Armature reaction at different load power factors

Armature reaction is the effect of the magnetic field set up by the armature (stator) current on the main field flux produced by the rotor poles. When the alternator is loaded, the three-phase armature currents produce a rotating mmf that rotates at synchronous speed along with the rotor. This mmf distorts, weakens or strengthens the main flux depending on the power factor of the load, and so changes the terminal voltage.

In the equivalent circuit, armature reaction is represented by a fictitious reactance $X_a$; together with the leakage reactance $X_l$ it forms the synchronous reactance $X_s = X_a + X_l$, and

$$\bar E = \bar V + \bar I (R_a + jX_s)$$

(i) Unity power factor (resistive) load

• The armature current is in phase with the emf, so each conductor carries its maximum current at the instant it is under the centre of a pole (where its emf is maximum). The armature mmf is then at 90° (in quadrature) to the main flux.
• The effect is cross-magnetising: flux is distorted (crowded at one pole tip, weakened at the other) but its average value changes little.
• The terminal voltage drops only slightly (mainly due to $IR_a$ and the small quadrature drop). $E$ is only a little greater than $V$.

 (a) Unity pf load
                    E
                  / |
                /   |  j I Xs
              /     |
            O-------+  V
            O------->  I  (in phase with V)

(ii) Lagging power factor (inductive) load

• For zero pf lagging, the current lags the emf by 90°; armature flux acts directly opposite to the main flux along the pole axis.
• The effect is demagnetising; the resultant air-gap flux and generated voltage fall.
• For a practical lagging pf (e.g. 0.8) the effect is partly cross-magnetising and partly demagnetising.
• The terminal voltage falls considerably with load; $V < E$, and regulation is large and positive. More field current is needed to keep $V$ constant.

 (b) Lagging pf load
                      E
                     /|
                   /  |  j I Xs
                 /    |
               O------+ V
                `-.
                   `-. I  (lags V by phi)

(iii) Leading power factor (capacitive) load

• For zero pf leading, the current leads the emf by 90°; the armature flux acts along the main flux.
• The effect is magnetising (strengthening); the air-gap flux increases.
• The terminal voltage rises with load; $V$ can be greater than $E$, so regulation can be negative. Less field current is needed.

 (c) Leading pf load
             I      E
              \    /'.
               \  /   '.  j I Xs
                \/      '.
                O----------+ V
      I leads V by phi;  E < V

Summary