Responding to roshni's Jul 26, query.... The relationship between an alternator's armature and field currents, properly called 'V-curves'.
Usually, it is provided by the machine manufacturer. However, if it is something you are tasked with, then:
Q1) A plot can be constructed from the machine's design parameters. Typically, the machine's synchronous reactance and stator resistance are
used. Furthermore, there are equation variances due to type of rotor construction, as implied in Sam Bones' Jul 26 reply.
Q2) Or, are you attempting to accomplish this task by means of a field-test?