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 `Omega` 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.

Explanation

Here step-up transformer is used at power plant and step down transformer ( 4000V - 220V) is used at the town substation. See the diagram given below.

(a) Here 800 kW power is delivered at town sub station by two way transmisstion line at 4000 V. Hence, current through this line is,
`I = ( P )/(V )`
`= (800 xx 10^(3))/( 4000) ( :. P = 800 kW )`
I = 200A
Resistance of above two way line is, `:. R = 15 Omega`
Power loss in the line wire is,
`P = I^(2) R`
`= ( 200)^(2) ( 15)`
`:. P. = 600 xx 10^(3) W = 600 kW`
( b) Total power supplied by the plant should be
`P _(t ) + P + P . `
`= 800 + 600`
`= 1400 kW`
(c ) Voltage drop across two way line.
= IR
= ( 200) ( 15)
3000 V
Voltage across the secondary coil of a transformer at power plant should be,
= 3000 + 4000
= 7000 V
Thus, at power station we should use a step, up transformer ( 440 V - 7000V )