Efficient Gradient-Based Optimization for Joint Layout Design and Control of Wind Turbines

A central challenge in the design of energy-efficient wind farms is the presence of wake effects between turbines. When a wind turbine harvests energy from free wind, it produces a turbulent region with reduced energy for downstream turbines. Strategies for increasing the efficiency of wind farms by mitigating wake effects have been the subject of much computational research. To this end, both the positioning of the turbines and their cooperative control must be taken into account. Since they are mutually dependent, increasing attention has been paid to the joint consideration of layout design and control. However, joint modeling approaches lead to large-scale and difficult optimization problems, which lack efficient solution strategies. This paper describes an efficient optimization framework for the joint design and steady-state control of wind turbines under a continuous wake effect model. Through a multi-level reformulation of the joint optimization problem, it shows how problem sub-structure can be efficiently exploited to yield order-of-magnitude reduction in convergence times over naive approaches and prior proposals.