v/f control scheme- basic concept

For controlling the speed of induction motors in various industry application variable frequency control drives are used
One of the main speed control scheme used is the v/f control mode
here i shall explain briefly why v/f control, why this ratio is to be maintained and all
before reading this blog i recommond  you to go through the basic working principle of induction motor

v/f control

we know the expression for synchronous speed Ns
Ns = 120*f/P..................(1)
where
f: frequency of supply voltage
P : No of Poles

for a given induction motor no poles is constant, so inorder to change the speed , supply frequency need to be changed, now the question is then why to change voltage too? whats the big deal in maintaining the v/f ratio?
here is the answer for it

we know the that the motor torque developed  , T is directly proportional to both flux Φ and Current I
ie T= constant *Φ*I.........................(2)

now the expression for induced emf in the rotor of induction motor

E = 4.44FZΦ.........................(3)
where z is total no of conductors
from this equation

Φ= E/Φ

approximating E to terminal voltage V

we get that Φ= V/Φ

Now in most motor applications the torque is to be maintained constant
if we change frequency alone, then the torque requiremens will not be met (check eqtn (2)
So at particular load, in order to get speed control along with maintaining the torqe, v/f ratio to be maintained