Inaccurate machine parameters can cause orientation errors and instability in field-oriented control schemes relying on model-based estimations. This paper analyzes the accuracy and stability of two field-oriented control schemes for a stand-alone doubly fed induction generator (DFIG), where the field orientation is affected by the stator inductance and stator/mutual inductance ratio. After deriving a reduced-order model accounting for parameter mismatch, the paper deduces a formula to calculate the field orientation error as a function of the inductance mismatch, revealing parameter sensitivities. A stability analysis is then carried out proving that overestimating the stator/magnetizing inductance ratio may trigger instabilities in case of a high load level, whereas underestimation allows always stable operation. The theoretical insight is supported with simulation and test results on a laboratory rig.