Forecasting of Solar Power Generation Using Machine Learning and Deep Learning Algorithms

doi:10.21203/rs.3.rs-4963709/v1

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Forecasting of Solar Power Generation Using Machine Learning and Deep Learning Algorithms

https://doi.org/10.21203/rs.3.rs-4963709/v1

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This study analyses the predictability of solar electricity generation using various machine and deep learning methods on large solar datasets from diverse cities in Saudi Arabia and the United States. According to our most recent article [1], the "Multilayer Perceptron" and "Random Forest" algorithms perform better in forecasting Saudi Arabia's solar power generation. This finding has been validated using additional datasets in the present study. Additionally, the effects of various hidden layer and neuron number combinations on MLP performance are examined. We found beyond a certain point, the number of hidden layers in an MLP became inversely correlated with its prediction accuracy. As the number of neurons in the model increases, the training duration also increases, generally improving predictability. The RMSE of deep learning algorithms such as the feedforward neural network (FFNN), convolutional neural network (CNN), and long short-term memory (LSTM) are compared against the MLP and Random Forest to evaluate their feasibility in estimating solar power generation. We found that FFNN and MLP provide almost similar results and Random Forest gives the best results among all the ML and DL algorithms for predicting solar power generation using our datasets. Future work may explore different aspects of the Random Forest model.

Solar electricity prediction

Regression analysis

Machine learning

Deep Learning

Multilayer Perceptron

The transition towards renewable energy sources has become a global priority to mitigate the impacts of climate change and reduce reliance on fossil fuels [2]. Among renewable energy options, solar power stands out for its abundant availability and significant potential for large-scale electricity production [3]. Accurate prediction of solar power generation is crucial for optimizing energy management, integrating renewable sources into the grid, and ensuring a stable energy supply. Leveraging data science and advanced algorithms has revolutionized solar energy prediction, providing sophisticated tools and techniques to analyze vast datasets and derive actionable insights. Key platforms like Weka, MATLAB, and Python have emerged as powerful tools for implementing machine learning (ML) and deep learning (DL) algorithms, offering a wide range of options for data preprocessing, model training, and performance evaluation [4, 5].

The literature on solar power prediction is rich with studies exploring various ML and DL algorithms. Traditional approaches have used statistical models and simpler machine-learning techniques such as decision trees and linear regression [6]. Recent advancements have shifted towards more complex models, including Multilayer Perceptron (MLP), Random Forest, Convolutional Neural Networks (CNN), Feedforward Neural Networks (FFNN), and Long Short-Term Memory (LSTM) networks [x8]. Despite significant progress, there remains a gap in understanding the comparative performance of these algorithms across different geographic regions with diverse climatic conditions. This study aims to address this research gap by evaluating the predictability of solar electricity generation using various ML and DL methods on large solar datasets from Dhahran (Saudi Arabia), Florida (USA), Oregon (USA), and Colorado (USA). By analyzing the performance of algorithms like MLP, Random Forest, FFNN, CNN, and LSTM, this research provides a comprehensive comparison and identifies the most effective models for different environments. Additionally, this work investigates the effects of different hidden layer and neuron number combinations on MLP performance, offering valuable insights for future algorithm optimization.

K-Nearest Neighbors (KNN)

KNN is an instance-based learning algorithm used for both regression and classification tasks. Its operating principle is that similar data points exist in close proximity. In classification tasks, it assigns a class to a data point based on the majority class among its 'k' nearest neighbors. In regression tasks, it predicts the output value by averaging the values of the 'k' nearest neighbors [7]. This algorithm has several advantages that make it appealing for machine learning tasks. It is straightforward to understand and implement, making it an excellent choice for beginners. Additionally, it does not require a separate training phase, allowing for quick setup. KNN is also flexible because it does not make any assumptions about the underlying data distribution, enabling it to adapt effectively to a wide range of data patterns [8]. However, KNN has some notable disadvantages. It performs slowly on large datasets because it computes the distance to all training data points for each prediction, and it requires significant memory to store all these points. The algorithm is also sensitive to irrelevant features, which can affect distance calculations and reduce prediction accuracy [8, 9].

Multilayer Perceptron (MLP)

A Multilayer Perceptron (MLP) is a type of feedforward neural network composed of an input layer, one or more hidden layers, and an output layer. Each layer consists of nodes (or neurons), with every node in one layer connected to every node in the next layer, forming a fully connected network [10] as shown in Fig. 1a.

