1. Introduction

The global transition toward sustainable energy sources underscores the critical importance of accurate forecasting for renewable energy systems [1]. Among these, photovoltaic (PV) power generation stands out as a prominent and rapidly growing renewable energy technology. However, the intermittent and variable nature of solar energy necessitates precise prediction methods to optimize its integration into the power grid and ensure reliable energy supply [2, 3]. Exploring PV systems is critical in the broader context of renewable energy utilization, particularly in addressing global energy challenges and transitioning toward sustainable energy sources. PV systems play a central role in the renewable energy landscape, serving as pivotal components in hybrid energy systems that integrate various renewable and traditional energy sources. Their significance extends to applications such as grid integration [4], energy forecasting [5–7], voltage regulation [8], battery lifetime maximization [9], and microgrid management [10, 11] where they contribute to enhancing the reliability and stability of energy supply. In addition to their role in energy generation, PV systems also drive innovation in energy optimization techniques, notably through the development of maximum power point tracking (MPPT) methodologies [12]. These techniques are essential for maximizing the efficiency of solar PV arrays, thereby increasing their power output and overall performance. By harnessing the potential of MPPT strategies, PV systems can better adapt to changing environmental conditions and optimize energy capture, making them more versatile and resilient in renewable energy ecosystems. Furthermore, the modeling of PV systems, which often involves the representation of complex electrical characteristics using multidiode equivalent circuits [13, 14], underscores the multifaceted nature of PV technology.

The prediction of PV power encompasses various classifications based on prediction procedures, spatial scales, forms, and methodologies [15]. Meteorological variables play a fundamental role in determining the output of PV systems, as solar irradiance, temperature, and other weather parameters directly influence energy production. Leveraging advancements in data analytics and machine learning (ML), researchers have increasingly explored hybrid approaches that integrate meteorological data into prediction models to enhance the accuracy of PV power forecasts. Notably, in recent years, deep learning (DL) methodologies have attracted considerable attention regarding their outstanding capabilities in extracting and transforming features, leading to notable advancements in PV power prediction [16]. Among these methodologies, long short-term memory (LSTM) stands out as a classical DL characterized by its distinctive architecture. This architecture facilitates the transfer of pertinent information utilizing memory units, rendering LSTM particularly suitable for PV power forecasting tasks [17]. Previous studies have struggled to improve forecasting accuracy by modifying the structure of LSTM networks. However, a groundbreaking study [18] incorporated LSTM into an autonomous PV day-ahead energy projection system and introduced a corrective approach that accounts for the connection between various PV energy production patterns of PV power generation. Moreover, convolutional neural networks (CNNs) demonstrate remarkable proficiency in extracting meaningful features from extensive training datasets. Utilizing multiple convolutional kernels as feature extractors, CNNs significantly enhance feature extraction performance.

The integration of many models is a potential way to capitalize on their individual strengths and efficiently leverage data gathered from PV power measurements and weather data series, as opposed to the limits faced with single-model forecasts. This integrated approach yields significant improvements in prediction accuracy. For instance, the fusion of CNN and LSTM models, as demonstrated in [19], showcases the superiority of the combined model over individual models. This was evidenced by experiments conducted on real-world datasets from Morocco, where the integrated CNN-LSTM model exhibited enhanced predictive capabilities. Similarly, in [20], the composite long short-term memory (CLSTM) model was optimized using an advanced sparrow searching optimization (SSO). Regarding parameters acquired through enhanced SSO, the CLSTM model outperformed individual neural networks such as backpropagation (BP), CNN, and LSTM, as well as unoptimized CLSTM models. In another study [21], a method was presented that combined CNN for extracting features with inputs from the Informer model, making use of methods for determining periodic feature correlation between historical information. The strategy results in accurate PV power predictions, highlighting the effectiveness of leveraging information source modeling techniques. The deterministic approach of point prediction method lacks the capability to account for the probability distribution and range of fluctuations in prediction outcomes. Particularly in intricate weather conditions, PV power generation experiences notable fluctuations within short time frames. This makes point prediction systems less accurate and makes it more difficult to maintain a secure and reliable electricity supply. In contrast, probabilistic density (PD) prediction provides an enhanced forecasting method such as quantile regression (QR) and kernel density estimation (KDE), which enable providers make better decisions by allowing them to establish intervals for prediction in regard to the PD function.

The paper’s structure is organized as follows: Section 2 provides a detailed description of the features present in the DKASC Hanwha Solar dataset, including PV output power and meteorological variables collected from sensors. Section 3 elaborates on the methodologies employed in the study, outlining the process of feature selection techniques, integration of meteorological data, and the utilization of multiple regression algorithms to develop the hybrid predictive model framework. The findings from the hybrid predictive model’s testing and assessment are examined in Section 4. Finally, Section 5 summarizes the main research findings and addresses the conclusions by summarizing the key outcomes of the research.

2. Feature Description and Data Set Overview

This study focuses on utilizing the DKASC Hanwha Solar dataset as the primary dataset [38]. The dataset includes the output power of the PV system (Hanwha Solar, 5.8 kW, poly-Si, Fixed, 2016) and meteorological data gathered from sensors between January 1 and December 31, 2020. Figure 1 shows the DKASC map and Hanwha Solar system location. The weather data comprise crucial meteorological variables, including radiation data, relative humidity, temperature, and rainfall. Everyday data gathered between 6:00 AM and 7:00 PM was kept for analysis to maintain result accuracy, taking into account the low power output in the early hours of the day. The dataset has a raw resolution of 5-min intervals, comprising 163 sampling points per day. The dataset, structured as a time series, consists of 57,450 samples with 10 distinct features. The study utilized a training-to-test ratio of 7:3 for model evaluation.

