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.
(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.

Explanation

Total electric power required, `rho=800`kW=`800xx10^(3)W`
Supply voltage, V=220V
Voltage at which electric plant is generating power, V=440V
Distance between the town and power, generating station, d=15km
Resistance of the two wire lines carrying power =`0.5Omega//km`
Total resistance of the wires, `R=(15+15) 0.5=15Omega`
A step-down transformer of rating 4000-220 V is used in the sub-station.
Input voltage `V_(1)=4000V`
Output voltage `V_(2)=220V`
Rms current in the wire lines is given as:
`l=(P)/(V_(1))`
`=(800xx10^(3))/(4000)=200A`
(a) Line power loss `=I^(2)R`
`=(200)^(2)xx15`
`=600xx10^(3)W`
=600kW
(b) Assuming that the power loss is negligible due to the leakage of the current:
Total power supplied by the plant =800kW+600kW
=1400kW
(c) Voltage drop in the power line `=IR=200xx15= 3000V`
Hence, total voltage transmitted from the plant =3000+4000
=7000V
Also, the power generated is 440V.
Hence, the rating of the step-up transformer situated at the power plant is 440V-700 V.