MLPs can be used for both classification and regression tasks across various fields. For example, in image recognition, they classify images into different categories; in speech recognition, they transcribe spoken words into text. They are also employed in financial forecasting to predict market trends and stock prices, and in the medical field, MLPs assist in diagnosing diseases based on patient data. Input data enters through the input layer and moves forward through the hidden layers, eventually reaching the output layer where it generates a result. Connections between neurons have weights, and each neuron includes a bias term. These parameters are tuned during training. The backpropagation algorithm calculates the gradient of the loss function concerning each weight and bias. Weights are then updated using an optimization algorithm like gradient descent to reduce prediction error. Neurons apply activation functions such as sigmoid, hyperbolic tangent (tanh), or rectified linear unit (ReLU) to introduce non-linearity, enabling the network to learn complex patterns.

Training Multilayer Perceptrons (MLPs) can be time-consuming and resource-intensive, especially with large datasets and deep networks [m3]. Large amounts of data are usually required to train MLPs effectively and prevent overfitting [m4]. Several factors need to be considered to ensure effective performance when implementing MLPs. Data preprocessing, such as normalizing or standardizing input data, can improve training convergence. Hyperparameter tuning, which involves selecting the appropriate architecture (number of layers and neurons) and hyperparameters (number of epochs, learning rate, batch size), often requires experimentation and cross-validation [11]. Multilayer Perceptrons (MLPs) can model complex relationships in data due to their multi-layer structure and non-linear activation functions. The architecture can be customized by varying the number of layers and neurons, making MLPs adaptable to various problems.

Random Forest

Random Forest is an ensemble learning algorithm that creates multiple decision trees during training and combines their results to improve accuracy and reduce overfitting. This algorithm applies to both regression and classification tasks [14]. Combining the predictions of several base estimators, it reduces variance and enhances generalization. Random Forest also provides insights into feature importance, allowing analysts to identify the most significant features. These characteristics highlight its effectiveness as a robust and adaptable tool in predictive modeling. During training, Random Forest uses bootstrap sampling to create random subsets of the training data. At each split, a random subset of features is selected to ensure diversity and reduce correlation among the trees. Each tree is built independently on different subsets of data and features (Fig. 1b). Random Forest achieves high accuracy by combining predictions from multiple decision trees, reducing variance and improving overall accuracy. This ensemble approach enhances the algorithm's robustness, significantly reducing the likelihood of overfitting compared to individual decision trees, especially with an adequate number of trees.

Despite its strengths, Random Forest has several drawbacks. First, training multiple decision trees can be computationally intensive, requiring substantial processing power and memory, which poses challenges for large datasets. Second, the ensemble nature reduces interpretability compared to individual decision trees, making it harder to understand how specific features influence predictions across the model. Finally, the complexity of Random Forest necessitates careful hyperparameter tuning, including the number of trees, tree depth, and feature selection criteria [15]. Effective implementation of Random Forest involves several critical considerations. Hyperparameter tuning is essential, with parameters such as the number of trees [r6], maximum depth, and minimum samples per leaf needing optimization for optimal performance. Handling imbalanced datasets is another important factor, where techniques like resampling or adjusting class weights can help maintain balance and improve predictive outcomes [16]. Leveraging parallel processing capabilities can significantly accelerate training times by allowing each decision tree to be built independently, enhancing overall computational efficiency.

M5 Tree

M5 Tree is a machine learning algorithm used for regression tasks. It builds decision trees by recursively splitting the dataset based on feature conditions to predict continuous numerical values. Unlike traditional decision trees, M5 Tree incorporates model tree nodes where linear regression models are used at the leaf nodes to improve accuracy. This hybrid approach allows M5 Tree to capture complex relationships in data while maintaining interpretability [17].

SMOReg

SMOReg, or Sequential Minimal Optimization for Regression, is a machine learning algorithm designed for regression tasks using support vector machines (SVM). It optimizes a set of linear equations derived from training data to find a regression function that best fits the data points. SMOReg operates by iteratively updating weights for support vectors until convergence, aiming to minimize prediction errors. This algorithm is particularly effective in tasks where the relationship between outputs and inputs is not linear and requires flexibility in defining decision boundaries [18]. However, SMOReg may be computationally intensive and sensitive to parameter tuning, impacting its efficiency and performance on large datasets.

