A small town with a demand of 800kW of electric power at 220V is situated 15km away from an electric plant generating power at 440V. The resistance of the two wire line carrying power is `0.5Omega` per km. the town gets power from the line through a 4000-220V 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.

Explanation

Power requirement of the twon is given by EI, where E is the voltage at the receiving end of the line and I is the line current
Here
`P = 800 xx 1000 W`
`E = 4000 V` then
`I = (P)/(E) = (800 xx 1000)/(4000) = 200A`
(a) Line power loss
`= I^(2)R = (200)^(2) xx (2 xx 15 xx 0.5)`
`= 600,000 W = 600 kW`
(b) Total power delivered by power plant
`= 800 + 600 = 1400 kW`
(c) Voltage at sending end of line
= Receiving end line voltage + voltage drop in line
`= 4000 + (I R) = 4000 + 200(2 xx 15 xx 0.5)`
`= 4000 + 3000 = 7000 V`
`therefore` Step up transformer of `(7000 V)/(440V)` is required