# Early Detection of Photovoltaic Panel Degradation through Artificial Neural Network
## 7 ANN Results with Simulated Degradation on _I-V_ Curves  
The capability of ANN to detect the degraded SDM parameters is tested in this section by still using emulated degraded curves. Even if this is a limitation with respect to  
Figure 11: Comparison of experimental data and reconstructed single-diode _I-V_ curve with estimated ANN parameters in healthy condition. In this case, the error area is 5%. Figure 12: Comparison of experimental data and reconstructed single-diode _I-V_ curve with estimated ANN parameters in healthy condition. In this case, the error area is 0.5%. using real degraded curves, it allows to corroborate the methods with a well-controlled degradation effect introduced artificially. For each k parameter (\(k\in[1,..,5]\)), the analysis is carried out by using the following procedure:  
* Select randomly \(N_{\text{{test}}}\) experimental healthy \(I\)-\(V\) curves from the NREL database (not used during the ANN training phases) and save the related SDM parameters as the vector \(\mathbf{p}\) and environmental conditions \((G,T)\). * For each selected case, do the following: 1. Apply a fixed degradation factor \(\alpha_{k}\) to the k-th parameter of \(\mathbf{p}\). 2. Generate the degraded \(I\)-\(V\) curve by using Equation (1). 3. From the degraded \(I\)-\(V\) curve, select the voltage and current of 3 points equally spaced around MPP and ordered in the vector \([V_{1},V_{2},V_{3},I_{1},I_{2},I_{3}]\). 4. ANN(level #1) estimates the healthy SDM parameters \(\mathbf{p_{H}}\) with \([G,T]\) as input vector. 5. ANN(level #2) estimates the degraded SDM parameters \(\mathbf{p_{deg}}\) with \([G,T,V_{1},V_{2},V_{3},I_{1},I_{2},I_{3}]\) as input vector. 6. Calculate the percentage of parameters variation as follows: \[\Delta\mathbf{p_{\%}}=\frac{\mathbf{p_{deg}}-\mathbf{p_{H}}}{\mathbf{p_{H}}} \cdot 100\] (12)  
Figures 13-16 show some comparison between the degraded \(I\)-\(V\) curves (blue lines) and the reconstructed \(I\)-\(V\) curves (light blue lines) obtained by using the \(\mathbf{p_{deg}}\) parameters estimated by means of ANN. In each figure, the healthy \(I\)-\(V\) curves (red lines) used to generate the degraded curves and the 3 points passed to the ANN for estimating the SDM degraded parameters are also reported. Of course, in an on-board operation, only steps **3-6** of the previous procedure are necessary since all ANN input are provided by the real-time measurements. As mentioned in Section 2.1, the sensitivity of the \(I\)-\(V\) curve with respect to each SDM parameter, especially close to the maximum power point, is strongly different. In particular, a variation of a few percentage points on \(I_{ph}\) and \(\eta\) produces a significant modification of the \(I\)-\(V\) curves, while the effect of \(I_{sat}\), \(R_{s}\) and \(R_{sh}\) is visible on the \(I\)-\(V\) curve only for larger percentage variations. For this reason, different percentages of degradation are considered in the examples shown in Figures 13-16. In Tables 5-9, the corresponding ANN identification results are reported. The vector (\(\mathbf{p_{deg}}\)) of degraded SDM parameters estimation is compared with the healthy SDM parameters estimation vector (\(\mathbf{p_{H}}\)) to calculate (\(\Delta\mathbf{p_{\%}}\)) and find out which parameter has the most significant percentage variation. It is worth noting that, in order to establish which kind of degradation is most relevant, the vector of maximum power variations \(\Delta\mathbf{P_{mpp,\%}}\), due to each parameter variation, is also shown in the tables. It is estimated numerically as follows:  
* Calculate the maximum power in healthy condition \(P_{mpp}^{H}\) by using the single diode model and healthy parameters (\(\mathbf{p_{H}}\)). * For \(k\in[1,5]\), do the following:
* Replace the parameter \(\mathbf{p_{H}}(k)\) with the corresponding degraded values \(\mathbf{p_{deg}}(k)\)
* Estimate the maximum power \(P_{mpp}^{k}\) by still using the SDM.