Comparative Analysis Using Multiple Regression Models for Forecasting Photovoltaic Power Generation

Abstract

Effective machine learning regression models are useful toolsets for managing and planning energy in PV grid-connected systems. Machine learning regression models, however, have been crucial in the analysis, forecasting, and prediction of numerous parameters that support the efficient management of the production and distribution of green energy. This article proposes multiple regression models for power prediction using the Sharda University PV dataset (2022 Edition). The proposed regression model is inspired by a unique data pre-processing technique for forecasting PV power generation. Performance metrics, namely mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), R²-score, and predicted vs. actual value plots, have been used to compare the performance of the different regression. Simulation results show that the multilayer perceptron regressor outperforms the other algorithms, with an RMSE of 17.870 and an R² score of 0.9377. Feature importance analysis has been performed to determine the most significant features that influence PV power generation.

1. Introduction

Due to the capacity to produce power without predominantly generating greenhouse gases, photovoltaic (PV) systems are being considered as an alternative form of clean energy. Precise PV power generation forecasts are crucial for effective electricity oversight, particularly for establishing and programming purposes [1]. Reliable forecasting of power generation, impacted by an assortment of variables, including the climate, radiation from the sun, and system effectiveness, is necessary for the effective operation of PV systems [2]. Accurate forecasting is crucial for effective energy management, planning, energy generation scheduling, and ensuring the power grid’s stability and reliability [3]. In recent years, conventional machine learning algorithms have emerged as powerful tools for forecasting PV power generation. Demand response, proactive maintenance, energy production, and load predicting are just a few applications where machine learning models are the go-to toolkit for researchers [4]. These models can capture complex nonlinear relationships between various factors influencing power generation and accurately predicting future values [5]. The use of deep learning, nevertheless, can be useful when dealing with time series data. Auto-Regressive Integrated Moving Averages (ARIMAs) methods are beneficial for instantaneous forecasting of powerful time series data. Artificial neural networks are far more potent than ARIMA models and quantitative approaches, particularly for modeling complicated interactions [6]. Because artificial neural networks have the appropriate properties for interacting with non-linear models, forecasting time series has become a more common application for supervised neural networks in recent years. Estimating PV output can be crucial for grid operators and energy providers to plan and optimize tasks like managing maintenance and regulating power demand. Machine learning regression models can offer forecasting and anomaly detection in PV plants in such cases. In this study, multiple regression models, such as linear regression (LR), a support vector regressor (SVR), a k-neighbor regressor (KNR), a decision tree regressor (DTR), a random forest regressor (DFR), a gradient boosting regressor (GBR), and a multilayer perceptron regressor (MLP), have been used for PV power generation forecasting with promising results [7]. The effectiveness of the proposed regression model has been compared with existing approaches.

1.1. Motivation and Contribution

To address the effectiveness and applications of regression models for forecasting PV power generation, a comparative analysis of multiple regression models used on a dataset has been proposed. The testbed architecture of the PV system installed in the SHARDA University campus is discussed in Figure 1 of the manuscript, followed by the dataset description. Some of the major contributions of the article are as follows:

• Realistic time series dataset is harvested from PV panels (with sensors) and installed on multiple buildings of the SHARDA University campus.
• A comparative study and a performance analysis of the LR, SVR, KNR, DTR, RFR, GBR, and MPR for power prediction are tested.
• A discussion of numerous case studies for PV power is presented to identify the important features favoring power prediction.

Figure 1. Testbed architecture of PV system at Sharda University.

Figure 1. Testbed architecture of PV system at Sharda University.

1.2. Acronyms Used

The abbreviations and short forms used throughout the article are presented in

Table 1. Abbreviations and short forms.

Acronym	Full Form
ANN	Artificial Neural Network
XAI	Extensible Artificial Intelligence
LSTM	Long Short-Term Memory
CNN	Convolutional Neural Network
ARIMA	Autoregressive Integrated Moving Average
PV	Photovoltaic
MLP	Multi-layer Perceptron Regressor
SARIMA	Seasonal Autoregressive Integrated Moving Average
SARIMAX	Seasonal Auto-Regressive Integrated Moving Average with Exogenous Factors
LR	Linear Regression
LAN	Local Area Network
SVR	Support Vector Regressor

of the manuscript.

