GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 45 of 65

Marks: +1, -0

A three-phase

50 {Hz}, 400 {kV}

transmission line is

300 {km}

long. The line inductance is

1 {mH} {/} {km}

per phase, and the capacitance is

0.01 µ {F} \/ {km}

per phase. The line is under open circuit condition at the receiving end and energized with

400 {kV}

at the sending end, the receiving end line voltage in

{kV}

(round off to two decimal places) will be_____________.

Solution:

Given data:
A

3-ϕ, 50 {Hz}, 400 {kV}

line
length of line,

l=300 {km}

inductance and capacitances,

{L}=1 {mH} {/} {km}, {C}=0.01 µ {F} {/} {km}

line was under open circuit condition
input voltage,

{V}_{ {s}}=400 {kV}( {LL})

No load receiving end voltage,

V_{ {r}_{ {y}}}=\;{V_{ {s}}}/{ {A}}

Parameter,

{A}=\cos β 1

(assuming line as lossless)
where

β= {w} √{ {LC}} {rad} {/} {km}

=2 π × 50 × √{1 × 10^{-3} × 0.01 × 10^{-6}}

=9.9345 × 10^{-4} {rad} {/} {km}

β 1 =9.9345 × 10^{-4} × 300 {rad}

=0.298037 {rad}

Now,

{A}=\cos β 1

=\cos 0.298037

=0.9559

finally,

{V}_{ {r}( {LL})} \;\; =\;{400}/{0.9559} {kV}

=418.447 {kV}

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