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This paper deals with the study and development of new control solutions of permanent-magnet synchronous motor (PMSM) drives specifically aimed to operate under sensorless vector control even during fault conditions. The phase imbalance produced by an open-phase fault leads to the failure of several sensorless estimation algorithms based on either machine models or high-frequency signal injection. Exploiting a recently proposed machine model for three-phase faulted PMSM drives, the practical implementation of sensorless vector controls for such drives under asymmetric conditions due to a single-phase open-circuit fault is performed. The effects of the magnetic/geometrical asymmetries during the fault are studied, and the techniques able to mitigate such effects on the rotor position information are provided. The rotor position estimation is achieved in a wide operating range during the fault as it is confirmed by experimental tests.