Question

A salient pole synchronous generator has $X_d=0.95pu$, $X_q=0.7p.u.$ The generator is connected to an infinite bus through a reactance of 0.2 p.u., the excitation voltage is 1.3 p.u., and infinite bus voltage is 1 p.u. at power angle of ${25}^{\circ }$. The power supplied to the bus is ______ p.u.

• A. 0.57

Answer 1

The correct option is A 0.57
Power supplied, $P=\frac{E_{f}V}{X_d}\sin \delta +\frac{V^2}{2}(\frac{1}{X_q}-\frac{1}{X_d})\sin 2\delta$

$X_{d\left(new\right)}=0.95+0.2=1.15p.u.$

$X_{q\left(new\right)}=0.7+0.2=0.9p.u.$

$\text{Power supplied,}P=\frac{1.3\times 1}{1.15}sin{25}^{\circ }+\frac{1}{2}[\frac{1}{0.9}-\frac{1}{1.15}]sin{50}^{\circ }$
$=0.5702p.u.$