Full power scale back-to-back power converter MSC GSC PMSG wind turbine system, with direct-drive configuration, is an attractive solution, particularly for off-shore wind energy applications. For such systems, (nonlinear) direct control, which requires neither a modulation process nor cascaded linear controllers, but will operate the system at very high control dynamics, is a very promising control class. In this work, we reviewed and experimentally Fig. 1. A simplified structure of a grid-tied direct-drive back-to-back power assessed the classical (C-), the duty-optimal (DO-), the ripple-re- converter PMSG wind turbine system, where x are the variables for grid g,m reduced (RR-) and the multi-vector direct model predictive torque (g) and machine (m) side, x ∈ {i, e, v, R, L} represents the current, grid and control (MV-DMPTC) solutions to deal with the generator side converter voltage (vector), resistance and inductance, respectively, Vd, ωm, control of grid-tied full power scale back-to-back power converter P, Q are the DC-link voltage and rotor speed, grid side active and reactive power, respectively. P and P is the power output of the wind turbine and t m generator, respectively. "MSC" and "GSC" represent "machine side con- verter" and "grid side converter". fault-ride through capabilities, and (v) reduced maintenance. These features make such WTSs attractive, in particular, for off-shore applications. Control schemes for the machine side convertor (MSC) of such systems (as shown in Fig. 1) can be divided into two classes (see, e.g., [2], [3]): (i) (Linear) control schemes (with modulator) (e.g. with space vector modulation (SVM)), such as (a) PI controller methods, e.g. field-oriented control (FOC) or (b) direct torque control (DTC) with modulator, and (c) deadbeat-like model predictive control (DBC) meth- ods; and (ii) (nonlinear) direct control schemes (without modulator) such as (a) DTC with switching table (ST-DTC) and (b) (nonlinear) direct model predictive control (DMPC) approaches. From the concept point of view, the first class (partially) approximates the plant (i.e., the power converters and drives) as a linear and continues system, thereby, apply- ing the "timed-average principle" with a modulator to em- ulate certain continues commands to the system. However, a switching power converter-fed energy conversion system is in essence a nonlinear and switching-mode plant. Modern digital controllers process a control algorithm in discrete format as well. Therefore, a more proper control philosophy shall be nonlinear direct control, which requires no linear and continuous approximation, but takes the nonlinear and switching-mode nature of the power converters and digital controllers into account and combines the modulation and switching sequence selection processes into a single step. Switching table based direct control (direct torque control (ST-DTC) [4], [5] for machine side, and direct power control for grid side), which was originally developed in the 1980s for induction motor drives, has already been a very matured concept. In such solutions, the switching se-