# Induction Motor Starting Torque Equation

Starting torque is the torque developed by a machine at the instant of starting. During the start of induction motor, slip(s) is 1 since speed of the rotor is zero and it is at standstill. At standstill condition, torque generated by the induction motor is the starting torque.

Torque developed by the rotor of induction motor is proportional to the magnetic flux, rotor current and power factor of the rotor circuit. Since the magnetic flux produced is proportional to the induced emf in the rotor. Therefore, we can write the mathematical expression for starting torque in induction motor as : Here E2 is the induced emf in rotor per phase, I2  is the rotor current per phase and is the power factor of the rotor per phase. We can write the above expression as: …. … .. eq. B

Here K is the constant of proportionality and its value is In above equation, ns is the synchronous speed in rps (revolution per second). The term “3’indicates the motor as a 3-Phase machine.

Putting the value of K in equation B, we have, For starting torque,

Rotor impedance per phase = Here, R2 is the resistance of rotor circuit and X2 is the rotor reactance per phase.

Power factor can be written as: Current I2 is simply the ratio of emf “E2”and impedance Z2 . Now, starting torque expression from eq. B is Putting the value of  I2  and in the above equation. Or By putting the value of  K, we have  In general, supply voltage V to the stator is kept constant which means that flux (per pole) setup by the stator is also fixed. Hence, emf (E2) induced in the rotor will also be constant.

The above equation can be written as: The above expression is the starting torque equation of induction motor. By analyzing the above equation, we can say that starting torque of induction motor is directly proportional to rotor resistance (R2) and inversely proportional to the reactance of rotor. Hence in order to have high starting torque, it is necessary to have large rotor resistance and low reactance.

Mathematical Expression for Maximum Starting Torque:

In order to find maximum starting torque of induction motor, we differentiate the starting torque equation w.r.t R2 and equate it to zero.

i.e.  Differentiating w.r.t  R2 Differentiating by U/ V method  Or, We can write as:   Simply, we can write as: The above expression is for the maximum starting torque in induction motor. By making rotor resistance equal to rotor reactance at standstill, we can achieve maximum starting torque in induction motor.