Economical sizing and multi-azimuth layout optimization of grid-connected rooftop photovoltaic systems using Mixed-Integer Programming

Abstract

Solar energy is expected to be a significant contributor to meet the increasing global energy demand. Rooftop photovoltaic (PV) systems account for a substantial portion of the global solar energy potential. However, optimizing the size and layout of these systems remains challenging. Existing approaches either focus on maximizing energy generation, heavily restrict the space of potential layouts, ignore inverter-type implications, or neglect practical aspects, such as minimizing self-shading. This paper presents a mixed-integer programming (MIP) model to address these limitations for PV systems installed on flat rooftops. The proposed model optimizes the net present value (NPV) and can produce multi-azimuth layouts while accounting for practical considerations, including mitigating self-shading, and ensuring rooftop walkability. The proposed model is adapted for systems that utilize micro-inverters or string-inverters. Two case studies are conducted to evaluate the performance of the proposed model. In one case study, the model is applied to a residential area. It is numerically shown that in some instances of capital costs and billing policies, the use of multi-azimuth layouts could significantly improve the NPV compared to the use of single-azimuth layouts with parallel rows of panels. The proposed model solutions are compared to an existing optimized installation in the second case study. The proposed model multi-azimuth layout solution improves the NPV by 10.17%. When restricted to single-azimuth layouts, the proposed model produces the same design as that of the existing installation in only a few seconds.