Irradiance Forecasting Research Articles

Precise solar radiation forecasting for sustainable energy integration: A hybrid CEEMD-SCM-GA-LGBM model for day-ahead power and hydrogen production

In response to the critical need for sustainable energy solutions, this study introduces a groundbreaking hybrid model for enhancing solar radiation forecasting, which is crucial for optimizing solar power integration and hydrogen production. Leveraging a sophisticated amalgamation of Ensemble Empirical Mode Decomposition (EEMD), Sample Entropy-based System Clustering Method (SCM), Genetic Algorithms (GA), and Light Gradient Boosting Machine (LGBM), the model sets a new benchmark in forecasting accuracy. Tested across diverse seasonal data from Jiangsu province, China, it outperforms conventional models like Multi-Layer Perceptron (MLP) and Long Short-Term Memory (LSTM) networks, achieving exceptional accuracy with an average coefficient of determination (R2) of 0.99, root mean square error (RMSE) of 31.17, and mean absolute error (MAE) of 24.03. The model's practical efficacy was validated through a simulated system comprising a photovoltaic array, a DC-DC converter, and an Alkaline electrolyzer, demonstrating a peak hydrogen production of 0.25 kg at 2:30 p.m. on June 18. This indicates the model's superior capability to forecast solar irradiance accurately, which is essential for enhancing the efficiency of solar energy systems and hydrogen generation. The CEEMD-SCM-GA-LGBM hybrid model's adoption is advocated for solar radiation forecasting, promising significant advancements in the integration of solar energy and the optimization of hydrogen production, aligning with global sustainability objectives.

Satellite‐Based Solar Irradiance Forecasting: Replacing Cloud Motion Vectors by Deep Learning

Satellite‐based (SAT) methods are widely used to forecast surface solar irradiance up to several hours ahead. Herein, a cloud index‐based version of the Heliosat method is applied to infer irradiance from Meteosat Second Generation images. The cloud index (CI) is derived from images in the visible range and quantifies the impact of clouds on surface solar irradiance. Conventional SAT methods utilize cloud motion vectors (CMVs) from consecutive CI images to predict future cloud conditions and subsequently retrieve irradiance. In this study, HelioNet is introduced—a convolutional neural network (CNN) with UNet architecture designed to predict future CI situations from sequences of preceding CI images. Forecasts of two HelioNet configurations are benchmarked against CMV and persistence over a full year (2023), with lead times (LT) up to 4 h. HelioNet15 min recursively generates forecasts at 15 min resolution. HelioNethybrid begins with forecasts at 15 min resolution for , then uses a 45 min resolved model to forecast all remaining LT steps. HelioNet15 min achieves root mean square error (RMSE) improvements of >15% over the CMV model within the first hour on image level. HelioNethybrid shows superior performance for all LT across all metrics considered, with an average RMSE improvement of >11% on image and 8% at irradiance level.

An attention fused sequence -to-sequence convolutional neural network for accurate solar irradiance forecasting and prediction using sky images

The challenge of accurately forecasting ultra-short-term solar irradiance for photovoltaic systems is complicated by rapidly changing weather, and while ground-based sky images offer potential improvements, effectively extracting spatiotemporal data from these images remains a significant hurdle for current computer vision models. A new hybrid model, "An Attention Fused Sequence-to-Sequence Convolutional Neural Network," is being developed to address this challenge. The model predicts intra-hour GHI, DNI, and DHI with a 10-min lead time by combining a Convolutional Neural Network (for spatial feature extraction from sky images), an attention mechanism (to focus on relevant regions), and a sequence-to-sequence model (for temporal feature extraction from time-series data). The proposed Model is trained using the NREL Solar Radiation Research Laboratory Dataset while evaluating the model with the Mean Bias Error, Mean Absolute Error, Root Mean Squared Error, R Squared, and forecasting skill score. The 10-min and sequence length 2 interval is considered to be the best performing across most of the evaluation metrics with an MBE value is 2.321 W/m2, MAE value of 39.490 W/m2, RMSE value of 62.086 W/m2, R2 value is 0.909 W/m2, FSS value of 23.589 W/m2 and an MBE of 4.876 W/m2, MAE of 56.887 W/m2, RMSE of 85.346 W/m2, R2 of 0.834 and FSS of 24.881 W/m2 respectively. Furthermore, the sensitivity analysis reveals that the proposed model's performance is influenced by both the sequence length and the lead time. The proposed framework outperforms other techniques for ultra-short-term PV generation forecasting, demonstrating its potential for practical deployment in PV systems to improve grid reliability and energy management.

