# Standard Transmission Lines (Waxwing, Partridge, etc.)



## R2KBA (Oct 12, 2011)

I'm having some difficulty understanding how to use this table of standard transmission lines in the Yarbrough/Camara book (the one with the code names like Waxwing, Partridge, etc... It gives inductive and capacitive reactances for 1-ft spacing. How does this differ for single-phase vs. 3-phase circuits. I know there is no such thing as "3 phase impedance", but I imagine that there would certainly be a difference in reactances of individual conductors if they were out of phase vs in phase relative to one another.

There are two cases I can think of for questions that could be asked on the exam. First, there could be a single-phase line (including one return) which may or may not have multiple bundled cables. Second, there could be a three phase line. I have seen examples in different places done both ways, but I find it hard to believe that the values in the table simply don't care about whether the system is 3 phase or single phase with a return line.

Does anyone know how to explain this?

Thanks.


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## ElecPwrPEOct11 (Oct 12, 2011)

I haven't seen any test questions (yet) on these 'code named' transmission lines. I'm curious what input others have.


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## mudpuppy (Oct 12, 2011)

The numbers in the table are a per-phase impedance of a three-phase line, with 1-ft spacing. I think these numbers are only listed in the table to provide a quick comparison of the relative reactances of the different conductors. Since a one-foot spacing is unlikely in a real-world transmission line, the actual impedances will have to be calculated for a specific example. A good power system analysis reference will cover how to do this, or Google turns up this reference which might be helpful: http://www.ee.iastate.edu/~jdm/EE456/UseOfTables.doc


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## R2KBA (Oct 12, 2011)

The examples I have been able to found (Camara) and others all use this table for a single-phase system, even though it is intended for 3phase. It just seems strange to me that the same values can be used for either system. Unless someone can tell me differently, I'll just assume that the values are equally valid for 3phase or 1phase systems, of course as long as the impedance is doubled for 1phase due to the return.


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## mudpuppy (Oct 12, 2011)

If you look at the equations to calculate the reactance of a transmission line, they actaully are the same for three-phase and single-phase systems, on a per-phase basis, assuming that your phase spacing is the same. . . i.e. the distance between conductors in the single-phase system must be the same as the geometric mean distance between all three conductors in the three-phase system.

I still caution you not to use the reacatance numbers directly from the tables unless you happen to have a line configuration with 1-foot spacing.

The equations from Camara (I have the 6th edition EERM) are:

Single phase *total inductance *of both conductors, Ll = 4*10-7 ln (D/GMR) in H/m (which you can easily convert to Ohms/m or Ohms/mi)

Three phase *per-phase inductance *Ll = 2 * 10-7 ln (De/GMR) in H/m

If you divide the single phase inductance by two to get a per-phase value, then there are the same.


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## R2KBA (Oct 12, 2011)

Thanks for pointing that out, I hadn't noticed before that those two equations only differ by a factor of two (and of course the distance vs mean distance). I suppose that confirms my assumption. And yes, it seems that you never get away with using the values from the table without that annoying correction factor...


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## DK PE (Oct 12, 2011)

In my old, old copy of Yarbrough (5th edition) they have the same 1ft. spacing table which by itself is practically useless. If you look in a real textbook (Stevenson, _Elements of Power System Analysis_ or later versions of Grainger/Stevenson), you will also find a "spacing factor" table following in which you just look up the spacing and add it to the 1ft. value to arrive at the line's properties.

Stevenson also has examples of both single-phase and three phase lines and, as a previous poster pointed out, the single phase is multiplied by two whereas the three phase is right out of the table.

Of course in real life today I doubt if many people look up _Osprey_ or _Drake _properties but who knows what would be tested. It may pay to have the table and know how to apply, it's not difficult.


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## ElecPwrPEOct11 (Oct 13, 2011)

Thanks for the comments everyone. I'm now going to be sure to do some practice problems of transmission line impedance.


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## R2KBA (Oct 13, 2011)

Right. The chances of it being on the test are slim, but as you said it is not difficult so therefore is not a bad time investment IMO.

I have the Grainger/Stevenson book, just not with me at the moment, but I will take a look when I get home. I did notice, however, that Camara p. 38-8 explicitly states that the table can be used for either single phase or two phase, and that the impedances must be doubled for single phase systems. I am now satisfied enough to feel prepared for this type of problem on the PE exam.

Also, I thought of a clue about how to explain conceptually how the table can be used for both single and balanced 3 phase: If you were to stick a core-balance CT/Ring CT around the two phases of a single phase line, you would get zero net current. If you did the same for 3phase, you would also get zero net current, so I suppose either way there is some sort of cancellation going on that also makes the impedances the same for both systems.


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## R2KBA (Oct 14, 2011)

Sorry everyone, I did some more research and I have to correct what I posted above. It turns out that there is only cancellation if the three phases are all equidistant from each other in an equilateral triangle formation. Otherwise there is different mutual inductance between each pair. I think I found the formulas, an I may attempt to solve DK PE's problem he just posted.


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## mudpuppy (Oct 14, 2011)

^Generally these problems assume the line is fully transposed. In fact, I work for a utility where the lines are not fully transposed but we still assume they are for modelling purposes.


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## R2KBA (Oct 14, 2011)

mudpuppy said:


> ^Generally these problems assume the line is fully transposed. In fact, I work for a utility where the lines are not fully transposed but we still assume they are for modelling purposes.


And this is basically what Grainger/Stevenson says, and you know how much he/they love to go into extreme detail on problems. I guess it's a pretty safe assumption to make then.


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