Introduction

As the global community confronts mounting challenges related to environmental sustainability, resource scarcity, and climate change, renewable energy has emerged as a pivotal solution to address these pressing issues (Owusu & Asumadu-Sarkodie, 2016; Singh, 2023). The consumption of fossil fuels is linked to severe environmental and health consequences, including air pollution, climate change, ecological imbalance, and the prevalence of serious diseases (Alizamir et al., 2023). In response, numerous developing countries have prioritized the transition to clean and renewable energy sources over recent decades (Pakulska, 2021). Among various renewable sources—such as wind, solar, hydropower, geothermal, biomass, and tidal and wave energy—solar energy has gained particular prominence due to its widespread availability and critical role in reducing greenhouse gas emissions (Babatunde et al., 2023; Chiranjeevi et al., 2023). This transition not only aids in environmental preservation but also presents economic benefits by promoting sustainable development and enhancing energy security (Gürel et al., 2023; Joseph, 2023). Furthermore, solar energy serves as a cleaner (Tang et al., 2018), more sustainable alternative to fossil fuels, aligning with international frameworks such as the Paris Agreement, which aims to limit global temperature increases by reducing dependence on non-renewable resources and advancing low-carbon energy systems (Park, Das & Park, 2015).

Solar energy systems are broadly categorized into photovoltaic (PV) systems and concentrated solar power (CSP) systems, both of which harness sunlight and convert it into usable energy. PV systems, in particular, have become the most widely adopted (Gürel et al., 2023; Zhang & Wei, 2019) due to their flexibility, ease of installation, and decreasing costs, which have made them suitable for a range of applications, including residential, commercial, and industrial use (Alkahtani, Aldhyani & Alsubari, 2023). Advancements in photovoltaic technology have improved efficiency and accessibility, accelerating global adoption (Bakır et al., 2022). This has contributed to its rapid adoption on a global scale, positively impacting energy systems in both developed and developing countries. Beyond electricity generation, solar energy has diverse applications across various sectors, underscoring its adaptability and far-reaching benefits. In agriculture, solar-powered systems support irrigation, crop monitoring, and greenhouse climate control, helping to improve productivity and resource efficiency. In healthcare, solar technology provides reliable energy sources in remote and underserved areas, enhancing access to essential medical services. Additionally, sectors such as tourism and urban planning incorporate solar installations to reduce carbon footprints and move towards energy independence. The integration of solar energy across these fields highlights its critical role in advancing sustainable development and underscores its potential to revolutionize global energy infrastructure (Guermoui et al., 2020).

Figure 1 highlights the significant growth in solar energy by depicting the total installed capacity of solar PV from 2000 to 2023. The increasing demand for solar energy necessitates accurate global horizontal irradiance (GHI) predictions, as the natural variability of solar energy presents notable challenges for seamless integration into power grids (Nam & Hur, 2019; Singh, Moger & Jena, 2022). Reliable GHI forecasting offers substantial benefits, including more efficient energy planning, reduced operational costs, and optimized power generation (Zhang & Wei, 2019; Chiranjeevi et al., 2023; Kumar, Namrata & Kumari, 2022). For instance, precise irradiance predictions enable energy providers to anticipate fluctuations, enhancing grid stability, minimizing reliance on backup power sources, and facilitating more effective energy dispatch. Consequently, many researchers have focused on producing daily solar radiation predictions to support these needs (Kasra et al., 2015; Rodríguez et al., 2018; Zhang & Wei, 2019). Beyond grid management, accurate solar forecasting yields economic advantages by minimizing energy wastage, improving the performance and reliability of solar installations, and supporting applications in other sectors, such as agriculture, where solar data aids in planning crop cycles and optimizing yields (Xing et al., 2023). These advantages underscore the vital role of GHI forecasting in maximizing the utility and sustainability of solar energy systems across diverse industries.

Given the critical need for reliable solar predictions, recent research has focused on advanced forecasting models, employing statistical methods, machine learning, and hybrid techniques to improve forecast accuracy. Nevertheless, further advancements are needed to address the inherent complexity (Kumar, Namrata & Kumari, 2022) of solar irradiance, which is influenced by a multitude of meteorological factors. This study addresses this gap by introducing a novel hybrid methodology that combines TCN and TE with ANN to improve GHI forecasting precision. The TCN+TE+ANN framework leverages TCN’s strength in managing sequential data and capturing temporal dependencies, while TE with ANN enhances generalization, together providing a robust and high-accuracy model capable of capturing complex temporal patterns in solar data.

