Asmall town with a demand of 800 kW of electric power at 220 V issituated 15 km away from an electric plant generating power at 440 V.The resistance of the two wire line carrying power is 0.5 Ω perkm. The town gets power from the line through a 4000-220 V step-downtransformer at a sub-station in the town.
(a) Estimatethe line power loss in the form of heat.
(b) Howmuch power must the plant supply, assuming there is negligible powerloss due to leakage?
(c) Characterisethe step up transformer at the plant.
Asmall town with a demand of 800 kW of electric power at 220 V issituated 15 km away from an electric plant generating power at 440 V.The resistance of the two wire line carrying power is 0.5 Ω perkm. The town gets power from the line through a 4000-220 V step-downtransformer at a sub-station in the town.
(a) Estimatethe line power loss in the form of heat.
(b) Howmuch power must the plant supply, assuming there is negligible powerloss due to leakage?
(c) Characterisethe step up transformer at the plant.
Total electric powerrequired, P = 800 kW = 800 × 103 W
Supply voltage, V= 220 V
Voltage at whichelectric plant is generating power, V' = 440 V
Distance between thetown and power generating station, d = 15 km
Resistance of the twowire lines carrying power = 0.5 Ω/km
Total resistance of thewires, R = (15 + 15)0.5 = 15 Ω
A step-down transformerof rating 4000 − 220 V is used in the sub-station.
Input voltage, V1= 4000 V
Output voltage, V2= 220 V
Rms current in the wirelines is given as:
(a) Line power loss = I2R
= (200)2 × 15
= 600 × 103 W
= 600 kW
(b) Assuming that the power loss is negligible due to theleakage of the current:
Totalpower supplied by the plant = 800 kW + 600 kW
=1400 kW
(c) Voltage drop in the power line = IR = 200 ×15 = 3000 V
Hence,total voltage transmitted from the plant = 3000 + 4000
= 7000 V
Also,the power generated is 440 V.
Hence,the rating of the step-up transformer situated at the power plant is440 V − 7000 V.
Total electric powerrequired, P = 800 kW = 800 × 103 W
Supply voltage, V= 220 V
Voltage at whichelectric plant is generating power, V' = 440 V
Distance between thetown and power generating station, d = 15 km
Resistance of the twowire lines carrying power = 0.5 Ω/km
Total resistance of thewires, R = (15 + 15)0.5 = 15 Ω
A step-down transformerof rating 4000 − 220 V is used in the sub-station.
Input voltage, V1= 4000 V
Output voltage, V2= 220 V
Rms current in the wirelines is given as:
(a) Line power loss = I2R
= (200)2 × 15
= 600 × 103 W
= 600 kW
(b) Assuming that the power loss is negligible due to theleakage of the current:
Totalpower supplied by the plant = 800 kW + 600 kW
=1400 kW
(c) Voltage drop in the power line = IR = 200 ×15 = 3000 V
Hence,total voltage transmitted from the plant = 3000 + 4000
= 7000 V
Also,the power generated is 440 V.
Hence,the rating of the step-up transformer situated at the power plant is440 V − 7000 V.
