Current increase in induction motor
Think of it: Iq is 90° rotated from Id. It represents reactive power. Reactive power is connected to slip in an induction motor and as you are using a VFD, the slip is held constant over a wide speed range, and so is Iq.

Above a certain speed your load requires more power than the motor can deliver. This is determined by the load's torque over speed characteristic. You still increase the frequency of the VFD, but you cannot speed up the drive. The only thing you increase that way is the slip. That's why your reactive power increases.

The VFD reacts by decreasing the voltage amplitude, as high reactive power could also mean oversaturation for a given motor.