In summary, this study aims to advance the field of solar irradiance forecasting by developing a high-precision, novel hybrid predictive model that supports the global shift toward renewable energy. Through its innovative approach, the study not only provides reliable solar energy forecasts but also has potential for informed decision-making in energy management, policy, and investment, thus reinforcing solar energy’s essential role in the pursuit of a sustainable energy future.

Related works

In recent years, significant advancements have been made in solar radiation forecasting, with a strong focus on developing hybrid models that combine machine learning and optimization techniques. These approaches aim to address the inherent challenges posed by the variability and non-linearity of solar radiation data, thereby enhancing prediction accuracy and facilitating the smoother integration of solar energy into power systems. Researchers have increasingly focused on hybrid methodologies that integrate deep learning models with meta-heuristic algorithms, as these combinations capitalize on the unique strengths of each approach—such as the adaptive learning capabilities of deep learning and the solution-finding efficiency of meta-heuristic techniques—to improve robustness and precision in solar irradiance forecasting (Ghimire et al., 2023). A comprehensive comparison of the proposed study with these existing models will be presented in the discussion chapter to highlight the distinct advantages and innovations of our approach.

Abdallah et al. (2023) proposed a hybrid framework combining variational mode decomposition (VMD), multi-functional recurrent fuzzy neural network (MFRFNN), and quantile regression forests (QRF) for daily global solar radiation (DGSR) prediction. VMD decomposes the DGSR time series into intrinsic mode functions (IMFs) to simplify patterns, MFRFNN captures non-linear and temporal dynamics within the IMFs, and QRF quantifies uncertainties, ensuring accurate and robust forecasting. Similarly, Peng et al. (2023b) developed a hybrid model integrating VMD, deep belief networks (DBN), and online sequential extreme learning machine (OS-ELM). VMD was used to reduce noise by decomposing solar radiation time series, while DBN and OS-ELM handled feature extraction and real-time prediction, respectively.

Chiranjeevi et al. (2023) presented a hybrid architecture combining long short-term memory (LSTM) autoencoders, convolutional neural network (CNN), and bidirectional LSTM (BiLSTM) with grid search optimization, demonstrating significant improvements in solar irradiation forecasting. Similarly, He et al. (2022) employed a hybrid model integrating CNN and BiLSTM networks to predict short-term photovoltaic system outputs, where CNN extracted spatial features, and BiLSTM captured sequence learning. Ghimire et al. (2023) proposed a related methodology that combines CNN and multi-layer perceptron (MLP) for global solar radiation (GSR) prediction. The CNN extracted spatial features, while the MLP refined these features to improve predictive performance. Hou et al. (2019) focused on a hybrid deep neural network, where CNN was used to extract spatial patterns from satellite imagery, and MLP integrated these patterns with temporal and location data for GSR estimation.

Peng et al. (2023a) evaluated multiple Machine Learning approaches, including MLP, LSTM, gradient boosting regression tree, and random forest (RF). They selected a hybrid RF-Informer framework that balanced accuracy and computational complexity, demonstrating high performance in solar radiation prediction. Alkahtani, Aldhyani & Alsubari (2023) applied a CNN-LSTM framework to meteorological data, creating an accurate solar radiation prediction model for renewable energy systems. Similarly, Xing et al. (2023) developed a hybrid model combining LSTM for time-series regression, DBN for feature extraction, and the mind evolutionary algorithm (MEA) for hyperparameter optimization. Inputs such as sunshine duration, temperature, and precipitation enhanced the model’s robustness and accuracy. Aslam et al. (2021) enhanced LSTM performance by implementing a two-stage attention mechanism (2AM) with Bayesian optimization for day-ahead photovoltaic power forecasting, optimizing hyperparameters to improve prediction accuracy.

