7.25 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 Ω 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) Characterize the step up transformer at the plant.
7.25 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 Ω 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) Characterize the step up transformer at the plant.
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1 Answer
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7.25 Total electric power required, P = 800 kW = 800 W
Supply voltage, V = 220 V
Electric plant generating voltage, V’ = 440 V
Distance between the town and power generating station, d = 15 km
Resistance of the two wires lines carrying power = 0.5 Ω /km
Total resistance of the wire, R = 2 = 15 Ω
Step-down transformer rating 4000 – 220 V, hence
Input voltage to the transformer, = 4000 V
Output voltage from the transformer, = 220 V
rms current in the wire lines is given as
I = = = 200 A
Line power loss = = 15 = 600 W = 600 kW
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