Solar irradiation forecast enhancement using clustering based CNN-BiLSTM-attention hybrid architecture with PSO

Accurate solar irradiation forecasting is essential for optimising solar energy use. This paper presents a novel forecasting approach: the ‘Clustering-based CNN-BiLSTM-Attention Hybrid Architecture with PSO’. It combines clustering, attention mechanisms, Convolutional Neural Networks (CNN), Bidirectional Long-Short Term Memory (BiLSTM) networks, and Particle Swarm Optimisation (PSO) into a unified framework. Clustering categorises days into groups, improving predictive capabilities. The CNN-BiLSTM model captures spatial and temporal features, identifying complex patterns. PSO optimises the hybrid model’s hyperparameters, while an attention mechanism assigns probability weights to relevant information, enhancing performance. By leveraging spatial and temporal patterns in solar data, the proposed model improves forecasting accuracy in univariate and multivariate analyses with multi-step predictions. Extensive tests on real-world datasets from various locations show the model’s effectiveness. For example, with NASA power data, the model achieves a Mean Absolute Error (MAE) of 24.028 W/m2, Root Mean Square Error (RMSE) of 43.025 W/m2, and an R 2 score of 0.984 for 1-hour ahead forecasting. The results show significant improvements over conventional methods.

A bidirectional gated recurrent unit based novel stacking ensemble regressor for foretelling the global horizontal irradiance

The rapid expansion of solar power generation has led to new challenges in solar intermittency, requiring precise forecasts of Global Horizontal Irradiance (GHI). Accurate GHI predictions are crucial for integrating sustainable energy sources into traditional electrical grid management. The article proposes an innovative solution, the novel Enhanced Stack Ensemble with a Bi-directional Gated Recurrent Unit (ESE-Bi-GRU), which uses machine learning (ML) boosting regressors such as Ada Boost, Cat Boost, Extreme Gradient Boost, and Gradient Boost, and Light Gradient Boost Machine acts as a base learner and the deep learning (DL) algorithms such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) for both directions are taken as a meta-learner. The predictive performance of the proposed ESE-Bi-GRU model is evaluated against individual models, showing significant reductions in mean absolute error (MAE) by 86.03 % and root mean squared error (RMSE) by 66.43 %. The model's ability to minimize prediction errors, such as MAE and RMSE holds promise for more effective planning and utilization of sporadic solar resources. By improving GHI forecast accuracy, the ESE-Bi-GRU model contributes to optimizing the integration of sustainable energy sources within the broader energy grid, fostering a more sustainable and environmentally conscious approach to energy management.

Leveraging advanced AI algorithms with transformer-infused recurrent neural networks to optimize solar irradiance forecasting

Solar energy (SE) is vital for renewable energy generation, but its natural fluctuations present difficulties in maintaining grid stability and planning. Accurate forecasting of solar irradiance (SI) is essential to address these challenges. The current research presents an innovative forecasting approach named as Transformer-Infused Recurrent Neural Network (TIR) model. This model integrates a Bi-Directional Long Short-Term Memory (BiLSTM) network for encoding and a Gated Recurrent Unit (GRU) network for decoding, incorporating attention mechanisms and positional encoding. This model is proposed to enhance SI forecasting accuracy by effectively utilizing meteorological weather data, handling overfitting, and managing data outliers and data complexity. To evaluate the model’s performance, a comprehensive comparative analysis is conducted, involving five algorithms: Artificial Neural Network (ANN), BiLSTM, GRU, hybrid BiLSTM-GRU, and Transformer models. The findings indicate that employing the TIR model leads to superior accuracy in the analyzed area, achieving R2 value of 0.9983, RMSE of 0.0140, and MAE of 0.0092. This performance surpasses those of the alternative models studied. The integration of BiLSTM and GRU algorithms with the attention mechanism and positional encoding has been optimized to enhance the forecasting of SI. This approach mitigates computational dependencies and minimizes the error terms within the model.

