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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.
An induction motor's speed follows its supply frequency, so changing frequency changes speed. But frequency cannot be changed on its own, because the flux in the motor's core depends on the ratio of voltage to frequency:
Φ ∝ V / f
Reduce the frequency while holding voltage constant and the flux rises, driving the core into saturation, collapsing the magnetising impedance and drawing enormous current. A variable-frequency drive therefore varies both together, holding V/f constant so that flux — and therefore available torque — stays roughly unchanged across the speed range.
For a 415 V, 50 Hz motor the ratio is 415/50 = 8.3 V/Hz. Running at 25 Hz means supplying about 207.5 V; at 30 Hz, about 249 V. The motor keeps full rated torque at half speed, but since power is torque times speed, available power halves to 3.75 kW. Constant V/f is a constant-torque, not a constant-power, régime.
Beyond the motor's rated frequency the drive cannot raise voltage further — it is already at the supply limit. Frequency keeps rising while voltage stays fixed, so V/f falls and flux weakens. Torque therefore drops in inverse proportion to speed, and power stays roughly constant. Running well above base speed is possible but comes with reduced torque, and mechanical limits on bearings and rotor balance apply too.
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.
That the drive changes voltage and frequency together so their ratio stays fixed. This keeps core flux, and therefore available torque, roughly constant as speed changes.
415/50 = 8.3 V/Hz. At 25 Hz the drive supplies about 207.5 V, and at 30 Hz about 249 V.
Flux is proportional to V/f, so holding voltage while lowering frequency raises flux and saturates the core. The magnetising impedance collapses and current rises sharply, which can destroy the motor.
Constant torque below base speed, and approximately constant power above it. Below base speed the drive holds V/f fixed; above it the voltage is already at its limit, so flux weakens and torque falls off with speed.
Because a self-ventilated motor's cooling fan is on its own shaft, so airflow falls with speed while losses do not. Sustained full-torque running at low speed needs either a derating or a separately-driven cooling fan.
Extra voltage the drive applies at very low frequencies to compensate for the stator resistance, which at those frequencies absorbs a significant share of the applied voltage that would otherwise produce flux. Without it, starting torque is poor.
Synchronous Speed & Slip • Starting Current • Motor Torque & Power • All Calculators