Time-shifted cost function design for more efficient dynamic wind farm flow control*

Dynamic wind farm flow control is the art and science to maximize the energy yield of large wind farms. In this paper we will address the problem of large time delays between control actions of the different turbines in the farm and the delayed impact on the downstream turbines. We propose and show how a time-shifted cost function approach can render the receding horizon optimization problem more efficient and can mitigate the unavoidable turn-pike effect. We further show how the resulting setup can be used to break the optimization problem apart into several smaller optimization tasks to reduce the computational load. We demonstrate that the proposed changes do allow an economic model predictive control strategy to engage into collaborative wind farm control for long term gains, while a more traditional cost function approach leads to greedy turbine behavior. As a result, we take a crucial step towards a mature implementation of dynamic model based wind farm flow control.