Resumen de Graph theory modelling of pv systems & contributions to the study of radial moore graphs

Jesus Miguel Ceresuela Torres

• In the first part, a characterization of photovoltaic elements using graph theory is proposed. The goal is to optimize the connection of photovoltaic modules to improve reliability and efficiency in energy generation. Directed graphs are used to represent the interconnections, developing an algorithm that generates and classifies photovoltaic arrays according to the reliability polynomial, adjusted to evaluate the expected power under random failures. An algorithm is also proposed to enhance the computational cost of the calculation of this polynomial in arrays characterized by Two Terminal Series Parallel (TTSP) graphs.

  The second part contributes to the degree-diameter problem, focusing on maximizing the number of vertices in a graph under constraints on connections and distances. Moore radial graphs are studied in mixed and undirected cases, proving the existence of two infinite families of these graphs and presenting new bounds and conjectures on their status. Additionally, an Integer Programming (IP) model is developed to identify new mixed radial Moore graphs.