Question

A 3-phase, 10 MVA, 13.8 KV, 50 Hz synchronous generator yields the following test data:
O.C. test field current = 842 A at rated voltage
S.C. test field current = 226 A at rated armature current
O.C. test revealed that the armature resistance per phase is $0.75\Omega$.
The value of adjusted synchronous reactance in p.u. will be

• A. 0.2
• B. 0.2956
• C. 0.2654
• D. 0.1084

Answer 1

The correct option is C 0.2654

$Z_{s\left(adjusted\right)}=\frac{V_{rated}/\sqrt{3}}{I_{sc}}{|}_{At{I}_{f}correspondingto{V}_{oc}=V_{rated}}$

rated armature current,
$\sqrt{3}{V}_{rated}{I}_{a\left(rated\right)}=10MVA$

$I_{a\left(rated\right)}=\frac{10\times {10}^3}{\sqrt{3}\times 13.8}=418.4A$

$I_{f\left(rated\right)}=842A$

$I_{sc}=\frac{418.4}{226}\times 842=1558.8A$

$Z_{s\left(adjusted\right)}=\frac{13.8\times {10}^3/\sqrt{3}}{1558.8}=5.11\Omega$

$X_{s\left(adjusted\right)}=\sqrt{Z_{s\left(adjusted\right)}^2-R_a^2}$

$=\sqrt{{5.11}^2-{0.75}^2}=5.054\Omega$

$X_{s\left(pu\right)}=5.054\times \frac{10}{(13.8{)}^2}=0.2654$