Enhancing solar irradiance forecasting for hydrogen production: The MEMD-ALO-BiLSTM hybrid machine learning model

This study focuses on an innovative hybrid machine-learning model for solar irradiance forecasting, targeting the integration of solar power into hydrogen production systems. Addressing the urgent need for sustainable energy transitions, the paper introduces the MEMD-ALO-BiLSTM model, designed to enhance solar irradiance prediction accuracy. This model uniquely combines Multivariate Empirical Mode Decomposition (MEMD), Ant Lion Optimizer (ALO), and Bidirectional Long Short-Term Memory (BiLSTM) techniques, setting a new benchmark in forecast precision across various seasonal datasets from Jiangsu Province, China. Demonstrating superior performance to traditional models, it achieves an exceptional coefficient of determination, averaging 0.99 for all seasons. Additionally, to prove the efficiency of the model three statistical tests were used, namely Wilcoxon, Friedman, and P-value. The research highlights the model's potential in optimizing photovoltaic systems and hydrogen production, thus contributing to carbon dioxide emission mitigation. Through comprehensive simulations of a residential system encompassing photovoltaic cells, compressors, and electrolyzers, the study underscores the practical feasibility and significant advancements the MEMD-ALO-BiLSTM model offers in the renewable energy sector, promoting a shift toward more reliable and efficient solar-powered hydrogen generation systems. Accordingly, the day-ahead values of photovoltaic-generated power and hydrogen production through the electrolyzer reached peak values at 1:00PM with approximately 75 kW and 1.4 kg, respectively.

EMD-based ultraviolet radiation prediction for sport events recommendation with environmental constraint

With the rising awareness of health and wellness, accurate ultraviolet (UV) radiation forecasts have become crucial for planning and conducting outdoor activities safely, particularly in the context of global sporting events arrangement and recommendation with definite constraint on environmental conditions. The dynamic nature of UV exposure, influenced by factors such as solar zenith angles, cloud cover, and atmospheric conditions, makes accurate UV radiation data forecasting difficult and challenging. To cope with these challenges, we present an innovative approach for predicting the UV radiation levels of a certain region during a certain time period using Empirical Mode Decomposition (EMD), a robust method for analyzing non-linear and non-stationary data. Our model is specifically designed for urban areas, where outdoor events are common, and integrates meteorological data with historical UV radiation records from specific geographic regions and time periods. The EMD-based model offers precise predictions of UV levels, essential for event organizers and city planners to make informed decisions regarding the scheduling, relocation and recommendation of events to minimize health risks associated with UV exposure. At last, the effectiveness of this model is validated through various experiments across different spatial and temporal contexts based on the Urban-Air dataset (recording 2,891,393 Air Quality Index data that cover four major Chinese cities), demonstrating its adaptability and accuracy under diverse environmental conditions.

PAOFCDN: A novel method for predictive analysis of solar irradiance

Solar photovoltaic power is the most feasible Renewable Energy Source (RES) for Pakistan, due to ample sunlight availability throughout the year. Since solar photovoltaic power is primarily dependent on solar irradiance, forecasting of solar irradiance is essential for reliable, secure and effective incorporation of solar photovoltaic power in power systems. Considering the importance of solar irradiance forecasting, in this study, predictive analysis of Islamabad’s solar irradiance is performed by using a novel proposed model named as Pelican Algorithm-based Optimized Fully-Connected Deep Network (PAOFCDN). The initial weights of Fully-Connected Deep Network (FCDN) are optimized through an effective optimization technique known as Pelican optimization. The accuracy of the optimized network PAOFCDN is enhanced many fold as compared to the FCDN network trained with randomly initialized weights. The inherent issue of poor generalization in FCDN is also resolved by optimization. The superior performance of PAOFCDN is evident from its comparative evaluation with existing benchmark methods, i.e., Long Short-Term Memory (LSTM), Support Vector Regression (SVR), Least Square Boosting (LSBoost) and standard FCDN. PAOFCDN achieves the least Normalized Root Mean Square Error (NRMSE) of 0.0503 as compared to 0.1179 of LSTM, 0.1256 of FCDN, and 0.2992 of SVR and LSBoost. The proposed model is applied to three real-world solar irradiance datasets having different resolutions of 10-minutes, hourly and daily. This study took the initiative of performing predictions on three datsets having multiple resolutions in perspective of south asia.

