Adjoint-based model predictive control for optimal energy extraction in waked wind farms

In this paper, a model predictive control (MPC) is proposed for wind farms to minimize wake-induced power losses. A constrained optimization problem is formulated to maximize the total power production of a wind farm. The developed controller employs a two-dimensional dynamic wind farm model to predict wake interactions in advance. An adjoint approach as an efficient tool is utilized to compute the gradient of the performance index for such a large-scale system. The wind turbine axial induction factors are considered as the control inputs to influence the overall performance by taking the wake interactions into account. A layout of a 2 x 3 wind farm is considered in this study. The parameterization of the controller is discussed in detail for a practical optimal energy extraction. The performance of the adjoint-based model predictive control (AMPC) is investigated with time-varying changes in wind direction. The simulation results show the effectiveness of the proposed approach. The computational complexity of the developed AMPC is also outlined with respect to the real time control implementation.