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 wirelines carrying power is 0.5 Ω 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.
RMS current in the coil I=P/V1=800×103/4000=200A (a) Power loss = I2R=2002×15=600kW (b) Total power supplied by the path is P=800+600=1400kW (c) Voltage drop is IR=3000 V Hence secondary voltage is 3000+4000=7000V Power generated is at primary voltage of 440V Hence the transformer rating is 440V−7000V
