Rotor Speed Current Frequency Torque And Emf
The difference between the speed of the stator, known as synchronous speed (Ns) and the actual rotor speed, N is known as the slip and is denoted by S. It is usually expressed as a fraction or % age of synchronous speed.
Fractional slip, S = Ns - N/Ns
Ns - N/Ns
Frequency of Rotor Current or EMF. The frequency of both the rotor emf and rotor current depends upon the rate of cutting flux by the rotor conductors i.e. on the relative speed between the stator revolving magnetic field and rotor and is given by the expression.
Where S is the slip and f is the supply frequency.
Rotor EMF. When the rotor is at standstill, the motor is equivalent to a 3-phase transformer with secondary short-circuited and so emf induced per phase in the rotor is given as
E2 = E1 X N2/N1
Where E1 is the applied voltage per phase to the stator winding and N1 and N2 are the number of turns per phase on stator and rotor respectively.
While the motor is running with slip S,m the induced emf in the rotor will be S times the induced emf in the rotor at standstill.
Rotor Current. If R2 and L2 are the resistance and inductance per phase of rotor and E2 is the induced emf at standstill, then rotor current per phase at standstill
I2 = E2/Z2 = E2/√R22 + X22
While the motor is running with slip S, ten the rotor phase reactance and rotor phase emf will be SX2 and SE2 respectively and rotor current will be as
I2 = SE2/√R22 + S2 X22
And power factor, cos Ø2 = R2/√R22 + S2 X22 At start S = 1 and, therefore, starting torque is given as
Tst = KR2 E22 / R22 +X22
Starting torque will be maximum when = R2/2X2