Equivalent circuit model and phasor diagram of a synchronous motor

Equivalent circuit model and phasor diagram of a synchronous motor

The equivalent-circuit model for one armature phase of a cylindrical rotor three phase synchronous motor is shown in Figure below exactly similar to that of a synchronous generator except that the current flows in to the armature from the supply. Applying Kirchhoff’s voltage law to Figure below

VT = IaRa + jIaXl + jIaXas + Ef 

Combining reactances, Xs = Xl + Xas 

VT = Ef + Ia(Ra + jXs)

or VT = Ef + IaZs

  where:                

Ra = armature resistance (/phase)            

Zs = synchronous impedance (/phase) 

VT = applied voltage/phase (V)                  

Ia = armature current/phase (A) 

A phasor diagram shown in Figure above, illustrates the method of determining the counter EMF which is obtained from the phasor equation;        

                                  Ef = VT − IaZs

The phase angle δ between the terminal voltage VT and the excitation voltage Ef in Figure above is usually termed the torque angle. The torque angle is also called the load angle or power angle.