1.3. Structure of the Article

The structure of the manuscript starts with the introduction containing the research statement, problem identification, and improvements required. The introduction contains three subsections: the first subsection represents the motivation and contribution; the second subsection presents acronyms used throughout the manuscript; and the third subsection depicts the structure of the manuscript. Section 2 of the manuscript presents a detailed literature review of the related articles. Section 3 of the manuscript depicts the Testbed architecture with a dataset description. The Data Acquisition Unit and Data Monitoring Unit (DTU) are the two core subsections of Section 3. Section 4 of the manuscript describes the proposed methodology, with various data preprocessing steps and multiple regression methods. Section 5 of the manuscript discusses the results obtained from two case studies, which are Case 1 and Case 2. Section 6 highlights a comparison of existing state-of-the-art regression modelling for PV power prediction. Section 7 of the manuscript presents the conclusion and future scope of the proposed research methodology.

2. Literature Survey

In this section, a literature survey has been conducted based on relevant research conducted in PV power forecasting using XAI and machine learning regression models.

Table 2. Background and literature review.

Case Studies	Methodologies	Regression Models Used	Dataset Description	Testbed Description
[8]	The study proposes two deep learning methods for irradiance predictions for the next hour.	LSTM and CNN networks are used.	-	-
[9]	To tackle the consequences of carbon dioxide and other pollutants, this work has provided a hybrid machine learning and quantitative programming approach that has a high rate of approximation and is used with sparse data.	The nine methods of ANN, autoregressive, ARIMA, SARIMA, SARIMAX, random forest, SVR, K-nearest neighbors, and LSTM were used to predict the harmful emissions of each gas.	-	-
[10]	The findings of PV power generation forecasts using linear, ridge, and Bayesian regression methods are presented in this work.	Linear regression, Ridge regression, and Bayesian regression.	The data collection approach uses the data records at 15 min intervals.	Skymet W.S.P.L.
[11]	According to the distinctions and commonalities, the paper sorts the nomenclature of PV energy forecast approaches, optimizers, and prediction frameworks into various groups.	The difficulties and probable paths for future study in PV power forecasting using machine learning algorithms are discussed by the authors.	Challenges faced in forecasting structure.	-
[12]	For point-to-point and intermediate modeling of PV power in the context of a smart grid ecosystem, a viable composite empirical wavelet transform (EWT)-based modified resilient Mexican hat wavelet kernel ridge regression (RMHWK) approach has been suggested.	EWT (empirical wavelet transform) and RKRR (robust Kernel Ridge regressor) methods are used by the researchers.	-	1 Megawatt PV Plant data of Odisha, India, validated using a dataset from Florida, USA.
[13]	Initially a time-series-based PV power projection (SPF) structure is developed using the nearby meteorology station’s forecasted weather data and its time component. For the proposed SPF, the long short-term memory (LSTM) method is applied in consideration of the data correlations in the data dimensions.	Long short-term memory (LSTM) with Gaussian process regression.	-	-
[14]	The paper suggests an overall regression neural network (GRNN) built around Grey Wolf optimization (GWO), which is anticipated to deliver better precise forecasts with faster computation.	To achieve meteorological aggregation and training the neural network. With GWO model, an autonomous map (SOM) is implemented.	Xiamen University Tan Kah Kee College, Zhangzhou China, and National Kaohsiung University of Science and Technology, Kaohsiung Taiwan.	Fifty-three thousand records each year are collected from various PV plants.
[15]	The weighted Gaussian procedure regression strategy is used in this investigation, and a novel method is suggested where data points with an elevated outlier likelihood are given a lower weight.	For data with large dimensions, a density-based local outlier identification approach is presented to make up for the degradation of the Euclidean distance outcome.	Dataset by Nanyang Technical University.	The testbed used in the research has six panel systems, distributed at various locations in a tropical rainforest region of Singapore.
[16]	This work involves performing hour-ahead PV power generation predictions.	Support vector regressor. Lasso regression and polynomial regression.	Data collected for 15 months are used in the study.	Virginia Tech Research Centre.
[17]	In this study, a non-parametric predictive machine learning method for PV electric power generation and forecasting in an anticipated timeframe of one to six hours is presented. To develop a gradient-boosted regression tree (GBRT) framework, 42 unique PV roofing setups, past power production, and pertinent climatic data are used.	Gradient-boosted regression tree and multi-site modelling.	-	Data has been collected from 46 distinctive PV installations.
[18]	To simulate the real-world practice of energy projections, the research provides a support vector regression approach to generate PV power estimates on an ongoing schedule for 24 h, extending over an entire calendar year.	Support vector regressor.	The dataset used in the research is from the Global Energy Forecasting Competition in the year 2014.	Precise PV power units installed in Australia.
[19]	The authors of the manuscript propose a strategy that employs the gradient boosting technique for reliable planning.	Gradient boost and k-nearest neighbor.	GEFCom 2014.	-
[20]	To project weekly PV power output, this study creates a genetic intermittent decomposition least-square support vector regression (ESDLS-SVR).	Least-square support vector regression, ARIMA, SARIMA, and GRNN.	Dataset by the Ministry of Science and Technology of the Republic of China incorporating Taiwan.	-
[21]	The manuscript introduces an online platform for power forecasting in PV systems used in various applications. This article is used to forecast hourly PV power estimates over 36 h spans.	Autoregressive models.	Data of a 15 min timelapse are used.	21 PV systems installed on building rooftops.

