It is defined as the rise in voltage when full-load is removed (\(I_f\) and \(N\) remaining the same) divided by the rated terminal voltage \[\boxed{\% \mbox{Voltage Reg.} = \dfrac{E_0-V}{V} \times 100}\]

The magnitude of the change in \(V\) depends not only on the load but also on the load power factor

Direct Method - for small machines

Indirect Method - for large machines

Alternator is driven at \(N_s\) and \(V\) is adjusted to rated value

Vary the load until watt-meter and ammeter indicates the rated values at desired p.f.

Throw the entire load off keeping the \(N\) and \(I_f\) constant

Open-circuit or no-load voltage \(E_0\) is read \[\% V.R. = \dfrac{E_0-V}{V} \times 100\]

Large machines the cost to find the regulation by direct loading becomes prohibitive.

All these methods require-

Armature resistance \(R_a\)

obtained by direct measurement (Voltmeter-ammeter or Wheatstone bridge)

Open-circuit/No-load Characteristic

Short-circuit characteristic (but ZPF lagging for Potier)

\[\begin{aligned} Z_s & = \dfrac{E_1(\mbox{open-circuit})}{I_1(\mbox{short-circuit})} ~~ X_s=\sqrt{Z_s^2-R_a^2}\\ E_{0}&=\sqrt{\left(V\cos\phi+IR_{a}\right)^{2}+\left(V\sin\phi+IX_{s}\right)^{2}} \end{aligned}\]

- Not accurate; \(Z_s\) found \(>\) than its value at normal voltage conditions and saturation.

\(X_a\) has not been treated separately but along with \(X_L\)

Converse of the EMF method: \(X_L\) is treated as an additional AR

Field A.T. required for \(V\) on F.L. is the vector sum of

O.C. test : Field A.T. required for \(V\) (or if \(R_a\) is to be taken into account, then \(V+IR_a\cos \phi\)) on no-load

S.C. test: Field A.T. to overcome demagnetising effect of AR on F.L. Field A.T. required to produce F.L. current on S.C balance the armature reaction and the impedance drop

\(Z_s\) drop neglected, \(R_a\) very small and \(X_s\) also small under S.C. condition

P.F. on S.C is almost zero lagging and field A.T. are used entirely to overcome AR which is wholly demagnetising

\(OA\) represents \(I_f\) for \(V\)

\(OC\) represents \(I_f\) required to produce F.L current on S.C

\(\overrightarrow{AB} = \overrightarrow{OC}\) drawn at \((90^{\circ})+\phi\) to \(OA\) (p.f. lagging)

Total \(I_f\) is \(OB\) for which the corresponding O.C. voltage is \(E_0\)

: give results less than the actual value

method based on separation of armature-leakage reactance drop and the armature reaction effects

gives more accurate results

makes use of first two methods

OCC and F.L. ZPF (not SCC)

ZPF curve - \(V\) against \(I_f\) when delivering \(I_{a,F.L}\) at zero p.f.

Note \(\boxed{E_0 = \left[V + I_a(R_a+jX_L)\right]+ \mbox{armature-reaction drop}}\) (assuming lagging p.f.)

Point \(B\) - wattmeter = \(0\)

Point \(A\) - SC test with F.L \(I_a\)

\(OA\) represents \(I_f\) = and opposite to demagnetising armature reaction and for balancing \(X_L\) drop at F.L.

From \(B\), draw \(BH\) = and \(\parallel\) \(OA\)

From \(H\), \(HD\) drawn \(\parallel\) initial straight part of NL curve, i.e. \(\parallel\) \(OC\), which is tangential to the NL curve

We get point \(D\) on NL curve, which corresponds to point \(B\) on F.L. ZPF curve

Triangle \(BHD\) is Potier triangle

Draw \(DE\) \(\perp\) \(BH\)

\(DE\) = \(IX_L\)

\(BE\), \(I_f\) to overcome demagnetising effect of AR at FL

\(EH\) for balancing \(X_L\) drop \(DE\)

\(E=DF=V+jIX_L\) (neglecting \(R_a\)); \(I_f = OF\)

\(NA = BE\) represents \(I_f\) needed to overcome AR

\(\overrightarrow{NA}+\overrightarrow{OF}\), \(I_f\) for \(E_0\), read from NL curve (\(NA=FG\))