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 line wires carrying power is `0.5 Omega` per km. The town gets power from the lines through a 4000-220 V step down transformer at a substation in the town.
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.

Explanation

Line resistance, R = 30`xx 0.5` = 15 ` Omega`
power demand = 800 KW
rms voltage at primary = 4000 V
rms current in the line, I = `("power")/("voltage")`
= `(800xx 1000)/(4000) = 200 ` A
(a) Line power loss
` P = i^(2)` R
= ` 200 x 200 xx 15 `
`= 600` kW
(b) Power supply by the plant = Power required at sub-station + loss power on transmission
= 800 + 600 = 1400 kW
(c ) Voltage drop on the line ` = I_(R) = 200 xx 15 = 3000` V
The step-up transformer at the plant is 440 V - (4000 + 3000) V = 440 - 7000 V.