## 3 Results
### Case Study
#### 3.1.6 Forecasting Errors  
Table 5 presents the regional load demand, \(LD\), and its respective forecasted values resulting from the proposed methodology, \(FLD\), along with the forecasted values obtained from CENACE, \(FLD\_C\), for the sample weekdays illustrated in Figures 9, 10, 11 and 12a. The last row shows the resulting MAPE values for each case. Similarly, Table 6 displays the same values for the sample weekend days presented in Figures 9, 10, 11 and 12b. As indicated, the difference between the forecasted values and historical data is minimal overall. In nearly all instances, the MAPE values obtained from the forecasted values using the proposed methodology are superior to those from CENACE. Figure 19: Historical and forecasted load demand data for the minimum load demand week corresponding to 25 December 2022. Figure 18: Historical and forecasted load demand data for the peak load demand week from 16 May 2022 to 22 May 2022. Thus, the proposed methodology for load demand forecasting enhances accuracy through the selected LSTM neural network training, which focuses on distinguishing the information used in similar-day methods while differentiating between weekdays and weekends. Moreover, the training data selection is more refined by grouping load demand patterns throughout the year obtained through K-means clustering applied to the load demand data. Finally, Table 7 shows the MAPE values derived from the forecasted values using the proposed methodology alongside the CENACE results for a holiday on 25 December 2022. The results indicate that the proposed methodology is quite promising, even during holidays. The days in each season were considered to provide a wide temporal range for evaluating the model's adaptability to seasonal effects. The results indicated the following:  
* Spring and autumn: These transitional seasons typically exhibit moderate demand, characterized by significant variability due to erratic weather changes. The model excelled during these times, accurately reflecting demand shifts related to both industrial activity and temperature-driven residential consumption. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Hour**}} & \multicolumn{4}{c}{**13 January 2022**} & \multicolumn{4}{c}{**21 April 2022**} & \multicolumn{4}{c}{**14 July 2022**} & \multicolumn{4}{c}{**6 October 2022**} \\ \hline \multirow{2}{*}{**Hour**} & **LD** & **FLD** & **FLD** & **LC** & **LD** & **FLD** & **FLD** & **FLD** & **FLD** & **FLD** & **FLD** \\  & \(\left  
* Summer: The model successfully captured the high demand for cooling devices and extended daylight hours. It accurately predicted peak loads during weekdays while slightly underestimating the weekend peaks driven by residential usage. * Winter: The average temperature in winter in eastern Mexico is relatively mild, around 20.6 \({}^{\circ}\)C. Due to these moderate conditions, the demand for heating devices is minimal among the population, unlike in colder regions, where heating significantly drives energy consumption. As a result, energy demand during the winter months remains stable, with little to no dramatic increases stemming from temperature-driven residential heating. This characteristic has significant implications for energy forecasting in the region: seasonal variations in demand are less pronounced during winter, with industrial, commercial, and general residential consumption following typical patterns. Unlike areas where energy demand spikes due to colder temperatures, in eastern Mexico, the primary fluctuations in energy usage during winter are likely associated with other factors, such as holiday periods or changes in daylight hours, rather than the direct impact of climate conditions.