Probability Mass Function of Energy for Light-Collecting Surfaces in Rough Geometries and Its Applications in Urban Energy and Photovoltaics

Sunlight throughout urban areas largely impacts local climate [sustainable development goal (SDG) 13], residents’ well-being (SDG 3), and access to clean energy (SDG 7). However, sunlight availability on various urban surfaces is affected by urban geometry. Here, in this work, a probabilistic framework to evaluate the interplay between sunlight and urban geometry is presented, and its immediate applications in urban energy studies are demonstrated. A probability mass function that predicts the energy production of a group of light-collecting surfaces, such as solar photovoltaic (PV) systems, installed in rough geometries, such as urban areas, is derived. Along the way, an expression for the sky view factor (SVF) is formulated within rough geometries as well as a link between the capacity factor of the residential PV fleet and urban geometry. The predictions of the mathematical framework are validated using the digital surface model and collected PV systems data in The Netherlands. This work primarily helps understand the underlying relation between the geometrical parameters of a rough surface and the received sunlight energy on a subset of that surface. Exemplified applications are swift SVF calculations and residential PV fleet yield predictions, which, respectively, support efficient urban energy assessments and privacy-preserving electrical grid management.