The added value of combining solar irradiance data and forecasts: A probabilistic benchmarking exercise

Despite the growing awareness in academia and industry of the importance of solar probabilistic forecasting for further enhancing the integration of variable photovoltaic power generation into electrical power grids, there is still no benchmark study comparing a wide range of solar probabilistic methods across various local climates. Having identified this research gap, experts involved in the activities of IEA PVPS T1611International Energy Agency - Photovoltaic Power Systems - Solar Resource for High Penetration and Large Scale Applications. agreed to establish a benchmarking exercise to evaluate the quality of intra-hour and intra-day probabilistic irradiance forecasts.The tested forecasting methodologies are based on different input data including ground measurements, satellite-based forecasts and Numerical Weather Predictions (NWP), and different statistical methods are employed to generate probabilistic forecasts from these. The exercise highlights different forecast quality depending on the method used, and more importantly, on the input data fed into the models.In particular, the benchmarking procedure reveals that the association of a point forecast that blends ground, satellite and NWP data with a statistical technique generates high-quality probabilistic forecasts. Therefore, in a subsequent step, an additional investigation was conducted to assess the added value of such a blended point forecast on forecast quality. Three new statistical methods were implemented using the blended point forecast as input.To ensure a fair evaluation of the different methods, we calculate a skill score that measures the performance of the proposed model relative to that of a trivial baseline model. The closer the skill score is to 100%, the more efficient the method is. Overall, skill scores of methods that use the blended point forecast ranges from 42% to 46% for the intra-hour scenario and 27% to 32% for the intra-day scenario. Conversely, methods that do not use the blended point forecast exhibit skill scores ranging from 33% to 43% for intra-hour forecasts and 8% to 16% for intra-day forecasts.These results suggest that using (a) blended point forecasts that optimally combine different sources of input data and (b) a post-processing with a statistical method to produce the quantile forecasts is an effective and consistent way to generate high-quality intra-hour or intra-day probabilistic forecasts.

Dataset for Machine Learning: Explicit All-Sky Image Features to Enhance Solar Irradiance Prediction

Prediction of solar irradiance is crucial for photovoltaic energy generation, as it helps mitigate intermittencies caused by atmospheric fluctuations such as clouds, wind, and temperature. Numerous studies have applied machine learning and deep learning techniques from artificial intelligence to address this challenge. Based on the recently proposed Hybrid Prediction Method (HPM), this paper presents an original and comprehensive dataset with nine attributes extracted from all-sky images developed using image processing techniques. This dataset and analysis of its attributes offer new avenues for research into solar irradiance forecasting. To ensure reproducibility, the data processing workflow and the standardized dataset have been meticulously detailed and made available to the scientific community to promote further research into prediction methods for photovoltaic energy generation.

Machine learning and deep learning models based grid search cross validation for short-term solar irradiance forecasting

In late 2023, the United Nations conference on climate change (COP28), which was held in Dubai, encouraged a quick move from fossil fuels to renewable energy. Solar energy is one of the most promising forms of energy that is both sustainable and renewable. Generally, photovoltaic systems transform solar irradiance into electricity. Unfortunately, instability and intermittency in solar radiation can lead to interruptions in electricity production. The accurate forecasting of solar irradiance guarantees sustainable power production even when solar irradiance is not present. Batteries can store solar energy to be used during periods of solar absence. Additionally, deterministic models take into account the specification of technical PV systems and may be not accurate for low solar irradiance. This paper presents a comparative study for the most common Deep Learning (DL) and Machine Learning (ML) algorithms employed for short-term solar irradiance forecasting. The dataset was gathered in Islamabad during a five-year period, from 2015 to 2019, at hourly intervals with accurate meteorological sensors. Furthermore, the Grid Search Cross Validation (GSCV) with five folds is introduced to ML and DL models for optimizing the hyperparameters of these models. Several performance metrics are used to assess the algorithms, such as the Adjusted R2 score, Normalized Root Mean Square Error (NRMSE), Mean Absolute Deviation (MAD), Mean Absolute Error (MAE) and Mean Square Error (MSE). The statistical analysis shows that CNN-LSTM outperforms its counterparts of nine well-known DL models with Adjusted R2 score value of 0.984. For ML algorithms, gradient boosting regression is an effective forecasting method with Adjusted R2 score value of 0.962, beating its rivals of six ML models. Furthermore, SHAP and LIME are examples of explainable Artificial Intelligence (XAI) utilized for understanding the reasons behind the obtained results.

