Estimate how much power is saved if the voltage is stepped up from 150 VV to 1500 VV and then down again, rather than simply transmitting at 150 VV . Assume the transformers are each 99%% efficient. Express your ans

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Question:

Suppose 79 kW is to arrive at a town over two 0.115 Ω lines. Estimate how much power is saved if the voltage is stepped up from 150 V to 1500 V and then down again, rather than simply transmitting at 150 V. Assume the transformers are each 99%% efficient. Express your ans up to two decimal points.

Power saved = 30772.58 W or 30.77 kW

Explanation:

Since the power loss depends upon current, we need to find the current at each voltage level.

Current at 150 V:

I = P/V = 79,000/150 = 526.67 A

Current at 1500 V:

Considering transformer efficiency of 99%

79,000/0.99 = 79797.97 W

I = P/V = 79,797.97/1500 = 53.19 A

Power loss at 150 V:

P = I²R = (526.67)²*0.115 = 31898.84 W

Power loss at 1500 V:

Here we have to consider both of the losses, due to the transmission line and due to transformer itself

P = I²R = (53.19)²*0.115 = 325.35 W

So the total power at the sending end would be

Receiving end power + losses

79,000 + 325.35 = 79,325 W

Power at the input of the transformer is

79,325/0.99 = 80126.26

Power lost in the transformer is

80,126.26 - 79,000 = 1126.26 W

So the power that can be saved by stepping up the voltage from 150 to 1500 V is

Power saved = 31898.84 - 1126.26

Power saved = 30772.58 W

Power saved = 30.77 kW

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