## 3 Case Study: Design and Implementation of the Photovoltaic Control System  
The modeling and design technique proposed in this paper is explained by a real-life case study example. Figure 8 shows the concept of a smart photovoltaic control system. The main aim of the presented concurrent system is to control the solar panels depending on their temperature and current power production in order to prevent the overloading of the electricity grid. As photovoltaic systems become more popular nowadays, the risk of grid overloading increases [90; 91]. Therefore, the presented concurrent control system permits the control of the production and allows for the reduction in the production by the dynamical switching on/off of particular solar cells.  
In the realm of renewable energy, smart photovoltaic (PV) control systems represent a significant leap forward in managing and optimizing energy production. However, the current landscape of these systems is characterized by a reliance on traditional control methodologies that are often rigid and unable to capitalize on the dynamic nature of solar energy fully. These conventional systems are limited by their rule-based algorithms which cannot adequately handle the variability and unpredictability inherent in solar irradiance and weather conditions. As a result, a substantial gap exists between the potential and actual performance of PV systems, leading to inefficiencies and energy losses [92]. The proposed hybrid approach seeks to bridge this gap by introducing a sophisticated layer of machine learning algorithms that can learn from data, predict future conditions, and make intelligent decisions in real time [92]. This approach is inspired by recent advancements in subsurface engineering environments, where intelligent decision-making strategies have been successfully applied to predict fire intensity and rockburst events. By adopting similar  
Figure 8: Model of a smart photovoltaic system.  
machine learning techniques, such as t-SNE for dimensionality reduction, K-Means Clustering for pattern recognition, and XGBoost for predictive modeling, the hybrid system aims to overcome the limitations of existing PV control methodologies [93]. This integration of machine learning not only enhances the adaptability and efficiency of the control system but also paves the way for a more resilient and responsive energy grid. Thus, the novelty of the hybrid approach lies in its potential to transform the smart PV control landscape, offering a solution that is both innovative and imperative for the advancement of sustainable energy systems [94].  
Going into the details of the proposed photovoltaic system, each panel of the presented photovoltaic system is composed of eight solar cells (modules), denoted by \(m_{1},\ m_{2},\ \dots,\ m_{8}\). Furthermore, each module contains built-in sensors that allow for the measurement of its temperature and current power production. The measured data are sent to the operational center. Depending on the needs, the operational center dynamically configures the system by adjusting the number of enabled solar cells. The system works as follows. Firstly, the system examines whether the particular solar cell is enabled or disabled. The measurement is performed only for the enabled modules. If such a condition is fulfilled, the current temperature and power production are read from the sensors. The obtained data are analyzed by the modeled concurrent control system according to the over-high temperature and overload of the power. Finally, the result is sent to the operational center, which makes a decision about switching on or off the particular panels to prevent the overloading of the electricity grid. To avoid improper measurements (e.g., in the case where the particular module is disabled), particular sensors are active only if the referred module is enabled. Let us formally specify the discussed smart photovoltaic system by an interpreted Petri net.