An Improved Spatiotemporal Time Series Modelling Procedure with Application to Forecasting of Solar Radiation

The demand for energy and associated services to meet sustainable agricultural and economic growth and improve human health and lifestyle is increasing day by day. Hence, there is a need for systematic and scientific prediction of solar and other renewable sources of energy to meet these requirements. The main purpose of this study is to propose a hybrid Space-Time Autoregressive Moving Average Artificial Neural Network (STARMA-ANN) model for the precise and accurate forecasting of solar radiation for better planning and policy making. This approach has been implemented at seven geographical locations of Bihar in India. Spatial weight matrices have been used to describe all seven geographical locations and incorporated into the STARMA model to reflect the spatial and temporal correlation. To deal with nonlinear dynamics in the spatiotemporal data, ANN technique has been applied on residuals of the fitted STARMA model. The results have demonstrated that the proposed hybrid model performs better prediction accuracy than using conventional STARMA model, especially for spatiotemporal data with nonlinear characteristics of solar radiation.

InFLuCs: Irradiance Forecasting Through Reinforcement Learning Tuned Cascaded Regressors

InFLuCs: Irradiance Forecasting Through Reinforcement Learning Tuned Cascaded Regressors

Ultra-short-term global horizontal irradiance forecasting based on a novel and hybrid GRU-TCN model

The need for energy is increasing globally due to a several factors, including population growth and economic development. Achieving this energy demand in the face of global warming and the depletion of fossil fuels requires the use of renewable energy. Photovoltaic energy is one of the renewable energy sources that is widely used in many nations across the world. Photovoltaic (PV) energy integration into the grid has significant benefits for the environment and economy, but at high penetration levels, its intermittent nature makes system stability difficult to maintain. Accurate ultra-short-term global horizontal irradiance forecasting is necessary in order to guarantee the most optimal use of photovoltaic power production sources. For GHI forecasting, a novel GRU-TCN-based model is proposed in this paper. It is composed of two neural networks: a temporal convolutional network and a gated recurrent unit. After extracting the temporal features from time-series solar irradiance data using GRU, the spatial features are obtained from the correlation matrix of different meteorological variables of the target and its neighbor position using TCN. Univariate and multivariate GRU-TCN models have been used for GHI ultra short-term forecasting. This paper compares the univariate and multivariate GRU-TCN models with TCN, LSTM, and GRU models based on three evaluation metrics in order to investigate how different combinations of variables affect the accuracy of the GRU-TCN models for one-step forecasting. The findings indicate the adoption of a univariate model using historical data of GHI is suitable to obtain reliable forecasting with 23.02 (W/m2) in MAE as opposed to the best multivariate model that achieved 25.67 (W/m2) in MAE. According to the results, the proposed model outperforms the other models assessed and offers a practical alternative for ultra-short-term GHI forecasting.

Solar Irradiance Forecasting for Informed Solar Systems Design and Financing Decisions

Solar Irradiance Forecasting for Informed Solar Systems Design and Financing Decisions

Artificial Intelligence-Based Improvement of Empirical Methods for Accurate Global Solar Radiation Forecast: Development and Comparative Analysis

Artificial intelligence (AI) technology has expanded its potential in environmental and renewable energy applications, particularly in the use of artificial neural networks (ANNs) as the most widely used technique. To address the shortage of solar measurement in various places worldwide, several solar radiation methods have been developed to forecast global solar radiation (GSR). With this consideration, this study aims to develop temperature-based GSR models using a commonly utilized approach in machine learning techniques, ANNs, to predict GSR using just temperature data. It also compares the performance of these models to the commonly used empirical technique. Additionally, it develops precise GSR models for five new sites and the entire region, which currently lacks AI-based models despite the presence of proposed solar energy plants in the area. The study also examines the impact of varying lengths of validation datasets on solar radiation models’ prediction and accuracy, which has received little attention. Furthermore, it investigates different ANN architectures for GSR estimation and introduces a comprehensive comparative study. The findings indicate that the most advanced models of both methods accurately predict GSR, with coefficient of determination, R2, values ranging from 96% to 98%. Moreover, the local and general formulas of the empirical model exhibit comparable performance at non-coastal sites. Conversely, the local and general ANN-based models perform almost identically, with a high ability to forecast GSR in any location, even during the winter months. Additionally, ANN architectures with fewer neurons in their single hidden layer generally outperform those with more. Furthermore, the efficacy and precision of the models, particularly ANN-based ones, are minimally impacted by the size of the validation data sets. This study also reveals that the performance of the empirical models was significantly influenced by weather conditions such as clouds and rain, especially at coastal sites. In contrast, the ANN-based models were less impacted by such weather variations, with a performance that was approximately 7% better than the empirical ones at coastal sites. The best-developed models, particularly the ANN-based models, are thus highly recommended. They enable the precise and rapid forecast of GSR, which is useful in the design and performance evaluation of various solar applications, with the temperature data continuously and easily recorded for various purposes.

