## 4 Results and Discussion
### Deep FF BPNN
In order to better understand the situation and investigate possible ways to improve forecasting accuracy, it is useful to plot, in the same figure, the respective fluctuation of ambient temperatures as recorded by the Psychico weather station during this period. The temperature during the night before the 16 th was seen to stay at about 23-26 \({}^{\circ}\)C. Beginning at 06:00 and during the morning hours, we observed a significant increase in ambient temperature, which continued to a maximum of 35 \({}^{\circ}\)C between 14:00 and 15:00. Then, a gradual drop in ambient temperature was observed after late afternoon. However, the temperature did not drop to its normal nocturnal levels during the second day and started to ascend earlier Sunday morning. This should place an unexpected burden on  
Figure 18: Prediction and validation of system’s demand for July 2022, FF-ANN after 81 epochs vs. Deep NN after 1000 epochs. the air-conditioning systems and produce a very pronounced morning peak for Saturday and Sunday. The high electricity consumption levels could be attributed to the very high increase of tourists in Greece during this period, which unexpectedly increased the filling rate of hotels and other tourist residences. A closer look at the comparison curves of Figure 19 reveals further instances of prediction failure. One of these events is 8 July, when a significant over-prediction of load occurred for both models (Figure 20). This should be correlated with the sudden drop in ambient temperatures, shown in the same figure in the example of the Psychico weather station, and a drop in humidity by shifting to NE winds, which suddenly reduced the need for air-conditioning. Both neural networks over-corrected their prediction for the next day, Friday 9 July, which obviously led to an over-prediction failure this time. Another important failure was observed on Wednesday, 20 July, when a sudden increase in ambient temperatures could not be addressed with the required fast response by both neural network models. A real-world application of the two FF ANN methods described was carried out according to the following procedure. The computer code was run at midnight of each day to predict the 24 h values of load for the next day. The input data for the FF ANN comprise the following variables and sets: (i) Heating degree days (one value predicted daily by the meteorological service for the Psychico meteorological station). (ii) Cooling degree days (one value daily for the Psychico meteorological station). (iii) Time series of the recorded hourly Greek system load values up to midnight. Data uncertainty exists only for the prediction of heating and cooling degree days for the next day, which is equivalent to the day-ahead prediction of the mean daily temperature. Improvements in the specific aspects of model performance would require a further increase in synergy between the machine learning models and empirical models, incorporating a faster response of the system's demand to weather conditions by means of an improved transfer function with responses on the order of one hour. To this end, it would be helpful to record the system's demand at an increased frequency (once every 15 min), following the example of other European countries [33]. Figure 19: Incident of Saturday 16–Monday 18 July: load prediction failure of both models during a weekend with high temperatures. Maximum relative error is \(-16.4\%\) for the FF ANN and \(-19.9\%\) for the deep NN.