# The Phasor Diagram of an Induction-Motor Phase

Under running conditions, the frequency of the current in the stator circuit is f and that of the current in the rotor circuit is f 2 = f s is, so no common phasor diagram may be constructed for the two circuits. However such a phasor diagram may be plotted if we assume an equivalent blocked rotor in the motor for which a model circuit representing one stator and rotor phase is shown in Fig. 19. This figure also shows the phasor diagram thus constructed and the phasor diagram for a stator phase carried over from Fig. 14 . unchanged . The reference vector is Φ̇r with respect to which the stator phase emf Ėl and the phase emf of the equivalent blocked rotor. Ė2,br , are in quadrature lagging .

With respect to - Ė2,br the rotor current 2 lags be­hind by an angle

φ2 = arctan [(ɷLleak,2/(rw2+ r2)]

= arctan (sɷLleak,2/rw2)

which is the same phase difference as is observed between - Ė2 and 2 when the rotor is revolving (see Fig 16) .

The secondary circuit includes a resistance

rw2 + r2 = rw2/s

and an inductive reactance ɷLleak.2 .Accordingly, Ė2,br consists of an active component, rw22/s , and a reactive component jɷLleak,22 .

The vector of the rotor phase current referred to the stator side is

'2 = (m2w2kw2/3wlkwl) 2

and the stator phase current is

1 = '2 + 1,nl

In the stator phase winding the referred current '2 corresponds to the rotor phase current 2 which it compensates . The magnetizing current 1,nl , which accounts for a part of the stator phase current, excites the revolving magnetic field of the motor. The magnetizing current phasor leads the magnetic flux phasor by an angle 6 owing to hysteresis and eddy-current losses in the core. The phasor diagram of one phase of an induction motor with its rotor blocked is in effect the same as the phasor diagram of a transformer (see Fig. 11).

The stator phase voltage phasor is plotted on the basis of the fol­lowing equation:

1 = - Ėl + rw11+ jleak.11