Explanation of v curve of sync machine
The magnetizing current of a synchronous machine is supplied by DC excitation current in the rotor. However, if the rotor excitation current is not sufficient for the motor to supply the voltage dictated by the grid connection with a given load current, the machine will experience a phase shift that result in magnetization being supplemented by reactive current in the armature.
If the excitation current exceeds the current required for operation under the given conditions, the armature will supply reactive current to connected loads.
The V curves are a series curves that show armature current vs. field current for various levels of output power. Superimposed on those curves is a set of curves for various values of leading and lagging power factor. Together, the curves show a range of power factors, armature currents and field currents that can be operationally achieved.
There are other limit of operation that could be superimposed to show the limits of stable operation, prime mover limitations and the thermal limits of the machine. Some of those limits may be indicated by simply limiting the extent of the V curves.