presents the current state of the art research, including recent research in the field of PV power forecasting with the help of regression modeling.

3. Testbed and Dataset Description

The dataset utilized in this study has been obtained from the data collection Centre at SU in Uttar Pradesh, India 28.4753° N, 77.4823° E, which is dispersed across several building rooftops. The dataset contains the records of the year (2022) from date 21 January 2022 to 21 December 2023, and it has a time-lapse of 15 min between each instance. The dataset has seven features namely hour, power (kW), irradiance (W/m²) (IRR), wind (km/h), ambient/panel temperature (°C), and PR representing performance percentage.

The architecture of the PV system is given in Figure 1 of the manuscript below, where the PV panels are distributed at several locations. Various subparts of the testbed have been discussed in detail in Section 3.1.

3.1. DAQ Unit

The DAQ unit and DMU are the main components of the chosen test bed. PV panels are installed at various locations on the building rooftops of various buildings on the SU campus. In addition, PV panels are equipped with radiation sensors, wind sensors, and temperature transmitters. All the installed sensors transmit data to the remote terminal unit.

3.2. DMU

The DMU is used as a strong surveillance system to guarantee the steady and dependable performance of any PV system. The DM unit also monitors several electricity production indices and fault occurrences. In the proposed system, data from RTUs are transmitted to a sub-control system, equipped with computer-aided monitoring for data generation and system monitoring.

4. Proposed Regression Methodology

The various building blocks of the proposed model are presented in Figure 2. It starts with taking the PV dataset as the input and performs multiple preprocessing steps on it. The preprocessed data frame is directed for data modeling and to the selected regressor at the end.

4.1. PV Dataset

The dataset used in this study was collected from multiple building rooftops at the SU data collection Centre in Uttar Pradesh, India (28.4753° N, 77.4823° E). With a time gap of fifteen minutes between each occurrence, the dataset includes the recordings for the year 2022 from 21 January 2022 to 31 December 2023. The dataset includes the following seven features: wind speed (km/h), power (kW), hour, ambient/panel temperature (degrees Celsius), irradiance (W/m²) (IRR), and PR, or performance percentage.

4.2. Data Pre-Processing

In response to the data distribution within the six features, the pre-processing steps embedded with regression models are depicted in Figure 3. The proposed regression model takes the PV dataset as input and dataset concatenation is an initial step taken towards pre-processing. After data-frame concatenation, the column “Ambient/Panel Temperature (°C)” is separated into ambient Temperature and panel temperature columns. Before feature selection, outliers are detected and handled within the data frame with normalized values. Furthermore, a correlation and heat map have been used to select important features and drop redundant features as shown in Figure 3. In the proposed work, two case studies have been considered for data analysis.

Case 1:—Data frame with all features and removing rows with Null (NaN) values.

Case 2:—Data frame without PR% and wind (km/h) feature.

The two case studies have been deliberated in Section 5 of the manuscript.

Figure 3. Pearson correlation and heat map of data frame.

Figure 3. Pearson correlation and heat map of data frame.