FFNN (Feedforward Neural Network)

A Feedforward Neural Network (FFNN) is a type of artificial neural network where information flows in one direction, from input nodes through hidden layers to output nodes. Each layer comprises nodes (neurons) connected to nodes in the next layer by weighted connections. During training, FFNNs adjust these weights based on error gradients to minimize prediction errors. They are widely used for tasks like classification and regression in fields such as finance, healthcare, and natural language processing [19]. FFNNs excel in capturing complex patterns in data and can generalize well, but they may struggle with handling sequential data and require extensive hyperparameter tuning to prevent overfitting [20].

CNN (Convolutional Neural Network)

A Convolutional Neural Network (CNN) is designed for processing grid-like data, such as images, and is used in tasks like image recognition and computer vision. CNNs employ convolutional layers that apply filters over input data to detect spatial patterns, followed by pooling layers to reduce dimensionality and increase computational efficiency [21]. They can be computationally intensive and require large amounts of training data to generalize effectively.

LSTM (Long Short-Term Memory)

An LSTM network is a type of recurrent neural network (RNN) designed to model sequential data by overcoming issues like the vanishing gradient problem that traditional RNNs often face [22]. LSTMs utilize a sophisticated gating mechanism to selectively retain or forget information across long sequences. This capability makes them highly suitable for tasks such as time series prediction, natural language processing, and speech recognition [23]. LSTMs excel in capturing long-term dependencies in data and they accommodate sequences of varying lengths during training. However, they may be prone to overfitting with small datasets and require careful tuning of hyperparameters like the number of layers and learning rates to achieve optimal performance.

This study uses four sets of data from two sources: KFUPM, Saudi Arabia [1], and NREL, DOE, USA [24]. The first dataset includes various meteorological information such as temperature, humidity, air pressure, air speed, and corresponding voltage yields from a crystalline solar panel in Dhahran, KSA. These data were recorded at 20-second intervals for 8 days, resulting in a total of 632 instances. The other three datasets measure the performance of single-crystalline silicon PV modules in three climatically diverse locations: Cocoa, Florida; Eugene, Oregon; and Golden, Colorado. These datasets include values for dry-bulb temperature, relative humidity, atmospheric pressure, daily accumulated precipitation, PV module back surface temperature, and soiling rate. The fill factor was determined from the open-circuit voltage, short-circuit current, and maximum power of the PV module. Measurements were taken at 5-minute intervals in Cocoa and Eugene or 15-minute intervals in Golden. Data collected over 12 months in Golden and six months in Cocoa and Eugene were evaluated in this study. Wind speed and direction were excluded because their instantaneous values at the time of the I-V curve measurement do not correlate with PV module temperature due to the lag in PV module cooling or heating because of its thermal mass. A flowchart of the methodology used in this study is shown in Fig. 2.

A GUI-based WEKA data mining software [12] was used to apply different machine-learning techniques. During data preprocessing, outliers and extreme values were removed using the ‘InterquartileRange’ filter, and the data were normalized. Default factors for extreme values and outliers were used. The data were split into 20% for testing and 80% for training to develop the model. KNN, MLP, M5Tree, SMOReg, and Random Forest algorithms were employed on the processed data, and the correlation coefficient (CC), mean absolute error (MAE), and root mean square error (RMSE) were obtained. Correlation coefficients are inversely proportional to various errors (RAE, RMSE). In this study, CC and RMSE values were primarily used to interpret the results. Although WEKA supports a deep learning (DL) module, MATLAB was preferred for employing DL algorithms because its DL toolbox offers a variety of activation functions for hidden layers and training options. Here, imageInputLayer, convolution2dlayer, reluLayer, fullyConnectedLayer, and regressionLayer are used in the CNN model. The ReLu activation function is mainly used to handle non-linearity in the test data and various types of input parameters in the model. ‘Adam’ optimizer is used with 1000 epochs to train the model. Normalized data were used as input for the DL algorithm evaluation.

4.1 Machine Learning Methods

The effect of data preprocessing, specifically the application of extreme value and outlier removal filter, on the correlation coefficient (CC) is shown in Fig. 3. Machine learning techniques were used to determine the correlation coefficients, keeping all the parameters of these algorithms at their default settings as set by the WEKA workbench. This operation was done twice, first while datasets contained outliers (Fig. 3a), and the second time, outliers were removed (Fig. 3b).

