This question has been posted here before, and the posted answer is wrong.Thanks but this does not answer my question. I understand the units of measure changes. It is the overall question itself. Intuitively it seems that power loss should factor in to distance but we don't see that included in any of the above answers - even though it is included in the question. What if the line was 50 KM long - how would that change things? The easy way is just to memorize the following equations, but I want my team to understand the concepts as well and I can't explain it to them.For part B, you are not looking at the units. You should do 1286 * 0.2 = 257.2 kV (like you did). But then, 1286 amps * 257.2 kV = 330,759 kW. The reason that the correct answer is in MW, is because the values that started the problem were given in MW. To convert your answer, know that 1 MW is 1000 kW. So it is 330.76 MW.My team and I are having a very hard time understanding how to solve for calculating power loss along a line. I think the terms / equations are similar to Ohms Law but not quite the same and that is mixing us up. Here is an example question for an older test:
A power plant in Chicago is generating 900 MW on 700 KV. Assuming the line is 100 kilometers long, with a resistance along the line of 0.2 ohms
A. What is the current flowing along the line?
Using Ohms Law, current is I=P/V 900 MW / 700 KV = 1286 amps
B. How much power is lost in the lines?
This is where we get confused. The answer key says find the voltage drop = current (amps) * resistance (ohms) 1286 * 0.2 = 257.2 kV. Then find power lost = amps * kV 1286 amps * 257.2 kV = 330.76 MW
We don't understand these equations and how does the line distance factor in?
C. What is the percentage of the power lost?
This should be easy taking the answer to B / 900 MW.
Can someone please help explain how to solve these kinds of problems or point us to resources to learn from? Thank you for the help.
For part C, you are correct, it is 330.76MW / 900MW = 36.75%.
I once had a teacher that took off points if we did not carry the units throughout the problem. We could only cross off the unit if they matched. This habit stuck with me, and it has really helped me, so try that.
I hope this helps
Voltage Drop = Current * Resistance
Power Loss = Current * Voltage Loss
Thanks for the help
(your poor suffering Industrial Engineer who should have apparently taken more Electrical Engineering classes)
You're correct that distance is a factor in power loss. For a constant gauge wire, it will have a constant resistivity - or resistance per unit length. So as the length increases, so does the distance.
But here, they've given the resistance - so that's the total resistance of the entire length. The given distance is irrelevant (although you could be asked to compute the resistivity).
For the above question itself, the answers should be:
A. I = P/V = 900 MW / 700 kV = 900e6 W / 700e3 V = 1286 A
B. The methodology in the solution is correct. Voltage Drop = Current * Resistance (Ohm's Law). The resistance is given, not the resistivity, so the distance is irrelevant here. So you just put in the 0.2 ohms.
So Vdrop = 1286 A * 0.2 ohm = 257.2 V (not kV!).
Then power lost = Vdrop * I = 257.2 V * 1286 A = 330.8 kW (not MW!).
Alternatively if you plug in symbolically, you get Vdrop = I * R, and P = Vdrop * I, so P = I * (I * R) or P = I^2 * R. Then P = (1286 A)^2 * 0.2 ohms.
C. Percent loss = 330.8 kW/900 MW = 330.8e3/900e6 = 0.0367% loss. The posted solution of 36.7% is wrong, and a line loss of over 1/3 would be absurd.
To answer your question about what if the line was 50 km - if it was 50 km but the resistance was still given as 0.2 ohms, the solution would not change.
But, if the same gauge line was used, and the resistance was not given, we could determine the resistance. The resistivity of the line is 0.2 ohms/100 km = 0.002 ohm/km. So if the distance was 50 km of the same line, the resistance would be 0.002 ohms/km * 50 km = 0.1 ohm. Then proceed as above.