Effect of excitation on synchronous motor

Principle

A synchronous motor runs at constant speed. For a constant load and constant supply voltage $V$, the power input $P = \sqrt3 V_L I\cos\phi$ stays constant, so the active component $I\cos\phi$ of the armature current stays constant. When the field excitation $I_f$ is changed, the back emf $E_f$ changes, and the current adjusts so that only its reactive component changes. This changes the power factor. (Armature resistance is neglected.)

The phasor relation for a motor is $\vec V = \vec E_f + j\vec I X_s$.

Three conditions

1. Normal excitation: $E_f \cos\delta = V$. The current is minimum, in phase with $V$, and the power factor is unity.
2. Under-excitation ($E_f$ smaller): the current lags the voltage. The motor draws reactive power from the supply like an inductive load: lagging power factor. The current is larger than at unity pf.
3. Over-excitation ($E_f$ larger): the current leads the voltage. The motor supplies reactive power to the supply: leading power factor. The current is again larger.

 Motor: V = Ef + jIXs   (V is the horizontal reference; Ef lags V by delta)

 (a) Under-excited: I lags V, Ef is short
 O------------------------> V
  `-._                    /
      `-._    Ef         / jIXs
          `-._          /
              `-._     /
                  `-._/

 (b) Normal: I in phase with V, Ef cos(delta) = V
 O------------------------> V
  `-._                    |
      `-._    Ef          | jIXs
          `-._            |
              `-._        |
                  `-._    |
                      `-._*

 (c) Over-excited: I leads V, Ef is long
 O------------------------> V
  `-._                     \
      `-._    Ef            \ jIXs
          `-._               \
              `-._            \
                  `-._         \
                      `-._      \
                          `-._   \
                              `-._*

In each case $jIX_s$ is drawn from the tip of $E_f$ to the tip of $V$, at $90^\circ$ ahead of $I$. Because the power is constant, $I\cos\phi$ is constant (the tip of $I$ moves along a line perpendicular to $V$), and $E_f\sin\delta$ is constant (the tip of $E_f$ moves along a line parallel to $V$).

Application

An over-excited synchronous motor running at no load is a synchronous condenser, used for power factor correction. The V-curve plots armature current against field current for each load; the minimum current of each curve corresponds to unity power factor.