I think you do not understand how a VFD works. It does just as it states. It changes only the AC frequency driving the motor. The motor is an inductive motor and its speed will follow the drive frequency change. The motor, however is wound for a given amount of impedance (AC resistance). The amount of impedance a coil has depends largely on the frequency it is being driven with, as it will have a fixed inductance. The formula is XL=2PsquarefL. So, as the frequency increases, the speed increases, the impedance increases, the current decreases along with the motor torque and motor efficiency. If the frequency is dropped lower, the speed decreases, the impedance decreases, the current increases, torque decreases and efficiency decreases. This is why a VFD driven motor is always sized larger, typically doubled. A VFD is NOT an efficient replacement for gears. The driving voltage never changes, only the frequency.
Nope, VFDs definitely change output voltage. They cannot raise it above their input voltage (except in the special case of 120>240V models with a voltage doubler), but they can output anywhere between 0V and Vin.
Consider putting 460V at 5Hz into a motor. It's going to saturate immediately, and you're going to be closer to DC braking than actually motoring.
So in general (there are more advanced methods), they keep the voltage proportional to the frequency.
460V/60Hz. 230V/30Hz. 115V/15Hz.
This maintains a constant voltage:frequency ratio, which is why this mode is usually called V/f or V/Hz. This is also called 'constant torque' - the motor can maintain full rated output torque from 0 to full speed, though they require extra cooling at low speeds as the fan is spinning slower. Note that as the motor is only outputting full torque despite being at e.g. half speed, the output power is only half also. You're correct that unlike gearing, they can't
increase the motor torque.
Fans and centrifugal pumps ('variable torque') are often run in parabolic or square V/f, where the voltage is reduced below this straight line in the middle, as the load uses less torque at lower speed. Reducing the voltage below this linear relationship gives slightly improved motor efficiency as it reduces iron (hysteresis mainly I believe) losses at the expense of more current so higher copper losses.
The impedance of an induction motor is, unlike a simple coil,
not constant. The rotor and slip speed has a significant effect.
More or less the sole reason VFDs are used in such huge numbers in industry and HVAC is that it is vastly more efficient to use a VFD than almost any other method of capacity control. Running a pump or fan at a lower speed for half flow uses much less energy than running the same load at full speed and 50% duty. Another approach used was to use dampers on the inlets to fans, restricting the flow. Less airflow reduces the motor load and therefore power consumption - but the motor is still spinning at full speed, now against an even higher static pressure. Using a VFD allows the fan to be slowed and the restrictors removed. Less pressure, less flow, more energy.
Motor-VFD combinations can be upwards of 80% efficient across most of their speed range. Sure, you can do better with gears or belts - but not a huge amount, and only if you're using a single speed.