Question

78 kW is to arrive at a town over two 0.060 ? lines. Estimate how much power is saved if the voltage is stepped up from 120 V to 2400 V and then down again, rather than simply transmitting at 120 V . Assume the transformers are each 99% efficient.

Answer 1

With no transformers, 78 kW/120V = 650 amps.

voltage loss is IR = 650 x (2*0.06) = 78 volts, so the power loss is 78x650= 50.7 kW

With transformers

78kW/.99 = 78.79 kW needed at receiving end.

78.79kW/2400V = 32.83 amps of current

voltage drop on line = 32.83 x (2*0.06) = 3.94 volts

power loss is 3.94 volts x 32.83 = 129.34 watts

that means power at source is 78.79 kW + 129.33 watts = 78.92 kW

transformer loss is 78.92 kW / .99 = 79.72 kW

power loss is 79.72–78 = 1.716 kW

difference is 50.7 kW – 1.716 kW = 48.98 kW