Motor adjustment to load and excitation effects

A synchronous motor always runs at synchronous speed $N_s = 120f/P$. When the shaft load changes it cannot slow down (as an induction motor does); instead the rotor shifts backwards in space by a larger load angle $\delta$, and the armature current changes to supply the new power.

Adjustment to change in load

1. At no load the rotor poles are almost in line with the stator field ($\delta \approx 0$), and the motor draws only enough current to meet losses.
2. When load torque increases, the rotor momentarily slows down. The rotor poles fall back with respect to the rotating stator field, so $\delta$ increases.
3. Back emf $E_f$ stays the same in magnitude (excitation unchanged) but moves further behind $V$. The resultant voltage $E_r = V - E_f$ grows, so armature current $I_a = E_r / jX_s$ increases.
4. Power drawn $P = \dfrac{3VE_f}{X_s}\sin\delta$ rises until it equals the new load plus losses. The rotor then runs again at $N_s$ with a larger fixed $\delta$.
5. If load exceeds $P_{max}$ (at $\delta = 90^\circ$ for a cylindrical rotor), the motor pulls out of step and stops.

          V (fixed)
   ------------------>
     \  delta1
      \--------> Ef (light load)
       \
        \ delta2 > delta1
         \------> Ef (heavy load, same length)

Effect of change in excitation (constant load)

With load (and hence $P = VI_a\cos\phi$) constant, $I_a\cos\phi$ is constant, so the tip of $I_a$ moves on a line perpendicular to $V$, and $E_f\sin\delta$ is also constant.

           I(lead)   I(unity)
             \         |
              \        |
  ------------ +-------+--------> V
                \      |
             I(lag)  locus of I tip
                      (I cos(phi) const)

• Raising the field current from a low value first reduces $I_a$ (lagging pf improves) until $I_a$ is minimum at unity pf.
• Further increase makes $I_a$ rise again with a leading pf.
• Plotting $I_a$ against field current gives the V-curves; the pf vs field current curve is an inverted V.

This is why an over-excited synchronous motor can act as a synchronous condenser to improve plant power factor.