An Intelligent Method for Day-Ahead Regional Load Demand Forecasting via Machine-Learning Analysis of Energy Consumption Patterns Across Daily, Weekly, and Annual Scales

Abstract

Electric power load forecasting is essential for the efficient operation and strategic planning of utilities. Decisions regarding the electric market, power generation, load management, and infrastructure development all rely on accurate load predictions. This work presents a novel methodology for day-ahead load forecasting. The approach employs a long short-term memory neural network (LSTM NN) trained on representative load and meteorological data from the region. Before training, the load dataset is grouped by its statistical seasonality through K-means clustering analysis. Clustering load demand, along with similar-day data management, enables more focused training of the LSTM network on uniform data subsets, enhancing the model’s ability to capture temporal patterns and reducing the complexity associated with high variability in demand data. A case study using hourly load demand time-series data provided by the Centro Nacional de Control de Energía (CENACE) is analyzed, and the mean absolute percentage error (MAPE) is calculated, showing lower MAPE than traditional methods. This hybrid approach demonstrates the potential of integrating clustering techniques with neural networks and representative meteorological data from the region to achieve more reliable and accurate regional day-ahead load forecasting.

1. Introduction

Climate change prompts us to adopt decarbonization measures that include using renewable energy, improving energy efficiency, and optimizing energy use [1,2]. These measures are essential for achieving the climate goals established in the Paris Agreement, specifically, reducing global greenhouse gas (GHG) emissions to limit the increase in global temperature to a maximum of 2 °C [3]. The inclusion of renewable energy sources and effective energy management takes place within energy systems, which generally consist of electrical loads that must be met by electrical generation. These electrical loads can range from just a few watts for an LED spotlight, several kilowatts for a house, tens of megawatts for a small city, a few gigawatts for a metropolis, to hundreds of gigawatts for industrialized countries.

A power system, such as an electrical grid, consists of interconnected electrical components that generate, transmit, distribute, and supply electrical energy. A well-functioning system requires extensive analyses, the most critical being an understanding of the electrical load it must meet through its various generators. Therefore, electrical load forecasting is essential for power systems, influencing everything from design and installation to operation and maintenance [4].

The dynamics of electric load demand are a complex issue influenced by various local factors, including the type of day, weather conditions, and economic, social, and political elements. To model load demand, representative load curves (RLCs) are used to evaluate demand on a daily, weekly, monthly, or annual basis [5,6]. For instance, in daily analysis, load demand fluctuations can be influenced by the type and time of day, temperature, rainfall, levels of industrial and agricultural activities, and social factors such as holidays and festivals.

Accurate energy load forecasting plays a critical role in the efficient operation of electrical grids, influencing decisions related to energy generation, load dispatch, infrastructure development, and maintenance scheduling [7]. For this reason, load forecasting has become a fundamental topic in our lives, and there is significant scientific activity focused on developing more accurate load forecasting methodologies at all time resolutions [8,9].

Load forecasting for utilities across various time horizons helps ensure the safety and stability of the power supply. Accurate load forecasting to maximize electrical power utilization contributes to cost savings and reductions in greenhouse gas emissions, as well as to the finance, infrastructure, operation, and maintenance of the grid. Indeed, a load prediction with a 1% error could result in operating costs amounting to millions of dollars per year [10,11]. The effectiveness of load demand forecasting relies on the forecast horizon, which corresponds to the time scale in the future for which the forecasts are made. The forecast horizons relate to the corresponding duration for which the forecasts are conducted, along with the frequency of data utilized for the forecast.

The forecast horizon is defined as “the length of time into the future for which forecasts are to be prepared”, in alignment with the definition from the statistical office of the European Union [12].

Table 1. Forecast horizons, types of forecasts, and typical applications in electrical power systems.

Forecast Horizon	Type of Forecast	Use of Load Demand Forecast
1 s to several s	Real-time (RT)	Power system dynamic and transient analysis. Real-time monitoring.
Several s to 1 min	Real-time/Very short-term	Real-time scheduling of generation (RT electricity dispatch), load frequency control, resource dispatch, auction-based electricity markets, PV storage control.
1 min to 30 min (1 h)	Very short-term	Deregulated power, energy pricing. Intra-hour forecast: operating regulation reserves, storage system optimization, grid quality and stability. Islanding with high solar penetration.
30 min to 6 h	Short-term	Unit commitment, economic dispatch, electricity market. Intra-day forecast: electricity trading, control of electric loads.
6 h to 24 h (1 day)	Short-term	Power system load scheduling, load balancing, automatic generation control (AGC), reserve planning and control.
1 day to 1 week	Short-term	Day-ahead forecast: Unit commitment and utilities planning, market transactions.
1 week to 1 month	Medium-term	Commitment analysis of the power units, scheduling of power systems maintenance.
1 month to 1 year	Long-term	Scheduling the maintenance of power system elements, electricity pricing. Fuel supply strategies.
1 year to several years	Long-term	Power system planning, expansion and operation management.

summarizes the forecast horizons, types of forecasts, and their typical applications in electric power systems [13,14,15]. Based on the time horizon, forecasts can be categorized into different types—real-time, very short-term, short-term, medium-term, and long-term—though there is no international consensus on this issue. Furthermore, various applications in electric power systems employ different types of load demand forecasts depending on the speed at which their data and information processes vary.

As power systems become more complex and renewable energy sources are integrated, developing robust short-term load forecasting (STLF) models is essential for ensuring grid reliability and stability [16]. In particular, day-ahead load forecasting (DALF) is crucial for power system operations, as it enables grid operators to schedule power generation efficiently, minimizing energy waste, ensuring complete supply coverage, and preventing economic losses at first glance. Furthermore, day-ahead load forecasting significantly aids in the integration of renewable energy by facilitating the management of variable renewable sources and improving demand-side management strategies. Moreover, forecasting electricity demand for the entire following day allows power grid operators to optimize power generation dispatch, manage reserve capacity to accommodate changing demand, and it provides power market traders with the necessary information to make informed decisions about buying and selling electricity in the day-ahead market, based on anticipated consumption over the next 24 h.

1.1. State of the Art of Day-Ahead Load Forecasting

Many studies have been published on short-term and day-ahead load forecasting.

Table 2. Summary of some of the relevant publications highlighting the technology utilized and their major findings.