4.3. Data Modelling

The data frame is divided into training and testing, with 80% for training and 20% for training. Power feature is selected as the target feature.

4.4. Regression Models

Various regression models have been used to predict the power production from the data. The performance of each of the regression models used is evaluated using MAE, MSE, RMSE, R² error, explained variance score, and prediction plots. Considered regression models have been explained in Section 4 hereafter.

4.4.1. Linear Regression

The strategies in linear regression assume that the desired result will be a linear blend of the attributes. If ỹ represents the anticipated value in the notated form, it may be given as

ỹ(W,X) = W₀ + W₁ × 1 + W₂ × 2 + … W_nX_n

(1)

The shape of the vector is w = (W₁, W₂, … W_n) as the coefficient and W₀ as the intercept throughout the function. To reduce the total of the residuals of squares among the targets found in the data frame and the ones forecasted using the linear estimation, linear regression builds an equation with coefficients W = (W₁, W₂, … ,W_n−1, W_n).

4.4.2. Support Vector Regressor

It is comparable to SVR, which uses the argument kernel = ‘linear’, but because it is constructed using “liblinear” instead of “libsvm”, it offers additional versatility in the selection of penalty and loss coefficients and can expand more effectively to large chunks of data samples. The input of both kinds is supported using this method [22].

For a trained dataset, if X is the input data and Y is the target variable, SVR aims to find coefficients a and b that minimize the cost function and can be illustrated as

$$\frac{1}{2}{|\left|a|\right|}^2+\mathrm{C}{\sum }_{i=1}^{n}L(y_i,f\left(x_i\right))$$

(2)

|a| = norm of the weight vector a; C = regularization parameter; L = loss function that penalizes errors.

4.4.3. K-Neighbor Regressor

The idea underlying nearest neighbor approaches is to select a set with several training instances that are situated most closely to the point of interest and subsequently estimate the designation based on them [23]. Regarding the scenario of radius-based neighbor learning, the number of observations can either rely on the regional concentration of points or be a customized constant (k-nearest neighbor learning). The distance can normally be expressed in any metric system unit; the most popular option is the conventional Euclidean distance. Since neighbors-based strategies merely “remember” everything about the training data instances, they are referred to as non-generalizing machine learning approaches [24]. Regression and time series prediction, where the desired factor is often an order of interval scaled values, can benefit from applying the k-NN classifying concept when the reliant parameter is categorical [25].

For a single input sample, a, the predicted output b is calculated as the average of the target values of the K nearest neighbor in the dataset and can be illustrated as

$$b\left(a\right)=\frac{1}{k}{\sum }_{i=1}^k{b}_i$$

(3)

here, $b\left(a\right)$ is the predicted output for input a, b_i is the target value of the i-th nearest neighbor, and k is the no of neighbors.

4.4.4. Decision Tree Regressor

A decision tree regressor develops a model in the form of a tree structure to estimate data in the future and generate useful continual output by observing the properties of an item. Seamless output denotes the absence of uniform output, i.e., the absence of representation by a discrete, well-known set of values [26]. The number of observations that must have been collected for a tree to contemplate shattering a node into two is known as the minimum sample split parameter. A structure splits until it reaches this value. The level of a decision tree needs to be maintained constantly because a shallower tree is going to possess significant bias along with little variance, whereas a more extensive tree would have high variance and low bias [27,28]. As a result, in our study, we tested using the splitting criterion as well as the maximum depth of the tree to generate a model that is as accurate as possible. The mathematical representation of a decision tree regressor $T_{\left(r\right)}$ is illustrated in

$$T_{\left(r\right)}=C_i$$

(4)

here

• $T_{\left(r\right)}$ represents predicted output for the input a using a decision tree.
• C_i is the constant value associated with the leaf node i.

4.4.5. Random Forest Regressor

Three primary phases make up the random forest development algorithm. Establishing B sample sets of dimensions N utilizing the baseline data, these sample sets might be swapped out and combined. For every sample in the dataset, we create a random forest tree Tb by iteratively continuing the subsequent procedures for each terminal node unless the minimal node count min is obtained:

• Pick m predictors randomly from the p covariates.
• Choose the top predictor for the split section out of the m identified predictors.
• Divide this location (node) into two minor nodes by establishing specific decision-making guidelines.

