Question

A 44 MVA, 10.5 kV, Y-connected three-phase salient pole synchronous generator has $X_d=1.83\Omega$ and $X_q=1.21\Omega$. It delivers the rated load at 0.8 p.f. lagging. The armature resistance is negligible, the load angle of the given alternator is ______ degrees (upto two decimal places).

• A. 16.69

Answer 1

The correct option is A 16.69
Given, 44 MVA, Y-connected, $3-\varphi$ salient pole synchronous generator.

It deliver a rated load at 0.8 p.f. lag,
$V=10.5kV,X_d=1.83\Omega$
$X_q=1.21\Omega$, Y-connected

$tan\psi =\frac{Vsin\varphi +I_a{X}_q}{Vcos\varphi +I_a{R}_a}$

$V_{ph}=\frac{V_L}{\sqrt{3}}=6062.17V$

$I_a=\frac{P}{\sqrt{3}{V}_L}=\frac{44\times {10}^6}{\sqrt{3}\times 10.5\times {10}^3}=2419.3\angle -{36.86}^{\circ }A$

$tan\psi =\frac{(6062.17\times 0.6)+(2419.3\times 1.21)}{(6062.17\times 0.8)+(2419.3\times 0)}$

$\psi ={53.546}^{\circ }$

$\psi =\delta +\varphi$

$\delta ={53.546}^{\circ }-{36.86}^{\circ }$

$={16.686}^{\circ }\simeq {16.69}^{\circ }$