Reference	Forecast Horizon	Data from	Tools	Features
Pindoriya et al., 2009 [17]	One hour ahead	California electricity market	Multilayer perceptron neural networks	Forecasting values are computed for test weeks in summer and winter, finding absolute percentage errors ranging from 3.29% to 0.01%.
Lahouar et al., 2015 [18]	One day ahead	Tunisian Power Company	Random forest	Information about the country’s weather or market is used according to expert knowledge. The forecasted values are calculated for weekdays and weekends, achieving a MAPE of less than 2.3%.
Konica et al., 2016 [19]	One day ahead	Albania	Fuzzy logic	Load demand is forecasted for various days of test weeks during the seasons.
Muzaffar et al., 2019 [20]	24 h, 7 days, and 30 days	Abu Dhabi	LSTM neural network	Exogenous variables, such as temperature, humidity, and wind speed, are used to train the LSTM NN. MAPE values of 1.522%, 2.16%, 5.97%, and 9.75% are found for forecasting horizons of 24 h, 28 h, 7 days, and 30 days.
Hafeez et al., 2020 [21]	One day ahead	FE, EKPC, and Daytown, USA	Factored conditional restricted Boltzmann machine	A hybrid model based on modified mutual information for extracting data features, a factored conditional restricted Boltzmann machine for load forecasting, and a genetic wind-driven optimization to enhance the performance is presented. MAPE values of less than 1% are obtained for the three grids.
Madhiarasan et al., 2021 [22]	24 h, 6 h, 30 min	Electric Reliability Council of Texas	Multilayer perceptron neural network	Electricity load, along with temperature, humidity, wind speed, solar irradiance, and pressure, is used to train the NN with different hidden layers, achieving excellent results with a mean square error (MSE) in the order of 1 × 10−8.
Vasenin et al., 2021 [23]	One day ahead and intra-day ahead	Several sites	Artificial intelligence, neural networks, fuzzy logic, data mining	This review presents the current day-ahead and intra-day power forecasts in the residential sector, showing that an accuracy of up to 98% can be achieved.
Coria et al., 2022 [24]	One hour ahead	CENACE, Mexico	Random forest	One-hour-ahead load forecasting is conducted for each of the seven regions of the National Interconnected System of Mexico, with MAPE ranging from 10.2% to 0.48%.
Pelekis et al., 2023 [25]	One day ahead	Portugal	Multilayer perceptron, N BEATS, long short-term memory, and convolutional NN	The load forecast values using different technologies yield MAPE values ranging from 2% to 3%. Neural basis expansion analysis (N-BEATS) provides load demand forecasts with a lower MAPE.
Pavlatos et al., 2023 [26]	One day ahead	Greece	Recurrent, LSTM, and GRU neural networks	Short-term forecasts can be successfully made by capturing the underlying patterns, resulting in a root mean square error of 0.033.
Tzortzis et al., 2024 [27]	One day ahead	European countries	Feed-forward neural network and clustering	Load profiles from various countries are clustered into four basic groups based on similarity. Load forecasting results indicate an improvement of up to 0.24% compared to the baseline results.
Nabavi et al., 2024 [28]	Short- to long-term	Iran and Germany	LSTM and discrete wavelet transformation	Ambient temperature, cloud cover, solar radiation, and precipitation, along with electricity load data, are used to train the model. Accurate results are achieved, with MAPE ranging from 0.59% to 4.2% for hour-ahead to year-ahead forecasts for Iran and from 0.29% to 3.02% for Germany.
Laitsos et al., 2024 [29]	One day ahead	Greek islands of Rhodes, Lesvos, and Chios	Multilayer perceptron, convolutional neural network, and ensemble learning model	Load data from the Greek islands of Rhodes and Lesvos are used to train and fine-tune the three sequence-to-sequence deep-learning models to forecast load data for Chios. The results show MAPE values ranging from 5% to 6%.

summarizes several significant publications, highlighting the technologies used and their key findings.

1.2. Proposed Approach Contributions

Traditional energy demand forecasting methods often rely on time-series models or regression-based techniques, but they have limited capacity to capture non-linear patterns and dependencies [30]. In recent years, machine-learning approaches, particularly artificial neural networks (ANNs), have become more prominent due to their ability to model complex relationships in data. Among these, long short-term memory (LSTM) neural networks, a type of recurrent neural networks (RNNs), have demonstrated superior performance in capturing long-term dependencies in sequential data, making them particularly effective for time-series forecasting, such as predicting energy demand [31].

However, the performance of LSTM networks can be further enhanced by integrating clustering techniques with load data, along with a similar-day approach for selecting training data. Clustering allows for the identification of underlying patterns or regimes in historical load data, which can improve the training process for neural networks and is widely utilized in contemporary scientific research [32]. In particular, it has been applied to load demand. For example, the classification of representative load curves based on similar features and site temperatures has been carried out in [33]. Furthermore, similar patterns of electricity usage have been uncovered through clustering analysis in [34], and short-term load forecasting has been implemented for random users in Nanjing by grouping users into clusters with similar consumption patterns and predicting energy consumption using a backpropagation neural network [35]. On the other hand, similar-day methods rely on examining historical days with similarities, including weekday index, weather conditions, coincidences of social events, festivities, disasters, anomalous events, and so on [36,37].

In this work, we propose an innovative approach that integrates K-means clustering and similar-day criteria with LSTM networks for day-ahead load demand forecasting. By grouping historical load data into clusters and utilizing similar days, the LSTM network is trained more effectively on relevant data patterns, particularly for weekdays and weekends, which potentially enhances forecasting accuracy. Furthermore, by defining representative regional climate conditions, weather information—an essential factor—augments the training process for improved forecasting accuracy.

1.3. Novelty

This work presents a novel intelligent methodology for day-ahead regional load forecasting. It utilizes a hybrid approach that integrates LSTM neural networks with K-means clustering and a similar-day strategy. The methodology aims to harness the strengths of these techniques: K-means clustering assists in pre-processing and grouping similar load patterns, while similar days enhance the classification of load patterns. In conjunction with representative regional climate conditions, they improve the training of the LSTM network, making it better equipped for modeling sequential dependencies in time-series forecasting.

This work is organized as follows. Section 2 presents the innovative methodology, illustrated by a flow diagram in Figure 1. Section 2.1 details the data preparation, while Section 2.2 thoroughly describes the process of identifying load demand seasonality and briefly outlines the fundamentals of cluster analysis. To refine the data for training the LSTM neural network, the similar-day methodology is discussed in Section 2.3. Section 2.4 outlines the calculation of representative weather conditions. Next, Section 2.5 describes the day-ahead load forecasting process, including the basic concepts underlying the operation of an LSTM neural network. Finally, Section 2.6 details the metric used to quantify the accuracy of the predictions. The proposed methodology is applied to a case study in Section 3, where the process is explicitly demonstrated step by step, along with its results in each subsection, following the order established in the previous section. Section 4 presents a discussion of the novel methodology and the results obtained. Lastly, Section 5 presents the conclusions of this work.

