Adjoint-based model predictive control of wind farms: Beyond the quasi steady-state power maximization

In this paper, we extend our closed-loop optimal control framework for wind farms to minimize wake-induced power losses. We develop an adjoint-based model predictive controller which employs a medium-fidelity 2D dynamic wind farm model. The wind turbine axial induction factors are considered here as the control inputs to influence the overall performance by taking wake interactions of the wind turbines into account. A constrained optimization problem is formulated to maximize the total power production of a given wind farm. An adjoint approach as an efficient tool is utilized to compute the gradient for such a large-scale system. The computed gradient is then modified to deal with the defined final set and practical constraints on the wind turbine control inputs. The performance of the wind farm controller is examined for a more realistic test case, a layout of a 2 x 3 wind farm with dynamical changes in wind direction. The effectiveness of the proposed approach is studied through simulations.