Why V/f ratio is kept constant for induction motor speed controlling

Let’s consider Induced EMF equation for single phase for an induction motor which is

Here kw and Nph are constant for given motor

Following diagram shows per phase equivalent circuit for 3 phase induction motor where Vs is supply voltage , r and X denote stator and rotor impedances.

When motor is running and neglecting the effect of r₁ and jX₁  we can derive

               

 

                              

Magnetic flux in the air gap plays an important role in determining the flow of power from the stator to rotor shaft and for better power transfer we must keep Air gap flux as high as possible.

If Air gap flux is below optimum value rotor current is decreased causing decrease of the torque leading to less efficiency. If the Air gap flux is higher the optimum value then the core is saturated causing unnecessary current drawing from the supply even destroying the winding.

Also assuming that motor is driving a constant load and when voltage and frequency is varied by keeping ratio between them constant then the motor torque is kept constant when speed changes. This is another advantage of keeping V/f constant.

So Air gap flux should be kept constant at maximum possible value for Safe operation, Good efficiency and for favorable output. So according to  to keep constant the ratio V/f is kept constant.