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This paper presents a new sensorless method and its stability study for the estimation of the mechanical rotor position of the wound-rotor induction machine. The main purpose of this study is to implement the control of the doubly fed induction generator (DFIG). The method is based on the model reference adaptive system and uses the electromagnetic torque as the working error variable. The method does not need any information about the stator or rotor fluxes, and so, it is only indirectly dependent of the flux dynamics. As other methods proposed recently, this can also be implemented in the rotor or in the stator reference frames and with hysteresis or with proportional-integral controllers. The stability analysis gives an instability region on the rotor current dq plane described by a circle whose diameter is the no-load stator current. The method is robust to parameter variations depending only weakly on a single parameter. Simulation and experimental results show that the method is appropriate for the vector control of the DFIG although needing an additional approach to stabilize the system in the instability region.