Offshore wind farm layout optimization with alignment constraints

Abstract. Wind farm layout optimization involves placing wind turbines in a defined domain to minimize the expected production losses due to wake effects within the wind farm. Due to navigational regulations and risks, tenders for offshore wind farms often impose so-called alignment constraints; i.e., wind turbines must be located at the intersections of a grid formed by parallelograms. The shape and orientation of these parallelograms are to be determined to minimize wake losses. Mathematically, this problem belongs to the class of non-convex, nonlinear mixed-integer programming problems, known to be highly complex. The literature has not yet investigated the wind farm layout optimization problem under alignment constraints. This paper makes two contributions. First, we propose a modelization of the annual energy production (AEP) maximization with alignment constraints as a mixed-integer nonlinear problem, where the continuous parameters are the parallelogram-based tiling parameters and the discrete variables are the turbines' positions at the tiling's intersections. Second, we provide a heuristic derived from the DEBO algorithm developed by the same team and presented in Thomas et al. (2023). The proposed method is the subject of international patent application number WO 2024/061627.