Bayesian Optimisation of a Two-Turbine Configuration Around a 2D Hill Using Large Eddy Simulations

When planning a new wind farm, optimising the turbine layout to maximise power output is crucial. Traditional approaches based on analytical wake models often fail in complex terrain. In such areas, wake-to-wake interactions and terrain-induced effects need to be taken into account via high-fidelity optimisation. Building on our prior research on how best to maximise offshore wind farm power production by both micro-siting (layout optimisation) and wake steering (yaw angle optimisation), this study focuses on the optimisation of two onshore wind turbines located around a 2D hill. The proposed approach is based on high-fidelity simulations (LES) to account for the complexity of the flow and on Bayesian optimisation (BO) to systematically and efficiently find the optimal configuration for the two turbines given a set of parameters. The LES are performed with the high-order finite-difference wind farm simulator WInc3D, which has been modified for this study to deal with complex terrains and turbines with yaw and tilt. Following the validation of the immersed boundary method (IBM) and wall modelling used to model the complex terrain and of a modified actuator disc model (ADM) to account for tilted turbines, two BO campaigns are presented in this study, with different sets of parameters to optimise. The main flow features and some statistics for each optimum case are discussed using the flow fields with and without the optimised configuration of the upstream turbine to analyse its impact on the downstream turbine and on the overall power of the system. For the first optimisation, the design variables include the wind turbines' streamwise locations and their hub heights (4 parameters). This optimisation study benefits from an elevated upstream turbine hub, leading to a significant power increase in the downstream turbine, thanks to an acceleration of the flow in front of the hill. For the second optimisation, the design space is modified based on the data from the first optimisation, by replacing the turbine's hub height with the possibility of changing the tilt angle of the upstream turbine (4 parameters). It is found that considerable power gains can be obtained while maintaining a modest upstream turbine hub height, by introducing a positive tilt angle in the upstream turbine. Overall, it is found that by setting up the turbines in ways that exploit the speed-up of the flow around the hill, both optimised layouts achieve considerable enhancements in power density over a reference configuration.