Lastly, determine the combination of the trees ${\left\{{\mathrm{T}}_{\mathrm{b}}\right\}}_1^{\mathrm{B}}$, where B is the total number of trees in the random forest.

$${\widehat{\mathrm{f}}}_{\mathrm{R}\mathrm{F}}=\frac{1}{\mathrm{B}}{\sum }_{\mathrm{b}=1}^{\mathrm{B}}{\mathrm{T}}_{\mathrm{b}}\left(\mathrm{x}\right)$$

(5)

• ${\widehat{\mathrm{f}}}_{\mathrm{R}\mathrm{F}}$ is the predicted output for the input X;
• B is the total number of trees left (base learners right) in the RFR$;$
• ${\sum }_{\mathrm{b}=1}^{\mathrm{B}}{\mathrm{T}}_{\mathrm{b}}\left(\mathrm{x}\right)$ is the prdiction of the b-the decision tree in the forest for input X.

The final prediction is the average of these individual tree predictions.

4.4.6. Gradient Boosting Regressor

The loss argument in the gradient boosting regressor allows the specification of a variety of loss functions in regression and squared error, which constitutes a typical loss function. A loss function is employed during the boosting procedure. The “squared error” and “Poisson” losses incorporate the “half least squares loss” and “half Poisson deviance” to make the mathematical calculation of the gradient simpler. Additionally, “Poisson” loss employs an internal log connection and needs y ≥ 0. Pinball loss is employed by “quantile”.

Mathematical representation for M weak learners and the prediction FM(i) for input (i) is given using

$$\mathrm{FM}(\mathrm{i})={\sum }_m^M{\beta }_m{h}_m\left(i\right)$$

(6)

FM(i) is the predicted output for (i) input using a gradient boost model with weak learners. $h_m$ is the prediction of the m-th weak learner for input (i), and ${\beta }_m$ is the weight assigned to the m-th weak learner. The update rule for the weights and the new weak learner is determined by minimizing a loss function, often using gradient descent.

4.4.7. Multilayer Perceptron Regressor

MLP has a layered configuration with input, hidden, and output layers, like the other neural networks. During the MLP classifier’s recurrent development process to adjust the parameters, the estimates of the loss function regarding the parameter estimation are generated at each observation time. The loss function may undergo a convolution operation that lowers the model’s coefficients to prevent overfitting [29]. It learns with a supporting function.

$$f\left(\mathrm{X}\right):R^m\to R^o$$

(7)

where “$R^m$” represents the input space, “$\to$” indicates mapping from the input space to the outer space, $R^o$ represents the outer space [30]. A data frame with the input X = ($x^1,x^2,x^3\dots x^n)$ and the target variable and y is provided. “$R^m$” represents the input space, “$\to$” indicates mapping from the input space to the outer space, $R^o$ represents the outer space [30]. The proposed MLP regressor is tuned with Adam as an optimizer, and loss is calculated using MAE and with a learning rate parameter of 0.01, across 250 epochs. The decimal value of 0.31 is used as the initial value for the validation split parameter on the training set of data. The information from the preceding layer is transformed by each neuron in the hidden layer using a weighted linear sum of weights and input sets.

5. Results

For the proposed model, the results section is divided into two case studies concerning the feature vector of the dataset. Pearson’s correlation method has been used to select and drop the features from the dataset. Pearson’s correlation method is simple and strategic to determine the strong and weak correlation between independent and dependent variables [31]. From Figure 4 of the manuscript, which is the correlation and heat map plot of the features, wind (km/h) and hour are visualized as weakly correlated and are dropped in two different cases. The two different case studies are

Case 1:—Data frame with all features and removing rows with null (NaN) values.

Case 2:—Data frame without PR% and wind (km/h) feature.

For each case study, the LR, SVR, KNR, DTR, RFR, MLP, and GBR are tested. The performance of each regression model is evaluated using the MAE, MSE, RMS, R² Score, and prediction plots (actual and predicted values).

Figure 4. MAE score plots of Case 1.

Figure 4. MAE score plots of Case 1.