Table 1 provides an illustration of the attributes’ description, and Figure 2 shows the distribution of meteorological data.

3. Methodology and the Proposed Approach

3.1. Regression Analysis Techniques

ML regression analysis is a predictive modeling technique used to understand the relationship between a dependent variable (often referred to as the target or output) and one or more independent variables (also known as features or inputs). The primary goal is to predict continuous values, as opposed to discrete labels, which are the focus of classification tasks. This analysis method is commonly employed across various fields, including sales forecasting, stock price estimation, credit scoring, and energy consumption prediction (e.g., forecasting energy usage in buildings or industrial processes). Regression analysis in ML comes in various forms, with the choice of method depending on the specific nature of the data.

There are various regression methods such as linear regression, ridge regression, Least Absolute Shrinkage and Selection Operator (LASSO) regression, Elastic Net, Extra Trees Regressor, random forest regressor, GB regressor, and XGBoost Regressor. To address of how these model process the used meteorological data for solar power prediction, the main steps can be summarized as follows:

Step 1. Data collection: Meteorological data (e.g., solar radiation, temperature, humidity, and wind speed) and the corresponding solar power output data are collected.

Step 2. Data preprocessing: Missing values are handled, outliers are removed, and any errors in the data are corrected. Also, features are normalized to ensure they are on a similar scale, which is particularly important for methods sensitive to feature scales.

Step 3. Feature selection process: The most relevant features for the model are identified and selected. Then, the raw data are transformed into meaningful features to improve model performance. In this step, various feature selection techniques are discussed such as PC, VIF, MI, SFS, BE, RFE, and EM. A general overview of the steps involved in applying feature selection techniques to identify the most influential factors for PV power prediction can be described as follows:

Step 3.1. Apply feature selection techniques:

• •

  Correlation analysis: PC is used to assess the linear relationships between each feature and the PV power output. Also, VIF is computed to detect multicollinearity and remove or combine features with high VIF values.

• •

  MI: The MI between each feature and the PV power output is calculated to measure the nonlinear dependency. Then, the features are ranked based on their MI scores and select the most relevant ones.

• •

  SFS: It starts with no features and iteratively adds features that improve model performance the most. Then, the model performance is evaluated at each step using cross-validation or a performance metric.

• •

  BE: It starts with all features and iteratively removes the least significant feature based on model performance. Then, metrics like p-values or feature importance scores are utilized to decide which features to remove.

• •

  RFE: The model is trained with all features, and they are ranked based on their importance. The least important features are iteratively removed, and the model is retrained until the desired number of features is reached.

• •

  EM: LASSO regression or tree-based models like random forests or XGBoost models are incorporated as part of the training process. Then, the feature importance directly from these models is selected.

Step 3.2. Evaluate the selected features: After utilizing various feature selection methods, each generates a set of selected features. These sets are then tested using a random forest regressor model, and the prediction accuracy is compared across the different methods (the results are tabulated and compared in Table 2).

Table 2. Output metrics for the final features selected by each feature selection method.

Method	No. of selected features	RMSE	R2
PC	5	0.166435	0.991222
VIF	4	0.192499	0.988257
MI	5	0.158889	0.992000
SFS	5	0.160618	0.991825
BE	6	0.164447	0.991430
RFE	4	0.168400	0.991014
EM	2	0.182029	0.989500

• Abbreviations: BE, backward elimination; EM, embedded method; MI, mutual information; PC, Pearson correlation; RFE, recursive feature elimination; RMSE, root mean square error; SFS, step forward selection; VIF, variance inflation factor.

Step 3.3. Finalize feature set: Based on the evaluation results, the feature selection methods that yield the highest accuracy are chosen, and their selected features are compared to identify common ones. A threshold value of 1 is used, so features selected by more than one method are considered, with these common features designated as primary features.

Step 4. Model training: The data are divided into training and test sets to assess model performance. Then, the chosen regression model is implemented to fit the training data, using the selected primary features to predict solar power output.

Step 5. Model evaluation: The trained model is evaluated on the test set to check its performance on unseen data. Also, the metrics of RMSE, mean absolute error (MAE), and R² are evaluated to assess accuracy.

Step 6. Prediction: The trained model is utilized to predict solar power output based on new or future meteorological data.

These steps provide a structured approach to utilizing meteorological data for solar power prediction, regardless of the specific regression technique used.

3.1.1. Linear Regression

Methods of regression play a key role in studying data. Of all, linear regression is most likely the most popular. Linear regression enables us to examine data in an easy-to-understand manner. Linear regression is the process of fitting an equation with straight lines to data that you observe. One variable is assumed to explain the other. A linear regression line’s equation is as follows [39]:

$$ (1)

In this case, X serves as the explanatory variable, and Y represents the dependent variable. The value of Y at X = 0 is the intercept, and the slope of the line is b. The least squares approach is the most popular strategy to determine a regression line [39]. This calculates the best line for data. It minimizes vertical distances squared from each point to line. Figure 3 shows an example of linear regression line and some data points.

3.1.2. Ridge Regression

Ridge regression is a specific method for analyzing multicollinear multiple regression data. A phenomenon known as multicollinearity occurs when a given degree of accuracy is reached in several regression models by linearly predicting one projected value along with others [40]. High correlations between more than two predicted variables are the basic cause of multicollinearity. A typical linear regression equation with numerous variables is [40]:

$$ (2)

This is a standard, multiple-variable linear regression equation. In this case, X is any predictor (independent variable), B is the regression coefficient associated with that independent variable, Y is the expected value (dependent variable), and X₀ is the value of the dependent variable (also known as the Y-intercept) when the independent variable equals zero.