Alizamir et al. (2023) studied on thirteen artificial intelligence models, including multivariate adaptive regression splines, extreme learning machines (ELM), Kernel ELM (KELM), online sequential ELM (OSELM), optimally pruned ELM (OPELM), outlier robust ELM (ORELM), and deep ELM (DELM). These models were further enhanced by integrating VMD, resulting in variants such as VMD-DELM, VMD-ORELM, and VMD-KELM for solar radiation estimation in Iraq. Aybar-Ruiz et al. (2016) proposed a neural-genetic hybrid algorithm, where a grouping genetic algorithm (GGA) was used for optimal feature selection, and ELM carried out the prediction task. Similarly, Fan et al. (2020) introduced a hybrid model combining support vector machines (SVM) with heuristic algorithms such as particle swarm optimization (PSO), bat algorithm (BAT), and whale optimization algorithm (WOA) to improve prediction accuracy, particularly in air-polluted regions.

Meng et al. (2021) employed a hybrid model incorporating a wavelet transform (WT) package and generative adversarial networks (GANs). The WT decomposed solar energy signals into sub-harmonics, while GANs predicted short-term energy trends, with the dragonfly algorithm (DA) optimizing the GAN’s performance. Similarly, Kasra et al. (2015) combined SVM with WT for daily and monthly solar radiation predictions, showcasing the efficacy of hybrid methods in addressing temporal variability. Zhang & Wei (2019) also introduced a hybrid approach integrating principal component analysis, WT, and ELM optimized using the BAT for daily solar radiation prediction. Ikram et al. (2022) introduced an improved model integrating the improved multi-verse optimizer (IMVO) with least squares support vector machines (LSSVM). IMVO optimized hyperparameters, such as kernel function width and regularization constants, to enhance prediction accuracy and computational efficiency.

Al Diego Pega, Hannah Mae San Agustin & Bonifacio Tobias (2022) introduced a hybrid model for forecasting DGSR time series. Their approach employed meteorological data and solar radiation samples from Dumaguete, Philippines, to evaluate the predictive accuracy of a nonlinear autoregressive network with exogenous inputs (NARX) combined with a gated recurrent unit (GRU) hybrid model.

Rahman, Rahman & Haque (2021) proposed an ANN-based model utilizing climatic variables such as temperature, humidity, wind speed, and solar radiation for hourly solar forecasting, highlighting ANN’s versatility in solar radiation prediction. Babatunde et al. (2023) introduced a hybrid model that integrates machine learning algorithms with a meta-heuristic optimization technique for solar radiation forecasting. Their model, benchmarked against traditional interpolation methods like linear and spline interpolation, outperformed established machine learning approaches such as RF and multivariate adaptive regression splines. Brahma & Wadhvani (2020) extended this direction by developing deep learning models based on multi-site data to address spatial variability in daily solar irradiance forecasting. Chaibi et al. (2022) demonstrated the utility of machine learning frameworks by combining RF and Bayesian optimization to forecast solar irradiance, incorporating feature selection to enhance accuracy. Malinowski, Leon & Abu-Rub (2017) conducted an extensive review of photovoltaic and thermal solar energy systems, discussing current advancements and trends in solar energy technologies. These studies emphasize the growing interest in hybrid models and machine learning techniques, which combine feature extraction, sequence modeling, and optimization to tackle the complexities of solar radiation prediction effectively.

In summary, the literature reveals a trend towards hybrid models in solar radiation forecasting, integrating deep learning architectures with optimization techniques to achieve higher prediction accuracy. Studies frequently combine models like CNN, LSTM, and SVM with optimization algorithms, underscoring the effectiveness of multi-layered, hybrid approaches in advancing the precision and robustness of solar radiation models.

Method

The methodological approach of this study primarily used the Python programming language. It is chosen for its extensive ecosystem of libraries and its versatility in handling complex data processing and machine learning tasks. A computer equipped with Intel i7 processor (14700KF) with a 33 M Cache, a base clock speed of 3.4 GHz up to 5.60 GHz. The system included 64 GB of RAM and an NVIDIA RTX 3060 GPU, which significantly accelerated the training and testing of the deep learning models. The GPU was especially beneficial for managing large datasets, facilitating fine-tuning, and supporting the complex structures of neural networks, resulting in reduced training time and enhanced model optimization in data-intensive tasks.

Model selection

The proposed model architecture combines three advanced models to create a novel hybrid methodology—TCN, TE, and ANN—each contributing unique capabilities to improve solar irradiance prediction accuracy.

