Distributed Fixed-Time Fatigue Minimization Control For Waked Wind Farms

This article focuses on addressing the challenge of distributed fixed-time optimization in wind farms, with the aim of reducing fatigue loads caused by the wake effect. The proposed approach involves a two-level wind farm control scheme, where each turbine is equipped with a local control module (LCM) for dynamic control, as well as a cooperative control module (CCM) to compute the turbine power set-point. To assess the fatigue loads on each wind turbine, effective indices are developed through quasi-static mathematical modeling and stochastic analysis. Considering that the wake effects create an aerodynamic coupling between fatigue loads in a given turbine and the output power of neighboring units, these indices are employed to define a local decoupled auxiliary cost function for each wind turbine. Through mild assumptions, it is demonstrated that this control strategy not only maintains the original optimization solution but also facilitates convex analysis of the global fatigue cost. To solve the problem, an algorithm with fixed-time convergence is proposed, utilizing Taylor linearization on the demand equality constraint. The findings are validated using the FLOw Redirection and Induction in Steady State (FLORIS) software tool, developed by NREL, which allows for the simulation of wind farm control and optimization structures.