Nonlinear optimal control of a multi-rotor wind power unit with PMSGs and AC/DC converters)

Abstract

A nonlinear optimal (H-infinity) control method is developed for a wind power unit that comprises twin turbines, permanent magnet synchronous generators (PMSGs) and AC/DC converters. By proving differential flatness properties for this system the associated setpoints definition problem is solved. The dynamic model of the wind power unit being initially expressed in a nonlinear and multivariable state-space form, undergoes approximate linearisation around a temporary operating point that is recomputed at each time-step of the control method. The linearisation relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearised state-space model of the wind power unit, a stabilising optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem of the wind power unit under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The global stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control of the wind power unit, without the need to measure its entire state vector, the H-infinity Kalman Filter is used as a robust state estimator.