2. Materials and Methods

Figure 1 illustrates the proposed methodology. The first step involves gathering hourly historical electrical load data from the region of interest. The larger the dataset, the more accurate the predictions will be. To capture the seasonality of the electrical load, it is preferable to work with datasets that cover more than three years. Next, a cluster analysis is performed on the dataset to identify its seasonality. After establishing the seasonality, the load demand dataset is divided into the identified seasons. Additionally, meteorological time-series datasets representative of the region are created and similarly grouped into the identified seasons. Then, for each season, an individual LSTM neural network is trained using data from similar days. By training the LSTM with data from each season that share similar characteristics, such as weekdays or weekends, the model learns more effectively, enhancing its ability to forecast day-ahead energy demand for the specific region under study. The following subsections outline this process in detail.

2.1. Data Pre-Processing

The first step is to clean and organize the dataset to eliminate any outliers, inconsistencies, or missing values that could introduce systematic errors. This pre-processing stage is essential for improving the quality of the input data and, consequently, the accuracy of the results. Normalizing the data ensures that all variables are on the same scale, as neural network and clustering algorithms are sensitive to the magnitude of input variables [38].

2.2. Load Demand Seasonality

Load demand seasonality refers to the periodic fluctuations in electricity load over specific timeframes (daily, weekly, monthly, or annually), which are reflected in time-series load data through regular and predictable variations. Load seasonality is heavily influenced by local factors, such as weather patterns, differences between weekdays and weekends, time of day, local customs and practices, holidays, vacations, and various political and social elements. The most notable seasonal patterns in energy consumption include (a) daily seasonality, which arises primarily because energy use during the day surpasses night usage, and consumption differs during typical office hours compared to non-office hours; (b) weekly seasonality, resulting from differing energy use on weekdays versus weekends, with weekdays showing higher consumption; and (c) annual seasonality, largely attributed to changes in climatic conditions, such as the increased use of air conditioners in summer and heaters in winter. However, there may be other seasonal patterns, whether one or many, that, once identified, can improve the understanding of energy consumption and enhance load forecasting.

Given energy consumption’s intense and complex dependence on local conditions, its seasonality can be found via clustering analysis of its historical data using machine-learning tools. In this case, the K-means algorithm clusters the energy consumption time-series data and finds the seasonality according to the similarities.

Clustering

K-means clustering is a well-established unsupervised learning algorithm that partitions data of $n$ observations $\{{\mathit{x}}_1, {\mathit{x}}_2,\dots ,{\mathit{x}}_n\}$, where each observation ${\mathit{x}}_j$, with $j=1,\dots ,n$, is a d-dimensional real vector, into distinct $k(\le n)$ sets of clusters $S=\{S_1, S_2, \dots ,S_k\}$ based on feature similarity. This is performed by minimizing the Euclidean distance between the vectors and the mean or centroid, ${\mathit{\mu }}_i$, of points in the cluster $S_i$, such that

$$\arg \min \sum _{i=1}^k\sum _{\mathit{x} \in S_i}{‖\mathit{x}-{\mathit{\mu }}_i‖}^2 ,$$

(1)

where ${\mathit{\mu }}_i={\displaystyle \frac{1}{\left|S_i\right|}}\sum _{\mathit{x}\in S_i}\mathit{x}$, $\left|S_i\right|$ is the size of $S_i$, and $‖·‖$ is the Euclidean norm [39].

K-means clustering is computationally efficient, especially when working with large datasets like energy demand records that contain hourly data over multiple years. The algorithm’s iterative process of assigning points to clusters and recalculating centroids is relatively fast compared to other clustering techniques, making it suitable for real-time or large-scale applications. Indeed, K-means offers simplicity, speed, and scalability, making it ideal for large energy-demand datasets. In the context of energy forecasting, clustering techniques can be highly beneficial for identifying patterns and segmenting historical load data for more accurate training in the forecasting processing. Among various clustering algorithms, K-means is widely used due to its simplicity and efficiency [40,41].

2.3. Similar-Day Approach

Similar-day load forecasting is a practical method commonly used in utilities for load forecasting [42]. This method designates a selection criterion to identify similar days from the past and uses their load to predict the load on the forecasting date. There are a wide variety of criteria, such as the day of the week, the day of the year, similar climate conditions, days with the same holiday, days with the same political conditions, days with the same social events, etc. One may choose as criterion one or two or more of these criteria. Then, a “similar day” is searched in a big database, and the load of the day most similar to the selected criterion is the one chosen for prediction.

The immediate difference in energy consumption patterns is the day of the week, i.e., weekdays or weekends. Thus, the proposed forecasting methodology uses the similar-day approach with the criterion of differentiating the days that belong to weekdays and to weekends. It is worth mentioning that this methodology does not apply to atypical days.

2.4. Representative Weather Conditions

As mentioned, energy consumption strongly depends on weather conditions. Climate conditions are easy to obtain for a specific site; there are many public sites with historical databases. However, in the case of power systems that cover a large region, climate conditions are not so direct to obtain.

In this methodology, the regional climate conditions are computed by the weighted average of the meteorological properties of the main load zones of the region. Given $n$ main load zones $L=\{l_1,l_2,\dots ,l_n\}$, with their corresponding weights $W=\{w_1,w_2,\dots ,w_n\}$, such that the total power system load $l_{tot}$ can be approximated by

$$l_{tot}~\sum _{i=1}^n{ l}_i ,$$

(2)

and

$$w_i={\displaystyle \frac{l_i}{l_{tot}}} ,$$

(3)

such that

$$\sum _{i=1}^n{w}_i=1$$

(4)

Then, the meteorological conditions characterizing the region are calculated by

$$P_{reg}={\displaystyle \frac{\sum _{i=1}^n{w}_i P_i}{w_i}}$$

(5)

where $P_i$ can be any of the meteorological variables, such as temperature, solar radiation, precipitation, etc., of the site where the load $i$ is located.

