Effect of Slip on Rotor Parameters : Part 3

Effect of Slip on Rotor Parameters

4. Effect on Rotor Power factor

       From rotor impedance, we can write the expression for the power factor of rotor at standstill and also in running condition.

       The impedance triangle on standstill condition is shown in the Fig1. From it we can write,

                        cos Φ₂ = Rotor power factor on standstill

                                    = R₂/Z₂ =R₂/√(R₂²+ X₂²)

       The impedance in running condition becomes Z_2r and the corresponding impedance triangle is shown in the Fig.2. From Fig. 2 we can write,

                        cos Φ₂r = Rotor power factor in running condition

                                     = R₂/Z_2r = R₂/√(R₂²+ (s X₂)²)

Key point : As rotor winding is inductive, the rotor p.f. is always lagging in nature.

Fig. 1

Fig. 2

5. Effect on Rotor Current

       Let                     I₂ = Rotor current per phase on standstill condition 

       The magnitude of I₂  depends on magnitude of E₂ and impedance Z₂  per phase.

                                  I₂  = (E₂  per phase)/(Z₂  per phase) A

       Substituting expression of Z₂ we get,

                                   I₂ = E₂ /√(R₂²+ X₂²)      A

       The equivalent rotor circuit on standstill is shown in the Fig.3. The Φ₂ is the angle between E₂ and I₂ which determines rotor p.f. on standstill.

Fig. 3

       In the running condition, Z₂ changes to Z_2r while the induced e.m.f. changes to E_2r. Hence the magnitude of current in the running condition is also different than on standstill. The equivalent circuit on running condition is shown in the Fig. 4.

                                 I_2r = Rotor current per phase in running condition

       The value of slip depends on speed which inturn depends on load on motor hence X_2r is shown variable in the equivalent circuit. From the equivalent we can write,

                                 I_2r =  E_2r/Z_2r = (s E₂)/√(R₂²+ (s X₂)²)      

       Φ_2r is the angle between E_2r and I_2r which decides p.f. in running condition .

Fig. 4

Key point : Putting s  = 1 in the expression obtained in running condition, the values at standstill can be obtained.