Current in Saturated motor(synchronous machine)

First of all, the synchronous machine d-q model is not a transformer model -it is, in fact a DC model of conditions as seen from the stator. You do have direct and quadrature axis mmfs and direct and quadrature axis fluxes are affected by saturation (and damping windings or their equivalents). This is, for steady state, a DC situation, unlike that of a transformer. The effect of saturation, as seen from the AC or stator side is one of a change in the internal voltage generated by the field current with respect to the unsaturated situation. In other words, stator mmf as seen from the rotor boosts or bucks the (DC) direct and/or quadrature mmf and the amount of boost or buck depends on saturation. This will not cause a distortion in the stator current as it appears as if it is a change in field current (or a change in reactances) If there are DC components in the stator currents, these will be seen as fundamental frequency components of the mmf as seen in the rotor but then damper winding currents (including eddy currents) will come into play as in a transformer. These will be reflected back as second harmonics in the stator and these can, in theory, be distorted by saturation but will one notice this distortion? Does your model deal with this?

Note that the usual saturation model for a synchronous machine is as expressed by Krause "Analysis of Electrical Machines" McGraw Hill, 1986, pp461-65.

The one thing that you can hold a a dogma is that: "the more you know about synchronous machines, the more you are aware of your ignorance"