Power Curve Tracking with Tip Speed Constraint using LQR Regulators

We consider the problem of power regulation for a variable speed wind turbine in the presence of a blade tip speed constraint, for example to limit noise emissions. We formulate a policy in the transition region between the classical regions II and III which accommodates the tip speed constraint, and we derive wind schedules for the rotor speed, blade pitch and aerodynamic torque. Based on these wind schedules, we formulate model-based controllers which are capable of performing power curve tracking throughout all wind speeds, in contrast with commonly adopted approaches which use switching controllers to cover the various operating regimes of the machine. The proposed regulation policies and control laws are demonstrated in a high fidelity simulation environment for a representative 3 MW machine. Notation u Input vector w Wind vector field x State vector y Output vector λ Vector of Lagrange multipliers β Blade pitch λ Tip-speed-ratio Ω Rotor speed ρ Air density A Rotor area CF Force coefficient CP Power coefficient CT Torque coefficien