A short 3 phase transmission line, connected to a 33kV, 50 Hz generating station at the sending end is required to supply a load of 10Megawatts at 0.8 power factor lagging, 30kV at the receiving end. If the minimum transmission line efficiency is to be limited to 96%, estimate the per phase values of resistance and inductance of the line.

Question
Asked Oct 16, 2019

A short 3 phase transmission line, connected to a 33kV, 50 Hz generating station at the sending end is required to supply a load of 10Megawatts at 0.8 power factor lagging, 30kV at the receiving end. If the minimum transmission line efficiency is to be limited to 96%, estimate the per phase values of resistance and inductance of the line.

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Step 1

As given in the question

Sending end voltage, v, (linevoltage) 33kv
33
-kv/phase
v. (phase voltage) -
receiving end voltage, v
(line voltage) 3Okv
30
-kv/phase
(phase voltage)
active power at output end,P, 10MW
load pf (cosø0.8
Efficiency-96%
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Sending end voltage, v, (linevoltage) 33kv 33 -kv/phase v. (phase voltage) - receiving end voltage, v (line voltage) 3Okv 30 -kv/phase (phase voltage) active power at output end,P, 10MW load pf (cosø0.8 Efficiency-96%

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Step 2

To calculate resistance steps is shown below

hence
P 3V2I cos
3I cos
plugging given value in the above formula
10x10
I =
3 x17.32x10x 0.8
I 240.56.4
hence
efficiency=
P loss
On plugging values of P and efficiency
loss 41.66x10w
Impedence for lagging load is
loss
And, R=
41.66x10
R=
ohms
240.562
R=7.2 ohms
7.2
therefore,resistance per phase
ohms
3
resistance per phase 2.4 ohms
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hence P 3V2I cos 3I cos plugging given value in the above formula 10x10 I = 3 x17.32x10x 0.8 I 240.56.4 hence efficiency= P loss On plugging values of P and efficiency loss 41.66x10w Impedence for lagging load is loss And, R= 41.66x10 R= ohms 240.562 R=7.2 ohms 7.2 therefore,resistance per phase ohms 3 resistance per phase 2.4 ohms

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Step 3

Now to calculate reactance s...

output power factor (given)is
cos36.87
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output power factor (given)is cos36.87

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