Control co-design of wind farms using joint yaw-induction control

Collective wind farm flow control and layout optimization have both demonstrated potential to increase farm energy production. Flow control and layout optimizations are interdependent. Therefore, optimizing control and layout simultaneously, known as control co-design, is necessary to achieve a globally optimal result. Here, we study the impact of control co-design on optimal turbine spacing, farm efficiency, cost of energy and lifetime farm profit. Co-design is investigated with three different control strategies: induction (thrust) control, yaw control and joint yaw-induction control. The high dimensional optimization problem is efficiently handled using gradient-based optimization with automatic differentiation of an analytical wind farm model. A generalized momentum model is used to accurately predict the induction and initial wake velocities of the turbine rotor depending on the yaw misalignment and thrust coefficient. Co-design optimizations are performed using an idealized actuator disk representation to capture the full theoretical range of possible operating setpoints as well as a blade element model representation to capture the impact of realistic rotor aerodynamics. We show that the mitigation of wake losses via collective control lowers the optimal turbine spacing of control co-designed wind farms resulting in reduced cost of energy, increased lifetime farm profit and reduced land use.