Electrical Engineering ⇒ Topic : Rotor E.M.F., Current and Power

Rotor e.m.f:-

When the rotor is stationary, an induction motor is equivalent to a 3-phase transformer with secondary short-circuited. Therefore, the induced e.m.f. per phase E₂ in the rotor at the instant of starting is given as :

                                                                          ............... (1)

where  E₁= applied voltage per phase to primary, i.e., stator winding,

           N₁= number of stator turns, and

           N₂ = number of rotor turns

When the rotor starts gaining speed,. the relative speed of the rotor with respect to stator flux, i.e., slip, is decreased. Hence induced e. m. f. in the rotor, which is directly proportional to the relative speed, i.e., slip, is also decreased and is given by sE₂. Hence for slip 's', the induced e.m.f. in the rotor is s times the induced e.m.f in the rotor at standstill.

Rotor current :

Let                   R₂ = rotor resistance/phase,

                        L₂ = rotor inductance/phase, and

                        E₂ = induced e.m.f. of rotor/phase at standstill

At standstill :

Induced e.m.f. of rotor/phase          = E₂

Rotor winding resistance/phase      = R₂

Rotor winding reactance/phase,X₂  = 2πL₂ where f is the supply frequency 

Rotor impedance/phase,           

Rotor current/phase                        = 

At slip 's' :

Induced e.m.f. of rotor/phase =sE₂

Rotor winding resistance        = R₂

Rotor winding reactance         = 2ΠfL₂= 2ΠsfL₂= s(2ΠfL₂) = sX₂

_{Rotor winding impedance/phase} 

_{Rotor current/phase,}           

                                                            ............ (2)

The rotor current I2 lags the rotor voltage E2 by rotor power factor angle  Φ₂

_{Power factor of rotor current,}

Power:-

                                        ..........(1)   

Eqn. (1) can be represented by a simple series circuit as shown in Figure 

                       Figure Rotor equivalent circuit of an induction motor

It is seen from this circuit that per phase power' input (gross) to rotor.

where                  

An examination of Figure  also shows that per phase power input to rotor is equal to  as the reactance X₂ consumes no power

P_g is t he power transferred from stator to rotor across the air gap. In view of this, P_g called tht. air-gap power. The expression for P_g may be written as

                                                                      = Rotor ohmic loss + internal mechanical power developed in rotor (P_mech)

                                                                                                 ...............  (a)

                                                                     .................. (b) 

                                      _{Rotor ohmic loss  =                          ..................   (c)}

_{Eqn. (12.11) reveals that ohmic loss}

_{Internal (or gross) torque developed per phase is given by}

                                        

_{Here is the synchronous speed in mechanical radians per second.}

The power available at the shaft can be obtained from P_g as follows : 

Output or shaft power, P_sh= P_m- mechanical losses (friction, and windage losses)

                                or P_sh= P_g- rotor ohmic loss - friction and windage losses.

Output or shaft torque

It stator input is known, then air-gap power P_g is given by

                                         P_g = stator power input - stator I²R loss - stator core loss