Accurate Forecasting of Global Horizontal Irradiance in Saudi Arabia: A Comparative Study of Machine Learning Predictive Models and Feature Selection Techniques

Accurate Forecasting of Global Horizontal Irradiance in Saudi Arabia: A Comparative Study of Machine Learning Predictive Models and Feature Selection Techniques

Evaluation of Scikit-Learn Machine Learning Algorithms for Improving CMA-WSP v2.0 Solar Radiation Prediction

This article aims to evaluate the performance of solar radiation forecasts produced by CMA-WSP v2.0 (version 2 of the China Meteorological Administration Wind and Solar Energy Prediction System) and to explore the application of machine learning algorithms from the scikit-learn Python library to improve the solar radiation prediction made by the CMA-WSP v2.0. It is found that the performance of the solar radiation forecasting from the CMA-WSP v2.0 is closely related to the weather conditions, with notable diurnal fluctuations. The mean absolute percentage error (MAPE) produced by the CMA-WSP v2.0 is approximately 74% between 11:00 and 13:00. However, the MAPE ranges from 193% to 242% at 07:00–08:00 and 17:00–18:00, which is greater than that observed at other daytime periods. The MAPE is relatively low (high) for both sunny and cloudy (overcast and rainy) conditions, with a high probability of an absolute percentage error below 25% (above 100%). The forecasts tend to underestimate (overestimate) the observed solar radiation in sunny and cloudy (overcast and rainy) conditions. By applying machine learning models (such as linear regression, decision trees, K-nearest neighbors, random forests regression, adaptive boosting, and gradient boosting regression) to revise the solar radiation forecasts, the MAPE produced by the CMA-WSP v2.0 is significantly reduced. The reduction in the MAPE is closely connected to the weather conditions. The models of K-nearest neighbors, random forests regression, and decision trees can reduce the MAPE in all weather conditions. The K-nearest neighbor model exhibits the most optimal performance among these models, particularly in rainy conditions. The random forest regression model demonstrates the second-best performance compared to that of the K-nearest neighbor model. The gradient boosting regression model has been observed to reduce the MAPE of the CMA-WSP v2.0 in all weather conditions except rainy. In contrast, the adaptive boosting (linear regression) model exhibited a diminished capacity to improve the CMA-WSP v2.0 solar radiation prediction, with a slight reduction in MAPE observed only in sunny (sunny and cloudy) conditions. In addition, the input feature selection has a considerable influence on the performance of the machine learning model. The incorporation of the time series data associated with the diurnal variation of solar radiation as an input feature can further improve the model’s performance.

An Enhanced Forecasting Method of Daily Solar Irradiance in Southwestern France: A Hybrid Nonlinear Autoregressive with Exogenous Inputs with Long Short-Term Memory Approach

The increasing global reliance on renewable energy sources, particularly solar energy, underscores the critical importance of accurate solar irradiance forecasting. As solar capacity continues to grow, precise predictions of solar irradiance become essential for optimizing the performance and reliability of photovoltaic (PV) systems. This study introduces a novel hybrid forecasting model that integrates Nonlinear Autoregressive with Exogenous Inputs (NARX) with Long Short-Term Memory (LSTM) networks. The purpose is to enhance the precision of predicting daily solar irradiance in fluctuating meteorological scenarios, particularly in southwestern France. The hybrid model employs the NARX model’s capacity to handle complex non-linear relationships and the LSTM’s aptitude to manage long-term dependencies in time-series data. The performance metrics of the hybrid NARX-LSTM model were thoroughly assessed, revealing a mean absolute error (MAE) of 9.58 W/m2, a root mean square error (RMSE) of 16.30 W/m2, and a Coefficient of Determination (R2) of 0.997. Consequently, the proposed hybrid model outperforms the benchmark model in all metrics, showing a significant improvement in prediction accuracy and better alignment with the observed data. These results highlight the model’s effectiveness in enhancing forecasting accuracy under unpredictable conditions, improving solar energy integration into power systems, and ensuring more reliable energy predictions.