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.