Photovoltaic (PV) technology is one of the most popular means of renewable generation, whose applications range from commercial and residential buildings to industrial facilities and grid infrastructures. The problem of determining a suitable layout for the PV arrays, on a given deployment region, is generally non-trivial and has a crucial importance in the planning phase of solar plants design and development. In this paper, we provide a mixed integer non-linear programming formulation of the PV arrays’ layout problem.

First, we define the astronomical and geometrical models, considering crucial factors such as self-shadowing and irradiance variability, depending on the geographical position of the solar plant and yearly time window. Subsequently, we formalize the mathematical optimization problem, whose constraints’ set is characterized by non-convexities. In order to propose a computationally tractable approach, we provide a tight parametrized convex relaxation. The resulting optimization resolution procedure is tested numerically, using realistic data, and benchmarked against the traditional global resolution approach, showing that the proposed methodology yields near-optimal solutions in lower computational time.

The paper is motivated by the need for efficient algorithmic procedures which can yield near-optimal solutions to the PV arrays layout problem. Due to the strong non-convexity of even simple instances, the existing methods heavily rely on global or stochastic solvers, which are computationally demanding, both in terms of resources and run-time. Our approach acts as a baseline, from which practitioners can derive more elaborate instances, by suitably modifying both the objective function and/or the constraints. In fact, we focus on the minimum set of necessary geometrical (e.g., arrays position model), astronomical (e.g., irradiance variation), and operational (e.g., power requirements) constraints which make the overall problem hard. The Appendices provide a guideline for suitably choosing the optimization parameters. All data and simulation code are available on a public repository.

This preprint has been accepted for publication in IEEE Transactions on Automation Science and Engineering.