3.1.3. LASSO Regression

L1 regularization, another name for LASSO regression, is a widely used method in ML and statistical modeling that estimates and predicts the associations between variables [41]. LASSO regression makes predictions more accurate by shrinking data values. It shrinks the values toward a central point like the mean. This helps the model make better predictions by reducing errors.

Because LASSO regression can automatically choose variables, it is perfect for predictive problems as it can simplify models and improve prediction accuracy [40]. However, because LASSO regression generates more bias by decreasing coefficients toward zero, ridge regression might perform better than LASSO regression. Because it picks a feature at random to include in the model, it also has issues with linked features in the data.

3.1.4. Elastic Net Regression

Elastic Net regression combines the best aspects of ridge and LASSO regression [42]. Elastic Net is a hybrid of LASSO and ridge, the two most often used regularized forms of linear regression. While LASSO uses an L1 penalty, ridge uses an L2 penalty. Elastic Net utilizes both the L2 and the L1 penalty, so you do not have to pick between these two models [42].

Elastic Net regression is used to deal with the problems of multicollinearity and overfitting, which are frequently seen in high-dimensional datasets. Comparing Elastic Net regression to LASSO and ridge regression, there are a number of benefits. For choosing features, Elastic Net performs feature selection, which facilitates model interpretation. It manages multicollinearity between variables by grouping them, which can be very useful in certain datasets. Finally, it balances ridge and LASSO regression to handle the bias-variance trade-off.

3.1.5. Extra Trees Regressor

Extra Trees (short for excessively randomized trees) Regressor is an ensemble supervised ML method that employs decision trees [43]. The additional trees algorithm, like the random forest approach, creates a huge number of decision trees, but it does so randomly and without replacement for each tree.

This creates a dataset where each tree has a unique sample. In addition, a certain set of features are chosen at random for each tree. The most significant and unique characteristic of Extra Trees is the random selection of a splitting value for a feature. Instead of splitting the data and determining a locally optimum value using entropy or Gini, the method selects a split value at random. The trees become diverse and uncorrelated as a result. Random forest is slower than this technique. A simplified representation of the Extra Trees approach regression procedure is presented in Figure 4.

3.1.6. Random Forest Regressor

It is an algorithm for supervised learning that provides regression using an ensemble learning technique. It is not a boosting approach; rather, it is a bagging technique [44]. Since the trees in random forests grow in parallel, there is no contact between them as they are growing. The random forests algorithm makes its final forecast by averaging the predictions of several decision trees that were trained on a dataset with a real tree structure.

Since the random forests algorithm performs well with high-dimensional data, missing values, and outliers, they are regarded as strong and powerful ML models. They also do not require a lot of hyperparameter tweaking and are comparatively simple to utilize.

3.1.7. GB Regressor

GB has become a popular ML technique for issues involving regression and classification. Several weak learners are combined into one stronger model using this ensemble learning technique [45, 46]. GB’s primary concept is to repeatedly add new, vulnerable learners to the model while training each one to fix the errors created by the prior ones [47]. Decision trees are commonly used in GB [48]. The loss function is commonly used as the objective function for GB classifiers, quantifying the difference between the expected and actual output. GB is a very useful technique for addressing missing data, outliers, and huge cardinality categories on the features with no requiring further processing. It is capable of detecting any nonlinear relationship that exists between the features and the model target.

3.1.8. XGBoost Regressor

XGBoost, or eXtreme GB, is a ML technique that is a part of the GB framework, which is a subset of ensemble learning. It makes use of regularization techniques to improve model generalization using decision trees as foundation learners. XGBoost is a popular choice for computationally demanding tasks including regression and classification due to its proficiency in feature importance analysis, management of missing information, and computational economy [49]. XGBoost creates a predictive model by repeatedly integrating the predictions of several different models, most frequently decision trees. The way the algorithm operates is by gradually adding weak learners to the ensemble, with each new learner concentrating on fixing any errors produced by the previous ones. During training, it minimizes a predetermined loss function using the gradient descent optimization method. The capacity to manage complicated relationships in data, regularization strategies to avoid overfitting, and the use of parallel processing for effective computing are some of the main characteristics of the XGBoost algorithm [50]. XGBoost is frequently employed in several domains due to its great prediction performance and adaptability across multiple datasets.

3.3. Proposed Approach

This part covers the general procedures of the suggested model, the feature selection method, and the key performance measures that are utilized to assess the suggested model’s efficacy.

3.3.1. Overview of the Proposed Model

Figure 5 provides an overview of the proposed model.

As is shown, the collected data are first analyzed to identify and address any missing values, which are then replaced with the most appropriate values. Different strategies for handling missing data include imputation or deletion. Specifically, if a missing value is detected in the active power column, the entire row is removed. For other missing values, the mean imputation is used, which involves calculating the mean of the observed values for each variable and substituting the missing values with this mean. After addressing the missing values, the data are standardized [55] to ensure that all features are on a comparable scale, preventing any single feature from disproportionately affecting the learning process. The standard scale method is employed for standardization [55], as described by Equation (6):

$$ (6)

where µ is the mean [55] given by Equation (7):

$$ (7)

and σ is the standard deviation [55] given by Equation (8):

$$ (8)

The dataset is then split into two categories: testing and training, wherein 70% of the data are used for the training phase and the remaining 30% are used for testing. To solve the overfitting problem, seven different feature selection methods PC, VIF, MI, SFS, BE, RFE, and EM are considered in order to choose the most relevant features and address the overfitting issue.

