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Detection of defects or beginning faults is a way to be able to prevent catastrophic faults. Here asymmetrical states of a doubly-fed induction machine, as for example a turn-to-turn fault, are modeled and simulated in state space with hybrid machine equations. These equations are reduced in order of less computation effort. To detect rotor turn-to-turn faults of the doubly-fed induction machine a Luenberger observer is developed and investigated by simulation. The results show a sensitive and fast detection of the fault.