Optimization of the distribution of small scale linear Fresnel reflectors on roofs of urban buildings

Abstract

• We present a new optimization method, related to the packing mathematical problem. • The objective is to maximize the collection area considering gaps and shadows. • The influence of the form and orientation of the available roof area is analysed. • The algorithms present good convergence and time efficiency figures. This paper analyses the optimization of the distribution of small-scale linear Fresnel reflectors on roofs of urban buildings. The effects of the two major design parameters (i.e., the form and orientation of the available roof area) on the performance of the reflectors are assessed. We present three new algorithms, related to the classical packing mathematical problem, to develop the optimization method. As decision variables, we use the mirror length and the mirror field width (bounded between upper and lower bounds), jointly with the spacing arrangement of the reflectors. The specific objective is to maximize the collection area considering gaps and shadows. To this end, we will optimize the arrangement, number and dimensions of the reflectors. Finally, we present examples based on real cases and analyse the convergence and accuracy of the algorithms, as well as the required computational effort.