The histograms indicate that CC values generally improve after removing outliers and extreme values, particularly for KNN, M5Tree, and MLP. The outlier removal filter appears to have a negligible impact on the SMOreg and Random Forest models. On the other hand, the performance of M5Tree seems highly sensitive to outlier removal filters. Among all the models, the SMOreg model performs the worst in predicting solar power production, while the Random Forest model yields the best correlation coefficient values, ranging from 0.85 to 0.99. Although researchers have claimed that Support Vector Machine (SVM) is a powerful tool for regression analysis, it does not perform well in this study. Here, we used SMO (sequential minimal optimization), which generally solves quadratic problems in SVMs. A future work may involve a detailed analysis of SVM model to accurately predict the generation of solar electricity.

This study focuses on the Multilayer Perceptron (MLP) module of WEKA workbench. In the following section, the role of hidden layer and neuron number in MLP is investigated. To study the effect of the number of neurons, we kept the number of hidden layers constant, as shown in Table 1. Here the number of neurons in each layer has been altered systematically. Also, the number of hidden layers is varied in the later section. The first column of Table 1 shows the number of default hidden layers in WEKA, where \(\:a=\left(nos.\:\:of\:atrributes+classes\right)/2.\) This means that for the Dharan data, \(\:a\) is 3, and for Cocoa, Eugene, and Golden, \(\:a\) is 4. The investigation matrix is designed in such a way that the number of neurons not only varies across different cases but also follows both ascending and descending orders to the order of the hidden layers.

Table 1

Matrix for the investigation of the effect of neuron number on the performance of MLP algorithm
Cases	Number of Neuron in Hidden Layer
Cases	1st layer	2nd layer	3rd layer
1	a	1	1
2	a	1	3
3	a	1	6
4	a	3	1
5	a	3	3
6	a	3	6
7	a	6	1
8	a	6	3
9	a	6	6

Figure 4 implies that data recorded in Dhahran and Golden do not show any dependency between the correlation coefficient and the different cases in Table 1 when using MLP. However, the correlation coefficient increases significantly for the data measured in Cocoa when the number of neurons in the second hidden layer is more than 3. For the data from Eugene, there is no distinguishable relationship with the number of neurons. Neuron number is ascending order according to the hidden layer increases CCs. Considering all the datasets and investigation cases, Case 6 appears to perform the best overall where 1st, 2nd, and 3rd hidden layer consists of \(\:a\), 3, and 6 number of neurons, respectively.

Table 2 is the investigation matrix, is organized to study the effect of the number of layers on the predictability of solar electricity generation. As we can see, the number of hidden layers is increased from 1 to 4, with each layer containing a different number of neurons. Here we formulate the matrix keeping the best neuron numbers (\(\:a\), 3, 6) of Figure. Addiotionally, number of neuron is increased in 3 hidden layer architure (case 13) to check the relavance of the result of Fig. 4. Figure 5 shows that the number of layers does not influence the data measured in Dhahran, Eugene, and Golden, provided the total number of hidden layers does not exceed 3 and each layer has a sufficient number of neurons to transfer information. However, one hidden layer does not work well for the data from Cocoa. Consequently, it can be concluded that MLP performs better in our study for cases 4 to 8 and it has the case 6 of Table 1.

Table 2

Matrix for the investigation of the effect of hidden layer numbers on the performance of MLP algorithm.
Cases	Number of Neuron in Hidden Layer
Cases	1st layer	2nd layer	3rd layer	4th layer
1	a
2	3
3	6
4	a	3
5	a	6
6	a	3	3
7	a	3	6
8	a	6	6
9	a	3	3	3
10	a	3	3	6
11	a	3	6	6
12	a	6	6	6
13	a	6	8

4.2 Deep Learning Methods

The performance of deep learning methods, namely feed-forward neural networks (FFNN), convolutional neural networks (CNN), and long short-term memory (LSTM) techniques, is evaluated in this section. Figure 6a plots the test data measured in Eugene against the corresponding data generated using FFNN, CNN, and LSTM. Similar sets of data for Golden are shown in Fig. 6b. Gray, blue, green, and violet symbols refer to the data obtained from the experiment, FFNN model, CNN model, and LSTM model, respectively. An enlarged view of these plots indicates that the results from the DL methods follow the pattern of the test data, with most predictions accurately estimating the test data. Discrepancies are particularly noticeable in the low fill factor region (Fig. 6a). Numerical data was also found to be shifted from the test data. A close view in Fig. 6b reveals that the test data do not follow a smooth path. Marion et al. [4] mentioned that the uncertainty in the measurement of the fill factor is 0.558%. Therefore, we may expect deviations to some extent in predicting the experimental data. Although the numerically generated curves qualitatively follow the experimental data, quantitative validation is still needed. Additionally, a performance test of the DL methods is required. In this context, Fig. 7 compares the test data against the numerical data generated from each DL model (FFNN, CNN, LSTM).

