A general algorithm for the optimization of photovoltaic modules layout on irregular rooftop shapes

Although the installation of photovoltaic systems on roofs is a successful investment, rooftop space availability has been identified as a significant limiting factor in achieving zero-energy buildings, especially by building components such as chimneys, elevator machine rooms, fans, plumbing vents, etc. This study presents a general algorithm for the optimal deployment of photovoltaic module rows installed on irregular flat roof shapes. The presented algorithm takes into account the irregular rooftop shape, the self-shading of photovoltaic modules, the inclusion of building components, commercial photovoltaic modules with different sizes, mounting systems with different configurations, distances required for maintenance, and the technical reports to minimize shading effects. The proposed algorithm allowed to increase in the amount of solar energy received by the photovoltaic modules. The optimization process takes into account the weather conditions at the specific location. The optimization algorithm was implemented using a specific Mathematica™ code in which the commands used in the development of the code were introduced to facilitate its replication. The optimization algorithm output provides the essential parameters for the optimal photovoltaic system design such as: the optimum number of mounting systems and their configuration, the optimum tilt angle of the mounting system and its dimensions, the photovoltaic module model, the maximum total area of the photovoltaic field and the maximum annual energy captured by the photovoltaic modules. We compared the mounting system layout obtained with the proposed algorithm with the tilt angle photovoltaic module layout recommended by three technical papers (IDAE Technical Report, Lorenzo’s equation and Jacobson’s equation) with respect to photovoltaic field area gain, energy gain and levelized cost of energy.The optimal photovoltaic module layout obtains the maximum photovoltaic field area gain of 35.52% with respect to the Jacobson’s equation and the minimum of 32.29% with respect to the IDAE Technical Report. The optimal photovoltaic module layout obtains the maximum energy gain of 27.83% with respect to the Jacobson’s equation and the minimum of 24.84% with respect to the IDAE Technical Report. The levelized cost of energy of the optimal PV module layout is lower than that of the other arrangements studied. The algorithm presented may be useful for decision-makers or policymakers in determining the optimal distribution of photovoltaic modules on irregular rooftop shapes.