The effective resistance of a 2200-V, 50-Hz, 440-kVA, 1-phase alternator is 0.5 Ω. On short circuit, a field current of 40 A gives a full load current of 200 A. The open circuit EMF for the same field excitation is 1200 V. Find the synchronous impedance.

Finding Synchronous Impedance (Zs) with the help of OCC and SCC:

Synchronous impedance is the ratio of Open circuit voltage per phase to the score circuit armature current at the same value of field current (Excitation).

• Let the rated field current is IA, and we have to find the Open circuit voltage and short circuit armature current at this value by plotting the graph as shown,

From the above characteristics,

At rated field current (IA),

Open Circuit Voltage (VOC) = OB

Short Circuit Current (ISC) = OC

Synchronous Impedance (Zs) = \(\dfrac{OB}{OC}\) Ω

From using the concept of, Z2 = R2 + X2, we easily find the Synchronous reactance.

And Armature resistance will find by using the Voltage Test Method or (VA or AV) method.

Application:

We have,

Field of of 40 A produced:

Open circuit voltage (V_oc) of 1200 V

And short circuit current (I_sc) of 200 A

Now graph can be drawn as,

Synchronous impedance is given as (Z) = \(\large{\frac{V_{oc}}{I_{sc}}|_{I_f\ =\ constant}}\)

Hence, Z = 1200/200 = 6.0 Ω