# Online Identification of Photovoltaic Source Parameters by Using a Genetic Algorithm
## Validation of the GA-Based SDM Parameter Identification Method  
This section presents the results obtained by compiling and running on a desktop PC (Intel i5-3470 quad-core processor, running at 3.2 GHz) the code written in C language to implement the GA andto calculate the guess solution. The aim is to test the code, to tune the genetic algorithm parameters and to validate the approach. A further section is dedicated to the details about the embedded system implementation. The procedure has been applied to the experimental data of a Sunowe Solar SF125x125-72-m(I) PV panel. The related datasheet parameters are given in Table 3.  
Figure 4 shows the experimental data used to test the proposed SDM parameter identification procedure. The white curves are the measured I-V curves, acquired in different irradiance and temperature conditions. The black points are the test points selected to be used by the proposed SDM parameter identification procedure. Specifically, the case related to Test #1 is discussed hereinafter, whereas the cases related to Tests #2 and #3 will be explained in Section 4. The module temperature (\(T\)) is measured by a sensor placed at the backside of the PV panel. This quantity is used in the identification procedure for calculating the guess solution. In the absence of such a sensor, \(T\) can be estimated by using the ambient temperature, as described in [25]. The guess solution for the first experimental case has been calculated by using Equations (7)-(11) with \(\beta_{I}=1.2\) and \(\beta_{V}=1.35\). The corresponding parameters are reported in Table 4.  
It is worth noting that different guess solutions can be calculated by changing the values of \(\beta_{I}\) and \(\beta_{V}\) within their respective ranges. The choice of the best guess solution can be made by evaluating the corresponding fitness with (6). For the case of Table 4, the fitness value is reported in the last column. In order to appreciate the benefit of using a restricted research space for the SDM parameter identification, the genetic algorithm has been launched twice: using the physical bounds of Table 1 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & \(I_{ph}\) **(A)** & \(I_{s}\) **(A)** & \(\eta\) & \(R_{s}\) **(\(\Omega\))** & \(R_{h}\) **(\(\Omega\))** & **Fitness** \\ \hline Test \#1 & 5.61 & \(5.58\times 10^{-8}\) & 1.05 & 0.833 & 51.5 & 1.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Guess solutions for the SDM parameters in Test #1. Figure 4: Experimental I-V curves of the Sunowe Solar SF125x125-72-m(I) PV panel, in different environmental conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(I_{sc}\) & 5.32 A & \(V_{cc}\) & 44.8 V \\ \(I_{MPP}\) & 5.03 A & \(V_{MPP}\) & 35.8 V \\ \(\alpha_{I}\) & 0.04 \%/\({}^{\circ}\)C & \(\alpha_{V}\) & \(-0.35\) \%/\({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sunowe Solar SF125x125-72-m(I) 180-W PV panel. and using the real boundary conditions of Table 2, calculated on the basis of the guess solution reported in Table 4. When the real boundary conditions are used, the guess solution is also included as an individual of the initial population; thus, a further improvement is obtained in the GA convergence. The parameters of the GA have been set as reported in Table 5; they have been selected on the basis of the fitness function behavior. In order to show the different behavior, Figure 5 shows the trend of the best individual's fitness with respect to the number of generations for the two above-mentioned scenarios: using only the physical bounds (Figure 5a) and using the real boundary constraints and the corresponding guess solution (Figure 5b). The figure is related to the case Test #1, but it is also representative of the other two cases. The improvement is evident in terms of the higher fitness value and faster convergence. Once the GA has returned the best solution, the latter has been used to reconstruct the I-V and P-V curves of the PV panel.