GATE Electrical Engineering (EE) 2018 Solved Paper

Question : 49 of 65

Marks: +1, -0

Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator and are and respectively. The per unit values of and line reactive power loss respectively are

$5.00,12.68,2.68$
$6.34,10.00,1.34$
$6.34,11.24,2.68$
$5.00,11.34,1.34$

Validate

Solution:

G_{2}

load demand is

20 {pu}, G_{2}

supplies only

15 .

Remaining supplied by

G_{1}

through transmission line.

P_{s} \;\; =|\;{V_{s} V_{R}}/{X_{L}}| \sin δ

5 \;\; =\;{1 × 1}/{0.1} \sin δ

δ \;\; =30^{∘}

Q_{5}=\;{V_{S}^{2}}/{X_{L}}-\;{V_{S} V_{R}}/{X_{L}} \cos δ

=\;{1^{2}}/{0.1}-\;{1 × 1}/{0.1} \cos 30^{∘}=1.34 {p} . {U}

Q_{R} \;\; =|\;{V_{s} V_{R}}/{X_{L}}| \cos δ-|\;{V_{R}^{2}}/{X_{L}}|

\;\; =|\;{1 × 1}/{0.1}| \cos 30^{∘}-\;{1^{2}}/{0.1}=-1.34 {p.u} .

Q_{\;\text "loss "\;} =Q_{S}-Q_{R}

=1.34-(-1.34)=2.68 {p.u.}

G_{1}

Q_{G 1} =Q_{\;\text "load "\;}+Q_{s}

=5+1.34=6.34 {p} . {u}

G_{2}

Q_{G 2} \;\; =Q_{\;\text "load "\;}+(-Q_{R})

=10-(-1.34)=11.34 {p} . {U}

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