Development of real-time optimal control of wind farms based on a LES plant model

The efficiency of energy extraction in large-scale wind farms strongly depends on turbine wake interactions. In the last decade, much research has been done into dynamic receding-horizon optimal control strategies to take these effects into account. However, due to the natural divergence of the adjoint simulation in chaotic turbulent systems, the extension of the optimization horizon to the order of the wind farm flow-through time remains a major challenge. Recently, it was found that sensitivities in chaotic systems can also be determined using shadow trajectories. We aim at developing such a shadowing algorithm that exploits the multiscale nature of the turbulent flow system to extend the horizon length, and apply it for real-time control. As a plant model, we consider a model based on large-eddy simulations that we complement with a bias term that takes into account the scale dependency of the LES approximation and improves the conditioning of the shadowing problem. The extended model is integrated in a preconditioned multiple shooting algorithm and combined with a scale-dependent multigrid solution strategy to solve the receding-horizon optimal control problem in realtime for larger time horizons. We also develop a fast LES-based state estimator and integrate it into the optimal control framework to achieve a practical control system suitable for real-time control. We test the approach in a virtual environment that is based on fine-grid simulations on a supercomputer.