Effect of excitation on armature current and pf

In a synchronous motor with constant load (constant power $P = 3VI\cos\phi$), varying the DC field current changes the back emf $E_b$. Since $V$ and $P$ are fixed, $I\cos\phi$ stays constant, so the tip of the current phasor moves along a line perpendicular to $V$, while $E_b\sin\delta$ also stays constant.

(a) Normal excitation

• Field current gives $E_b$ such that the current is in phase with $V$: unity pf.
• Armature current is minimum for that load.

(b) Under-excitation

• $E_b$ is smaller; the resultant voltage $E_r = V - E_b$ swings so that the current lags $V$.
• Armature current is larger than at normal excitation; the motor draws lagging reactive power (magnetising current) from the supply.

(c) Over-excitation

• $E_b$ is larger; the current leads $V$.
• Armature current again increases; the motor supplies reactive power to the supply (synchronous condenser action).

 Phasors at constant load (V reference, Rs = 0)

   I3 (lead, over-excited)
     \
      \     I1 (upf, normal)
  O----+------> V      I tip moves on the
      /                vertical line I cos(phi)
     /                 = constant
   I2 (lag, under-excited)

V-curves and inverted V-curves

  Ia                         pf
  |  \       /  full load    |      _
  |   \     /                |    /   \  (inverted V)
  |  \ \   / /               |   /     \
  |   \_\_/_/  no load       |  /       \
  +------------> If          +--------------> If
  lag | upf | lead          lag  upf  lead

• V-curves: $I_a$ vs $I_f$ at constant load, shaped like a "V". The minimum point of each curve is at unity pf. The left side (under-excited) is lagging, the right side (over-excited) is leading. Higher load gives a higher curve.
• Inverted V-curves: pf vs $I_f$; the peak is unity pf. The locus of minimum points (unity pf) shifts to the right as load increases, since more excitation is needed at higher load.

This property lets an over-excited synchronous motor drive its load and also correct the plant power factor.