3.3.2. Feature Selection

The DKASC Hanwha Solar dataset comprises 10 columns, as detailed in Section 2. Columns 2 through nine contain meteorological data, which includes eight features that we need to analyze carefully to select only the most important ones for maximizing power prediction accuracy. We employ various feature selection methods, generating a set of selected features for each method. Each set of selected features is tested using a random forest regressor model, and the accuracy of power predictions is compared across methods. The feature selection methods that yield the highest accuracy are chosen, and the sets of selected features are then compared to identify common features, which are designated as primary features. Utilizing these most relevant features can enhance model performance by focusing on the most informative data.

The primary features used by ML models are constructed based on the list of selected features based on seven different techniques: PC, VIF, MI, SFS, BE, RFE, and EM. A robust strategy is to test models using alternative ways to choose features (and quantities of features) and choose the one that yields a model having the greatest efficiency. There are actually numerous methods to rate features and choose features according to these scores. Compared to linear regression, random forest is a robust ML technique that may produce superior outcomes. It consists of a group of decision trees, which are far more effective than linear models at capturing nonlinear correlations between data and goal variables. This section will compare various models constructed from features chosen using the seven distinct ways to an evaluation of a random forest regressor model with all features.

Figure 6 displays the heatmap regarding the PC coefficient, to assess how linear the relationship is between two variables. In this map, darker colors indicate strong positive correlations, while lighter colors indicate strong negative correlations.

As seen in Figure 6, the PC coefficient heatmap provides a more understandable representation of the dependency between variables. From PC heatmap, Weather Relative Humidity, Global Horizontal Radiation, Diffuse Horizontal Radiation, Radiation Global Tilted, and Radiation Diffuse Tilted based on the degree of association are chosen. Additionally, the VIF is utilized as a measure to determine the degree of multicollinearity among multiple regression variables. The following features were chosen using VIF: Radiation Global Tilted, Weather Daily Rainfall, Diffuse Horizontal Radiation, and Weather Relative Humidity. Also, MI is utilized to measure how much knowing one thing helps reduce the uncertainty about the other. It is a way to quantify the connection between two quantities. Data visualization is a great follow-up to utility ranking. Figure 7 illustrates the MI score, and features with a high score are selected. Radiation Global Tilted, Global Horizontal Radiation, Radiation Diffuse Tilted, Diffuse Horizontal Radiation, and Weather Temperature Celsius are the features that have been chosen.

Moreover, Weather Temperature Celsius, Weather Relative Humidity, Global Horizontal Radiation, Radiation Global Tilted, and Radiation Diffuse Tilted are the features that were chosen using the SFS technique. The following features were chosen using the BE technique: Wind Direction, Global Horizontal Radiation, Weather Temperature Celsius, Weather Relative Humidity, Daily Rainfall, and Radiation Global Tilted. The features selected by RFE technique are Weather Relative Humidity, Global Horizontal Radiation, Radiation Global Tilted, and Radiation Diffuse Tilted. There are two features only selected by EM technique, Global Horizontal Radiation, and Radiation Global Tilted. Finally, Table 3 displays the selected features for each feature selection method. By examining the selection counts, we can identify the common features that were selected across different methods.

Table 3. Selected features for each feature selection method.

Method	Column number/features								No. of selected features for each method
	2	3	4	5	6	7	8	9
PC	—	√	√	√	—	—	√	√	5
VIF	—	√	—	√	—	√	√	—	4
MI	√	—	√	√	—	—	√	√	5
SFS	√	√	√	—	—	—	√	√	5
BE	√	√	√	—	√	√	√	—	6
RFE	—	√	√	—	—	—	√	√	4
EM	—	—	√	—	—	—	√	—	2
Selection count	3	5	6	3	1	2	7	4

• Abbreviations: BE, backward elimination; EM, embedded method; MI, mutual information; PC, Pearson correlation; RFE, recursive feature elimination; SFS, step forward selection; VIF, variance inflation factor.

The table provides a comprehensive overview of features selected by various feature selection methods for PV power prediction. It reveals that Global Horizontal Radiation and Radiation Global Tilted are consistently identified across most methods, underscoring their significant influence on PV power output. These features are selected by seven and six methods, respectively, indicating their robust relevance. Weather Temperature Celsius, Weather Relative Humidity, and Radiation Diffuse Tilted also appear frequently, suggesting they contribute importantly but with less consistency across methods. Notably, BE is the most inclusive, selecting six features, including additional ones like Wind Direction and Daily Rainfall, which are not chosen by other methods. This broad selection indicates BE’s tendency to retain a larger set of features before eliminating them. In contrast, the EM is the most selective, choosing only two features, reflecting its focus on the most impactful variables. The Selection Count shows that while Global Horizontal Radiation stands out with the highest frequency, features like Weather Temperature Celsius and Weather Relative Humidity have moderate counts, highlighting their variable importance.

We then test the selected features from each feature selection method using a random forest regressor model and compare the results. Table 2 presents the outcomes for the final selected features.

The results in Table 2 reveal the impact of different feature selection techniques on the performance of regression models, assessed through RMSE and R² metrics. Among the techniques, MI exhibits the most impressive performance, with the lowest RMSE of 0.158889 and the highest R² of 0.992000. This suggests that the features selected by MI provide the most accurate and explanatory model. SFS and PC analysis also deliver robust results, with SFS achieving an RMSE of 0.160618 and R² of 0.991825, and PC analysis yielding an RMSE of 0. 166435 and R² of 0.991222. These techniques effectively balance the number of features with model performance, ensuring that critical information is retained without unnecessary complexity.

