1. Introduction
Renewable energies, with solar power at the forefront, are essential to meeting the challenge of a sustainable energy supply [
1,
2]. However, the unpredictable nature of sunlight prevents the full potential of solar energy from being exploited [
3,
4]. To overcome this problem, Maximum Power Point Tracking (MPPT) technology and reliable weather forecasts optimize the PV system efficiency and energy production [
5,
6]. MPPT ensures that solar panels operate at maximum power under varying sunlight conditions [
7,
8]. Accurate weather forecasts allow proactive adjustments to MPPT algorithms and system operations [
9,
10]. The integration of MPPT technology and reliable weather forecasts significantly improves the energy yield and efficiency of solar installations [
11,
12]. These advances pave the way for a sustainable solar-powered energy future [
13,
14].
Conventional MPPT algorithms, such as Perturb and Observe (P&O), Hill Climbing (HC), and Incremental Conductance (IC), often struggle to efficiently track the Maximum Power Point (MPP) under stochastic conditions [
15,
16]. These limitations can lead to significant energy losses and reduced system efficiency [
17,
18].
Advanced MPPTs such as particle swarm optimization (PSO) and JAYA outperform but are not well-suited to addressing large and complex optimization challenges and are prone to triggering at local optima [
19,
20]. PSO can converge prematurely to sub-optimal solutions [
21], while JAYA’s sensitivity to initial conditions and limited exploration of the search space can hamper its effectiveness [
22]. The large search space inherent in the genetic algorithm (GA) parameter optimization process can significantly hamper the system speed and increase the complexity [
23].
These limitations can lead to significant energy losses in solar energy systems, particularly in dynamic environments with fluctuating irradiance and partial shading [
24].
This research addresses the challenge of optimizing operational processes under uncertainty by applying a methodology described in [
25]. Stochastic optimization problems are addressed by transforming them into equivalent deterministic formulations, in particular, in scenarios with fully admissible solutions. The approach introduces a deterministic optimization problem presented as a minimum-risk problem (MRP), solved efficiently using non-linear mathematical programming methods. This methodology is then applied to derive optimal decision frameworks for simplified industrial applications, with a specific case study demonstrating the practical application in the optimization of solar energy systems.
In addition, the growing need to predict future trends in various fields has fuelled a strong demand for forecasting techniques. In this context, ANNs have emerged as powerful tools. ANNs have been successfully applied in various fields, including tourism (e.g., forecasting tourist numbers or hotel stays [
26]), financial trading [
27], and the energy sector (e.g., forecasting renewable energy production and energy consumption [
28,
29,
30]). Numerous studies consistently demonstrate the superior performance of ANNs, particularly when dealing with high-frequency data, compared to traditional forecasting methods.
In [
31], the performance of the ANN model was evaluated against various models documented in the literature, including Quadratic Support Vector Machine (QSVM), Decision Tree [
32], Convolution Neural Network–Bi-Direction Long Short-Term Memory (CNN-BILSTM) [
33], Deep Learning (DL) [
34], Adaptive Neuron Fuzzy Inference System (ANFIS) [
35], Group Method of Data Handling (GMDH) [
36], and ANFIS-PSO [
37], to predict different types of solar radiation. The evaluation used the Mean Squared Error (MSE) and regression(R) criteria to ensure a complete and accurate comparison. The results of this comparative analysis unequivocally demonstrated the superior accuracy of the ANN model compared with the aforementioned models. In particular, the study highlighted the challenges associated with determining hyper-parameters and specific parameters in the other models, a concern mitigated by the relative ease of implementation of the ANN model.
In many studies, researchers have frequently used the proportional integration (PI) controller to regulate the controller duty cycle. Specifically, in research [
38], the Fuzzy-PI method was used for control and, in another study [
39], a combination of ANN and PI was implemented. Despite the effectiveness of the PI controller, it faces challenges related to its inherent linearity, which complicates its applicability to non-linear systems, as well as the tuning complexities associated with selecting optimal parameters. Alternatively, sliding mode control (SMC) is emerging as a robust and versatile control method recognized for its ability to handle uncertainties and disturbances in dynamic systems.
