In this paper, a dynamic state space model of a DFIG with stator inter-turn short circuit fault is proposed. This model can quantitatively describe the fault at any level in any single phase. Both healthy and faulty conditions can be simulated by using this model. Base on this model, an observer based fault detection and diagnosis (FDD) scheme is developed, which can not only provide a rapid detection when fault occurs but also give an accurate diagnosis of the fault position and level. In order to ensure the observer stability under a wide rang of the speed variation of DFIGs, a time varying Kalman like gain supplied with measured rotor speed is applied to the observers. Moreover, an exponential adaptive observer is employed to provide a desirable estimation of fault level. The simulation results demonstrate the effectiveness of this approach in detecting and diagnosing the faults under both stationary and speed varying operations. The latter is particularly important for fault detection of wind turbine DFIGs.