## 4 Results and Discussion
### Deep FF BPNN  
The training progress of the two-hidden layers' FF-BPNN was tested by setting a different number of maximum epochs in the range 20-2000. The computation time was about an order of magnitude higher than the simple FF ANN; that is, it takes about 2 min to run 1000 epochs on a standard laptop PC. The results are presented in Figure 16 in terms of the attained RMSE of the normalized predicted values of load demand, which is seen to stabilize at a little higher than 0.025 for 2022 predictions. The normal evolution of convergence can be observed in this Figure without any signs of over-fitting. The model is seen to gradually assimilate the useful information contained in the training data. A high rate of drop in RMSE was observed for the first 400 epochs, which was set as the duration of the learning drop period (Table 2). The respective results of  
Figure 14: FF-ANN forecasting: Box-plot of the error distribution of forecasted load as function of the hour of day for 2022. Figure 15: FF-ANN forecasting: Box-plot of the error distribution of forecasted load as function of the day of week for the year 2022.  
the predicted versus actual demand are presented in Figure 17 for the example of January 2022. The values of the selected performance metrics for 2022 are shown in the same Figure: MAPE, \(\mu\) = 3.56% with \(\sigma\) = 0.42%; nRMSE, \(\mu\) = 0.049 with \(\sigma\) = 0.006. Compared with the shallow FF ANN model presented in Figures 12 and 13, the mean value of MAPE was a little lower, however, it was higher than the official predictions. However, the standard deviation of MAPE was observably higher than the respective values for both the FF ANN and the official predictions. This may be due to a somewhat higher tendency of the deep networks for data over-fitting, which is not a problem here anyway, as explained above. Figure 16: Training progress of deep feed-forward neural network after 20-2000 epochs, as seen by the prediction RMSE for 2022. Figure 17: Prediction and validation of system’s demand for January 2022, FF-ANN after 81 epochs versus deep NN after 1000 epochs. Modeling error metrics are shown for deep FNN predictions for the whole year 2022. These values were only a little better than those obtained with the simple FF ANN model, as shown in Figure 12. That is, the additional complexity and CPU time required to run the deep FNN model (a few minutes run on a laptop compared to less than a minute for the FF ANN) did not seem to reward. For comparison, the respective predicted values with the simple FF ANN are drawn in the same diagram. It seems that both types of models incorporated, to a high degree, the information contained in the training dataset. This observation is further supported by the fact that the error metrics of both models are directly comparable to those of the Greek system's operator's forecasting (Figure 1). Moreover, an optical comparison of the two figures points to the similar forecasting behavior of all three models. Similar instances of prediction failures with various types of ANN have been frequently reported by other researchers in different countries [19]. Thus, the cause of specific, short periods of prediction failure should be attributed to the lack of some additional types of training input. In order to further research this issue, we start with a comparison of the two alternative models' performance against the actual demand for July 2022 (Figure 18). As already reported in Section 2, July and August are more demanding in terms of forecasting, because of the high fluctuations in electricity demand for air conditioning. On the other hand, the models are proven effective in predicting the system's peak demand exceeding 9 GW during 25-28 July. However, both models fail to predict the high levels of demand for the weekend 16-17 July, as shown in detail in Figure 19. The maximum relative error in prediction stays at the same high levels with the official prediction (see Figure 7).