Optimal design of wind farms in complex terrains using computational fluid dynamics and adjoint methods

Optimal design of wind farms in complex terrains has never been fully addressed because of the complex flow phenomena generated by the turbine wakes, the terrain itself, and their mutual interaction. To capture these effects, Computational Fluid Dynamics (CFD) simulation models are necessary, but their direct use with traditional optimization algorithms is prevented by their high computational cost. By using a gradient-based algorithm and an adjoint method for the gradient calculations, we present a methodology for the optimization of wind farm layouts that enables the use of CFD models to accurately simulate wake effects and terrain-induced flow characteristics. As opposed to previous studies, this methodology is general in its formulation and can handle different wind farm configurations, wind resource distributions and terrain topography. Benefits of an optimal wind farm design that employs CFD models are demonstrated for idealized and real cases, where significant improvements in annual energy production are realized by optimally siting turbines over complex terrains exploiting both turbine- and terrain-induced flow features. We ultimately show that this innovative methodology is feasible with current computational resources and an optimization process can be completed within days.