5.1. Case 1:—Data Frame with All Features

The PR% feature of the dataset contains a hefty amount of NaN values, so all NaN-valued rows from it have been dropped. Time slots during the night were all representing NaN values in the PR% column. Replacing NaN values with substitute statistical outcomes was not an option and could have inserted bias in the dataset. However, the power generation using the PV system at night is zero. In this case study, the rows representing NaN in the PR% column are dropped. A comparison of various errors for Case 1 using the regression method has been presented in

Table 3. MAE, MSE, RMSE, and R² error outcomes in Case 1.

Regression Method	MAE	MSE	RMSE	R2 Score
LR	16.047	517.434	22.747	0.8990
SVR	15.170	547.968	23.408	0.8931
KNR	11.710	370.1811	19.2400	0.9278
DTR	13.1296	586.275	24.213	0.8856
random forest regression	10.0267	298.475	17.776	0.9417
MLP	11.507	319.36	17.870	0.9377
GBR	11.627	329.415	18.149	0.9357

. and score plots for the MAE, MSE, RMSE, and R² are illustrated in Figure 4, Figure 5, Figure 6 and Figure 7. The comparison of actual values and prediction values for Case 1 using various models is plotted in Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14.

The efficacy and performance of the various ML regression models are presented in the form of MAE, MSE, RMSE, and R² scores. Figure 4 of the article depicts the MAE scores obtained from various regression methods. The vertical axis represents the numeric values ranging from 0 to 18, and the values of MAE obtained using each regressor model are presented in the plot.

In contrast, Figure 5 depicts the MSE scores obtained from various regression methods. The vertical axis represents the numeric values ranging from 0 to 700, and the value of MSE obtained using each regressor model is presented in the plot.

Figure 5. MSE score plots of Case 1.

Figure 5. MSE score plots of Case 1.

Similarly, Figure 6 depicts the RMSE scores obtained from various regression methods. The vertical axis represents the numeric values ranging from 0 to 700, and the values of RMSE obtained using each regressor model are presented in the plot.

Figure 6. RMSE score plots of Case 1.

Figure 6. RMSE score plots of Case 1.

Figure 7 of the study illustrates the R² values acquired from numerous regression approaches. The vertical axis indicates the numeric values ranging from 0.82 to 1.0, and R² values obtained using each regressor model are shown in the plot.

Figure 7. Root square error score plots of Case 1.

Figure 7. Root square error score plots of Case 1.

Figure 8 depicts the actual vs. predicted plots using LR. Figure 9 depicts the actual vs. predicted plots using SVR for Case 1. In a regression problem, the actual vs predicted plot visually assesses model performance. The red dotted diagonal line signifies perfect predictions, with blue points ideally aligning closely. Scattered points deviating from this line indicate model inaccuracies, highlighting potential performance issues. A clustered alignment around the diagonal line signifies robust model performance.

Figure 8. Actual and predicted plots using LR.

Figure 8. Actual and predicted plots using LR.

Figure 9. Actual and predicted plots using SVR.

Figure 9. Actual and predicted plots using SVR.

Figure 10 depicts the actual vs. predicted plots using the MLP regressor, and Figure 11 depicts the actual vs. predicted plots using GBR for Case 1.

Figure 10. Actual and predicted plots using MLP.

Figure 10. Actual and predicted plots using MLP.

Figure 11. Actual and predicted plots using GBR.

Figure 11. Actual and predicted plots using GBR.

Figure 12 depicts the actual vs. predicted plots using RFR, and Figure 13 depicts the actual vs. predicted plots using DTR for Case 1.

Figure 12. Actual and predicted plots using RFR.

Figure 12. Actual and predicted plots using RFR.

Figure 13. Actual and predicted plots using DTR.

Figure 13. Actual and predicted plots using DTR.

Figure 14 depicts the actual vs. predicted plots using KNR for Case 1.

Figure 14. Actual and predicted plots using KNR.

Figure 14. Actual and predicted plots using KNR.

5.2. Case 2:—Data Frame without Wind (Km/h) and PR% Features

Dropping rows from the dataset with NaN values in the PR% column, the row count of the dataset remains 14,220 from 25,656. To improve the performance of regression models, PR% with maximum NaN values and wind (Km/h) with a weak correlation with the power feature are dropped. The regression matrices are presented in

Table 4. MAE, MSE, RMSE, and R² error outcomes in Case 2.

