Emphasis of this article is on variable-speed pitch-controlled wind turbines with multi-pole permanent magnet synchronous generator (PMSG) and on their extremely soft drive-train shafts. A model and a control strategy for a full back-to-back converter wind turbine with multi-pole PMSG are described. The model comprises submodels of the aerodynamic rotor, the drive-train by a two-mass model, the permanent magnet generator and the full-scale converter system. The control strategy, which embraces both the wind turbine control itself and the control of the full-scale converter, has tasks to control independently the active and reactive powers, to assist the power system and to ensure a stable normal operation of the wind turbine itself. A multi-pole PMSG connected to the grid through a full-scale converter has no inherent damping, and therefore, such configuration can become practically unstable, if no damping by means of external measures is applied. In this work, the frequency converter is designed to damp actively the drive-train oscillations, thus ensuring stable operation. The dynamic performance of the presented model and control strategy is assessed and emphasized in normal operation conditions by means of simulations in the power system simulation tool DIgSILENT. the world. At the moment, substantial documentation exists on modelling and control issues for the doubly fed induction generator (DFIG) wind turbine. But this is not the case for wind turbines with synchronous generator and full-scale power converter.This article primarily addresses one particular topology of wind turbines with synchronous generator, namely the direct-driven variable-speed wind turbine equipped with multi-pole permanent magnet synchronous generator (PMSG) and full-scale power converter. This concept, announced as more and more attractive by wind turbine manufacturers, is feasible for MW class wind turbines and thus suitable for application in large wind farms.Traditionally, wind turbine generators are operating best at high speeds and require step-up gearboxes. However, as the gearbox is very expensive and needs a lot of maintenance, the idea of gearless, i.e. directdriven wind energy system has gained interest in the recent years, especially for offshore applications, where a low maintenance solution is an attractive option. A direct-driven generator connected to the grid through a full-scale converter can operate at very low speeds, typically 10-25 rpm for wind turbines in the MW range. However, such a low shaft speed operation is generally a drawback for electric generators, owing to the fact that a high torque is needed to produce the required power. Standard generators can therefore not be used, and generators have to be developed specifi cally for this application. In order to provide the high torque, directdriven generators must be designed with a large rotor diameter and a high number of poles to get suitable frequency ratio. 2 As multi-pole asynchronous generators would require a too large magnetizing current (i.e. poorer p...