Conversely, the EM selects only two features, resulting in the highest RMSE of 0.182029 and the lowest R² of 0.989500 among the methods. This indicates that while fewer features simplify the model, they may also omit essential information, reducing predictive accuracy and explanatory power. Similarly, the VIF and RFE techniques, which select four features each, show moderately lower performance metrics. VIF’s RMSE is 0.192499 with an R² of 0.988257, while RFE’s RMSE is 0.168400 with an R² of 0.991014, suggesting that these methods might exclude some informative features or introduce redundancy.

In this study, PC, MI, SFS, and BE based on RMSE values are selected and implemented to draw the following figure to describe the features importance. Figure 8 illustrates the importance of various features as determined by the selected feature selection techniques. Table 4 displays the features selected by the PC, MI, SFS, and BE methods, with the selection count used to assess and describe feature importance.

Table 4. Selected features for PC, MI, SFS, and BE.

Method	Column number/features
	2	3	4	5	6	7	8	9
PC	—	√	√	√	—	—	√	√
MI	√	—	√	√	—	—	√	√
SFS	√	√	√	—	—	—	√	√
BE	√	√	√	—	√	√	√	—
Selection count	3	3	4	2	1	1	4	3

• Abbreviations: BE, backward elimination; MI, mutual information; PC, Pearson correlation; SFS, step forward selection.

After this assessment, the features are filtered to retain only those with an information gain above a specific threshold. This threshold was determined through extensive experimentation to maximize prediction accuracy, ultimately setting the threshold at 1. Consequently, features selected by more than one method are considered. The final input features, designated as Primary Features, include Radiation Global Titled, Global Horizontal Radiation, Weather Temperature Celsius, Weather Relative Humidity, Radiation Diffuse Titled, and Diffuse Horizontal Radiation.

3.3.3. Regression Models

After identifying the most relevant features through feature selection methods, the less important and irrelevant features were eliminated. This process refined the dataset, reducing it to seven columns: six columns corresponding to the key meteorological variables (the input features) and one column representing the PV power output, which serves as the prediction target.

Next, data standardization was performed to ensure that all features were on the same scale and range, preventing any single feature from disproportionately influencing the model’s predictions. This step was essential for improving the accuracy and performance of many ML algorithms, especially those sensitive to feature scaling. Standardization also involved correcting any data inconsistencies and handling outliers, thereby improving the overall quality and reliability of the dataset. Table 5 provides a snapshot of the dataset after the standardization process. The data presented includes 10 randomly selected rows, showcasing the standardized values for each of the six key features.

Table 5. The data after the standardization process.

Row index	Diffuse Horizontal Radiation	Global Horizontal Radiation	Radiation Diffuse Tilted	Radiation Global Tilted	Weather Relative Humidity	Weather Temperature Celsius
498	−0.024379	1.440419	−0.191172	1.294711	−0.531889	0.235946
2996	−0.972909	−1.256791	−0.296669	1.367570	−1.187329	−3.243804
1023	3.622827	0.999440	3.583228	0.892936	−0.731438	0.602466
5050	−0.969549	−1.254162	1.272719	−0.301553	−1.266024	−3.314420
3645	−0.966517	−1.255915	1.779339	1.001072	−1.354223	−3.394903
4750	0.120411	1.457192	−0.055305	1.312147	−0.712017	0.734318
1132	0.409328	−0.808236	0.322156	−0.963642	2.998456	0.069261
5324	−0.925316	−1.244115	0.432101	−0.968838	−1.367583	−3.407290
4021	−0.400967	−0.097872	−0.529834	−0.335821	−0.868302	0.487791
740	−0.495449	−0.139009	−0.600254	−0.251373	0.684165	−0.050749

After the standardization process, the dataset was randomly split into two subsets: 70% of the data was allocated for training, and the remaining 30% was set aside for testing. This split ensures that the model can learn from the majority of the data while being evaluated on unseen data to assess its generalization capability. The primary goal of the model is to analyze the numerical meteorological data (such as temperature, radiation, and humidity) and establish patterns or relationships between these variables and the electrical energy generated by solar cells. Once these relationships are identified, the model can predict the energy output based on new meteorological data, even if it has not encountered those specific inputs during training.

In this study, scikit-learn’s prebuilt estimators (open-source Python library for ML models [56, 57]) were used which provides a comprehensive set of tools for both supervised and unsupervised learning. Each estimator is trained on the data using its fit method. The input to the fit method is the sample matrix X (which includes the meteorological features, where each row represents an individual observation and each column represents a feature), and the target values Y, which correspond to the actual PV power output. Once trained, the estimator can predict target values for new, unseen data, based on the learned patterns from the training data. In this study, the sample matrix includes six columns representing the primary features, with the target variable being the generated electrical energy. The estimator is trained using 70% of the data. Once trained, the estimator can predict target values for new input data without requiring retraining.

Following training, the model was tested using the remaining 30% of the dataset. The new data matrix (X) was input into the model, and the resulting predicted values (Y) were compared with actual values to assess prediction error. Table 6 shows the predicted and original data for 10 randomly selected samples when training and testing the linear regression model used from the scikit-learn library.

Table 6. Linear regression model predicted samples.

Row index	Actual PV power	Predicted PV power
3956	4.906299	4.918425
867	4.127600	4.226289
1414	0.995533	0.942023
2840	4.750800	4.755520
4870	1.360933	1.381778
1162	2.667434	2.668501
324	4.048267	4.122180
831	1.075600	1.244946
1333	3.521366	3.546563
2014	4.638200	4.648940

• Abbreviation: PV, photovoltaic.