2.5. Day-Ahead Load Forecasting

Many techniques have been used and methodologies proposed for day-ahead load forecasting, which is the most significant forecasting method for the day-to-day operation of electricity systems and electricity markets. DALF is a challenging task, as electricity load time series are highly non-linear, non-stationary, random, and they present multiple seasonal patterns. In this novel methodology, we use a long short-term memory neural network to forecast the day-ahead electricity load time series of a region.

LSTM NN

LSTM NN is a recurrent neural network able to deal with long-term dependencies and retain extended information. LSTM NN selectively remembers or forgets information over time, allowing the neural networks (NNs) to recall relevant context and dependencies over long sequences. The LSTM NN’s basic architecture is shown in Figure 2 and consists of (a) the cell that stores the state of a sequence and is able to keep or forget information; (b) the input gate that determines the information to be stored in the cell; (c) the output gate that decides the next hidden state; and (d) the forget gate that decides the information that should be kept or discarded. These kinds of NNs allow information to be kept for long periods and sequences with time intervals between events to be processed more efficiently.

Let $h_t$ and $c_t$ be the hidden and the cell state, respectively, of the LSTM NN at a time step $t$, and let $x_t$ be the input vector. The LSTM NN obtains the input vector and the previous state. The forget gate $f_t$ decides which information to discard from the cell state based on $c_{t-1}$. On the other hand, the input gate $i_t$ decides which information to store in the cell gate. Next, using the previous information, the old cell state is updated to the new cell state $c_t$. Finally, the output gate $o_t$ decides the output based on the cell state. The LSTM operation is given by

$$\begin{array}{cc}{f}_t& =\sigma \left( W_f x_t+U_f h_{t-1}+b_f\right),\\ i_t& = \sigma \left(W_i x_t+U_i h_{t-1}+b_i\right),\\ o_t& =\sigma \left(W_o x_t+U_o h_{t-1}+b_o\right),\\ c_t& =f_t c_{t-1}+i_t \mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h} \left(W_c x_t+U_c h_{t-1}+b_c\right) ,\\ h_t& = o_t\tanh \left(c_t\right).\end{array}$$

(6)

where $\sigma$ is the Sigmoid function; $W_g$ is the respective weight for the gate $g$; $U_g$ is the recurrent connection between the previous hidden layer and the current layer for the gate $g$; $b_g$ is the respective bias of the gate $g$; and $t$ corresponds to the time step.

The main advantages of LSTM NN are the ability to learn long-term dependencies and the capacity to handle sequential data with time steps of different lengths.

Thus, for DALF purposes, the LSTM NN is trained with electrical load data and representative meteorological data time series for each season, as shown in Figure 3.

In time-series forecasting tasks, particularly with LSTM neural networks, incorporating time-related features, such as hours, days, or months, is essential. However, these features are cyclical, i.e., hours repeat every 24 h, and months repeat every 12 months. Encoding them as raw integers can mislead the network because it implies a linear relationship between successive values. Indeed, after 23 h, the value cycles back to 0. Cyclical encoding transforms these features into a pair of sine and cosine values to preserve their cyclical nature, allowing the LSTM to better capture temporal patterns and dependencies. This method enhances the neural network’s ability to recognize recurring trends, improving the model’s learning process and overall predictive performance. By encoding time-related data cyclically, we ensure that the LSTM captures seasonal and temporal dependencies more effectively, leading to more precise demand prediction forecasting.

Integrating K-means clustering with an LSTM NN leverages the strengths of both methods. Clustering enhances the quality of input data, and the LSTM NN architecture excels at modeling sequential dependencies.

2.6. Forecasting Error

Forecasting errors are used to quantify the accuracy of prediction. The mean absolute percentage error (MAPE) is frequently used in reporting the accuracy of electrical load forecasts [43]. MAPE quantifies the discrepancy between the real observed value and the forecasted value and is calculated as follows

$$MAPE={\displaystyle \frac{1}{n}} \sum _{i=1}^n\left|{\displaystyle \frac{Y_i-{\widehat{Y}}_i}{Y_i}}\right|\times 100$$

(7)

where $n$ is the number of observations, and $Y_i$ and ${\widehat{Y}}_i$ are the observed and predicted values for the ith observation. The MAPE value reveals the average percentage error for all observations. A good prediction is reflected in a low MAPE value.

3. Results

This section illustrates the effectiveness of the proposed methodology through its application in a case study in Mexico, with the corresponding results presented. The Centro Nacional de Control de Energía (CENACE) is the national system operator of the Sistema Eléctrico Nacional (SEN) that supplies electricity to the country. The SEN electrical generation system is composed of fossil and clean power plants, as well as their transmission and distribution, involving high- and low-voltage power plants, and their commercialization nationwide. The SEN is divided into eight regions to enhance energy management and facilitate a regional-level analysis of energy resources.

3.1. 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, Veracruz, Oaxaca, Puebla, Tlaxcala, Guerrero, and Morelos, covering a total area of 370,000 km², 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 km².
• 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 ($g_1,g_2,\dots ,g_n$), followed by adding or subtracting the energy associated with power flow in tie lines ${E tl}_i$ with neighboring areas (${tl}_1, {tl}_2, \dots ,{tl}_m$), which correspond to the gray areas surrounding the green one, and finally, subtracting network losses ($Nl$) as given by

$$D=\sum _{i=1}^n{E g}_i+\sum _{i=1}^m{E tl}_i-Nl ,$$

(8)

which is described in Figure 5.

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 Villahermosa, 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 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. For instance, low-pressure systems can trigger storms, while high-pressure systems are typically associated with heat waves; both significantly influence energy usage for heating or cooling. Wind speed plays a crucial role in energy generation in areas with integrated wind power and also affects perceived temperatures. Strong winds can enhance wind power production, reducing demand from traditional sources, whereas weaker winds might increase energy consumption from alternative sources. Furthermore, wind influences perceived temperature, further shaping the energy demand for temperature regulation.

Finally, precipitable water measures the amount of water vapor in the atmosphere, influencing weather conditions such as cloud cover and storms, which in turn affect both solar energy availability and energy demand. By incorporating these data, the model can more effectively predict how weather disruptions—like rain, storms, or heavy cloud cover—will impact short-term energy consumption pattern [46,47].

By integrating these meteorological variables into the LSTM neural network, the model can more accurately represent the external environmental conditions that drive energy demand, resulting in more reliable and dynamic forecasting capabilities, particularly in response to shifting weather patterns.

The data used in this study were sourced from publicly available datasets, including the National Center for Energy Control (CENACE) [44] and the National Solar Radiation Database (NSRDB) [48].

