In this paper, we present an analytical model of the currents flowing in a 5-phase PMSM. The analytical expressions of the currents are derived both in the stationary and the synchronous frames. This analytical model depends on the fault effect parameters: phase shift, amplitude modification and bias. The flexibility of the model allows analysing the different fault signatures in any of the reference frames whatever the coupling of the windings (isolated or non isolated neutral). At first, this analytical model has been validated by comparison with a numerical model obtained from simulations. Afterwards it has been used to evaluate the fault effect on the transformed currents. The results have shown that depending on the fault type, the current waveforms exhibit changes (additional components, mean or variance changes) and the current vector trajectory is also distorted. Therefore, the fault signature may be extracted from features in the time, frequency or time-frequency domain. The results have also shown that the fault features should be tracked in all the frames.