## 3 Results
### Case Study
#### 3.1.5 Results of Proposed Day-Ahead Load Forecasting Methodology with Real Data  
The LSTM neural network was implemented in Python 3.13.0a3 using the open-source library TensorFlow, specifically Keras [50]. The architecture of the LSTM neural network utilized for day-ahead regional load forecasting features two hidden layers: the first consists of 64 neurons with a hyperbolic tangent activation function, while the second comprises 32 neurons with a linear activation function, as indicated in Table 4. The inputs to the LSTM neural network represent the load demand data, and in this analysis, we consider key \begin{table}
\begin{tabular}{c c} \hline \hline
**Season** & **Mean Temperature (\({}^{\circ}\)C)** \\ \hline Winter & 20 \\ Spring & 26 \\ Summer & 24 \\ Autumn & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean temperature per season in the eastern region of Mexico from 2016 to 2022.  
factors such as temperature, relative humidity, global horizontal irradiance (GHI), pressure, wind speed, and precipitable water for the region, as depicted in Figure 3.  
The training was conducted for 10, 30, 50, 80, and 100 epochs. The best performance was achieved with 100 epochs, taking approximately 25 min, which improved the training MAPE values by up to 4%. Our previous study observed that the proposed LSTM neural network exhibited reduced predictive accuracy during moderate or low energy consumption periods [51]. In the following, the day-ahead load forecasting values are computed for a weekday, Thursday, and a weekend, Sunday, for each season in 2022. Figure 11a illustrates the energy consumption and forecasted values for the winter season. 13 January 2022 falls on a Thursday. As observed, the energy consumption in the region dips to nearly 4800 MWh/h around 5 AM. It then gradually increases until it reaches an almost stable value of 5800 MWh/h around 3 PM. Following that, a more pronounced rise occurs until it hits the maximum demand of nearly 6400 MWh/h before 9 PM. In contrast, Figure 11b illustrates a different pattern for the weekend day of 16 January 2022, which is a Sunday. Early in the day, demand increases sharply, peaking at nearly 5200 MWh/h around 1 AM. It then declines, reaching the lowest demand at 6 AM, and remains relatively stable with minimal growth until 6 PM. Afterward, there is a rapid increase, reaching the maximum demand of 5800 MWh/h at 9 PM before dropping sharply. The winter season brings milder climate conditions to the region; there is no extreme cold weather or rain, resulting in lower energy consumption compared to other seasons. As shown in Figure 11a,b, the overall difference between the forecasted values and historical data is minimal. The most significant discrepancies arise during rapid changes in demand behavior. Ultimately, the forecasted curve closely resembles the fluctuations in demand patterns throughout the day. Figure 12a illustrates the load demand and forecasted values for the spring season. 21 April 2022 is a Thursday. As observed, there is a drop in demand to 6250 MWh/h around 5 AM. Subsequently, it gradually increases until the demand exceeds 7000 MWh/h around 4 PM, followed by a drop at 6 PM and a subsequent sharp increase up to 7500 MWh/h by 9 PM. In contrast, Figure 12b illustrates a different pattern for the weekend day of 24 April 2022, which is a Sunday. Early in the day, the demand begins at 6800 MWh/h and decreases to nearly 5500 MWh/h by 7 AM. It then gradually rises to 6200 MWh/h by 6 PM and swiftly increases to 7500 MWh/h by 9 PM before declining again. The spring season is the warmest time of the year in the region, as shown by the highest energy consumption compared to other seasons, illustrated by the previous figures.