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) Characterise the step-up transformer at the plant.
a) Power required, P = 800 kW = 800 × 103 W
Total resistance of two wire lines
R = 2 × 15 × 0.5 = 15 Ω.
Since supply is through 4000 – 230 V transformer
As,
where, IV is the rms value of the current.
Line power loss in the form of heat is,
= (IP)2 Resistance of line
= (200)2 0.5 15 2
= 60 104 W
= 600 kW
(b) If there is no power loss due to leakage,
then the essential plant power supply is
= 800 + 600
= 1400 kW
(c) Voltage drop on the line =
Voltage from transmission = 3000 + 4000 = 7000 V.
Since, the power is generated at 440 volt, the step-up transformer needed at the plant is 440 V - 7000 V.