This research also leverages multiple ML models from the scikit-learn library, including ridge regression, LASSO Regression, Elastic Net, Extra Trees Regressor, random forest regressor, and GB regressor. Each of these models is trained on 70% of the dataset, just like the linear regression model, allowing them to learn the patterns between the key meteorological features and the generated PV power. After training, the models are tested on the remaining 30% of the data to evaluate their performance on unseen data. For each model, the prediction process involves taking the test set input (which includes the meteorological features) and generating predicted values for the PV power output. These predicted values are then compared with the actual values to assess how well each model performs. The tables (Tables 7–12) present a random sample of predicted PV power values for each of the models used, highlighting their performance on individual test samples.

Table 7. Ridge regression model predicted samples.

Row index	Actual PV power	Predicted PV power
852	1.065667	1.344560
3651	0.088667	0.160171
4111	1.380267	1.699295
1237	4.433100	4.103973
307	1.076400	1.484775
107	0.183467	0.210443
2925	0.000000	0.054042
5181	2.684367	2.515708
3180	2.754433	2.545339
4429	4.131333	4.207422

• Abbreviation: PV, photovoltaic.

Table 8. LASSO regression model predicted samples.

Row index	Actual PV power	Predicted PV power
1699	1.934400	1.629623
3529	0.583133	0.454784
722	4.142833	4.298744
840	3.989933	3.800298
4514	1.711667	1.738500
3897	0.000000	0.811547
5358	0.000000	0.053930
2020	1.610000	1.622825
4830	4.713334	4.917562
2104	4.046600	4.126561

• Abbreviations: LASSO, Least Absolute Shrinkage and Selection Operator; PV, photovoltaic.

Table 9. Elastic Net model predicted samples.

Row index	Actual PV power	Predicted PV power
206	0.009067	−0.014759
3418	3.448400	3.478625
3395	4.879633	5.030806
4220	0.743067	0.662497
1119	3.808200	3.632128
4493	4.169366	4.029801
72	4.483334	4.788738
1046	2.856467	2.687984
4757	0.000000	0.063725
2161	3.260300	3.127507

• Abbreviation: PV, photovoltaic.

Table 10. Extra Trees Regressor model predicted samples.

Row index	Actual PV power	Predicted PV power
402	4.880700	4.827788
1345	0.860333	0.822132
1807	3.062900	3.110857
2470	4.976267	4.989662
1950	2.564233	2.582682
3403	4.422999	4.522958
2306	2.747400	2.775152
3512	0.105500	0.101361
2198	0.014067	0.016680
4108	4.490734	4.502964

• Abbreviation: PV, photovoltaic.

Table 11. Random forest regressor model predicted samples.

Row index	Actual PV power	Predicted PV power
3778	3.098900	3.111685
3833	2.495766	2.516712
3391	3.707500	3.720703
3994	0.866733	0.836290
5346	0.212933	0.180451
277	3.789867	3.873528
3035	5.033367	5.063702
2751	0.000000	0.000000
4430	5.194300	4.765915
210	2.027300	2.014854

• Abbreviation: PV, photovoltaic.

Table 12. GB regressor model predicted samples.

Row index	Actual PV power	Predicted PV power
668	4.780767	4.911787
5273	4.740500	4.692913
752	5.055233	5.053923
3244	3.388200	3.609603
2874	0.000000	0.001427
2563	2.226067	2.488140
4510	0.214533	0.149639
1910	3.673167	3.674817
321	4.610366	4.597660
4582	1.556167	1.649106

• Abbreviations: GB, gradient boosting; PV, photovoltaic.

The XGBoost library was employed to implement the XGBoost Regressor, a highly optimized GB tool designed for efficient and scalable ML model training. The model was trained on the designated training data and evaluated on the test set. Table 13 provides a random sample of PV power predictions made by it.

Table 13. The XGBoost Regressor model predicted samples.

Row index	Actual PV power	Predicted PV power
4200	0.734000	0.748405
1221	4.255466	4.190846
3067	3.947300	3.963487
4067	3.661800	3.558964
5141	0.000000	0.017265
3123	4.576834	4.526834
5382	0.418500	0.388340
4756	5.104000	5.104790
2704	4.469967	4.434934
737	0.957767	0.872789

• Abbreviations: PV, photovoltaic; XGBoost, eXtreme Gradient Boosting.

3.3.4. Performance Measure Indices

The performance of the regression models was evaluated through various statistical metrics, calculated by comparing the predicted outputs from each algorithm against the reference test data. One key metric used was the RMSE, defined by Equation (9). In this equation, N represents the number of data points, X denotes the target or reference output, and X’ signifies the output predicted by the algorithm [58]:

$$ (9)

The MAE, defined in Equation (10), with the same variable definitions as RMSE is as follows:

$$ (10)

The R² value is defined in Equation (11), where N is number of data points, X is the observed dependent variable, X’ is the predicted value of the dependent variable, and $$ is the mean of the dependent variable [58]:

$$ (11)

A lower RMSE and MAE reflect greater prediction accuracy. Similarly, an R² value approaching 1 indicates that the predictions are highly accurate [58]. There is always going to be a difference between the RMSE and MAE; the larger the gap, the more variance there is in the individual errors within the sample.

