A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is 0.5 W per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub-station in the town. (a) Estimate the line power loss in the form of heat. (b) How much power must the plant supply, assuming there is negligible power loss due to leakage? (c) Characterise the step up transformer at the plant.
Answers
Electric power=P = 800 kW = 800 × 10³ W
Supply voltage, V = 220 V
Voltage at which electric plant is generating power, V' = 440 V
Distance =d = 15 km
Resistance of the two wire lines carrying power = 0.5 Ω/km
Total resistance of the wires, R = (15 + 15)0.5 = 15 Ω
A step-down transformer of rating 4000 − 220 V is used in the sub-station.
Input voltage=V1 = 4000 V
Output voltage=V2 = 220 V
rms current in the wire lines is given as:
I=P/V1
=800x 10³/4000
=200A
a) Line Power Loss = I² R
= (200)x 200 x15
=600 x 10³ W
=600kW
b) Let us assume the power loss is negligible due to leakage of current :
Total Power supplied by Plant = 800kW+600kW=1400 kW
c) Voltage drop in the power Line= IR=200x15 =3000V
Voltage transmitted from plant =3000+4000=7000V
Power generated is 400V
d)Characterise the step up transformer at the plant:
The rating of step up transformer situated at Power plant is 400V-7000V