3.1.1. Load Data Pre-Processing

In any process involving artificial neural networks, normalizing the input data before training is essential. This accelerates learning, leads to faster convergence, and reduces the risk of overfitting [49]. In this case, all measured data followed a Gaussian distribution. For instance, Figure 7 illustrates the standardization of energy demand data, which centers the values around a mean of just under 5 GWh/h and a standard deviation of approximately 1 GWh/h, providing the optimal scaling method for normalization. This remarkable natural behavior is due to the fact that residential load behavior dominates regional load demand.

Figure 8 illustrates GCRORI’s daily hourly load profiles from 2016 to 2022. Note that a few profiles deviate from the majority’s behavior and tend toward zero at the end of the day. These profiles are anomalous due to a malfunction in the measuring devices.

By clustering similar load profiles, the training process can be optimized to identify more subtle temporal patterns, resulting in more accurate load demand forecasting. This approach not only enhances the model’s predictive accuracy but also enables a more targeted strategy for addressing various types of load patterns that might otherwise be overlooked in a generic training method.

3.1.2. Load Demand Regional Seasonality

The K-means clustering method is frequently used to group data based on similarities. This facilitates the analysis of daily load profiles and their interrelationships, providing valuable insights into the underlying demand patterns. In this study, we explore how K-means clustering enhanced the performance of the LSTM neural network for day-ahead load forecasting.

As illustrated in Figure 9, the K-means clustering algorithm effectively segregates daily load profiles into four distinct clusters, each representing similar load demand conditions throughout the day. This segmentation is visually evident, as the load profiles within each cluster exhibit consistent patterns and levels of energy demand, indicating that the clustering process had successfully grouped days with comparable demand characteristics. The graph demonstrates the distribution of energy demand across various hours of the day, with each color band denoting a different cluster identified by the K-means algorithm. The clustering captures the inherent variability in daily energy demand, with distinct clusters corresponding to different demand levels and shapes. For instance, one cluster may represent typical weekdays with moderate demand, while another could represent high-demand or low-demand days, such as weekends or special events.

Figure 10 provides a detailed view of the identified clusters. The first group exhibits a steady load demand throughout the day, with a slight increase during peak hours, as illustrated in Figure 10a. This suggests that these days coincide with the warmer months when cooling devices are consistently in use. The second group displays a similar pattern to the previous one but with more pronounced peaks, as shown in Figure 10b. This indicates that these days align with the hottest days of the year, characterized by high energy consumption peaks due to intense cooling needs. The next cluster shows a relatively stable load demand throughout the day, typical of the cooler autumn months when neither heating nor cooling is heavily utilized, as illustrated in Figure 10c. Finally, the last cluster depicts the lowest energy demand associated with winter months during which the need for energy decreases due to mild temperatures, leading to reduced use of heating and cooling devices, as displayed in Figure 10d.

Table 3. Mean temperature per season in the eastern region of Mexico from 2016 to 2022.

Season	Mean Temperature (°C)
Winter	20
Spring	26
Summer	24
Autumn	22

shows the seasonal average temperature in the eastern region of Mexico, indicating that the region’s average temperature varies between 20 and 26 °C. This range affects residential energy consumption due to heating and cooling requirements.

The clear stratification of load profiles into these clusters indicates that the K-means algorithm had identified significant patterns in the data. Each cluster’s homogeneity suggests that the algorithm had grouped days that not only share similar demand magnitudes but also show comparable daily trends and fluctuations. This is crucial for improving the accuracy and robustness of any predictive modeling efforts, such as training an LSTM neural network. By focusing on these clusters, the model can be trained more effectively, capturing the nuanced behavior of load profiles specific to each cluster rather than taking a generalized approach that might miss these important differences. Therefore, the K-means algorithm’s ability to segregate daily load profiles into intuitively logical clusters highlights its value in energy demand analysis.

3.1.3. Similar-Day Approach

To rigorously evaluate the performance of the proposed day-ahead regional load forecasting methodology, four distinct days from each season of 2022 were selected. These days were carefully chosen to represent a variety of demand scenarios, including weekdays, weekends, and holidays, each presenting unique challenges for forecasting due to fluctuations in energy consumption patterns. This selection ensured that the evaluation encompasses a wide range of typical and atypical demand behaviors, providing a comprehensive validation of the model’s overall performance when applied to different consumption patterns:

• Weekdays typically exhibit predictable, higher demand during work hours, which gradually declines in the evening.
• Weekends often show decreased demand, with varying peaks based on the time of day and outside activities.
• Holidays exhibit irregular patterns, typically featuring decreased industrial and commercial activity but possibly increased residential consumption.

3.1.4. Representative Weather Conditions

Electrical load demand greatly depends on meteorological conditions. The representative climatological conditions of the area are determined by considering these conditions at the zones associated with the primary loading areas, specifically the cities of Cuernavaca, Puebla, Veracruz, Villahermosa, and Poza Rica. Subsequently, the weighted average value of these factors—namely temperature, relative humidity, global horizontal irradiance (GHI), pressure, wind speed, and precipitable water—is calculated in accordance with Equation (5).

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. Architecture of the LSTM model. Neurons and activation functions of hidden layer 1 (H1) and hidden layer 2 (H2).

Models	H1 Neurons	H2 Neurons	H1 Activation Function	H2 Activation Function
LSTM—Cluster-based training	64	32	Hyperbolic tangent	Linear

. The inputs to the LSTM neural network represent the load demand data, and in this analysis, we consider key 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.

The results obtained for both types of days in this season indicate that the prediction is generally accurate, except during significant shifts in the demand trend, such as peaks.

Figure 13a illustrates the load demand and forecasted values for the summer season. 14 July 2022 is a Thursday. The load demand begins at approximately 6800 MWh, decreases to nearly 6000 MWh/h by 5 PM, and then rises again to 6800 MWh/h by 3 PM, maintaining that level until 6 PM. Afterward, there is a swift increase to nearly 7400 MWh/h around 9 PM, followed by another decline. In comparison, Figure 13b shows the load demand and forecasted values for 17 July 2022, which is a Sunday. As observed, the pattern is quite similar to that in Figure 11a. Load demand starts from a slightly lower value than on the weekday, at nearly 6750 MWh/h, decreases to 5500 MWh/h by 7 AM, and then begins to rise steadily to nearly 6500 MWh/h. It shifts to 6250 MWh/h around 5 PM before showing a sharp increase to reach 7500 MWh/h around 9 PM before decreasing again. The summer season coincides with the rainy season in the region and is milder than the previous season, leading to lower energy consumption compared to spring.

