Analysis of turbulent flow properties and energy fluxes in optimally controlled wind-farm boundary layers

Abstract

In the present work our focus is to improve the performance of a wind farm by coordinated control of all turbines with the aim to increase the overall energy extraction by the farm. To this end, we couple flow simulations performed using Large Eddy Simulations (LES) with gradient based optimization to control individual turbines in a farm. The control parameters are the disk-based thrust coefficient of individual turbines as a function of time. They indirectly represent the effect of control actions that would correspond to blade-pitching of the turbines. We employ a receding-horizon predictive control setting and solve the optimization problem iteratively at each time horizon based on the gradient information obtained from the evolution of the flow field and the adjoint computation. We find that the extracted farm power increases by approximately 16% for a cost functional that is based on total energy extraction. However, this energy is gained from a slow deceleration of the boundary layer which is sustained for approximately 1 hour. We further analyze the turbulent stresses and compare to wind farms without optimal control.