Potier method of voltage regulation

The Potier (zero power factor, ZPF) method finds regulation by separating the leakage reactance drop and the armature reaction mmf, and it allows for saturation. It is more accurate than the EMF and MMF methods.

Tests and curves needed

1. Open-circuit characteristic (OCC): $E$ vs field current $I_f$.
2. Zero power factor characteristic (ZPFC): terminal voltage vs $I_f$ with full-load current at zero pf lagging (purely inductive load). Two points are enough: the short-circuit point A (V = 0) and one point P at rated voltage.
3. Armature resistance $R_a$.

Potier triangle

  V                        OCC
  |                  __.--''
  |               .-'
  |             .'  R
  |           .'   /|           ZPFC
  |         .'    / |        __.-'
  |       .'     /  |    _.-'
  |      /     Q----S-----P  (rated V,
  |     /                      rated I)
  +----A---------------------> If
  O  (short-circuit point)
     QP = OA, QR parallel to air-gap line

• From P draw PQ horizontally to the left, equal to OA.
• From Q draw a line parallel to the air-gap (linear) part of the OCC, meeting the OCC at R.
• Drop a perpendicular RS onto PQ. Triangle PRS is the Potier triangle:
  • $RS$ = leakage reactance drop $IX_L$, so $X_L = RS/I$ (Potier reactance);
  • $SP$ = field current equivalent to armature reaction mmf ($F_a$).

Finding regulation (phasor steps)

1. Take $V$ as reference, current $I$ at the given pf.
2. Air-gap emf: $\bar E_g = \bar V + \bar I(R_a + jX_L)$.
3. From the OCC read the field current $F_g$ needed for $E_g$; it leads $E_g$ by 90°.
4. Add the armature-reaction field current $F_a$ (from the triangle), drawn opposite to $I$ (to cancel the armature mmf), to $F_g$: the resultant field current is $\bar F_r = \bar F_g + \bar F_a$, i.e. $$F_r = \sqrt{F_g^2 + F_a^2 + 2F_gF_a\cos(90^\circ - \theta)}$$ where $\theta$ is the angle between $E_g$ and $I$ (lagging pf).
5. From the OCC read $E_0$ for $F_r$. Then $$\%\text{Reg} = \frac{E_0 - V}{V}\times100$$