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This paper presents an observer based fault detection approach for stator inter-turn short circuit fault in DFIGs. A state space model is developed based on d-q axis theory, which can represent both the healthy and faulty conditions. A global exponential adaptive observer is constructed using this model, which allows estimating the fraction of short circuited winding as well as the rotor speed. To further improve the dynamic performance of rotor speed estimation, an exponential estimator gain is introduced. The simulation results demonstrate that this approach has effectiveness on fault detection under transient conditions and strong robustness against the speed and load variations. This advantage has significance on condition monitoring of wind turbine DFIGs, since the DFIGs predominantly operate under transient conditions.