TCN: It plays a foundational role in the model by extracting temporal features from the sequential input data. TCNs are designed to capture complex temporal dependencies across various time scales, which is essential for effective time-series forecasting tasks such as solar irradiance prediction. Unlike recurrent networks, which process data sequentially, TCNs apply convolutional operations that enable parallel processing of time steps, resulting in faster training and improved scalability (Bai, Kolter & Koltun, 2018). By leveraging dilated convolutions, TCNs can identify patterns over long sequences, allowing the model to consider both recent and historical patterns when forecasting irradiance levels—a critical feature given the fluctuating nature of solar radiation (Lea et al., 2017).

The TCN processes the sequential input data by utilizing convolutional layers with dilation to capture temporal dependencies. It is responsible for extracting patterns over the time dimension, making it suitable for time-series forecasting.

TE: It is initially developed for natural language tasks, have proven effective at identifying complex dependencies within time-series data as well (Vaswani, 2017). By dynamically assigning attention to relevant data points, the Transformer Encoder makes it possible for the model to prioritize key information and improve the focus of the prediction (Devlin, 2018). The TE layer follows the TCN and applies attention to the features extracted. Attention mechanisms allow the model to focus on specific time steps with features.

In the model, the TE layer is applied to the features extracted by the TCN. It captures relationships and patterns between different features, enhancing the extracted representations.

ANN: In the final stage, ANN uses fully connected layers (Dense layers) to produce the GHI prediction. This component takes the refined features from the TE and generates the prediction output. Fully connected layers are well-suited for this task because they combine information from previous layers and capture any remaining non-linear relationships, which ultimately results in accurate solar irradiance predictions (Goodfellow, Bengio & Courville, 2016).

The architecture of the proposed model is visually represented in Fig. 2 which provides a structural overview of TCN, TE Block, and ANN components. The diagram illustrates the sequential flow and interaction between these three primary layers: TCN for extracting temporal features, TE Block for applying attention to selectively emphasize relevant time steps with features, and ANN for generating the final GHI prediction. This visual representation highlights how each component builds upon the previous layer’s output, illustrating the layered approach designed to optimize time-series forecasting.

Results

The performance of the proposed model was evaluated across three major solar energy production sites: Desert Sunlight, Copper Mountain, and Solar Star. Each location was chosen for its significance in solar power generation within the U.S., ensuring that the model’s predictions were tested across varied environmental conditions.

Table 4 presents the performance metrics for the Desert Sunlight location, Table 5 summarizes the metrics for Copper Mountain, and Table 6 details the metrics for Solar Star. These tables provide a comprehensive overview of the proposed hybrid model’s performance at each point of the site, including key metrics such as MAE, MSE, RMSE, and R². Additionally, the tables present the average of the results, the coefficient of variation (%), and the interquartile range (IQR) for each location, offering further insights into the variability and consistency of the model’s performance. The results displayed in these tables demonstrate the model’s effectiveness in solar irradiance prediction across different locations.

Table 7 provides a detailed statistical summary of the model’s performance metrics, presenting key values such as the minimum, maximum, standard deviation, and average of the results from all locations (69 data points). Additionally, the table includes the coefficient of variation (%), which highlights the relative variability of the results, and the IQR, offering a measure of the spread of the data around the median. These comprehensive statistics enable a deeper understanding of the distribution and consistency of the model’s performance metrics, facilitating a more nuanced evaluation of its predictive reliability and robustness across different scenarios.

To provide a comprehensive overview of the proposed model’s performance during training and testing, visual plots were generated for one point of each location. These visualizations include the learning curve, error distribution histogram, residual plot, and scatter plot. The learning curves demonstrate the training and validation loss over epochs, showcasing model convergence and indicating potential overfitting. The error distribution histograms illustrate the distribution of prediction errors, providing insights into how well the errors are centered around zero. Residual plots depict the residuals (differences between actual and predicted values) across the range of predicted values, aiding in the identification of any patterns that might suggest model bias or unaccounted variance. Scatter plots display the relationship between actual and predicted values, where a close clustering of points along the line of perfect prediction indicates higher predictive accuracy. Together, these visualizations demonstrate that the model effectively learns from the training data and maintains strong predictive performance on unseen test data.

Figures 3, 4 and 5 collectively illustrate the learning curves, error distribution histograms, residual plots, and scatter plots for the three solar sites: Desert Sunlight, Copper Mountain, and Solar Star, respectively. These visualizations showcase consistent training convergence, balanced prediction errors, and accurate residual distributions with minimal deviation, highlighting the model’s robustness and generalization capability across all sites.