This season’s forecasting results appear promising, highlighting a small discrepancy in the peak values.

Figure 14 illustrates energy consumption along with the forecasted values for autumn days, specifically 6 and 9 October 2022. The load patterns for weekdays and weekends closely resemble those of previous seasons, showing variations in both maximum and minimum load demand values. The minimum load demand is approximately 5600 MWh/h for a weekday and 5250 MWh/h for a weekend day, as shown in Figure 14a and Figure 14b, respectively. Similarly, the maximum load demand values approach nearly 7000 MWh/h and 6750 MWh/h for Thursday and Sunday, as indicated in Figure 14a and Figure 14b, respectively. Once again, the predicted trend in load demand mirrors the actual data, closely aligning with real behavior during smooth changes in the trend and deviating when the changes are more abrupt.

Figure 15 shows the energy consumption values registered on 21 May 2022, which corresponds to the day with maximum load demand during the year.

Finally, Figure 16 presents the forecasting results for a holiday on 25 December 2022. The prediction is successful for most of the day, with a slight deviation around 6 AM. The quantification of these forecasting results will be detailed in the next subsection.

These findings emphasize the importance of using a clustering approach in our methodology. By segmenting the data according to demand patterns, identifying statistical seasonality, and differentiating typical weekdays from holidays, the training process of the LSTM model can be significantly enhanced, leading to improved forecast accuracy, even in challenging situations like low or moderate consumption.

Furthermore, to illustrate the effectiveness of this method, load forecasts were obtained over an extended period, and three significant weeks of the year were identified. These weeks, along with the main reasons for their selection, are as follows:

• The Easter week. During this time, load profiles exhibit different patterns compared to typical weekdays due to the holidays.
• The week of maximum load demand occurs annually. Among these weekdays, 21 May 2022 recorded the highest load demand value of the year.
• The week of the annual minimum load demand featured one weekday that recorded the lowest load demand value of the entire year, specifically 25 December 2022.

Figure 17 illustrates the registered energy load demand alongside the forecasted values for Easter week. Both curves align closely during most hours of the day, with slight differences during peak load periods where the forecasted values exceed the actual daily peaks.

Figure 18 illustrates the registered energy load demand alongside the forecasted values for the annual maximum load demand week. Both curves align for most hours of the day, revealing slight differences in the minima and maxima of the valleys. As mentioned earlier, the maximum yearly load demand was recorded on 21 May at 10 PM, reaching 8208 MWh/h.

Figure 19 shows the measured energy load demand along with the forecasted values for the weekly minimum load demand throughout the year. Both curves align for most hours of the day, with slight differences noted on the night of 24 December 2022. On 25 December 2022, between 7 AM and 9 AM, the absolute minimum of the yearly load demand occurs, reaching 3597 MWh/h at 8 AM.

The next subsection quantifies the accuracy of these results by calculating the corresponding MAPE values and comparing them to those derived from the forecasted values calculated by CENACE.

3.1.6. Forecasting Errors

Table 5. Historical load demand data and forecasted load demand values obtained using the proposed methodology and CENACE’s methodologies for weekdays across all four seasons.

	13 January 2022			21 April 2022			14 July 2022			6 October 2022
Hour	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$
1 AM	5198	5202	5184.12	6921	6976	6837.18	6422	6538	6762.1	5968	5981	5970.63
2 AM	5004	5031	4995.55	6700	6701	6634.41	6311	6252	6567.53	5730	5767	5854.23
3 AM	4923	4909	4891.1	6497	6520	6472.38	6369	6177	6392.69	5641	5664	5738.63
4 AM	4894	4874	4827.26	6361	6374	6344.4	6269	6256	6273.73	5588	5600	5656.87
5 AM	4838	4905	4812.6	6287	6275	6282.04	6189	6193	6171.7	5584	5555	5685.79
6 AM	4954	4911	4899.47	6258	6228	6180.19	6195	6155	6182.44	5741	5607	5779.26
7 AM	5089	5040	5042.23	6175	6214	6129.2	6060	6182	6085.84	5797	5811	5835.07
8 AM	5105	5187	5066.97	6231	6187	6269.68	6150	6070	6211.8	5967	5916	5902.74
9 AM	5234	5211	5249.86	6458	6343	6413.5	6317	6266	6359.28	6051	5959	5992.23
10 AM	5393	5370	5403.51	6575	6614	6571.67	6359	6424	6528.03	6061	6162	6106.77
11 AM	5494	5502	5525.28	6718	6714	6705.23	6507	6478	6631.71	6173	6204	6124.94
12 PM	5584	5571	5596.49	6834	6893	6804.99	6613	6651	6759.51	6276	6269	6198.29
1 PM	5676	5653	5668.19	6905	6976	6879.69	6658	6723	6901.08	6351	6379	6254.67
2 PM	5710	5731	5729.86	7010	7047	6952.8	6742	6758	7008.56	6438	6394	6331.36
3 PM	5725	5747	5771.48	7084	7122	6998.57	6839	6816	7073.33	6511	6502	6331.36
4 PM	5751	5743	5822.5	7156	7139	7027.01	6819	6895	7101.17	6457	6529	6342.1
5 PM	5759	5727	5832.25	7061	7162	6985.61	6845	6808	7086.04	6497	6399	6290.15
6 PM	5809	5815	5858.16	6848	7028	6890.02	6759	6833	6968.22	6396	6421	6203.85
7 PM	6130	6144	6298.61	7028	6880	7016.22	6858	6726	7032.64	6707	6471	6484.04
8 PM	6310	6334	6397.58	7555	7453	7395.81	7359	7040	7484.97	6978	7171	6801.12
9 PM	6146	6212	6300.07	7550	7920	7457.55	7483	7569	7652.07	6944	6842	6692.26
10 PM	5856	5981	6102.98	7497	7554	7394.36	7398	7229	7558.73	6750	6632	6519.82
11 PM	5605	5652	5904.06	7322	7436	7195.94	7177	7112	7354.32	6560	6442	6270.72
12 AM	5427	5359	5664.82	6946	7145	7067.39	6821	6856	6911.31	6210	6203	6164.04
MAPE		0.63%	1.34%		1.11%	0.88%		1.18%	2.22%		1.04%	1.88%

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 Figure 9, Figure 10, Figure 11 and Figure 12a. The last row shows the resulting MAPE values for each case. Similarly,

Table 6. Historical load demand data and forecasted load demand values obtained using the proposed methodology and CENACE’s methodologies for weekend days across all four seasons.

