Nonlinear control of associations including wind turbine, PMSG and AC/DC/AC converters

We are considering the problem of controlling wind turbine synchronous generators driven through AC/DC rectifiers and DC/AC inverters. The control objectives are threefold: (i) forcing the turbine speed to track a reference signal, (ii) regulating the DC Link voltage, (iii) enforcing power factor correction (PFC) with respect to the power network. First, a nonlinear model of the whole controlled system is developed in the Park-coordinates. Then, a nonlinear multi-loop controller is synthesized using the backstepping design technique. A formal analysis based on Lyapunov stability and average theory is developed to describe the control system performances. In addition to closed-loop global asymptotic stability, it is proved that all control objectives (turbine speed tracking, DC link voltage regulation, and unitary power factor) are asymptotically achieved up to small harmonic errors (ripples). The amplitudes of these harmonic errors depend on the power network frequency: the larger the power net frequency the smaller the error amplitudes. The above results are confirmed by simulations which, besides, show that the proposed regulator is quite robust with respect to uncertain changes of wind speed.