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

Abstract

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.