Synchronous generator load characteristics, capacitive load

Load characteristics of a synchronous generator

The load characteristic (external characteristic) is the plot of terminal voltage $V$ against load current $I$ at constant speed, constant field current and constant power factor.

 V
 |            leading pf (rises)
 |         _.-'
 |  ______-----   unity pf (small fall)
 |        `-._
 |            `-._  lagging pf (falls)
 +----------------------> I

• Lagging pf (inductive): the armature reaction is demagnetising, and the synchronous impedance drop also reduces the voltage, so $V$ falls considerably with load.
• Unity pf: the armature reaction is mainly cross-magnetising; $V$ falls slightly.
• Leading pf (capacitive): the armature reaction is magnetising, so $V$ rises with load.

Why $V > E$ with capacitive load

The phasor equation for a generator is $\vec E = \vec V + \vec I(R_a + jX_s)$, where $X_s$ includes the armature reaction reactance ($X_s = X_{ar} + X_l$).

• With leading current, the armature flux aids the main field flux (magnetising armature reaction). In the phasor diagram this appears as a reactance drop $jIX_s$ that acts in the opposite sense to the lagging case.
• The drop $j\vec I X_s$ leads $\vec I$ by $90^\circ$, and $\vec I$ itself leads $\vec V$, so $j\vec I X_s$ has a component directed opposite to $\vec V$. In $\vec E = \vec V + j\vec I X_s$ the second term therefore reduces the magnitude, so $E < V$.

                     *  tip of E
                 .-'  \
             .-'       \   jIXs (leads I by 90 deg)
         .-'  E         \
     .-'                 \
 O------------------------> V
    I leads V by phi;  E = V + jIXs is shorter than V

Neglecting $R_a$, with $I$ leading $V$ by angle $\phi$ (and $IX_s$ small compared with $V$):

$$E \approx V - I X_s \sin\phi \quad\Rightarrow\quad V \approx E + IX_s\sin\phi > E$$

The same result is seen physically: the capacitive load current produces a field that adds to the main field, so the net flux (and the terminal voltage) is greater than that due to the field current alone. This is a Ferranti-like voltage rise, and it is why the voltage regulation is negative for leading pf.