Why V/f Ratio Is Kept Constant in VFD?

Speed of Induction Motor

VFD means variable frequency drive. VFD is used with an induction motor for speed control, process optimization, and energy saving.

Before understanding the reason why V/f ratio is kept constant in vfd, we first understand the working of the induction motor. V/f control is also called V/Hz control or scalar control.

The difference between synchronous speed and the actual speed of the motor is called slip. The speed of the induction motor can be calculated with the following formula.  

speed of induction motor formula


Ns = 120f/P- The Synchronous speed of the motor
f = Frequency
s = Slip of the motor
P = Number of poles.

Factors affecting Speed of Induction Motor

  • Frequency
  • No. of poles
  • Slip 

Speed regulation of induction motor with a change in voltage alone has certain limitations, and with this method, the speed can be governed in the range of 90% to 100% of the rated speed.

If the voltage is reduced below 90% of the rated voltage, the torque of the motor gets reduced drastically as the torque of the motor is proportional to the square of the applied voltage, and at this reduced voltage, the motor can stall if load demands more torque than the maximum torque delivering capacity of the motor.

torque and flux relationship in induction motor

With the reduction of stator voltage, the flux in the air gap of the motor gets reduced and, as a result, the torque-delivering capacity of the motor gets reduced.

The method of speed reduction up to the limited speed range with stator voltage reduction can be done if the driven load demands less torque at reduced speed.

Speed regulation by changing the frequency is the best method to govern the speed of the motor.


Stator voltage is also increased or decreased proportionately with an increase or decrease of the frequency with Pulse width modulator(PWM) inverter to maintain the constant flux in the motor. The PWM waveform is as given below.

PWM Inverter waveform in vfd

The width of the PWM waveform increase or decreases with an increase or decrease in the frequency. Thus, the smaller widths of PWM produce lower resultant voltage and, the larger pulse width produces higher resultant voltage.

How does the PWM Inverter maintain constant V/f Ratio in VFD?

Let us understand the concept of keeping the V/f ratio constant in vfd through an example. If 440 volts,1500 RPM, 50 Hz rating motor operate at 50 Hz, then the speed of the motor is around 1480 RPM. The V/f ratio is (440/50) 8.8.

If the motor is to operate at 740 RPM, then the frequency is 25 Hz, and corresponding to this frequency the voltage is 220 Volts. In this case, V/f ratio is (220/25) 8.8. In this way, the PWM inverter maintains the constant v/f ratio or constant flux, and thus, the motor delivers constant torque.

how does pwm inverter keeps constant v/f ratio in vfd

Thus the output voltage of the inverter increase linearly with an increase in the frequency. Thus the V/f ratio is kept constant.

vf pattern

What is Slip Control of an Induction Motor?

With slip control, the speed of the slip ring induction motor can be governed. Speed control through slip control causes copper loss in the rotor. The rotor copper loss or the slip power of the rotor can be recovered with the slip power recovery system(SPRS).

When the speed of the induction motor is regulated by regulating frequency, the stator voltage is also increased/decreased in proportion to change in the frequency. The increase or decrease in the voltage with frequency does not contribute to the speed variation of the induction motor; however, it is essential to regulate the voltage with a change in frequency. Let us understand the reason for this.

The winding of the stator is wound on the magnetic core. The flux is produced when the sinusoidal voltage is applied at the stator terminal; the produced magnetic flux in the core that travels through the air gap between stator and rotor gets linked to the rotor winding.

V/f ratio Constant in VFD

The flux produced in the motor core can be calculated with the formula as given below.

why vf ratio is kept constant in VFD

According to Faraday’s law of electromagnetic induction, the self EMF induced generated in the stator is expressed as; 

mathematical proof of why v/f ratio is kept constant in vfd

Where erms is the back EMF/phase produced in the stator, f-frequency, and n- Number of turns in the stator coil.

derivation of flux  formula in induction motor

Thus, the flux in the stator core is proportional to the ratio of V/f. That is why we keep v/f ratio constant in VFD.

Effect on motor performance if V/f ratio or flux is not maintained constant in the air gap of motor

If speed is increased by increasing frequency, the voltage has to be increased in the same proportion with the increase in frequency to maintain the constant flux in the core in order to avoid the overheating of the core.

What happens if the flux is increased above rated  flux capacity? 

If the voltage is not decreased with a decrease in frequency, the flux in the core will go above its rated design capacity and the core of the motor will get saturated. The saturation of the core will lead to a temperature rise of the core, and eventually, the winding insulation will break down.

For example- If we operate the motor of 440 Volts, 50 Hz rating at full speed, then the ratio of V/f is 440/50=8.8. Now we reduce the speed of the motor by half of its rated speed by changing the frequency only. In this case, the ratio of V/f is 440/25=17.6.

In the second case, core flux is two times the rated flux capacity. The core can not carry the flux above its capacity and it will cause the failure of the core on account of core insulation failure. This is the reason why v/f ratio is kept constant in VFD.

If the voltage is not increased with an increase in frequency the flux in the stator core is reduced from its rated average flux rating, and the motor will not able to produce the rated torque up to the base speed.

What happens if the flux is decreased below rated  flux capacity? 

In the application where speed is required to be increased above the base speed of the motor, the frequency is increased above 50 Hz., however, it is not practically possible to increase the voltage above 440 volts in the case of 440 Volts drives. Beyond the base speed of the motor, it is not possible to keep the V/f ratio constant in VFD.

Speed control above base speed is possible with weakening the main stator flux as V/ F ratio gets reduced. 

Up to the base speed( Rated speed), the motor operates in the constant torque region. In this region, the power varies with an increase in speed. Beyond base speed, the flux gets weakens and the motor operates in the constant power region. The constant power region is also called the flux weakening region.

constant torque and power mode of induction motor

This procedure of speed control above the base speed of the motor can be used for increasing the speed of the drives which require less running torque above the base speed operation. Increasing speed above the base speed of the motor will lead to a decrease in the torque.

With flux weakening, the motor speed can be increased above 10 % of the rated base speed of the motor. However, the motor design data must be checked before doing the speed regulation through flux weakening.

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