Mathematical Algorithms and Applications in the Analysis of Photovoltaic Systems

This paper analyzes mathematical modeling and the production of electrical energy using photovoltaic panels. It begins with general considerations and the fundamental principles of mathematical modeling in photovoltaics, emphasizing the importance of optimizing the performance of photovoltaic systems. The radiometric properties of incident light and their impact on the efficiency of photovoltaic panels are discussed. The focus is on the photovoltaic cell, analyzed through the I-V characteristic, construction, and carrier concentration, crucial elements for energy conversion efficiency. The paper explores the role of optics in the performance of photovoltaic cells, detailing the interaction of light with different media and the importance of optical design. Finally, the fundamentals of solar geometry are presented, essential for modeling the sun's trajectory and the optimal positioning of panels. This paper provides an overview of the key elements influencing the performance of photovoltaic systems, offering researchers and practitioners the necessary knowledge to optimize these systems and advance renewable energy technologies.