What is the influence of the DC voltage of an inverter on the control of a PMSM?
The influence of a DC voltage source is negligible for the control of the PMSM. For sure, considering that V_dc >= 2*V_phase. Indeed, if this condition is true, the DC voltage won't have any effect on the V_phase if the inverter is correctly modelled. There are two main factors to take into account when modelling the inverter: 


The input voltage to the inverter must be normalized using a gain = 1/V_dc
There is a modulation factor that must be also applied in the gain. It may vary depending on the formulation used.


It is also important to understand well the Space Vector Pulse Width modulation. A very helpful post was this one

Finally be aware not to overmodulate the signal (when modulated voltage becomes higher than triangular signal of the inverter).