Fibonacci solar tree: Mathematical modeling of the solar incidence as a function of its constructive variables

Abstract

Solar trees are three-dimensional engineered structures that mimic natural trees, with trunks, branches, and photovoltaic leaves, constituting a way of verticalizing solar plants. That is a trend emerging to replace the conventional horizontal system, enabling to generate more energy in a smaller area. However, in a solar tree, there are losses in light capture due to the shading that upper leaves cast over the lower ones. In this work, we propose the configurable Fibonacci Solar Tree design, which is inspired by natural trees and aims to minimize shading losses. In addition, we analyze the behavior of the configurable Fibonacci solar tree in relation to its constructive variables (i.e. height, leaf area, number of leaves, projection radius), and propose a methodology to obtain an equation for the average annual solar incidence as a function of them. For this, automation of the computational simulation process of the efficiency concerning the variables is carried out, obtaining a large volume of instances, which allows the interested party to decide on the best tree according to their criteria. The results are promising, with a Fibonacci solar tree showing solar irradiation 12.8% higher than the best model available in the literature to date.