Synchronous motor drawing lagging and leading current

A synchronous motor runs at constant speed whatever its excitation. For a constant load (constant input power $VI\cos\phi$), changing the field current changes the back emf $E_b$, and hence the magnitude and power factor of the armature current. So the same motor can behave as an inductive (lagging) or a capacitive (leading) load.

Motor equation (per phase, $R_a$ neglected):

$$\bar V = \bar E_b + jX_s\bar I \qquad\text{or}\qquad \bar I = \frac{\bar V - \bar E_b}{jX_s}$$

The resultant voltage $\bar E_r = \bar V - \bar E_b$ drives the current, which lags $E_r$ by 90°.

1. Under-excitation ($E_b < V$): lagging pf (inductive)

           V
   O-------------->
    \`-.        /
     \  `-.   / Er = jIXs
      \    `/
   I   \   Eb (short)
  (lags V)

• $E_b\cos\delta < V$; the motor draws a lagging current.
• The field is too weak, so the armature takes a lagging (magnetising) current from the supply to make up the missing flux. The motor then behaves like an induction motor or an inductor.

2. Normal excitation ($E_b \approx V$): unity pf

• Field current is just enough for the required flux; current is in phase with $V$ and is minimum for that load.

   O--------------> V
   O-------->  I (in phase)
     \       /
      Eb    / Er

3. Over-excitation ($E_b > V$): leading pf (capacitive)

     I (leads V)
      ^       V
      |  O---------->
      |    \        .
      |      \    . Er
      |   Eb (long)

• $E_b > V$; the resultant $E_r$ makes the current lead $V$.
• The motor supplies reactive power to the system and acts as a capacitor. Running at no load like this, it is called a synchronous condenser, used for power-factor improvement and voltage control.

Summary

These variations are shown by the V-curves (armature current vs field current at constant load), whose lowest point is at unity pf.