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Effect of Slip on Rotor Parameters : Part2

Effect of Slip on Rotor Parameters
2. Effect of Slip on Magnitude of Rotor Induced E.M.F
       We have seen that when rotor is standstill, s  = 1, relative speed is maximum and maximum e.m.f. gets induced in the rotor. Let this e.m.f. be,
                E2 = Rotor induced e.m.f. per phase on standstill condition
        As rotor gains speed, the relative speed between rotor and rotating magnetic field decreases and hence induced e.m.f. in rotor also decreases as it is proportional to the relative speed Ns - N. Let this e.m.f. be,
               E2r = Rotor induced e.m.f. per phase in running condition 
Now        E2r α Ns while E2r α Ns - N
       Dividing the two proportionality equations,
              E2r/E2= ( Ns - N)/Ns    but (Ns - N)/N = slip s
              E2r/E2 = s
              E2r = s E2
       The magnitude of the induced e.m.f in the rotor also reduces by slip times the magnitude of induced e.m.f. at standstill condition.

3. Effect on Rotor Resistance and Reactance
       The rotor winding has its own resistance and the inductance. In case of squirrel cage rotor, the rotor resistance is very very small and generally neglected but slip ring rotor has its own resistance which can be controlled by adding external resistance through slip rings. In general let,
                                                R2 = Rotor resistance per phase onstandstill
                                                X2 = Rotor reactance per phase on standstill
       Now at standstill,               fr = f    hence if L2 is the inductance of rotor per phase,
                                                X2 = 2πfr L2   = 2πf L2   Ω/ph
       While                                R2 = Rotor resistance in Ω/ph
       Now in running condition,  fr = s f   hence,
                                                X2r = 2πfr L2 = 2πfs L2   = s .(2πf L2)
                                                X2r = s X2
where                                       X2r  = Rotor reactance in running condition
       Thus resistance as independent of frequency remains same at standstill and in running condition. While the rotor reactance decreases by slip times the rotor reactance at standstill.
       Hence we can write rotor impedance per phase as :
                              Z2 = Rotor impedance on standstill (N = 0) condition
                                  = R2 + j X2 Ω/ph
                               Z2 = √( R22+ X2)2) Ω/ph            ...... magnitude
       While                Z2r = Rotor impedance in running condition 
                                      = R2 + j X2r = R2 + j (s X2) Ω/ph
                                Z2r = √(R22+ (s X2)2)      Ω/ph       ...... magnitude
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