Analysis Of Phasor Diagram Of Synchronous Motor

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 Ф 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 Ф.

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  Ф

where R_a = Resistance of stator per phase

X_s  = Synchronous reactance of stator per phase

i.e.        Ф = tan^-1 (X_s/R_a)

and      | Z_s| = Ф(R_a² + R_s²) Ф

This angle ‘Ф’ is called internal machine angle or an impedance angle.

The significant of ‘Ф’ is that it tells us that phasor I_aph lags behind E_Rph i.e. I_a Z_s by angle Ф. 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 Ф. Practically R_a is very small compared to X_a and hence Ф tends to 90^o.

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

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

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

Fig. 1 Phasor diagram under normal working condition