For the most part what happens on the LINE side of a VFD has little effect on what happens on the load side, but then again all the same rules apply with respect to the line side. So what I mean is that;
1 - If voltage goes up what happens to current?
Assuming you do not exceed the input voltage tolerance of the VFD and damage it, when the voltage goes up the current would drop. Power would remain the same.
2 - If the frequency goes up what happens to current and voltage?
If the frequency goes up on the LINE side of the VFD, nothing happens to the current and voltage on the load side, again assuming the input tolerance of the VFD is not exceeded. But again, the POWER that the VFD draws from the line as a result of the load remains the same.
It might help to think of VFDs this way: the VFD is like a generator that puts out a NEW energy source for the motor down stream of it and the LINE supply to the VFD is nothing more than a raw material source feeding that generator. There is no longer a direct connection from line to load. That's why it's easy to use a VFD as a phase converter to run 3 phase motors from a single phase source. The VFD may not even know if it has all three phases connected to it (other than the current increases on the remaining 2 phases by the sq. root of 3).
The only line side issue that has a serious effect on the load is that the VFD cannot create voltage potential that does not already exist; it cannot BOOST voltage by itself*. So for instance if you have a 230V source and a 460V motor, you use a boost transformer to get the line to 460V first, then the VFD can vary it to any level LOWER than that.
*Some VFDs can boost voltage by a few percent. There are also small VFDs (1HP and under) that are specially designed to boost up to 2X by using a "voltage doubler" effect in the rectifier, so for instance they can take 115V single phase in and put out 230V 3 phase. There are also a rare few that can do this at higher voltages but it is not the norm.