Discussion

This study aimed to develop and evaluate a novel hybrid model that integrates TCN, TE, and ANN for solar irradiance prediction. The motivation for this work arose from the challenges inherent in solar radiation forecasting, particularly the need for models capable of capturing complex temporal dependencies and prioritizing relevant features. Accurate solar irradiance prediction is crucial for various applications, including optimizing energy management, enhancing grid stability, and facilitating the seamless integration of solar power into existing energy systems. Its importance extends to improving decision-making in renewable energy planning and supporting sustainable energy infrastructure.

For the Desert Sunlight area, the proposed model utilized data from five different stations. The results, summarized in Table 4, indicate promising performance, with an average MAE of 0.02985, MSE of 0.00302, RMSE of 0.05488, and a high R² of 0.96428. All coefficient of variation values, except for MSE, were below 10%, signifying stability and reliability and suggesting consistent results (Montgomery, 2019). The coefficient of variation for MSE was between 10–20%, which is indicative of acceptable moderate variability (Montgomery, 2019). Additionally, very low IQR values were obtained, suggesting that the data points are closely clustered around the median, indicating minimal variability within the central distribution.

For the Copper Mountain area, the proposed model was evaluated using data from 13 different stations. The results, as presented in Table 5, show an average MAE of 0.033095, MSE of 0.003907, RMSE of 0.062513, and an R² of 0.952050. The coefficient of variation values for MAE (3.67%), MSE (6.08%), RMSE (3.04%), and R² (0.30%) all indicate strong stability and reliability, with low variability across most metrics. These results suggest consistent and dependable model performance (Montgomery, 2019). The IQR values were also notably low, with MAE at 0.00168, MSE at 0.00035, RMSE at 0.00277, and R² at 0.00356, indicating that data points are tightly clustered around the median and demonstrating minimal variability within the core of the data distribution (Montgomery, 2019).

For the Solar Star area, the proposed model was tested using data from 51 different stations. The results, detailed in Table 6, showed an average MAE of 0.02865, MSE of 0.00277, RMSE of 0.05266, and R² of 0.96840. The Coefficient of Variation for the metrics indicated reliable performance, with MAE at 6.06%, MSE at 9.39%, RMSE at 4.65%, and R² at 0.31%. These CV values highlight the model’s stability, suggesting consistent predictions across the extensive dataset. The IQR values were low—MAE at 0.002065, MSE at 0.00030, RMSE at 0.00287, and R² at 0.00352—indicating tightly grouped data points around the median and minimal variability within the central distribution, further underscoring the model’s robustness and precision in solar irradiance forecasting.

Table 7 provides a comprehensive summary of the proposed model’s performance across all 69 evaluated locations, showcasing consistent predictive accuracy. The quantitative results are promising, with a minimum MAE of 0.02510, MSE of 0.00228, RMSE of 0.04776, and a maximum R² of 0.97417. The standard deviation values indicate minimal variability across locations, suggesting stable model performance. The coefficient of variation supports the model’s reliability, with percentages of 8.25% for MAE, 17.19% for MSE, 8.34% for RMSE, and 0.74% for R². Additionally, the low IQR values demonstrate that data points were closely clustered around the median, confirming consistent performance and reduced variability across all 69 sites. These findings collectively underscore the model’s robustness and potential for effective solar irradiance prediction.

The performance visualization plots for each location (Figures 3, 4, and 5) further illustrate the model’s reliability. The learning curves indicate stable training and validation losses, suggesting that the early stopping mechanism successfully prevented overfitting. The error distribution histograms show errors that are centered around zero, confirming that the predictions are unbiased. Residual plots display no significant patterns, indicating that the model adequately captured the relationships between the features and the target variable. Finally, the scatter plots illustrate a close alignment of predicted and actual values, reinforcing the model’s predictive strength.

The results illustrate that combining TCN, TE, and ANN leverages the unique strengths of each component. TCNs extract detailed temporal features, the Transformer applies attention to enhance relevant patterns, and the ANN refines and outputs the prediction. This layered approach contributes to the model’s ability to generalize across different locations. Additionally, the chronological test split of approximately 26 months of data ensures the robustness of the evaluation by simulating real-world forecasting scenarios. The high R² values obtained across all locations, reaching up to 0.97 for some data points, underscore the model’s capability to explain a significant portion of the variance in solar irradiance, outperforming traditional and many hybrid models in existing literature.

