Excitation system and changing excitation at constant load

The excitation system of a synchronous motor is the DC source and its control (DC exciter, static rectifier or brushless exciter, with field regulator) that supplies the field current to the rotor poles; it decides the back emf $E_f$ and hence the motor's power factor.

Effect of changing excitation at constant load

With constant load, $VI_a\cos\phi$ and $E_f\sin\delta$ are constant. Only the reactive part of $I_a$ changes.

         Ia3 (over: lead)
           \        Ia2 (normal: upf)
            \       |
  -----------\------+--------> V
              \     |
          Ia1 (under: lag)
   tip of Ia moves on a line normal to V

The phasor diagram for the voltages shows the same effect. Since $E_f\sin\delta$ is constant, the tip of $E_f$ moves on a line parallel to $V$ as excitation changes:

  Ef1 (under)  Ef2 (normal)  Ef3 (over)
   .-----------.-------------.   <- locus of Ef tip (parallel to V)
   |           |             |
   O----------------------------> V
   Er = V - Ef joins the tip of Ef to the tip of V;
   Ia = Er / jXs lags Er by 90 deg

As field current rises, $I_a$ first falls to a minimum (unity pf) and then rises with leading pf, giving the V-curve.