# Electronic – Power loss during transmission

powertransmission

I have no background of electrical engineering so if my question sounds stupid then accept my apology in advance. I want to calculate the power loss during the transmission. I am using the simple formula which is

$$P_{loss} = Resistance \cdot I^2$$

Where P is power loss
Resistance is in Ohms
and I is the current

Replacing the I by P / V
Where V is the voltage
now the formula looks like

$$P_{loss} = Resistance \cdot \Big( \frac{P}{V} \Big)^2$$

If the value of resistance is 5.24 Ohms and voltage is 50 kV and the value of P is 940 kW then I get the value of P(loss) = 1852 W which does not seem intuitive.

Looking for your guidance (if i am calculating wrong). Accept my apology in advance if my question bothers you.

#### Best Answer

=> Short answer: Sounds reasonable.

Common approach would be: Try to approach this way: What causes the power loss if you transmit power along a line?

For simple, resistive loads (based on Ohms law: \$U = R \cdot I\$ and \$P = U \cdot I\$)

• The current flowing through the line (which is the current that you may use as well to power a device connected at the end of the line):

$$P_{loss} = R_{line} \cdot I_{line}^2$$

or

• The voltage drop along the line (from where you feed in the power [start] to where you extract it [usually end of the line] - NOT the voltage between line and ground, which I assume you 50kV are)

$$P_{loss} = \frac{V_{along\;line}^2} {R_{line}}$$

However, since you seem only to know the load and line-to-ground voltage, using

$$P = I_{line} \cdot V_{line,gnd}$$

to substitute the current is correct. The resistance appears reasonable for a longer medium voltage line and < 1 % ohmic losses is not that bad.

If you are interested, take a look at this page:

AC Transmission Line Losses, by Curt Harting

For AC: Use RMS values. If you have a multiple phase system, make sure you dont confuse line-to-line and line-to-ground voltages... Also the skin effect has to be taken into account.

General advice: If you are referring to values per length, use a dash: [P'] = W/m and also use them if you write something like "P = ...".