Integer programming for optimal yaw control of wind farms

Abstract. It is well-known that wakes caused by wind turbines within a wind farm negatively impact the power generation and mechanical load of downstream turbines. This is already partially considered in the farm layout. Nevertheless, the strong interactions between individual turbines provide further opportunities to mitigate adverse effects during operation, e.g., by repeatedly adjusting axial induction or yaw offsets to wind conditions. We propose a mathematical approach that covers the farm by patterns based on a smaller, precomputable so-called upstream section, in the form of integer programming for faster globally optimal farm-level yaw control (under some mild assumptions, such as discretized yaw offsets, chosen size of the upstream section, and homogeneous layout structure). While we prove the wind farm yaw problem to be strongly 𝒩𝒫 hard in general, we demonstrate through numerical experiments that our method enables optimal farm-level yaw control under real-world control update periods. In particular, the approach remains efficient if turbines are deactivated, and it scales well with farm width.