Computational design and optimization of wind farms using analytical derivatives

This paper presents a multidisciplinary framework for computational design and optimization of coupled offshore wind farm layout and support structure using analytical derivatives. Gradient-based optimization with exact analytical derivatives scales well with large design problems, and it is the preferred approach over gradient-free techniques. We used the second order Larsen model to simulate the wake in the wind farm. Combined with an energy production model and Weibull wind distribution function, the annual energy production of the wind farm is computed. Timoshenko beam elements model the support structure including the soil-structure interaction. Airy’s wave theory with Wheeler stretching is utilized for modeling the wave kinematics and to obtain the hydrodynamic loads using Morison’s equation. Cost models are used to evaluate the levelized cost of energy as the objective function. The design constraints are the support structure buckling, modal-frequency, and stresses. To evaluate the effectiveness of the proposed approach, we performed an optimization of a feasible baseline design consisting of 6 Vestas V80 wind turbines. Compared to the baseline design, our results show that the coupled layout and support structure approach reduces the levelized cost of energy by 1.4%. This efficient computational framework allows the concurrent design of the wind farm layout and support structure with thousands design variables, and it suitable for detailed design of offshore wind farms.