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A variable-frequency drive (VFD) controls an induction motor's speed by changing the supply frequency. To keep the magnetic flux — and therefore the torque capability — constant, the drive holds the voltage-to-frequency (V/f) ratio constant: as it lowers the frequency it lowers the voltage in proportion. The motor speed follows the synchronous speed Nsync = 120·f/poles, so halving the frequency roughly halves the speed while maintaining full torque.
| Quantity | Formula |
|---|---|
| V/f ratio | V/f = Vrated / frated |
| Output voltage | V(f) = (V/f) × f (up to Vrated) |
| Synchronous speed | Nsync = 120 × f / poles |
| Shaft speed | N ≈ Nsync − slip speed |
Below the rated (base) frequency the drive works in the constant-torque region, holding V/f constant. Above base frequency the voltage cannot rise past the rated value, so V/f falls and the motor enters the field-weakening / constant-power region — higher speed but reduced torque. A small voltage boost is usually added at very low frequency to overcome winding resistance.
V/f (volts-per-hertz) control is the basic method a VFD uses to run an induction motor: it changes the frequency to set the speed while changing the voltage in proportion to keep the magnetic flux and torque capability constant.
Divide the rated voltage by the rated frequency: V/f = Vrated/frated. A 400 V, 50 Hz motor has a V/f ratio of 8 volts per hertz.
The synchronous speed is N = 120×f/poles, so speed is proportional to frequency. Lowering the frequency lowers the speed; the actual shaft speed is slightly below synchronous by the slip.
Nsync = 120 × frequency / number of poles. At 50 Hz a 4-pole motor runs at 1500 rpm synchronous; a 2-pole at 3000 rpm.
Magnetic flux is proportional to voltage divided by frequency. Holding V/f constant keeps the flux at its design value, so the motor maintains full torque capability and does not saturate or overheat as speed changes.
The drive cannot raise voltage above the rated value, so V/f drops and the flux weakens. The motor enters the constant-power (field-weakening) region: it can go faster but produces less torque.
At very low frequency the winding resistance drops a significant share of the voltage, weakening the flux. Drives add a small low-speed voltage boost to compensate and preserve starting torque.
Yes. By starting at low frequency and voltage, a VFD can bring the motor up to speed while keeping the current near full-load value, avoiding the 6–8× inrush of direct-on-line starting.
For centrifugal loads the power follows the cube of speed, so running at 80% speed uses only about half the power. This cube law makes VFDs highly effective for variable-flow pumps and fans.
Slip is the small difference between synchronous and actual speed needed to produce torque. In the constant-torque region the slip speed (in rpm) stays roughly constant, so the shaft speed tracks the synchronous speed minus a fixed offset.
Yes, by raising the frequency above the rated value, but only in the field-weakening region with reduced torque, and within the mechanical and bearing limits of the motor. Check the manufacturer's maximum speed.
No. V/f (scalar) control is simple and open-loop. Vector (field-oriented) control regulates torque and flux independently for much better low-speed torque and dynamic response, at the cost of complexity and often a speed sensor.
Synchronous Speed & Slip • Starting Current • Motor Torque & Power • All Calculators