Question

A 20 kVA, 400 V, 50 Hz three phase star connected synchronous generator has effective armature resistance and synchronous reactance 0.5 $\Omega$/phase and 3 $\Omega$/phase respectively. Voltage regulation for 0.8 leading power factor at full load_____%(Answer up to 2 decimal places)

• A. -10.86

Answer 1

The correct option is A -10.86
$\text{Excitation emf,}\overrightarrow{E_f}=\overrightarrow{V}+\overrightarrow{I_a}{Z}_s$

$\text{Armature current,}{I}_a=\frac{20\times {10}^3}{\sqrt{3}\times 400}=28.87A$

$\overrightarrow{E_f}=\frac{400}{\sqrt{3}}+\left(28.87\angle {36.87}^{\circ }\right)\times (0.5+j3)$

$\overrightarrow{E_f}=205.85\angle {22.25}^{\circ }V$

$\text{Voltage regulation =}\frac{|E_f|-|V|}{|V|}\times 100\%$

$=\frac{205.85-\left(\frac{400}{\sqrt{3}}\right)}{\frac{400}{\sqrt{3}}}\times 100\%=-10.86\%$