2 R\_s R\_{sh} I\_{d1} I\_{d2} I\_{ph} \end{bmatrix} \tag{3}$$

where *Id*1, *Id*2, and *Iph* are the reversal saturation currents of the diodes and photon current; *q* is the electronic charge; *A*<sup>1</sup> and *A*<sup>2</sup> are the diodes' ideality factors; *T* denotes the temperature in Kelvin; *K* refers to the Boltzmann constant; and *Rsh* and *Rs* are the shunt and series resistances.