4. Results and Discussion

The models in this study were developed using Python on the Google Colab platform, leveraging several ML libraries, including Numpy, Pandas, and scikit-learn. The Google Colab environment utilized an AMD EPYC 7B12 processor (2250 MHz), 12.67 GB of RAM, and a Linux operating system. Initially, data preprocessing was performed, which involved cleaning the dataset by replacing all missing values with the most suitable estimates after thoroughly analyzing the dataset. Before applying ML algorithms, the data was standardized. Various feature selection methods, such as PC, VIF, MI, SFS, BE, RFE, and EM, were then applied to refine the dataset.

The dataset was split into training and testing sets with a 70:30 ratio, allocating 70% of the data (39,572 records) for training and 30% (16,960 records) for testing. Finally, both traditional and hybrid ML algorithms were implemented to evaluate the models’ performance including linear regression, ridge regression, LASSO regression, Elastic Net, Extra Trees Regressor, random forest regressor, GB regressor, XGBoost regressor, and hybrid model of XGBoost Regressor, Extra Trees Regressor, and GB regressor are applied to the dataset. The following table shows the results for all regression algorithms. The results indicate a clear trade-off between training time and model accuracy. While traditional linear models are extremely fast to train, they offer lower accuracy, as evidenced by their higher RMSE and lower R² values. In contrast, more complex models like Extra Trees Regressor, random forest regressor, GB regressor, and XGBoost Regressor provide significantly better accuracy but require longer training times. The hybrid model, with its superior accuracy, reflects the effectiveness of combining multiple robust algorithms to capture intricate patterns in the data, albeit at a higher computational cost.

Table 14 showcases the performance of various traditional and hybrid ML algorithms applied to a dataset, evaluated using metrics such as training time, RMSE, MAE, and R². Linear, ridge, LASSO regressions, and Elastic Net exhibit the shortest training times, with ridge regression being the fastest at 0.000590 s. These models yield similar performance metrics, with RMSE values around 0.305 and R² values near 0.970. The MAE values are also close, around 0.196, indicating consistent but moderate predictive accuracy. Despite their rapid training times, these models are less accurate compared to more complex algorithms, making them suitable for scenarios where speed is more critical than precision. On the other side, ensemble methods such as Extra Trees Regressor, random forest regressor, and GB regressor demonstrate significantly improved performance over linear models. Extra Trees Regressor, for instance, achieves an RMSE of 0.109884 and an R² of 0.996156, with an MAE of 0.056846. Random forest regressor and GB regressor also perform well, with RMSE values of 0.116084 and 0.114795, respectively, and corresponding R² values above 0.995. These models, however, require longer training times, reflecting their complexity and computational demands. Moreover, XGBoost Regressor stands out with a strong performance, achieving an RMSE of 0.111622 and an R² of 0.996034, coupled with a relatively short training time of 1.574913 s. This balance of accuracy and efficiency makes XGBoost Regressor a robust choice for many applications. The hybrid model, which combines XGBoost Regressor, Extra Trees Regressor, and GB regressor, achieves the best overall results with the lowest RMSE of 0.108735 and the highest R² of 0.996228. The MAE of 0.058998 further underscores its exceptional accuracy. However, the hybrid model has the longest training time at 144.4991 s, indicating the high computational cost of integrating multiple algorithms.

Figure 9 contrasts predicted and actual values. If the model is well-fitted, the data points will be firmly grouped along the diagonal line. This shows that the actual and predicted values are closely related. In this plot, the data points are closely spaced along the diagonal, which suggests that the hybrid model’s predictions are accurate and consistent.

Figure 10 describes the relationship between the error values and its density. XGBoost Regressor, Extra Trees Regressor, and GB regressor for hybrid model based on the result they achieve are selected.

Figure 11 shows RMSE, R², and MAE values for algorithms. Both RMSE and R² are metrics used to evaluate the fit of a linear regression model to a dataset. RMSE measures the model’s predictive accuracy by quantifying the absolute difference between observed and predicted values of the response variable. In contrast, R² assesses how well the predictor variables account for the variability in the response variable. In addition, Figure 12 displays the average generated and predicted power per day for every month of the year while Figure 13 illustrates the average actual and prediction power per month, and Figure 14 shows the maximum value for actual and prediction power for every hour for December.

The dataset of 361 days in a year was divided into three categories of comparable day samples: sunny, cloudy, and rainy using Gaussian mixture model (GMM) [59]. Identical days were identified for the raw PV power samples using the GMM clustering technique, as described in [58]. Table 15 shows some samples clustering of sunny, cloudy, and rainy days. In particular, there were 62 days with rain, 120 days with clouds, and 179 days with sunshine. As shown, the RMSE for the sunny days cluster, consisting of 179 days, was 0.079076, indicating high predictive accuracy. The R² value of 0.998007 suggests that the model explains almost all the variance in the data, reflecting excellent model performance. The training time for this cluster was 70.663 s, which is relatively moderate compared to the unclustered dataset. For the cloudy day cluster, with 120 days, the outcomes showed an RMSE of 0.144806 and an R² value of 0.992314. While these metrics indicate good predictive performance, they are slightly less impressive than those for the sunny days cluster. Also, the rainy day cluster, encompassing 62 days, had an RMSE of 0.086474 and an R² value of 0.997731. This cluster also shows high predictive accuracy, with performance metrics close to those of the sunny days cluster. Finally, the unclustered dataset of 361 days had an RMSE of 0.108735 and an R² of 0.996228. The training time was the highest at 144.499 s. These results show that clustering the data into sunny, cloudy, and rainy categories improves predictive accuracy and reduces training time. The unclustered dataset’s higher RMSE suggests that treating all weather conditions uniformly introduces more variability and prediction errors, which clustering helps to mitigate.

