Transformers for Efficient Power Transmission | Calculating Line Loss

[andrew410]

A transmission line that has a resistance per unit length of 4.5*10^-4 ohms/m is to be used to transmit 5 MW over 400 miles (6.44*10^5 m). The output voltage of the generator is 4.5 kV.
a) What is the line loss if a transformer is used to step up the voltage to 500 kV?
b) What fraction of the input power is lost to the line under thses circumstances?

For part A, I used P1=I1^2*R and solved it for I1. Then I used I1*V1 = I2*V2 and solved it for I2. Next, I got the power using I2 and subtracted P1 with the power that I just got. The answer is wrong though...
Can anyone help please? Thx! :)

 

[dextercioby]

I don't know how u define the "line loss",but you can easily compute the lost power due to Joule effect.

What is the current running through the wire in both cases...?Give the method & result.

Daniel.

 

[thepatientmental]

a) To calculate the line loss, we first need to find the current (I1) flowing through the transmission line. Using the formula P1 = I1^2 * R, we can rearrange it to get I1 = √(P1/R). Plugging in the given values, we get I1 = √(5*10^6/4.5*10^-4) = 106.07 A.

Next, we can use the formula I1*V1 = I2*V2 to find the current (I2) flowing through the transformer. Since the output voltage of the generator (V1) is 4.5 kV, we get I2 = I1*V1/V2 = 106.07*4.5/500 = 0.954 A.

Now, we can calculate the power lost in the line by using the formula Ploss = I2^2*R = (0.954)^2*4.5*10^-4 = 0.0041 MW or 4.1 kW.

b) The fraction of input power lost to the line can be calculated by dividing the line loss by the input power. In this case, the input power is 5 MW, so the fraction of power lost is 0.0041 MW/5 MW = 0.00082 or 0.082%. This means that only a very small fraction of the input power is lost in the transmission line.

Note: It is important to note that the above calculations assume ideal conditions and do not take into account any other losses such as in the transformer itself or due to other factors such as capacitance and inductance.