	16 January 2022			24 April 2022			17 July 2022			9 October 2022
Hour	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$
1 AM	5190	5288	5197.39	6524	6517	6699.13	6390	6379	6378.47	5789	5776	5898.49
2 AM	4997	5062	5024.36	6312	6298	6404.19	6292	6189	6177.6	5598	5589	5705.45
3 AM	4826	4897	4848.03	6158	6143	6252.78	6089	6123	6048.09	5499	5473	5532.51
4 AM	4719	4775	4751.98	6004	6042	6096.04	5944	5982	5939.11	5323	5443	5349.68
5 AM	4645	4713	4669.44	5936	5942	6025.37	5816	5873	5856.86	5333	5320	5295.32
6 AM	4643	4681	4720.46	5830	5895	5961.84	5686	5761	5781.62	5342	5371	5270.5
7 AM	4709	4698	4639.62	5593	5806	5752.92	5491	5648	5576	5318	5379	5213.26
8 AM	4684	4775	4541.75	5597	5631	5744.94	5473	5482	5630.96	5321	5374	5184.17
9 AM	4712	4748	4679.93	5675	5729	5741.57	5563	5570	5712.13	5400	5412	5245.03
10 AM	4776	4811	4791.76	5755	5833	5807.85	5717	5694	5789.35	5425	5523	5357.58
11 AM	4815	4859	4879.54	5827	5933	5868.27	5819	5853	5868.26	5487	5510	5384.61
12 PM	4852	4881	4927.74	5882	5994	5950.25	5893	5928	5933.64	5581	5580	5452.19
1 PM	4866	4919	4968.25	6029	6037	6028.47	6018	6012	5993.3	5617	5661	5545.95
2 PM	4876	4937	5013.95	6103	6180	6045.44	6061	6129	6067.34	5734	5686	5638.04
3 PM	4857	4951	5025.44	6192	6206	6092.56	6161	6129	6151.16	5738	5840	5718.62
4 PM	4879	4934	5037.35	6232	6302	6117.23	6241	6255	6198.94	5815	5787	5790.63
5 PM	4890	4939	4995.24	6260	6298	6186.95	6165	6248	6240.17	5822	5877	5851.07
6 PM	4991	4969	5079.81	6299	6304	6190.82	6285	6120	6260.92	5909	5821	5968.86
7 PM	5550	5256	5670.74	6574	6391	6677.9	6504	6412	6443.43	6531	6055	6481.87
8 PM	5849	5741	5993.73	7339	6883	7468.31	7196	6569	7147.46	6853	7107	6943.06
9 PM	5775	5662	5957.49	7507	7707	7552.27	7461	7517	7297.27	6728	6765	6903.09
10 PM	5569	5472	5711.16	7422	7306	7413.44	7360	7025	7202.55	6501	6536	6616.68
11 PM	5217	5220	5367.65	7095	7193	7121.96	7086	7008	6899.46	6162	6258	6260.44
12 AM	4911	4906	5018.18	6793	6827	6750.49	6737	6677	6587.86	5914	5903	5993.28
MAPE		1.302%	1.81%		1.31%	1.360%		1.39%	1.20%		1.19%	1.43%

displays the same values for the sample weekend days presented in Figure 9, Figure 10, Figure 11 and Figure 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.

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. Historical load demand data and forecasted load demand values obtained using our methodology and CENACE’s methodologies for a holiday.

	21 May 2022			25 December 2022
Hour	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	LD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$	FLD_C $\left[\frac{\mathbf{M}\mathbf{W}\mathbf{h}}{\mathbf{h}}\right]$
1 AM	7424	7446	7259	4312	4251	4215.3
2 AM	7241	7213	7013	4151	4168	4070.66
3 AM	7011	7060	6823	4020	4096	3939.73
4 AM	6781	6875	6620	3906	4035	3869.01
5 AM	6640	6680	6469	3809	3972	3830.89
6 AM	6551	6550	6423	3813	3905	3790.62
7 AM	6283	6468	6267	3747	3918	3703.93
8 AM	6352	6263	6418	3731	3844	3590.1
9 AM	6542	6474	6564	3864	3835	3591.26
10 AM	6743	6678	6723	3961	3996	3680.32
11 AM	6936	6915	6851	4084	4064	3791.13
12 PM	7071	7104	6976	4157	4197	3901.03
1 PM	7110	7238	7031	4209	4237	3962.35
2 PM	7145	7252	7060	4232	4285	4017.6
3 PM	7198	7272	7068	4319	4296	4078.67
4 PM	7235	7272	7033	4383	4373	4116.33
5 PM	7205	7256	6938	4469	4424	4080.12
6 PM	7154	7180	6890	4584	4625	4202.25
7 PM	7300	7157	7104	4997	4918	4734.12
8 PM	8019	7471	7813	5169	5189	4940.35
9 PM	8208	8295	7921	5102	5061	4874.54
10 PM	8094	7842	7817	4910	4866	4735.24
11 PM	7842	7898	7561	4747	4626	4544.67
12 AM	7510	7631	7430	4451	4440	4264.78
MAPE		1.32%	2.11%		1.48%	4.4%

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.
• 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 °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.

Table 8. Historical load demand data and forecasted load demand values obtained using our methodology and CENACE’s methodologies for the three weeks under study.

Week	MAPE	MAPE_C
Easter	1.25%	2.49%
Maximum load demand	1.15%	1.17%
Minimum load demand	1.14%	2.13%

displays the MAPE values for the forecasted load demand using the proposed methodology alongside the CENACE results for the three weeks illustrated in Figure 17, Figure 18 and Figure 19. As shown in the first row, the MAPE for the Easter week is 1.25%, while the value calculated using CENACE’s forecasted values is 2.49%, resulting in an improvement of nearly 50% in accuracy. Additionally, the third row presents the MAPE for the minimum load week, achieving a value of 1.14% compared to CENACE’s forecasted value of 2.13%, yielding an improvement of more than 46% in accuracy. Finally, the second row shows the MAPE for the minimum load demand week, which is 1.15% compared to the 1.17% obtained from CENACE, resulting in an improvement of 1.7% in accuracy.

4. Discussion

Although one of the most common machines used for load demand forecasting is LSTM neural networks, as shown in the literature, what sets the different works apart is the training process. The information used for training is crucial for achieving accurate forecasting results. The more suitable the information, the better the outcome will be.

