torque-speed characteristics of induction motors
Keeping the V/f constant while reducing the frequency is accomplished by reducing the terminal voltage while reducing the frequency. Maximum torque is produced when the magnetizing current is maximum. Magnetizing current is essentially the voltage across the magnetizing branch of the equivalent circuit divided by the magnetizing reactance I = V/X. A Since magnetizing reactance is X = 2 * Pi * f * L, I is proportional to V/f.

However V across the magnetizing reactance is not the terminal voltage. It is the voltage across the magnetizing reactance. The voltage drop across the stator resistance reduces the voltage across the magnetizing reactance. When the frequency is reduced, the terminal voltage is reduced, but the voltage drop across the stator resistance remains constant because the current is relatively constant. That means the V/f across the magnetizing reactance decreases even though the terminal V/f is constant.

The current through the stator resistance includes both the magnetizing current and the rotor current. However the rotor current is determined by the torque delivered to the load. If that remains constant, the current in the stator resistance is relatively constant.

The voltage drop across the stator leakage reactance also effects the V/f across the magnetizing reactance.

I have not included a diagram of the equivalent circuit, but anyone doing this type on analysis should have a mental image of that.