An original analytical expression is presented in this paper to obtain optimal currents minimizing the copper losses of a multi-phase Permanent Magnet Synchronous Motor (PMSM) under fault conditions. Based on the existing solutions [i]opt1 (without zero sequence of current constraint) and [i]opt2 (with zero sequence constraint), this new expression of currents [i]opt3 is obtained by means of a geometrical representation and can be applied to open-circuit, defect of current regulation, current saturation and machine phase short-circuit fault. Simulation results are presented to validate the proposed approach.