In order to illustrate how the suggested model outperforms conventional models in terms of prediction, several classical models are applied including LSTM, CNN, recurrent neural network (RNN), extreme learning machine (ELM), and QR and kernel density estimation deep learning networks (QRKDDNs) for comparison. Using the Rainy dataset as an example, each model is validated 10 times, and Table 16 displays the prediction results.

From Table 16, the proposed model stands out with the lowest RMSE of 0.086474 and the highest R² value of 0.997731, clearly outperforming all other models in terms of predictive accuracy. Additionally, it has the shortest training time at 25.202 s, showcasing its efficiency. The QR-ELM model has a training time of 53 s, which is more than double that of the proposed model. It records an RMSE of 1.085463 and an R² value of 0.825938. These metrics indicate significantly lower accuracy, with the model explaining much less of the variance in the data compared to the proposed model. The QR-CNN model takes 71 s to train, yielding an RMSE of 0.624928 and an R² of 0.874490. Although it performs better than the QR-ELM model, it still falls short of the proposed model in both prediction accuracy and efficiency. With a training time of 118 s, the QR-LSTM model achieves an RMSE of 0.874331 and an R² value of 0.857201. This model requires significantly more time to train and yet offers less accurate predictions than the proposed model. The QR-RNN model has a training time of 137 s, an RMSE of 0.562490, and an R² value of 0.929510. While its R² value is higher than those of some other classical models, indicating better accuracy, it is still less efficient and accurate compared to the proposed model. The QRKDDN model, with a training time of 154 s, shows an RMSE of 0.301985 and an R² value of 0.972064. Although this model performs better than the other classical models, it is still not as accurate or efficient as the proposed model. These results underscore the effectiveness of the proposed model, which not only predicts with greater accuracy but also does so more efficiently. This makes it particularly suitable for applications requiring real-time or near-real-time predictions, where both accuracy and speed are crucial. The comparative analysis confirms that the proposed model is a robust alternative to traditional approaches, offering substantial improvements in predictive performance and operational efficiency.

The model was set up and run 10 times to evaluate the computational efficiency of the proposed model with the comparative models used by the author [58] for the same data set. The comparative model’s schematic diagram and full description are included in the reference; however, they are not included in this study due to space limitations. Table 17 shows the average running time that resulted. The proposed model consistently demonstrates superior computational efficiency across all weather conditions. For sunny days, the proposed model has an average training time of 70.663 s, significantly lower than any of the comparative models. The QR-GRU model, the fastest among the comparatives, takes 187 s [58], which is more than double the time of the proposed model. On cloudy days, the proposed model again shows remarkable efficiency with an average training time of 47.044 s. The closest comparative model, QR-GRU, requires 166 s, while the QR-BiGRU takes 208 s [58]. The efficiency of the proposed model is most pronounced on rainy days, where it achieves an average training time of just 25.202 s. This is less than a quarter of the time needed by the QR-GRU model, which requires 108 s. The more complex QR-CNN-BiGRU and QR-CNN-BiLSTM-attention models take even longer, with training times of 151 and 204 s, respectively [58]. These results emphasize the proposed model’s advantage in computational efficiency without compromising predictive performance. The reduced training times make the proposed model ideal for real-time applications and scenarios where rapid retraining is necessary. This efficiency, combined with its previously demonstrated accuracy, positions the proposed model as a robust and practical solution in the field of predictive modeling.

5. Conclusion

In this paper, an accurate forecasting methodology is presented for the successful integration of renewable energy systems, particularly solar power generation. It introduces a pioneering hybrid predictive model framework that combines meteorological data, feature selection techniques, and multiple regression algorithms to enhance the accuracy of PV power prediction. The study is implemented on a PV system (Hanwha Solar, 5.8 kW, poly-Si, Fixed, 2016) and meteorological data gathered from sensors between January 1 and December 31, 2020. Through extensive experimentation and evaluation, the hybrid model incorporating XGBoost Regressor, Extra Trees Regressor, and GB regressor outperforms other regression algorithms, achieving a remarkable RMSE of 0.108735 and a high R² value of 0.996228. The findings emphasize how crucial it is to incorporate meteorological information into renewable energy forecasts in order to facilitate sustainable energy management and planning. The hybrid predictive model framework that has been suggested improves the forecast of solar power, facilitating grid integration and resource allocation for sustainable energy management. By clustering data into sunny, cloudy, and rainy categories, predictive accuracy improves and training time decreases. The higher RMSE of the unclustered dataset indicates that treating all weather conditions uniformly increases variability and errors, which clustering mitigates. The model’s computational efficiency and maintained predictive performance make it suitable for real-time applications requiring quick retraining. The model’s efficiency combined with its established accuracy makes it a reliable and useful tool for predictive modeling.

Future research stemming from this study entails delving deeper into advanced feature selection techniques and the integration of DL models not only for PV power prediction but also for applications in other renewable energy sources such as wind and hydroelectric power. Additionally, incorporating external factors like grid demand and market prices into the predictive model could enhance its applicability in broader power system planning and energy management contexts. Real-time forecasting strategies could not only improve PV power predictions but also aid in optimizing battery charging and discharging cycles for grid stability. Moreover, integrating uncertainty quantification methods could assist in assessing the reliability of predictions not only for PV power but also for battery state of charge estimations and grid load forecasts. Lastly, deploying the model in real-world settings could offer insights into its effectiveness in optimizing renewable energy generation and storage systems, contributing to enhanced operational efficiency and grid stability in sustainable power systems.

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

No funding was received for this manuscript.