Effect of excitation on synchronous motor

In a synchronous motor, the field excitation (field current I_f) controls the back emf E_b. At constant supply voltage V and constant load (constant power input), changing I_f changes the armature current I_a and the power factor, but not the speed.

Basis

Per phase, E_r = V − E_b (phasor difference) and I_a = E_r / Z_s, where Z_s = R_a + jX_s. For constant load, the input power per phase V·I_a·cos φ is constant, so the in-phase component I_a cos φ is constant. Only the quadrature component changes with excitation. R_a is neglected in the diagrams, so E_r = jX_s·I_a and I_a lags E_r by 90°. E_b lags V by the load angle δ. E_r is drawn from the tip of E_b to the tip of V.

Phasor diagrams (V as reference, motor mode)

 (a) Under-excited: Eb < V, Ia LAGS V

   O-------------------------------------->V
    \ ------                           //
     \      -----                    //  Er
      \          -----            ///
       \          Eb  ------    //
        \  Ia               -->/
         \
          \
           v

 (b) Normal excitation: Ia IN PHASE with V (unity pf, minimum Ia)

   O-------------------------------------->V    Ia along V
       --------                           |
               --------                   |  Er
                       --------           |
                     Eb        --------   |
                                       --->

 (c) Over-excited: Eb > V, Ia LEADS V

          ^  Ia
         /
        /
      //
     /
    /
   O-------------------------------------->V
        -----------                         \\
                   ---------                  \\  Er
                            -----------         \\
                        Eb             ---------  \\
                                                ----->

 In every case Er = V - Eb = jXs·Ia, so Ia is 90° behind Er;
 Ia cosφ stays the same for constant load.

Explanation

• With reduced I_f, E_b is small (less than V). The resultant emf E_r = V − E_b is large and points up and to the right of the E_b tip, so I_a, which is 90° behind E_r, lags V. The motor draws magnetising (lagging reactive) current from the supply, because part of the main flux must be supplied by the stator. This is the lagging pf mode.
• As I_f is increased, E_b rises, E_r shrinks and I_a falls. At one value of I_f, E_r is at right angles to V, and I_a is minimum and in phase with V: unity pf.
• Further increase of I_f (over-excitation) makes E_r larger again, but it now points up and to the left, so I_a leads V. The motor delivers lagging reactive power to the line, i.e. it acts as a capacitor. This is the leading pf mode.

Operating in leading or lagging mode

• To run at leading pf, raise the d.c. field current above the value for unity pf (over-excite). This is used for power-factor correction; a machine run this way without a mechanical load is called a synchronous condenser.
• To run at lagging pf, reduce the field current below that value (under-excite). This is rarely done, as the stability margin is poorer.
• The plot of I_a against I_f for a constant load is the V-curve. Its minimum point is at unity pf.