## 3 Results
### Normal Operation  
First, the performance data of the PVS1 system are applied to the ANN n1. The network n1 is trained by data of inverter 4 of PVS1. Simulated values are compared with measured values from inverter 4 and the results are presented in Figure 1. The PBIAS fluctuated between \(-3.7\) to 1.2 and nRMSE between 2.23 to 5.05 according to Table 3. The size of the samples involved in the daily calculations varied from 47 to 53. Figure 2 shows the fitting quality of the simulated and actual values in normal operation. The daily mean absolute error varies in the range from 103.63 to 213.82 W. The peak DC power in each inverter is 12,480 W and the maximum AC values for the respective period presented in Figure 1 did not exceed 11,000 W. The values of the statistical metrics \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Date** & **N** & **RMSE** & **MBE** & **MAPE** & **MAE** & **nRMSE** \\ \hline
2014-06-04 & 47 & 22.69 & 103.74 & 3.07 & 109.36 & 3.91 \\
2014-06-05 & 51 & 23.49 & 102.59 & 1.65 & 118.47 & 2.33 \\
2014-06-06 & 50 & 40.39 & 190.42 & 3.30 & 213.82 & 4.36 \\
2014-06-07 & 51 & 26.35 & 130.98 & 2.20 & 154.16 & 2.81 \\
2014-06-08 & 49 & 33.76 & 171.73 & 3.70 & 172.06 & 4.16 \\
2014-06-09 & 49 & 21.63 & 106.82 & 2.68 & 119.55 & 3.25 \\
2014-06-10 & 49 & 24.15 & 117.27 & 1.84 & 143.88 & 2.36 \\
2014-06-11 & 50 & 36.67 & 74.18 & 1.20 & 129.42 & 3.74 \\
2014-06-12 & 48 & 47.54 & 150.79 & 2.61 & 194.21 & 5.05 \\
2014-06-13 & 49 & 22.07 & 88.65 & 1.55 & 103.63 & 2.40 \\
2014-06-14 & 49 & 27.99 & 152.86 & 3.34 & 152.86 & 3.58 \\
2014-06-15 & 48 & 26.05 & 149.96 & 3.60 & 150.29 & 3.39 \\
2014-06-16 & 50 & 21.29 & 74.08 & 1.22 & 119.36 & 2.23 \\
2014-06-17 & 53 & 17.85 & 115.58 & 3.65 & 115.58 & 3.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical metrics of the inverter 4 of PVS1 for the period 5 June 2014 to 17 June 2014 (normal operation). that express the fitting accuracy are detailed in Table 3. The reported values of nRMSE, MAPE and the number of samples define a threshold for normal operation. Deviation from these values may indicate a possible fault. Especially, the values of MBE are positive, indicating a systematic over-prediction of output. These facts operate as indicators for faults either in PV system or in measurement equipment. According to the obtained statistical metrics of Table 3, the FF ANN fits the data with acceptable accuracy, since both MAPE and nRMSE are well below 5%. Adopting deep neural networks as CNN could further improve accuracy. However, what is important here is to set the basis for a fault detection methodology, where the obtained accuracy suffices and the fast convergence with low computational expenditure is very desirable. It is important to investigate the behavior of the other inverters of the same system when compared to simulated values for n1 network, which is trained from inverter 4. In Figure 3, a comparison in power output of eight inverters is compared to the respective simulated values. A comparison of the simulated values (Pf) with those measured at all inverters of PVS1 (Figure 3) indicates a very good agreement. The MAPE of the other inverters fluctuated between 0.06-3.56, while nRMSE 1.57 to 3.29%. The precise values of the statistical deviations shown in Table 4 indicate that MAPE and nRMSE of inverter 4 are at the same levels. This fact proves that an ANN simulation trained for one inverter of the n1 network in normal operation matches with high accuracy the behavior of all inverters. As shown in the technical data of the Appendix A, each inverter has the same number of strings, same number of panels and same type of PV panels.