To contextualize the performance of the proposed TCN+TE+ANN model, Table 8 compares it with a range of previously developed models for solar irradiance prediction. The table summarizes each study’s methodology, station count, data period, temporal resolution, number of samples, and performance metrics.

Key performance highlights can be listed as follows:

Innovative architecture: The integration of TCN, TE, and ANNs allows the model to effectively extract temporal features, focus on relevant data points, and refine predictions.

Performance metrics: The proposed model achieves excellent predictive performance, with R² values ranging from 0.94768 to 0.97417, RMSE between 0.04776 and 0.06543 W/m², and MAE between 0.02510 and 0.03526 W/m². These metrics indicate a high level of accuracy and minimal error.

Temporal resolution and dataset scope: The proposed study is distinguished by its large dataset of over 13.9 million samples, spanning 22 years of high-frequency (30-min) data from 69 data points. This is one of the most comprehensive datasets in terms of both temporal resolution and station coverage compared to the other studies, which often focus on daily or hourly data with fewer samples and shorter time periods. Unlike many previous studies that predominantly use daily data, this study employs a 30-min temporal resolution. This finer granularity allows the model to capture short-term variations in solar irradiance, which are critical for operational decision-making in real-time energy systems.

While the proposed model excels in many aspects, some limitations are worth noting such as station count, limited geographic diversity, and Real-Time Adaptation. Although this study analyzes 69 points across three locations, expanding the station count in future studies could further validate the generalizability of the model. Even though the study includes three major solar energy production sites—Desert Sunlight, Copper Mountain, and Solar Star—the geographic coverage is confined to US. This restricts the model’s validation across varying global climates, such as tropical, arid, or continental regions, which may exhibit different solar irradiance patterns. The model relies on historical data and does not currently incorporate real-time updates or adaptive mechanisms. In operational scenarios, such as grid management, real-time forecasting could be crucial to respond to rapid weather changes. Incorporating adaptive learning techniques could improve the model’s responsiveness and practical utility.

While various hybrid models in prior studies have combined CNNs, LSTMs, and attention mechanisms for solar irradiance forecasting, our model introduces a novel sequence by employing TCN for temporal feature extraction, followed by TE for attention-based refinement, and concluding with ANN for final prediction. To our knowledge, this TCN → TE → ANN configuration has not been previously applied in this domain. Unlike CNNs or LSTMs, TCNs offer more stable training and superior long-term temporal learning, and our use of a TE block directly on TCN-derived features enhances attention across time steps in a way not observed in prior work. This architectural distinction, along with the scale and granularity of our dataset, underpins the originality of this study.

The sequential architecture of TCN → TE → ANN is motivated by the distinct roles each component plays in temporal learning. Temporal convolutional networks (TCNs) are well-suited to capture both short- and long-range dependencies in time-series data using dilated convolutions, offering greater stability and parallelism than recurrent models. Following this, the Transformer Encoder (TE) focuses attention on the most relevant segments of the temporal representation, refining the signal based on internal attention mechanisms. Finally, the ANN component transforms the high-level temporal-attention features into scalar outputs through dense layers. This layered architecture mimics a hierarchical learning strategy—from raw temporal encoding (TCN), to selective weighting (TE), to output transformation (ANN)—which supports both theoretical soundness and practical performance.

The proposed study sets a new benchmark in solar irradiance prediction by combining innovative architecture with comprehensive spatial and temporal coverage. This study’s findings emphasize the value of hybrid models that integrate advanced TCN, TE, and ANN for solving complex forecasting problems. The model’s demonstrated performance highlights its potential for real-world applications, particularly in settings requiring high-frequency solar radiation predictions to support grid operations, energy storage scheduling, and investment scenario modeling. While this study does not include real-world deployment, the proposed framework can serve as a foundation for future tools aimed at supporting decision-making in energy management, policy, and operational planning.

