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The stability of a doubly-fed induction generator (DFIG) under vector control in stator voltage orientation (SVO) is investigated. Prior art has tended to assume that the inner current loop dynamics can be neglected when an SVO is employed. As a result, the poorly damped poles of the DFIG system were considered unaffected by the inner current loop tuning. The state-space model of the machine including the inner current closed loop dynamics is developed for schemes where different feed-forward compensation terms are used. The interaction between inner current loop dynamics and damping of the critical poles of the system is illustrated through analysis and simulation. The main outcome of the analysis is that the stability of the machine system in an SVO depends solely on the parameters of the proportional-integral controllers. Erroneous tuning can lead to instability, irrespective of the particular feed-forward compensation scheme, which could cause the disconnection of the machine as a result of rotor current oscillations of unacceptable magnitude in an actual case. The main contribution is to provide the necessary methodology in order to ensure the stable operation of a DFIG under SVO vector control.