In synchronous machines, the V curve (also spelled as V-curve) is the graph showing the relation of armature current as a function of field current in synchronous motors keeping the load constant. The name comes from an observation made by W. M. Mordey in 1893 that the curve resembles a letter V.
The lowest point of the curve corresponds to the unity power factor. For a motor, points on the left of the minimum correspond to underexcitation (and therefore the armature current would "lag" the voltage), on the right - to overexcitation (and "lead"). Typically multiple V curves are plotted based on the experiments, each corresponding to its own load value.
The data from the V curves can be used to set up the synchronous motor to correct the power factor of the overall system, as the power factor of the motor can be changed by simply adjusting the field current. While performing the correction, the motor can either provide the mechanical power also, or run in the idle mode ("float"), working as a synchronous condenser.
The inverted V curve is a graph showing the relation of power factor as a function of field current. The shape of this curve resembles a dome.