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GATE Electrical Engineering (EE) 2020 Solved Paper
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© examsnet.com
Question : 54
Total: 65
Bus 1 with voltage magnitude
V
1
=
1.1
p
.
u
.
is sending reactive power
Q
12
towards bus 2 with voltage magnitude
V
2
=
1
p.u. through a lossless transmission line of reactance
X
. Keeping the voltage at bus 2 fixed at 1 p.u., magnitude of voltage at bus 1 is changed, so that the reactive power
Q
12
sent from bus 1 is increased by
20
%
.
Real power flow through the line under both the conditions is zero. The new value of the voltage magnitude,
V
1
, in p.u. (rounded off to 2 decimal places), at bus 1 is____________.
Your Answer:
Validate
Solution:
Q
12
=
|
V
1
|
2
x
−
|
V
1
|
|
V
2
|
X
cos
δ
For a highly stable system,
δ
is very small,
cos
δ
∼
e
q
1
Q
12
=
|
V
1
|
2
x
−
|
V
1
|
|
V
2
|
X
Q
12
=
|
V
1
|
x
−
(
|
V
1
|
−
|
V
2
|
)
.....(1)
Let, for
Q
12
→
102
Q
12
(
20
%
increase)
V
1
→
V
1
′
Then,
1.2
Q
12
Q
12
=
|
V
1
′
|
(
|
V
1
′
|
|
V
2
′
|
)
X
×
X
|
V
1
|
(
|
V
1
|
−
|
V
2
|
)
1.2
=
|
V
1
′
|
(
|
V
1
′
|
−
1
)
1.1
(
1.1
−
1
)
|
V
′
1
|
2
−
|
V
′
1
|
−
0.132
=
4
∼
e
q
1.12
(Rounded off to two decimal places)
© examsnet.com
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