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

Question

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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Thiên Thanh 5 months 2021-08-27T06:39:32+00:00 1 Answers 18 views 0

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    2021-08-27T06:40:39+00:00

    The question is incomplete! The complete question along with answer and explanation is provided below.

    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.

    Answer:

    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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