Question

A 4 MVA, 6.6 kV 3-phase star connected, synchronous generator has 16-poles. Its direct and quadrature axis synchronous reactances are 10 $\Omega$ and 4 $\Omega$ respectively. Generator is supplying full load at 0.8 pf lagging. Which of the below given statements are true?

• A. The value of reluctance power, P is 1.2 MW.
• B. The reluctance power is dependent on the direct axis reactance and quadrature axis reactance.
• C. The value of armature current will be 350 A.
• D. The value of loading angle, $\delta ={5.86}^{\circ }.$

Answer 1

Answer: (B), (C)

The value of armature current will be 350 A.

Reluctance power, $P=V^2\left(\frac{X_d-X_q}{2X_d{X}_q}\right)sin2\delta$

Excitation emf, $\overrightarrow{E_f}=\overrightarrow{V}+j\overrightarrow{I_a}{X}_q$

Armature current, $I_a=\frac{4\times {10}^6}{\sqrt{3}\times 6600}=350A$
$\overrightarrow{E_f}=\frac{6600}{\sqrt{3}}+j(350\angle -co{s}^{-1}(0.8\left)\right)\times 4$

$=4783.48\angle {13.54}^{\circ }V$

Load angle, $\delta ={13.54}^{\circ }$

Reluctance power, $P=\left(6600{)}^2\left[\frac{10-4}{2\times 10\times 4}\right]sin\right(2\times 13.54)$

$P=1.487MW$