## 4 Results and Discussion
### Ff Ann  
As an example, the actual demand values, on an hourly basis, are compared with the day-ahead predictions with the FF ANN for January 2022 in Figure 12. The computation time was less than 30 s and the code converged after less than 100 epochs. The values of the respective statistical metrics for 2022 are shown in the same Figure to quantify the prediction accuracy. The RMSE was 3.08 MW, MAPE was 3.66%, nRMSE was 0.049, and MAE was 204 MW. Finally, MBE was 29 MW, which indicates a small over-prediction. On a qualitative basis, it is interesting to see that the quality of prediction for January 2022 was comparable to the prediction of the Greek system's operator, presented in Figure 1. Again, the most pronounced prediction failures are observed with regard to the morning peaks. It should be mentioned here that the specific, comparable levels of prediction accuracy were attained by a true day-ahead computation. That is, all 24 h of the next day were predicted. No correction at noon was applied in this case.  
Figure 12: Prediction with the FF ANN and validation of the Greek system’s demand for January 2022. MAPE and nRMSE means and standard deviations refer to the full year 2022.  
Further, it is interesting to look at the variance of the most important error metrics in these predictions. To this end, Figure 13 presents the variation of the monthly MAPE and nRMSE values for the official forecasts in comparison with the respective figures for the FF ANN predictions. Although the mean values of MAPE and nRMSE were lower for the official predictions, the standard deviations were observably higher than the respective error figures of the FF ANN predictions. The reduced standard deviations in the FF ANN prediction error metrics are a good indication for the lack of data overfitting problems.  
Apart from the visual, qualitative inspection of prediction quality, it is interesting to statistically assess the effects of the hour of the day and the day of the week in the FF ANN prediction errors. In this context, Figure 13 presents a box plot of the error distribution of forecasted load as a function of the hour of the day for 2022. A closer look at the box plots of this figure confirms the intuitive observation that the prediction of the nighttime base load is most confident. The other important finding is that the maximum prediction error, reaching values of the order of 15%, was observed for the hours 16:00-18:00, which correspond to the interval of returning from work. Again, this is expected by visual observation and affects the prediction accuracy of the late afternoon peak of the Greek system, which is the most difficult to address. This suggests that a significant part of the research effort should be directed to the improved prediction of the peak load for the daily load curve.  
As a second step in this direction, Figure 14 presents a box plot of the error distribution of forecasted load as a function of the day of the week for 2022.  
A comparison of the respective error box-plots in Figure 15 reveals that the weekdays where the maximum prediction error is observed are Saturday (#7) and Monday (#2). The reduced accuracy in the prediction of Saturday may be attributed to the fact that Saturday and Sunday are both categorized as weekend days. However, although the behavior of the system's load on Sundays is very particular, lying in between the behavior of weekdays and Sundays. Thus, it would be helpful to find a way to inform the artificial neural network during the training about these differences. Simply allocating a third category for Saturday was tested but did not improve the model's prediction capabilities.  
Figure 13: Comparison of the variation of monthly MAPE and nRMSE for the official forecasts and the FF ANN forecast during 2022.