Separating load profiles into clearly defined clusters reveals distinct operational regimes within the energy demand data. Therefore, clustering provides valuable insights into the underlying factors influencing these regimes, such as weather conditions, economic activities, or social behaviors. Understanding these patterns is essential for utilities and grid operators, as it enables more targeted and efficient demand management strategies. Moreover, the clusters reflect different energy consumption levels and illustrate the temporal structure of demand throughout the day. This refined understanding of the load profiles enhances the predictive capabilities of models and supports better decision-making processes in energy management. Furthermore, the similar-day methodology, in its various forms, is a widely used method for day-ahead load demand forecasting. This approach, which combines the technique of distinguishing between weekdays and weekends with clustering analysis, significantly enhances the relevant training information for the LSTM neural network.

Load demand is significantly influenced by weather conditions, with temperature being one of the most important factors. Therefore, it is essential to incorporate this information to achieve accurate forecasting results. A critical challenge in regional load forecasting arises when considering meteorological conditions across the entire region of interest, especially if it is a large area with varying local weather patterns. Thus, utilizing representative meteorological data by calculating a weighted average from the sites with higher loads in the region, as proposed in this approach, offers a solution to the challenge of integrating diverse climate conditions within a region.

Even though it was demonstrated that the proposed methodology yields better results than CENACE, it is valuable to compare it with methodologies employing similar paradigms. Research was undertaken on load demand forecasting for very short-, short-, medium-, and long-term load demands using LSTM neural networks. In particular, some of the most recent studies published on day-ahead load demand forecasting utilize LSTM neural networks as the primary machine-learning tool for achieving accurate predictions, as these networks are designed to capture long-term dependencies in sequential data. Table 6 summarizes recent research that employs this recurrent network, either independently or in conjunction with another tool, for day-ahead load demand forecasting alongside the proposed approach presented.

As seen in

Table 9. Some of the day-ahead load forecasting methodologies utilizing LSTM neural networks reported in the literature.

Reference	Approach	Load Dataset	Input Variables	Accuracy of Prediction
Kong et al., 2017 [52]	LSTM	A set of households in Australia	Historical load time series	MAPE values ranging from 21.99% to 26.85%.
Bouktif et al., 2018 [53]	LSTM + RNN + GA	Metropolitan zone in France	Historical load time series	CV(RMSE) = 0.78%.
Nespoli et al., 2020 [54]	LSTM	Industry in Italy	Historical load time series	nRMSE = 2.30.
Mughees et al., 2021 [55]	Bi-LSTM S2S	Residential region in Pakistan	Historical load time series	MAPE values ranging from 3.67% to 5.92%.
Wood et al., 2023 [56]	LSTM + EMD + K-means clustering	Residence, hotel, manufacturing plant, EV charging station, distribution network, transmission network in USA and Italy	Historical load time series	They obtain RMSE values lower than the benchmark models, ranging from −6.3% to 73% improvement over the benchmarks.
Atef et al., 2020 [57]	Uni-LSTM + Bi-LSTM	Power system network in Switzerland	Historical load data	MAPE values ranging from 0.22% to 3.895%.
Ortega et al., 2023 [51]	LSTM	Power system network in GRCORI	Historical load and temperature time series	MAPE values ranging from 0.36% to 3.58%.
Nabavi et al., 2024 [28]	LSTM + DWT + NARX + SVM	Power system network in Germany and Iran	Historical load and meteorological time series and social events	MAPE values ranging from 0.29% to 4.2%.
This approach	LSTM + K-means clustering + similar days	Power system network in GRCORI	Historical load and meteorological time series	MAPE values ranging from 0.63% to 1.48%.

, the main characteristics that differentiate the proposed day-ahead regional load forecasting methodology are as follows:

• It is used for regional load forecasting, regardless of the extension of the region.
• It defines and uses representative regional weather data, regardless of the extension of the region.
• It can achieve better accuracy in its forecasting results, as shown by the MAPE values.
• Its methodology is less complex compared with the other regional load forecasting methodologies.

5. Conclusions

The proposed methodology proved effective in providing day-ahead regional load demand forecasts with an acceptable error margin. In all forecasted scenarios, the mean absolute percentage error (MAPE) was below the acceptable threshold for forecasting performance in CENACE, which is 4%; indeed, all computed MAPEs were below 1.5%. For the various scenarios analyzed, on most days and during most hours, the load demand forecasts generated by the proposed methodology were more accurate than those forecasted by CENACE.

The presented methodology was demonstrated over three interesting weeks due to the challenges in forecasting periods of maximum and minimum load demand, as well as periods of high variability in the load levels, such as those reported during Easter week. These periods correspond to the most difficult operating scenarios and thus deserve special attention from both GCRORI and, in general, all power system operators.

The enhanced accuracy achieved in load prediction using the proposed day-ahead load forecasting model is particularly significant under complex operating conditions. For example, during peak load demand periods, power system elements often need to operate at or even exceed their nominal capacities, especially power transformers and transmission lines. Such conditions can lead to disturbances in the system, potentially resulting in significant blackouts. Conversely, during low peak load demand periods, certain power system elements, such as transmission lines and compensation devices like STATCOMs and static VAR compensators, as well as shunt capacitors and reactors, must be employed to maintain nodal voltages within secure ranges. In a longitudinal power grid, like that of GCRORI, the power transmission lines operate below their surge impedance loading (SIL). Consequently, they behave like shunt capacitors, injecting reactive power (Q) into the grid and raising nodal voltages. Therefore, in this minimum peak load scenario, the power transmission lines often need to be disconnected.

Furthermore, due to climate change, historical load patterns are becoming increasingly ineffective because of the unpredictable nature of loads on similar days or even months. In addition, the GCRORI power system has been affected by hurricanes from the Gulf of Mexico and the Pacific Ocean. Thus, we suggest the following directions for future work:

• Utilize data from extreme weather events to train the proposed day-ahead load forecasting model and enhance load forecasting during hurricanes, cyclones, and other severe conditions.
• The proposed day-ahead load forecasting model could serve as a valuable tool as uncertainty in weather behavior increases, as observed in the last two years (2023 and 2024).
• The proposed day-ahead load forecasting model would serve as a valuable tool for smaller load zones in Mexico compared to regional zones known as load zones.
• The proposed day-ahead load forecasting model could be applied to other CENACE regions, the entire SEN, and other power systems around the world.