Optimal control of wind farm power extraction in large eddy simulations

In the present work we couple flow simulations performed using Large Eddy Simulations (LES) with gradient based optimization to control individual turbine in a farm, so as to achieve an increase in the total power output. The controls in our optimization problem are the disk-based thrust coefficients C′ T,n of individual turbines as function of time. We use a gradient-based algorithm for the optimization and the gradients are computed using the adjoint method; the adjoint equations are formulated directly from the LES equation and the cost functional. 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. In this paper we further elaborate the optimization techniques, interpret the simulation of adjoint field and present results for the wind-farm boundary layer cases. We find that the extracted farm power increases by approximately 20%, during optimal control. However, the increased power output is also responsible for an increase in turbulent dissipation, and a deceleration of the boundary layer. These issues are further discussed.