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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 Z2r 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/Z2r = 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 Z2r while the induced e.m.f. changes to E2r. 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.
                                 I2r = Rotor current per phase in running condition
       The value of slip depends on speed which inturn depends on load on motor hence X2r is shown variable in the equivalent circuit. From the equivalent we can write,
                                 I2r =  E2r/Z2r = (s E2)/√(R22+ (s X2)2)      
       Φ2r is the angle between E2r and I2r 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.
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