Calculate the fraction of power generated that is lost in the lines

[joej]

If 30 MW of power at 45kV (rms) arrives at a town from a generator via 4-ohm transmission lines, calculate the fraction of power generated that is lost in the lines.

okay I think I'm not completely understanding what I'm supposed to do in this question, or I'm missing something as from my calculations there is more than 100% power loss

P/V = I

30,000,000W/45,000V = 666.7 A

Pl = I^2 x R

666.7^2 x 4 = 1777955.56V = 1778kV


probably something completely stupid that I'm doing here so would appreciate it if someone can set me straight, thnx


----edit-----

sorry stupidity strikes again... forgot that the power lost comes out in W not V

duh! sorry again, it's fine now

 

[Gamma]

more than 100% power loss

% Power loss = 1778/30 000 * 100 = 5.9 %


Gamma.

 

[Andrew Mason]

If 30 MW of power at 45kV (rms) arrives at a town from a generator via 4-ohm transmission lines, calculate the fraction of power generated that is lost in the lines.

okay I think I'm not completely understanding what I'm supposed to do in this question, or I'm missing something as from my calculations there is more than 100% power loss

Power loss is in Watts not volts. I^2R = V_{drop}^2/R gives you the power loss in watts. I prefer to work with the voltage drop. So:

Voltage drop is IR = 666.7 x 4 = 2666.67 V.

(ie. the voltage drops to 42333.3 volts at the town). So the power lost in the lines is 2666.67^2/4 = 1.78E6 Watts or 1.78 MW. As a fraction of the total power the line loss is 1.78/30 = 5.9%

AM