Varying excitation and V curves

At constant load and supply voltage, the field current $I_f$ of a synchronous motor controls the back emf $E_f$; this changes the armature current and the power factor, but not the speed or the active power.

Effect of varying excitation

Input power per phase $P = VI_a\cos\phi$ is constant, so the active component $I_a\cos\phi$ is constant; the tip of the $I_a$ phasor moves along a line perpendicular to $V$. Also $E_f\sin\delta$ is constant, so the tip of $E_f$ moves on a line parallel to $V$.

          Ia3 (lead)      Ia2 (upf)
            \               |
             \              |
  ------------+-------------+--------> V
               \            |  locus of Ia tip
             Ia1 (lag)      |  (Ia cos(phi) const)

1. Under-excitation ($E_f < V$): $I_a$ lags $V$; it has a large lagging reactive component. Current is high, pf lagging.
2. Increasing $I_f$: the lagging component falls, so $I_a$ decreases and pf improves.
3. Normal excitation: $I_a$ is in phase with $V$; current is minimum, pf = unity.
4. Over-excitation ($E_f > V$): $I_a$ leads $V$ and grows again; pf leading. The motor now supplies reactive power to the system.

V-curves

Plotting $I_a$ against $I_f$ for constant power output gives V-shaped curves.

 Ia
  |F                F   F = full load
  | F              F    H = half load
  |H F          F  H    N = no load
  | H  F  F  F    H
  |N  H        H  N
  | N    H  H   N
  |   N  N  N
  +------------------- If
    lagging | leading
         upf (minima)

• One V-curve for each load (no load, half load, full load); higher load curves lie higher and to the right.
• The minimum point of each curve corresponds to unity pf. The line joining them is the unity pf compounding curve; points left of it are lagging, right are leading.
• Plotting pf against $I_f$ gives inverted V-curves, with peak (pf = 1) at normal excitation.

Significance of V-curves

1. Show the field current needed for unity pf (minimum current, least copper loss) at any load.
2. Show how much leading kVAR an over-excited motor can supply, so it can be used as a synchronous condenser for power factor correction.
3. Show the limits of operation: the left end of each curve (very low $I_f$) approaches the stability limit, where the motor would pull out of step.
4. Help the operator choose excitation to keep armature current within rating.
5. Used to determine the excitation required for voltage control at substations.