Optimal Design of Efficient Rooftop Photovoltaic Arrays

This paper addresses a major challenge in the residential solar industry: automated design of cost-effective, efficient rooftop photovoltaic (PV) installations. Optimal designs choose system components, locations, and wiring to minimize cost while meeting desired energy output and complying with all physical and legal constraints. We present a novel lower bound for the energy produced by a PV installation, which admits efficient optimization via integer linear programming. The resulting algorithm can design systems with a variety of solar hardware, including microinverters, string inverters, and direct current (DC) optimizers, and optimize for complex shading patterns. Prior to our work, solar installers designed PV installations by hand. Our algorithm automates PV design using operations research (OR) techniques and has been used to create more than 70,000 designs for PV installations. We compare the performance of our optimal designs to designs produced by solar-installation experts at the National Renewable Energy Laboratory. Our algorithm designs faster, cheaper, more energy-efficient installations than expert installers, producing designs in tens of seconds, where experts require tens of minutes. The optimized designs deliver the required energy output at lower cost in more than 70% of cases and on average increase the energy produced per dollar invested. These results indicate that rooftop solar PV installations could produce 2% more energy at the same installation cost, or 820 gigawatt hours more energy per year.