Voltage Equation of an Alternator

In a d.c. generators, we have seen that due to the armature resistance drop and brush drop it is not possible to have all the induced e.m.f. available across the load. The voltage available to the load is called terminal voltage. The concept is same in case of alternators. The entire induced e.m.f. can not be made available to the load due to the various internal voltage drops. So the voltage available to the load is called terminal voltage denoted as. In case of three phase alternators as all the phases are identical, the equations and the phasor diagrams are expressed on per phase basis.

       So if E_ph is the induced e.m.f. per phase in the alternator, there are following voltage drops occur in an alternator.

i) The drop across armature resistance I_a R_a both I_a and R_a are per phase values.

ii) The drop across synchronous reactance  I_a X_s, both  I_a and X_s are per phase values.

       After supplying these drops, the remaining voltage of E_ph is available as the terminal voltage V_ph.

Note : Now drop I_a R_a is always in phase with I_a due to a resistive drop while current I_a lags by 90^o with respect to drop  I_a X_s as it is a drop across purely inductive reactance.

       Hence all these quantities can not be added or subtracted algebraically but must be added or subtracted vectorially considering their individual phases. But we can write a voltage equation in its phasor from as,

       This is called voltage equation of an alternator.

       From this equation, we can draw the phasor diagram for various load power factor conditions and establish the relationship between E_ph and V_ph, in terms of armature current i.e. load current and the power factor cos(Φ).