Convex Economic Model Predictive Control for Blade Loads Mitigation on Wind Turbines

Abstract

Economic model predictive control (EMPC) has received increasing attention in the wind energy community due to its ability to trade off economic objectives with ease. However, for wind turbine applications, inherent nonlinearities, such as from aerodynamics, pose difficulties in attaining a convex optimal control problem (OCP), by which real-time deployment is not only possible but also a globally optimal solution is guaranteed. A variable transformation can be utilized to obtain a convex OCP, where nominal variables, such as rotational speed, pitch angle, and torque, are exchanged with an alternative set in terms of power and energy. The ensuing convex EMPC (CEMPC) possesses linear dynamics, convex constraints, and concave economic objectives and has been successfully employed to address power control and tower fatigue alleviation. This work focuses on extending the blade loads mitigation aspect of the CEMPC framework by exploiting its individual pitch control (IPC) capabilities, resulting in a novel CEMPC-IPC technique. This extension is made possible by reformulating static blade and rotor moments in terms of individual blade aerodynamic powers and rotational kinetic energy of the drivetrain. The effectiveness of the proposed method is showcased in a mid-fidelity wind turbine simulation environment in various wind cases, in which comparisons with a basic CEMPC without load mitigation capability and a baseline IPC are made. Results indicate that CEMPC-IPC can achieve better reduction in rotating blade loads, as well as similar performance in the mitigation of shaft and yaw bearing loads, with the added advantage of convenient economic objectives trade-off tuning.

Analysis and multi-objective optimisation of wind turbine torque control strategies

“…While the Kω 2 strategy provides satisfactory performance, it is inflexible in providing a granular tradeoff between power and load objectives for present-day wind turbines. Therefore, modern large-scale wind turbines are controlled by more advanced WSE-TSR tracking schemes (Mulders et al, 2023), and wind turbine manufacturers are currently exploring the possibilities of applying model predictive control (MPC) to provide such flexibility (Hovgaard et al, 2015;Pamososuryo et al, 2023). This work focuses on comparing the baseline strategy, with the first being the WSE-TSR tracking control scheme, which is also often referred to as a power coefficient C p -tracking scheme in other works (Bossanyi, 2000).…”