Question

A 30 MVA, 11 kV, 50 Hz, 6 pole star connected alternator has
$Z_s=0.005+j0.70$ pu. The power factor when the alternator is delivering rated current at rated voltage with excitation emf 1.5 pu is ______lag. (Answer up to 3 decimal places)

• A. 0.844

Answer 1

The correct option is A 0.844
Here, $I_a=1.0pu$
$V_t=1.0pu$
$r_a=0.005pu$
$X_s=0.7pu$,
$E_f=1.5pu$
$Z=0.7\angle {89.59}^0$

$E_f^2=(V_t\cos \varphi +I_a{r}_a{)}^2+(V_t\sin \varphi +I_a{X}_s{)}^2$

$E_f^2=(V_t^2+I_a^2{Z}^2+2I_a{V}_t{r}_a\cos \varphi )+2I_a{V}_t{X}_s\sin \varphi$

${1.5}^2=1^2+0.49+2[0.005\cos \varphi +0.7\sin \varphi ]$

$0.005\cos \varphi +0.7\sin \varphi =0.38$

$0.7sin(\varphi +0.4092)=0.38$

$\varphi +0.4092=32.878$

$\varphi ={32.47}^0$

$pf=\cos \varphi$

$=0.8436lag$