## 2 Materials and Method
### Dark I-V Curves  
Solar PV cells convert sunlight into electricity. All potential combinations of current and voltage pairs of points of the PV device under certain conditions of irradiance and temperature are represented in an I-V curve. There are different models that describe the electrical behavior of the I-V curve of a PV device. The one exponential model is widely used and it includes the series and shunt resistances, as detailed in the following Equation (1) [10; 21]. Figure 1 shows the equivalent circuit of the one-diode model of a PV cell under illumination conditions (a) and dark conditions (b). \[I=\ I_{L}-I_{0}\bigg{[}\exp\bigg{(}\frac{V+I\ R_{s}}{n\ v_{t}}\bigg{)}-1\bigg{]} -\bigg{(}\frac{V+I\ R_{s}}{R_{sh}}\bigg{)} \tag{1}\]In Equation (1), \(I_{L}\) is the photogenerated current, \(I_{0}\) is the saturation current of the diode, \(n\) is the diode ideality factor, \(R_{s}\) is the series resistance, \(R_{sh}\) is the shunt resistance, and \(v_{l}\) is the thermal voltage (\(K\)\(T/e\)) with \(k\) as the Boltzmann constant, \(e\) as the electron charge, and T as the temperature in Kelvin. In the dark conditions model circuit, as the photogenerated current \(I_{L}\) due to illumination is zero, the current generator is missing. In Figure 2, there is a common I-V curve under illumination represented in the fourth quadrant, which overlaps the dark diode current with the photogenerated current due to illumination and the dark I-V curve in the first quadrant. The main characteristic points of the curve in illumination are marked in this figure. The criteria that have been considered in this research are that the current is negative when the PV device is generating power (fourth quadrant). As it has been remarked in the introduction, the measurement at dark conditions has the clear advantage that it is performed when the plant is not in operation, giving very important information about the characteristics of the device. It allows analyzing various failure modes, determining solar cell parameters, and monitoring the degradation of modules and it is used as a diagnosis to detect or characterize certain defects and failure modes. The application of the model of Equation (1) with the calculation of the parameters for the dark I-V curve can give information about the changes of a PV module performance, indicating that some failure or degradation has occurred. To illustrate how the variation of the parameters affect the dark I-V curve, Figure 3a,b show the changes in the dark I-V curve of a standard PV cell in which each one of the model parameters of Equation (1) has been changed one at a time. Parameters are expressed in relation to the area for being more comparable, so current is presented in mA/cm\({}^{2}\), and \(J_{0}\) represents the diode saturation current density. The reference curve corresponds to a standard cell with the following parameters: \(J_{0}\) = 1.5 * 10\({}^{-9}\) A/cm\({}^{2}\), \(n\) = 1.5, \(R_{s}\) = 0.6 \(\Omega\) cm\({}^{2}\), and \(R_{sh}\) = 60.000 \(\Omega\) cm\({}^{2}\). From  
Figure 1: One-diode model of a photovoltaic (PV) cell under illumination conditions (**a**) and dark conditions (**b**), including the series and shunt resistances. Figure 2: Illuminated and dark current–voltage (I-V) curves with their characteristic points. these initial values, parameters have been changed to simulate worse device behavior by increasing \(R_{s}\), \(J_{0}\), and \(n\), and decreasing \(R_{sh}\). The graph has been split into two parts to better appreciate the modifications that the change of each parameter introduces in the I-V curve. For the case of variations in \"\(n\)\" and \(R_{sh}\), the graph is presented in logarithm scale to better distinguish its influence and the voltage area in which these changes produce their effect. The variations of the curves presented in Figure 3 can be indicative of certain degradation modes.