All the test data recorded in Dhahran, Cocoa, Eugene, and Golden are plotted in the graphs of Figs. 7a, 7b, and 7c. Figures 7a, 7b, and 7c show the numerically predicted data from FFNN, CNN, and LSTM techniques, respectively. We found that FFNN, CNN, and LSTM are capable of predicting 97.52%, 92.13%, and 96.98% of the test data within a deviation of ± 30%, respectively. A common trend in all the graphs is that the numerical data overestimate the experimental data, which is particularly clear for CNN in Fig. 7b. The test data from Golden and Dhahran show the minimum deviation, whereas the data from Eugene show the most deviation. FFNN requires relatively less computational power compared to LSTM. Therefore, we can conclude that FFNN is the most effective deep learning method for predicting the test data from Dhahran, Eugene, Cocoa, and Golden.

Here we combine RMSE values of the best-performing ML models and all the DL models. The results are shown in Fig. 8. The best combination of the number of hidden layers and the number of neurons from this study (case 7, Table 2) was used to calculate RMSE values using both MLP and FFNN methods. An additional condition (case 13, Table 2) was also studied to check the consistency of the effects of hidden layers and neuron numbers.

The comparison between FFNN in case 7 and case 13 in terms of RMSE confirms that a neural architecture with 3 hidden layers and a moderate number of neurons in each layer performs the best. Conversely, the performance of MLP for cases 7 and 13 is slightly worse than that of FFNN, possibly due to differences in layer activation functions and data training options. Here it is to be noted that the neural architecture FFNN is very similar to that of the MLP model. The MLP is a type of multilayer FFNN. The CNN yields the worst results, particularly for the datasets recorded in Eugene which also confirms the result of Fig. 7b. Among all the ML and DL methods, the Random Forest model has been found to predict the test data most efficiently in terms of RMSE value and computational cost and the second most efficient method is FFNN.

Predicting future solar energy based on existing meteorological data is of great interest to the solar industry and researchers. Advanced tools are currently employed to model solar power estimation. One limitation is the lack of systematically generated data, which hinders the development of a generalized model. Another challenge is selecting a model that is both accurate and cost-effective. This study investigates the performance of various machine learning and deep learning algorithms, including KNN, Random Forest, Multilayer Perceptron (MLP), M5 Tree, SMOreg, Feedforward Neural Network (FFNN), Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM) in predicting solar power. The effect of different combinations of neurons and hidden layers in the MLP algorithm on solar power estimation was also examined. Input and output data were collected from four different regions: Dhahran (Saudi Arabia), Florida, Oregon, and Colorado (USA). At a certain point, the prediction accuracy of an MLP becomes inversely related to the number of hidden layers. However, as the number of neurons in the model increases and the training period lengthens, predictability frequently improves. Our findings indicate that MLP and FFNN produce nearly identical results, while Random Forest outperforms all other ML and DL models using default settings. Future research could explore the influence of different variables in the Random Forest model to determine the optimal settings for predicting solar power.

Conflict of Interest

There is no conflict of interest.

Author Contribution

D.S. conceptualized, collected raw data, performed calculation, analysed data, processed data, wrote a part of the first draft, and reviewed. R.K. wrote a part of the first draft.

Acknowledgement

Authors are grateful for the thoughtful assistance in reviewing the article provided by Dr. Md. Arifuzzaman and Dr. Mohammad Kamal Hossain from King Faisal University and King Fahd University of Petroleum and Minerals, respectively.

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No competing interests reported.

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Forecasting of Solar Power Generation Using Machine Learning and Deep Learning Algorithms

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Abstract

Figures

1. Introduction

2. Description of Prediction Algorithms

3. Data Collection and Preparation

4. Results and Discussion

4.1 Machine Learning Methods

4.2 Deep Learning Methods

Conclusion

Declarations

Conflict of Interest

Author Contribution

Acknowledgement

References

Additional Declarations

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