# Determine the resistance of electric transmission lines

How could I determine the resistance of electric transmission lines?

I face a lot of problems in determining the resistance of electric transmission lines, for example:

"if we need to deliver an amount of power from a power station to a factory to be used there, and the distance between them is 1000km, and we would use transmission lines, and the resistance per km is 0.25Ω.......etc."

When I start to solve the problem and try to determine the whole resistance of the transmission lines, I do this:

R(tot.)= 0.25*1000 = 250Ω.

But what I find is that this step is wrong, and the total resistance will be determined as this:

R(tot.)= 2*0.25*1000 = 500Ω.

That is what I find in my text book, and that confused me, and I would like if someone helped me and explains this. Are there always two lines to connect power stations and the consumers, because I find that "2" used in the equation, in every solution to a problem like the one above?

• Yes, there are supply and return lines. In some areas there are crude systems with only a supply and earth is used as the return, but traditionally there are 2 conductors. – John D Dec 1 '16 at 19:31
• @JohnD , and they are connect in series, so we multiplying the value by 2, not dividing them on 2, or what is the case? – Asmaa Dec 1 '16 at 19:43
• @Asmaa think of it another way. A circuit has to be a closed loop to conduct a current, so the current has to travel from the power station to the factory, and then back again (*). How much wire is there in the complete circuit? – Tom Carpenter Dec 1 '16 at 20:06
• @TomCarpenter, if you mean by the complete circuit that one connecting the power station and the factory, there would be two wires, according to what you said, but if you mean the number of wires given in the problem, it is unknown, the problem doesn't give me the number of the wires. – Asmaa Dec 1 '16 at 20:11
• @Li-aung Yip I think you're making the mistake of confusing the textbook-problem world with actual real life. – AndrejaKo Dec 2 '16 at 14:11

## 2 Answers

In a circuit current must flow in a complete loop so there is one wire going out and one wire coming back so the total resistance is double what is calculated for one wire. That's why the answer is 500 ohms not 250.

Resistance is not usually the limiting factor on a transmission line.

It is more common to be limited by current-carrying capacity.

In any case, the procedure for calculating three-phase overhead transmission line impedance, including resistive and inductive components, can be found in multiple books.

For a free book, try the Network Protection and Automation Guide, which is freely available in PDF form from Schneider. See chapter 5.18, Equivalent Circuits and Parameters of Power System Plant - Overhead lines and cables.

If you have a library available, try the Westinghouse / ABB Electric Transmission and Distribution Handbook, Chapter 3 - Characteristics of Aerial Lines.

Otherwise, try any book on power system analysis, i.e. Anderson's Analysis of Faulted Power Systems - Chapter 4 Sequence Impedance of Transmission Lines.