Question

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.

Answer 1

RMS current in the coil

$I=P/V_1=800\times {10}^3/4000=200A$

(a)

Power loss = $I^{2}R={200}^2\times 15=600kW$

(b)

Total power supplied by the path is $P=800+600=1400kW$

(c)

Voltage drop is $IR=3000V$

Hence secondary voltage is $3000+4000=7000V$

Power generated is at primary voltage of $440V$

Hence the transformer rating is $440V-7000V$