## 2 Materials and Methods
### Typical Load Curves of the Greek System, Seasonal Effects  
To understand the behavior of the 24 h total electric load curve, its evolution during a Friday of January is shown in Figure 2. The total system's load drops during the night, stabilizing at about 3.9 GW. The minimum values are before dawn, from 3:00 to 5:00 in the morning. This base load level makes up for the night consumption, which covers the following main activity:  
* Urban, road, and highway lighting;
* Industrial production continuing to the night shift;
* Base load of the residential sector. * Refrigeration loads for the industrial, commercial, and residential sectors. In the period 05:00-09:00, we observe the morning ramp. During the noon hours, the demand drops below 5.4 GW. From 16:00 to 18:00, the afternoon ramp leads to a demand plateau close to 6.3 GW between 18:00 and 20:00. Next, it is useful to study the patterns of another day, which is a Monday in November (Figure 3). Figure 2: Initial day-ahead prediction, modified noon prediction, and actual load curve on a weekday in January 2023 [34]. The modified noon prediction reduces 24 h MAE from 177 to 131 MW, MAPE from 3.35% to 2.47%, and RMSE from 0.041 to 0.035. The behavior of the demand curve during the night is about the same. However, the base load during the night drops below 3.5 GW. The morning ramp during this weekday is characteristic, with a total demand increase of 1.25 GW between 05:00 and 08:00. The morning ramp continues more gradually to the first load peak of the day (about 10:00 AM). This corresponds to the following activity:  
* Industrial activity starts for the morning shift. * Commercial and services activity starts. * People prepare and go to work. * Students prepare and go to school. * Space heating starts after the night shut down. After 9:00 AM, we observe an approximate consumption plateau, which results in a daily minimum at about 3:00 PM. Following the noon hours, we observe a gradual increase in consumption, which leads to the second ramp of the day and leads to the second consumption peak at 18:00-19:00 (because of the winter time and the early advent of evening, while this peak goes up to 21:00-22:00 during summer time). This second peak reaches 5.5 GW during this mild late autumn day but may reach 8.5 GW or more during winter (Figure 1) due to the part of space heating supplied by electricity. After 8 PM, we observe a gradual reduction in the electric load, which takes its night levels after 02:00. The system's load levels may drop significantly lower during the neutral months of April-May and October, respectively, which do not require electricity consumption for space heating in the residential and part of the commercial sector. An example of this performance is presented in Figure 4 for the month of April, 2022, where the minimum demand during the night drops close to 3 GW and the evening peak drops to less than 6 GW during late April, where ambient temperatures are of the order of 20-24 \({}^{\circ}\)C during the day. Figure 3: Evolution of the Greek system load on a typical Monday of November, 2022. Predicted versus actual hourly load values [35]. Further, it is interesting to observe in Figure 5 a pronounced load prediction failure of the Greek system's operator for the period 20-22 April (Wednesday to Friday, hours 2640-2712). An observation of the weather data for typical places in central Greece shows a sudden weather improvement after a rainy and cold weekend. A closer observation of this period in Figure 5 indicates that the day-ahead prediction routinely over-predicts the demand for the 20 th, 21 st, and half of the 22 nd of April. Figure 4: Greek system load during April 2022, day-ahead predicted versus actual values (MW) [35]. Figure 5: Load prediction failure during the period Wednesday 20 to Friday 22 April, 2022 (sudden weather improvement) [35]. Maximum relative error is 11.9%. Only after the noon correction in the prediction of the afternoon system's demand the error vanishes, and the prediction accuracy returns to high levels.