The proposed TCN+TE+ANN hybrid model is designed to extract deep temporal features and attention-based representations from high-frequency solar irradiance data, which requires a moderate level of computational resources. The model was trained on a workstation equipped with an Intel® Core™ i7-14700KF processor, 64 GB RAM, and an NVIDIA RTX 3060 GPU. Training the full model—including hyperparameter tuning—took approximately 10 to 12 h, demonstrating its feasibility for research-scale and periodic retraining scenarios. While this setup is suitable for offline training and periodic updates, deployment in real-time or resource-constrained environments may not be feasible with the full architecture. To address this, future implementations could adopt simplified versions of the model. Options include using:

• A TCN-only architecture, which retains strong temporal modeling while reducing complexity;

• A lightweight ANN model trained on selected time-windowed features;

• Quantized or pruned versions of the current model to reduce memory and inference time;

• Integration with on-device learning frameworks such as TensorFlow Lite or ONNX Runtime.

These alternatives offer practical trade-offs between accuracy and computational efficiency and are well-suited for embedded or edge-level deployment scenarios such as microgrids and mobile solar monitoring systems.

While the current model architecture inherently captures temporal dependencies through the use of TCN and TE, future research could explore the use of cyclical temporal features—such as time of day or day of year—encoded via sine and cosine transformations. These representations may be particularly useful for models that do not explicitly handle temporal sequences, offering a way to capture seasonality and diurnal patterns in solar irradiance more effectively.

Due to the absence of publicly available code or detailed configurations for many of the comparative models referenced, this study did not replicate baseline methods for statistical testing. As a result, formal significance testing could not be conducted under controlled, identical conditions. In future work, the development of a shared evaluation benchmark using open-source implementations across hybrid models would allow for more rigorous, statistically grounded comparisons.

While the proposed model demonstrates significant improvements in predictive accuracy over prior methods, the current study does not quantify the downstream operational impact of these improvements—such as energy savings, avoided curtailment, or improved grid stability. Estimating these effects would require integration with grid simulation tools or real-time operational datasets. Future research could bridge this gap by assessing how improved solar irradiance predictions affect specific energy management outcomes, including economic dispatch, battery scheduling, and demand-side control.

Although the model achieved consistently strong performance across all three sites, small variations in prediction accuracy were observed. Copper Mountain had a slightly higher average MAE (0.03310 W/m²) compared to Desert Sunlight (0.02985 W/m²) and Solar Star (0.02865 W/m²), possibly reflecting localized atmospheric complexity or sensor differences. The overall range of MAE values (0.02510–0.03526 W/m²) and standard deviation (0.00244) indicate a robust and stable model. Nonetheless, these findings suggest that minor performance differences could be further reduced through location-specific tuning or the inclusion of additional meteorological inputs.

Conclusions

As discussed earlier, this study introduces a state-of-the-art hybrid model integrating TCN, TE, and ANN to improve the accuracy of GHI prediction. By leveraging the unique strengths of each component, the proposed TCN+TE+ANN architecture demonstrates significant advancements in predictive accuracy, as evidenced by the high R² values and low error metrics achieved across three major solar energy production sites in the US. The utilization of a 22-year dataset with a 30-min temporal resolution highlights the model’s robustness and its ability to capture both short- and long-term patterns in solar irradiance effectively.

A comparative analysis with previous studies underscores the superiority of the proposed model in terms of performance, dataset scope, and temporal resolution, setting a new standard in solar energy forecasting. Despite these contributions, the study acknowledges certain limitations. First, the geographic focus on U.S. solar sites restricts the validation of the model’s generalizability to other regions with different climatic conditions. Future research should explore the application of the model to datasets from diverse geographic zones such as tropical, continental, or high-latitude regions, including publicly available datasets from Europe (e.g., CAMS), Asia (e.g., Indian Solar Radiation Atlas), or Africa. This would help assess the model’s robustness under varying meteorological and atmospheric conditions and support its broader applicability in global solar forecasting. Second, the computational complexity of the hybrid architecture may pose challenges for deployment in resource-constrained environments. Addressing these limitations in future research could involve expanding the geographic diversity of the dataset to include varied global climates and developing more lightweight model alternatives to balance accuracy and computational efficiency.

The findings of this study highlight the transformative potential of advanced hybrid models in renewable energy forecasting, particularly in improving operational decision-making, grid management, and energy policy development. By providing reliable, high-frequency solar irradiance predictions, this work contributes to the global transition toward sustainable energy systems and aligns with broader goals of environmental preservation and energy independence.

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