Many approaches have been explored by researchers to improve the efficiency of photovoltaic systems. In [
40], the authors presented a PV-TE hybrid system, combining photovoltaic (PV) and thermal (TE) cells, as a solution to the energy efficiency problems of PV technology. In parallel, ref. [
41] used a fuzzy method to find the Maximum Power Point (MPP), while [
42] used mathematical models for gradient optimization specifically adapted to photovoltaic panels. Despite their effectiveness, these methods do not address stochastic challenges due to the dynamic nature of the environment. Various prediction techniques, including physical methods, have been proposed, but they have some limitations. For example, as reported in [
43], physical and indirect forecasting methods struggle to accurately predict future weather conditions. However, in [
41], artificial intelligence emerged as a promising avenue for forecasting.
This paper presents significant advances in the applications of control systems for renewable energy sources. A key aspect of this work is taking advantage of artificial neural networks (ANNs) for temperature and solar radiation forecasting. The adoption of artificial neural networks is justified by their versatility and proven effectiveness in various domains, highlighting their suitability for this particular field. In addition, the paper proposes a new approach using the MRP-SMC method to control DC–DC converters, aligning with the essential principle of Maximum Power Point Tracking (MPPT). This innovative methodology improves converter performance, thus optimizing energy extraction in renewable energy systems.
This paper introduces two pivotal contributions to the field. First, it harnesses the power of artificial neural networks (ANNs) to accurately predict temperature and solar radiation levels, taking advantage of their well-established effectiveness in a multitude of domains. Secondly, it adopts an innovative MRP-SMC-based approach to control DC–DC converters according to the principles of Maximum Power Point Tracking (MPPT). The MRP method skillfully addresses the stochastic challenges arising from unpredictable weather conditions, while sliding mode control (SMC) excels in its ability to managing the uncertainties and disturbances inherent in dynamic systems. By seamlessly integrating these two methodologies, the paper improves the ability to explore the point of maximum power and precisely regulate the flow of energy within renewable energy systems. This holistic approach not only improves efficiency but also enhances the reliability of these systems, paving the way for sustainable energy solutions in the face of changing environmental dynamics.
The paper is structured as follows:
Section 2 delves into the methodology, discussing the theoretical framework of the PV model and boost converter, as well as the predictive system and controllers utilized for MPPT.
Section 3 outlines the neural-network-based predictive models employed, while
Section 4 presents an analysis of the PV characteristics and controller performance. In
Section 5, a comparative study is conducted between the proposed forecasting method and methods relying on the time series, alongside a comparison of the proposed MPPT method with the JAYA technique to evaluate the efficiency of the combined strategy. Finally,
Section 6 concludes with a summary of the research’s main achievements.
3. Neural-Network-Based Predictive Models
Artificial intelligence, especially NNs, is becoming more popular for forecasting because they are good at it. NNs work similarly to the brain, with interconnected parts that help them process information. They are being used in many industries, including forecasting, and they are showing great promise in making accurate predictions. The structure of the NN is represented in
Figure 4.
The ANNs process information through a multi-layer architecture. The input layer receives the raw data, which are then transformed, and features are extracted in hidden layers using activation functions. The output layer produces the final prediction. The number of hidden layers, biases, and pooling layers are adjusted based on the complexity of the problem to improve performance. Customizing the network layers and neurons is crucial for each specific problem and dataset. This process is represented by Equation (22).
where
Y: the output layer;
σ: The activation function;
Wi,j represents the weight linking the ith neuron in the preceding layer to the jth neuron in the current layer;
Xj: The output of the ith neuron in the previous layer;
β: Biases.
To predict temperature and solar irradiance, we use an NN with the sigmoid activation function, which introduces non-linearity and ensures output values stay between 0 and 1, making it suitable for these continuous variables.
The process begins with data collection from the Department of Systems Engineering and Automation at Vitoria College of Engineering using a specialized sensor. The data are pre-processed, transformed, and standardized for input to the neural network. A statistical analysis informs the network design, which includes specific input, hidden, and output layers. The network is then trained using the efficient Scaled Conjugate Gradient (SCG) algorithm with adaptive learning rates and second-order optimization. Key metrics such as MSE and R monitor the training progress until the validation error stabilizes. Once trained, the network predicts the temperature and solar radiation (T and G) of new data. Rigorous validation and testing ensure accuracy and reliability, including partitioning data into training, validation, and test sets to adjust weights, prevent over-fitting, and objectively evaluate the performance. This approach ensures accurate forecasts. The following
Figure 5 and
Figure 6 show the NN performance.
