This paper proposes a novel variable speed control strategy of a particular 5-phase Permanent Magnet Synchronous Generator (PMSG) in healthy and faulty modes by taking into account the constraints on voltages and currents. These constraints are related to the converter and machine design. The considered faults are open-circuited phases (one phase, two adjacent phases and two non-adjacent phases). A variable speed control strategy is presented, including flux weakening operations. Based on analytical formulations, a numerical computation is proposed to bring out the torque−speed characteristics. This method allows the determination of the current references which ensure the functioning of a 5-phase PMSG at variable speed while keeping phase voltages and currents below their limits. Theoretical, numerical and experimental results are presented. These results are compared in order to validate the proposed approach.