## 1 Introduction
### The Solar Cell/Panel Equivalent Circuit Models
extract the values of parameters \(I_{pv}\), \(I_{0}\) and \(a\) in Equation (1). The \(I\)-\(V\) curve resulting from this model crosses the aforementioned maximum power point, but it is not assured that this condition is reached at this point. 2. 1-diode/1-resistor model (indicated as 1D/1R in Figures 2 and 3, and Tables 2 and 3): the three characteristic points and the slope of the \(I\)-\(V\) curve at maximum power point are used as the four conditions needed to extract the values of parameters \(I_{pv}\), \(I_{0}\), \(a\) and \(R_{s}\) in Equation (2). 3. 1-diode/2-resistor model, two procedures are used in this case: 1. Four conditions procedure (indicated as 1D/2R-1 in Figures 2 and 3, and Tables 2 and 3): the three characteristic points and the slope of the \(I\)-\(V\) curve at maximum power point, together with a pre-established value of the ideality factor (reasonably, in the bracket from \(a\) = 1.1 to \(a\) = 1.3 [8]), are used as the four conditions needed to extract the values of parameters \(I_{pv}\), \(I_{0}\), \(R_{s}\) and \(R_{sh}\) in Equation (3). 2. Five boundary conditions procedure (indicated as 1D/2R-2 in Figures 2 and 3, and Tables 2 and 3): the three characteristic points, the slope of the \(I\)-\(V\) curve at maximum power point, and the inverse of the slope of the \(I\)-\(V\) curve at the short-circuit point, \(R_{sh0}\), are used as the five conditions needed to extract the values of parameters \(I_{pv}\), \(I_{0}\), \(a\), \(R_{s}\) and \(R_{sh}\) in Equation (3). 4. 2-diode/2-resistor model (indicated as 2D/2R in Figures 2 and 3, and Tables 2 and 3): the three characteristic points, the slope of the \(I\)-\(V\) curve at maximum power point, and the inverse of the slope of the \(I\)-\(V\) curve at the short-circuit and open-circuit points, \(R_{sh0}\) and \(R_{s0}\), together with the pre-established value of the ideality factor corresponding to the second diode (\(a_{2}\) = 2.0), are used as the four conditions needed to extract the values of parameters \(I_{pv}\), \(I_{01}\), \(I_{02}\), \(a_{1}\), \(R_{s}\) and \(R_{sh}\) in Equation (4). As mentioned, the parameters extracted are included in Tables 2 and 3. They can be compared with the ones from other authors that used [PERSON] et al. experimental data [4] to describe their solar cell/panel equivalent circuit parameter extraction procedures. The accuracy of each curve, defined by the comparison with the testing result, \(\Delta I=I_{exp}-I\), is shown in the bottom graph of Figures 2 and 3. Besides, in order to compare the five equivalent circuits, a normalized root mean square error (RMSE) has been also included in Tables 2 and 3:  
\[\xi=\frac{\text{RMSE}}{I_{sc}}=\frac{1}{I_{sc}}\sqrt{\frac{1}{m}\sum_{j=1}^{m }\Bigl{(}I_{cal,j}-I_{j}\Bigr{)}^{2}}. \tag{5}\]  
This comparison parameter is based on the RMSE proposed by [PERSON] and [PERSON] [9; 10]. The use of the normalized root mean square error allows the comparison between results from different photovoltaic technologies and configurations. From the figures and the tables, it can be observed that the more complicated the model is, the best results are obtained in terms of accuracy. However, it should be pointed out that the 2-diode/2-resistor model fitted to the Photowatt PWP201 solar panel shows a negative value of one of the diode reverse saturation currents. This result indicates that the model does not reflect the physical properties of the solar panel, although mathematically it fits the testing results very well. Figure 3: Photowatt PWP201 solar panel. **(top)**: _I-V_ curves (testing data and equivalent circuit models). **(bottom)**: Accuracy of the equivalent circuit models. Figure 2: R.T.C. France silicon cell. **(top)**: _I-V_ curves (testing data and equivalent circuit models). **(bottom)**: Accuracy of the equivalent circuit models.