During training, errors started repeating after 600 epochs, so the test was stopped at 677 epochs when the gradient was 0.0098. This repetition showed that the data were becoming more important. Epoch 200 was chosen as the baseline, and its weights were used as the final weights. Validation was carried out from Epoch 6 to 677, with errors repeating six times before stopping (see
Figure 7).
From
Figure 7, the red points represent the neural network’s performance on the validation dataset at each epoch, while the blue line indicates its performance on the training dataset over the epochs.
Figure 8 illustrates the temperature and irradiance prediction outcomes, showcasing the efficacy of the proposed neural-network-based prediction methodology. Rigorously evaluated using real-world data, the technique undergoes a meticulous comparison between the experimental and predicted temperature, as well as irradiance values. The primary goal is to minimize the disparity between the anticipated outcomes and observed data. Encouragingly, a discernible alignment emerges between the predicted values and actual observations, signifying a robust agreement between the predictions and real results.
An analysis of
Figure 8 reveals a good agreement between the predicted values and observed results for temperature, with a minimum error of about 0.16 for solar radiation. The results confirm the reliability and robustness of the forecasting process, and confirm its effectiveness in capturing complex dynamics with a high degree of accuracy.
The efficacy of neural networks heavily relies on hyper-parameters. Previous studies, referenced as [
48,
49], have explored various techniques such as the Bayesian Gaussian substitution process, boosted gradient regression trees, random forest, and heuristic algorithms to identify optimal hyper-parameter configurations. In this current investigation, diverse neural network architectures underwent training and cross-validation. This process involved weight optimization using the back-propagation algorithm, while considering the impact of the number of epochs and hidden-layer NNs’ performance.
Through experimentation, the most efficient configuration was determined to be a two-layer feedback network with 15 hidden-layer neurons, trained for 1000 epochs using the SCG algorithm. The dataset comprised 60,538 temperatures and solar radiation values, with 70% allocated to training and 30% to validation and testing sets. The network demonstrated its suitability for regression tasks, evidenced by an MSE of 0.0044 and R of 0.99, as depicted in
Figure 5 and
Figure 6, respectively. These results indicate a strong correlation between the network’s outcomes and the desired objectives, with minimal error.
4. Results
Appendix B and
Appendix C detail the specifications of the SG340P PV panel and the boost converter, with a resistor used as the load. The initial step was to assess the SG340P panel’s performance under various temperature and radiation levels.
Figure 9 presents the IV and PV characteristics recorded under these different conditions.
To accurately evaluate the performance of the Minimum-Risk Problem (MRP) algorithm under different conditions, we conducted a series of tests at different levels of temperature and solar radiation.
Figure 10 provides details of the test parameters.
The
PPV curve shows the power generated by the PV panel without tracking, while the
PMPP represents the maximum power achieved with the proposed tracking technique.
Figure 11 demonstrates that the PV power curve does not reach its maximum potential. However, the strength of the MPP detection algorithm lies in its precise identification of the Maximum Power Point (MPP), even during sudden fluctuations, a challenge for other methods. This highlights its exceptional ability to adapt to dynamic conditions.
Figure 12 illustrates the overall design. The effectiveness of the new neural-network-based prediction technique is evaluated by comparing the actual and predicted temperature and irradiation values, aiming to minimize the difference between the target and the predicted values.
We used the predicted temperature and radiation (Tf and Gf) from
Figure 13 to simulate the model and forecast the system’s behavior under these conditions.
Figure 14 shows the control signal and the error between the reference current (I
mpp) and the boost input current. The duty cycle changes along with the MPPT variations. This demonstrates the controller’s ability to adjust to changing system conditions.
The small error shows that the SMC is accurate and effective in controlling the process.
Figure 15,
Figure 16 and
Figure 17 display, respectively, the voltage, current, and power results for our model, using a load with a resistance of 30 Ω.
The previous figures demonstrate the optimization method’s success in reaching the maximum point. The method adapts well to predicted changes, as seen in
Figure 13. The SMC effectively tracks changes from both the optimizer and the PV panel, showing a strong performance during dynamic system transitions.