## 3 Results
### Case Study  
This study focuses on the region of the Gerencia de Control Regional Oriental (GCRORI), one of CENACE's eight regions. It includes the states of Chiapas, Tabasco, Vera'caruz, Oaxaca, Puebla, Tlaxcala, Guerrero, and Morelos, covering a total area of 370,000 km\({}^{2}\), as illustrated in the green region of Figure 4.  
In this study, hourly energy demand and meteorological factors from 2016 to 2022 were utilized, including temperature, relative humidity, global horizontal irradiance (GHI), pressure, wind speed, and precipitable water. The inclusion of these meteorological factors is crucial for improving the accuracy of energy demand forecasting, as weather conditions directly impact electricity consumption patterns. The main features of GCRORI are as follows:  
* Extension of 370,000 km\({}^{2}\). * 12 million users. * Annual energy consumption of approximately 55,000 GWh. * Daily peak load consistently falls between 20:00 and 22:00 h.
* The annual peak load occurs during spring or summer in the same period. * Both coastlines--the Gulf of Mexico and the Pacific Ocean--experience tropical storms and hurricanes annually. In GCRORI, the meteorological variables and load demand are highly correlated. In this study, both variables are assumed to have a single value for each hour--total load demand (hourly integrated energy)--and a single value for meteorological variables. The load demand \(D\) is determined through an energy balance, calculated by summing the total energy \(E\ g_{i}\) generated by all generation units in GCRORI (\(g_{1},g_{2},\ldots,g_{n}\)), followed by adding or subtracting the energy associated with power flow in tie lines \(E\ tl_{i}\) with neighboring areas (\(tl_{1},\ tl_{2},\ \ldots,tl_{m}\)), which correspond to the gray areas surrounding the green one, and finally, subtracting network losses (\(Nl\)) as given by  
\[D=\sum_{i=1}^{n}E\ g_{i}+\sum_{i=1}^{m}E\ tl_{i}-Nl\ \, \tag{8}\]  
which is described in Figure 5.  
Figure 4: Map of the SEN. The highlighted area represents the region of study [44; 45]. As mentioned previously, the hourly representative single-value meteorological variables are derived by considering the most significant load zones based on their load magnitude and geographical location, which include Villahhermosa, Veracruz, Poza Rica, Puebla, and Cuernavaca, as illustrated in Figure 6. The meteorological variables of each city are weighted using Equation (5) to obtain the representative single-value meteorological variables for the entire region encompassing the GCRORI. Temperature plays a significant role; extreme heat or cold can greatly increase the usage of heating, ventilation, and air conditioning (HVAC) systems, leading to spikes in energy demand. By incorporating temperature data, the model can better capture these fluctuations, resulting in more precise forecasts during seasonal or daily temperature changes. Similarly, relative humidity affects human comfort and the efficiency of HVAC systems. High humidity, for instance, raises perceived heat and increases cooling requirements. By considering humidity, the model can more accurately adjust its predictions for energy use in warmer and/or more humid conditions. GHI, which measures solar energy reaching the earth's surface, is another critical factor. In areas where solar energy contributes to the  
Figure 5: Representation of energy balance to determine the single-value hourly load demand for the entire region of the GCRORI. Figure 6: Main load zones for calculating the representative single-value meteorological variables for the entire GCRORI region. electricity grid, high GHI values decrease reliance on conventional energy sources, while low GHI values increase that dependence. Including GHI enables the model to adjust predictions based on solar power availability, which directly impacts overall energy demand. Changes in atmospheric pressure are often linked to weather patterns that affect energy consumption.