Regression Method	MAE	MSE	RMSE	R2 Score
LR	10.435	314.922	17.746	0.945
SVR	8.817	379.194	19.472	0.934
KNR	6.497	212.448	14.575	0.963
DTR	0.138	212.448	14.575	0.963
random forest regression	6.234	199.386	14.120	0.965
MLP	7.394	235.224	15.337	0.962
GBR	7.227	215.640	14.684	0.959

.

The efficacy and performance of the various ML regression models are presented in the form of MAE, MSE, RMSE, and R² scores. Figure 15 of the article depicts the MAE scores obtained from various regression methods. The vertical axis represents the numeric values ranging from 0 to 18, and the values of MAE obtained using each regressor model are presented in the plot.

In contrast, Figure 16 depicts the MSE scores obtained from various regression methods. The vertical axis represents the numeric values ranging from 0 to 700, and the values of MSE obtained using each regressor model are presented in the plot.

Similarly, Figure 17 depicts the RMSE scores obtained using various regression methods. The vertical axis represents the numeric values ranging from 0 to 30, and the values of RMSE obtained using each regressor model are presented in the plot.

Figure 18 illustrates the R² values acquired from numerous regression approaches. The vertical axis indicates the numeric values ranging from 0.82 to 1.0, and the values of R² obtained using each regressor model are shown in the plot.

Figure 19 depicts the actual vs. predicted plots using LR; Figure 20 depicts the actual vs. predicted plots using SVR for Case 2.

Figure 21 depicts the actual vs. predicted plots using MLP, and Figure 22 depicts the actual vs. predicted plots using GBR for Case 2.

Figure 23 depicts the actual vs. predicted plots using RFR, and Figure 24 depicts the actual vs. predicted plots using DTR for Case 2.

Figure 25 depicts the actual vs. predicted plots using LR for Case 2.

6. Discussion

This section highlights a comparison of existing state-of-the-art regression modelling for PV power prediction using the R² regression metric in

Table 5. Comparison analysis of various research articles vs. proposed methodology.

Case Study	Feature Selection Method	Regression Type	Features Used	Maximum R2	Dataset Used
[30]	Tree-based feature importance and principal component analysis.	Artificial neural network and random forest.	Temperature, humidity, day, and time.	0.9355	Metrological data of Hawaii United States of America (2016)
[31]	Wavelet transformation-based decomposition technique.	WT-LSTM, LSTM, Ridge regression, Lasso regression and elastic-net regression.	Cloudy index, visibility, temperature, dew point, humidity, wind speed, atmospheric, pressure, altimeter, PV output power.	0.9505	Urbana Champaign, Illinois
[32]	Correlation heatmap and Bayesian optimization.	LSTM	41 different features are used with variation.	0.8917	German dataset
Proposed Model	Pearson’s correlation and heatmap.	LR,	Hour, power, IRR (W/m2), wind km/h, ambient temperature, and panel temperature.	0.9650	SHARDA University PV Dataset (2022 Edition)
		SVR,
		KNR,
		DTR,
		RFR,
		GBR, and
		MLP

.

Compared to the cited research articles in Table 5, the proposed model has outperformed various regression methodologies in PV power prediction. However, the novelty of the model is determined by the portability of the best-performing regression method. The proposed model has harnessed 0.9650 of R² value and uses a novel preprocessing strategy and steps. The feature engineering step in the proposed model used co-relation values to extract important features from the dataset.

7. Conclusions

This study demonstrates the propensity of the regression models to forecast PV power generation in PV systems. The Sharda PV dataset offers a variety of properties that have helped the proposed model significantly understand the correlation between these variables, which are significant in a majority of PV datasets used in research. The model’s efficacy and accuracy point to it becoming a crucial component in how enterprises develop and operate AI-powered PV grid systems. Given the opportunity for extra parameters in the dataset for model training, the proposed model could achieve higher success rates in addition to metrological properties. It is concluded that the proposed model can be useful for future research and serves as a foundation for improving PV power predictions. Numerous studies have examined the impact and participation of different deep learning models and ensemble approaches, and the findings have been encouraging. The authors intend to use deep learning methods and ensemble methods in future to develop and improve the model and its efficiency. Using the proposed model for datasets with a wide variety of feature vectors is also possible in the future.