Optimal dynamic induction control of a pair of inline wind turbines

We study dynamic induction control for mitigating the wake losses of a pair of inline wind turbines. In order to explore control strategies that account for unsteady interactions with the flow, we employ optimal control and adjoint-based optimization in combination with large-eddy simulations. The turbines are represented with an actuator line model. We consider a simple uniform inflow case with two NREL 5 MW turbines spaced 5 diameters apart and find that optimal control leads to 25% gains compared to standard Maximum-Power-Point Tracking (MPPT). It is further found that only the control dynamics of the first turbine are changed, improving wake mixing, while the second turbine controller remains close to the MPPT control. We further synthesize the optimal generator torque and blade pitch controls of the first turbine into a signal that can be periodically used as an open-loop controller, with a Strouhal number of 0.38, while realizing the same gains as the original optimal control signal. Further analysis of the improved wake mixing resulting from the open-loop signal reveals periodic shedding of a three-vortex ring system, which interacts and merges downstream of the first turbine, increasing entrainment of high-speed momentum into the wake. The sensitivity of the open-loop signal to inlet turbulence levels and turbine spacing is also investigated. At low to medium turbulence levels, the control remains effective, while at higher levels, the coherence of the vortex rings degrades too fast for them to remain effective. Published by AIP Publishing.