# Parameter Estimation of the Bishop Photovoltaic Model Using a Genetic Algorithm
## 4 Results  
### Experimental Stage  
The ERDM-SOLAR 10/12 panel was selected to validate the parameter estimation processes. Table 1 reports the most important data sheet parameters. Additionally, to analyze the variation of the parameters of each panel technology, two panels of the same reference (one mc-SI and one pc-SI) were used. In each case, a cell with 50% shaded area was selected to experimentally obtain its I-V curve in both the first and second quadrants. The procedure to obtain the curve at cell level is described as follows:  
* The bypass diode included in the junction box of the PV panel was removed. * Two I-V curves had to be obtained from the PV panel terminals; both were named with the corresponding location of the cell in the PV panel (see Figure 6a). The first one, \(NS_{BS}\) curve, was taken without shading. The second curve was obtained by covering a percentage of the cell area, in this case corresponding to 50% (\(S_{BS}\)); Figure 6b shows those curves. Both curves should be taken under similar irradiation and temperature conditions. * Figure 7a presents a 36-cell serial array, where a single cell is shaded. The behavior corresponding to the shaded cell is the blue curve, while the red curve represents the I-V curve of the remaining 35 cells. Given its series connection, the output current was the same through all cells, but the output voltage was the sum of the voltages of the 35 cells without shading and the voltage of the shaded cell for the other curve. In this way, the I-V curve of the shaded cell was reconstructed through the difference between the two I-V curves obtained, i.e., with and without shading. Later, it was necessary to scale the voltage of the curve without shading \(V_{BS}\) to match the 35 cells without shading of the other curve (the one with a single shaded cell), as follows: \(V_{BS}^{35}=V_{BS}\cdot\frac{(35)}{36}\). * It was necessary to create a current vector with the highest value between the minimum currents of both curves as a minimum limit. The lowest value was chosen among the maximum currents of both curves as the upper limit. The current vector interpolated both curves (shaded I-V curve and unshaded scaled) to allow their subtraction to be performed, thus obtaining the current for the shaded cell. An example of this procedure is shown in Figure 7b, where the result of the experimental I-V curve of the shaded B5 cell is shown. The experimental I-V data required in this process were obtained performing a programmed voltage sweep on an electronic load using the experimental setup shown in Figure 8, where an oscilloscope (right photo) recorded the current and voltage of the cell (left photo) and small PV modules were short-circuited (center photo) to estimate the irradiance value. Thus, the experimental I-V curves of both mc-SI and pc-SI cells were generated under real operating conditions, with an irradiance of 1008 W/m\({}^{2}\) and a temperature of 320.65 K; Figure 9 shows the experimental I-V curves. The R&S RTE1204 oscilloscope used in the experiments had an accuracy for DC measurements of \(\pm 1.5\%\)[40]; hence, this precision must be propagated to the estimated values. Moreover, the short-circuit current was measured in another panel with the same characteristics to guarantee that the curves were obtained for similar irradiation. In this way, if the current did not change considerably, \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline \(V_{mp}\) & 0.48 V \\ \(I_{mp}\) & 0.55 \\ \(V_{oc}\) & 0.59 V \\ \(I_{sc}\) & 0.58 A \\ \(P_{max}\) & 0.26 W \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Datasheet parameters for ERDM-SOLAR 10/12 panel. it can be assumed that the irradiation did not change either. This was also ensured by taking at least three curves for each experiment and, if there were differences among the three curves, the data were discarded and the experiment was performed again.