Jay Goit

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

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.

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.

Robust and Stable Periodic Flight of Power Generating Kite Systems in Turbulent Wind Flow Field

Abstract Power-generating kite systems extract energy from the wind by periodically pulling a generator on the ground while flying fast in a crosswind direction. Kite systems are intrinsically unstable, and subject to atmospheric turbulences. As an alternative to closed-loop control, this paper investigates the open-loop stabilization and robustification of a kite system using techniques based on the solution of Lyapunov differential equation. A wind flow is computed as a solution to a time-dependent three dimensional Navier-Stokes equation. Open-loop stable trajectories for the power-generating kite system are computed based on the statistical properties of the wind field, and are robustified with respect to the system constraints. The stability and robustness of the resulting trajectories are assessed by simulating the system using the computed time- and space-dependent turbulent wind flow.

A framework for optimization of turbulent wind-farm boundary layers and application to optimal control of wind-farm energy extraction

A PDE-based optimization framework is presented that allows optimization of turbulent wind-farm boundary layers. It consists of a state-of-the-art large-eddy simulation code that allows the time-resolved simulation of the three-dimensional turbulent flow in the atmospheric boundary layer, together with the adjoint (backward) sensitivity equations to this nonlinear system of PDEs (i.e. the incompressible Navier-Stokes equations). Both the forward and the backward system are efficiently parallelized for supercomputing, and are combined with state-of-the-art gradient-based optimization methods. We use this tool to investigate the use of optimal coordinated control of wind-farm boundary-layer interaction with the aim of increasing the total energy extraction in wind farms. The individual wind turbines are considered as flow actuators and their energy extraction is dynamically regulated in time so as to optimally influence the flow field. Earlier work on wind-farm optimal control in the fully developed regime (Goit & Meyers 2015, J. Fluid Mech. 768, 550) is discussed, and extended towards wind farms in which inflow effects are important.