Power capability curve of alternator

The power capability curve (capability chart or P–Q diagram) of an alternator shows the region of active power $P$ and reactive power $Q$ in which the machine can run continuously without exceeding any thermal or stability limit, at rated voltage.

   P (MW)
    |          prime mover limit
    |      ______________________
    |     |                      \   field current limit
    |     |   armature current    \  (arc, lagging side)
    |     |   limit (circle)       \
    |     |        rated point      |
    | stability                     |
    | limit                         |
  --+-----+----------O--------------+----> Q
    lead  -3V^2/Xs   origin        lag
   (absorb)                      (supply)

Main components (limits)

1. Armature (stator) current limit: a circle centred at the origin with radius = rated MVA ($S = 3VI_{rated}$). Exceeding it overheats the stator winding.
2. Field (rotor) current limit: an arc centred at $(-3V^2/X_s, 0)$ on the Q-axis, with radius $3EV/X_s$ for maximum field current. It limits operation at lagging pf (over-excitation) to protect the rotor winding.
3. Prime mover (turbine) limit: a horizontal line at the maximum mechanical power of the turbine.
4. Steady-state stability limit: a line at $\delta = 90^\circ$ (in practice with a margin, about 70°) on the leading side, limiting under-excited operation.
5. Minimum excitation / under-excitation limit and stator end-core heating limit on the leading side.

The rated operating point (rated MVA at rated pf, e.g. 0.85 lag) lies where the armature and field current limits meet. The safe operating area is the region enclosed by all these limits.