Question

Answer the following question.
A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of the two wirelines carrying power is 0.5 Ω per km. The town gets the power from the line through a 4000-220 V step-down transformer at a sub-station in the town. Estimate the line power loss in the form of heat. 

Answer 1

Total electric power required,

P = 1200 kW = `1,200 xx 10^3 W`

Supply voltage, V = 220 V 
The voltage at which electric plant is generating power, V = 440 V  
Distance between the town and power generating station, d = 20 km 
The resistance of the two-wire lines carrying power  = 0.5  Ω/km
The total resistance of the wires, R = (20 + 20)0.5 = 20 Ω

A step-down transformer of rating 4000 - 220 V is used in the sub-station.

Input voltage, V₁ = 4000 V
Output voltage, V₂ = 220 V
Rms current in the wire lines is given as:

`I = P/V_1 = (1200 xx 10^3)/4000 = 300 A`

Line power loss = `I^2R`

`= 300^2 xx 20`

= `1800 xx 10^3`W
= 1800 kW.