Power Loss in electric power transmission network .. V^2/R OR I^2*R?/board:37-100-

To delieve electric power to the user, a transmission line is needed.
The power loss is due to the resistor(e.g. r=1.0Ω in the above picture) from the transmission line.

$P\equiv IV$ , It can be re-write as $P=I V =I_R (I_R R)=I_R^2 R$ or $P=IV=\frac{V_R}{R}V=\frac{V_R^2}{R}$
However, you need to use the voltage across the resistor $V_R$ or the current flow through the resistor $I_R$ .

If you want to calculate the power loss of the transmission line with $P=V_t^2/R$ ,
then the voltage should be the voltage from the transmission line (not the total voltage).
It is not the same as the voltage from the power plant.

From the above picture:
The source voltage is V, the resistor of the transmission line is r=1.0Ω, and the resistor of the transformer is 99Ω. So the voltage on the transmission line is only $V_t=V \frac{r}{r+R}=V\frac{1}{1+99} =\frac{V}{100}$ .

For the transmission line, the resistor from the transform will change according to voltage ratio between transformer. It is not a constant so a simulation was created to help you understand it.
The power loss can be calculated from $P_{loss}=I_r V_r= I_r^2 r$ and The power delivered $P=I_r V$
$P_{loss}=I_r^2 r=(\frac{P}{V})^2 r= \frac{P^2}{V^2}r$
And the percentage of power loss can be calculated as $\frac{P_{loss}}{P}= \frac{P }{V^2}r$
which is inverse proportional to $V^2$

Please check out Why we need High Voltage Transmission Line

Related Topics
	Subject	Started by	Replies	Views	Last post
	in ejs how to show to number as a power of 10? misc	Fred Chuit	2	11141	July 23, 2008, 03:18:56 pm by Fred Chuit
	Cosmic Rays trapped Into Power Lines Magnetic Field Request for physics Simulations	nalzayed	2	10962	December 12, 2008, 09:55:05 pm by nalzayed
	A loop rotating in a magnetic field (How electric power generator works!) Electromagnetism	Fu-Kwun Hwang	5	57609	December 12, 2009, 11:46:40 am by Fu-Kwun Hwang
	A loop rotating in a magnetic field (How electric power generator works! electromagnetism	ahmedelshfie	7	8350	April 22, 2010, 05:19:06 pm by ahmedelshfie
	Three-phase electric power and load Electronic	Fu-Kwun Hwang	2	21497	March 14, 2011, 08:47:30 am by ahmedelshfie

	Author	Topic: Power Loss in electric power transmission network .. V^2/R OR I^2*R?/board:37-100- (Read 85061 times)
0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).