A two-step topology and layout wind farm optimization approach

A novel two-step approach is presented to optimize the placement of wind turbines within a wind farm. The goal is to maximize the annual energy production, while the topology and layout of the wind turbines are optimized in sequence with a two-step procedure using gradient-based algorithms. In particular, in the first step the topology of the wind farm is optimized. A grid of potential wind turbine locations is defined, and continuous density variables ranging from zero to one are assigned to each location. The variables indicate the presence or absence of a wind turbine. Throughout the topology optimization process, we penalize the intermediate values of these variables, implicitly pushing the algorithm towards crisp 0-1 final layouts. Constraints are imposed on the minimum and maximum number of wind turbines and the spacing between them. Subsequently, in the second step, we refine the wind farm layout by optimizing the coordinates (x, y) of the wind turbines, which are initialized based on the optimal topology obtained in the first step. Numerical findings demonstrate the capability of the proposed approach to identify non-intuitive optimized wind farm layouts, with reasonable computational resources and time.