Question

A 1000 kVA, 6.6 kV, 3-phase star connected synchronous generator has a synchronous reactance of $25\Omega$ per phase. It supplies full load current at 0.8 lagging pf and rated terminal voltage. The terminal voltage (line) for the same excitation when the generator supplies full load current at 0.8 leading pf is_________.

• A. 9.15 kV
• B. 11.15 kV
• C. 2.48 kV
• D. 6.43 kV

Answer 1

The correct option is B 11.15 kV

$I_a$ (rated) $=\frac{1000}{\sqrt{3}\times 6.6}=87.5A$

$V_t=\frac{6600}{\sqrt{3}}=3810.6V$

Operation at 0.8 lagging pf rated terminal voltage
$\overrightarrow{E_f}=V_t+j{I}_a{X}_s$

$=3810.6+j87.5(0.8-j0.6)25$

$=5123+j1750=5413.7\angle {18.86}^{\circ }$

$\therefore |E_f|=5413.7V$

Operation at 0.8 leading pf with excitation remaining unchanged

Also $j{I}_a{X}_s=j87.5(j0.8+j0.6)\times 25$

$=2187.5\angle {126.87}^{\circ }$

$=2187.5\angle {53.13}^{\circ }$


From the phasor diagram:
$\frac{5413.7}{\sin 53.13}=\frac{2187.5}{\sin \delta }$

$\delta ={18.8}^{\circ }$

Also, $\frac{V_t}{\sin {108.1}^{\circ }}=\frac{2187.5}{0.323}$

$\Rightarrow V_t=6437.3V$ $\left(or\right)11.15kV\left(line\right)$