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Combination of Resistors

A power syste...

Question

A power system has two buses which are interconnected by a cable of reactance j0.04 pu. The buses individually have two generators connected to them as shown below with $| V_{1} | = | V_{2} | = 1 p u .$ If load demand at bus 1 and 2 are respectively
$S_{D_{1}} = (30 + j 10) p u a n d S_{D_{2}} = (25 + j 10) p u .$ The value of total reactive power of generating station $G_{1} w h e n δ = 20^{\circ}$ will be ______pu.

A

13.50

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B

25.50

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C

11.50

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D

30.50

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Solution

The correct option is C 11.50
For given system:

Total reactive power at,
$G_{1} = R e a c t i v e p o w e r d e m a n d a t B u s 1 + R e a c t i v e p o w e r b e i n g t r a n s f e r r e d t o B u s 2$
Reactive power demand at bus 1 = 10 pu
Reactive power transferred to bus 2,

$Q_{s} = \frac{| V_{s} |}{X} (| V_{s} | - | V_{R} | c o s δ)$
$Q_{s} = \frac{!}{0.04} (1 - 1 \times c o s 20^{\circ}) = 1.508 p u$

$∴ T o t a l r e a c t i v e p o w e r a t G_{1} w i l l b e Q_{G 1} = 1.508 + 10 = 11.508 p u$

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