V-curve and inverted V-curve

V-curve

A V-curve of a synchronous motor is the graph of armature current $I_a$ against field current $I_f$, at constant supply voltage and constant load (mechanical output). The curve has the shape of the letter V.

• The lowest point of each curve is at unity power factor, where the armature current is minimum.
• To the left (under-excited) the current lags the voltage; the pf is lagging, and $I_a$ increases as $I_f$ is reduced.
• To the right (over-excited) the current leads; the pf is leading, and $I_a$ increases as $I_f$ is increased.
• Curves are drawn for no load, half load, full load, etc. A higher load gives a curve higher up, and its minimum point moves to a larger field current.
• The dotted line joining the minima is the unity power factor line; the region to its left is lagging pf and the region to its right is leading pf.

  Ia
   |\                         /
   | \   full load          /
   |  \                    /
   |   \     half load    /
   |    \    \          / /
   |     \    \  no   / /
   |      \    \ load/ /
   +-------\----*---/------> If
   lagging   unity pf  leading
   (under)  (min Ia)  (over)

Inverted V-curve

The inverted V-curve is the plot of power factor against field current at constant load. The power factor rises as the field current increases from the under-excited region, reaches its maximum value of unity at the same field current at which the V-curve is at its minimum, and then falls again (now leading) as the field current is raised further. The shape is like an inverted V.

  pf
  1.0|        /\
     |      /    \
     |    /        \
     |  /            \
     +-----------------> If
     lag    unity   lead

These curves show that a synchronous motor can be operated at any power factor by changing its excitation, so it is used for power factor correction (as a synchronous condenser).