Phasor Diagram

 Consider a phasor diagram with normal excitation i.e. such a current through field winding which will produce flux that will adjust magnitude of E_bph same as V_ph.

       Let δ be the load angle corresponding to the load on the motor. So from the exact opposing position of E_bph with respect to V_ph. E_bph gets displaced by angle δ.

       Vector difference of E_bph and V_ph, gives the phasor which represents I_a Z_s, called E_Rph.

       Now  Z_s = R_a + j X_s  Ω

       where R_a = Resistance of stator per phase

                 X_s  = Synchronous reactance of stator per phase

       i.e.        θ = tan^-1 (X_s/R_a)

       and      | Z_s | = √(R_a² + R_s²) Ω

       This angle 'θ' is called internal machine angle or an impedance angle.

       The significant of 'θ' is that it tells us that phasor I_aph lags behind E_Rph i.e. I_a Z_sby angle θ. Current always lags in case of inductive impedance with respect to voltage drop across that impedance. So phasor I_aph  can be shown lagging with respect to E_Rph by angle θ. Practically R_a is very small compared to X_a and hence θ tends to 90^o.

       Note : The power factor at which motor is running, gets decided by the angle between V_ph and I_aph shown. This angle is denoted as Φ and called power factor angle.

       and cos Φ = Power factor at which motor is working.

       The nature of this p.f. is lagging if Iaph lags V_ph by angle Φ. While it is leading if Iaph leads V_ph by angle Φ. Phasor diagram indicating all the details is shown in the Fig.1.

Fig. 1 Phasor diagram under normal working condition