Reactance of Transposed vs Un-Transposed Line

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mbrooke

mbrooke

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Question. Does the reactance for B phase (middle phase) relative to that of A and C differ in an un-transposed 70 mile line and why/why not? Would the reactance change if the line was transposed evenly such that every phase ended up with even shunt capacitance relative to each other? Would transposition increase the surge impedance loading or have no effect on it?

Two configurations of where "A" "B" and "C" phase are present have been included for reference and discussion purposes. Assume 138kV for all circuits.





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You are trying to take site to places few on here will ever go.
Not saying topics are not worth discussing, just limited number of guys to hold interest.

I believe the eng tips site addresses these questions quicker for you.

Youtube has many videos that discuss this and goes through the calc technics.
 
mbrooke said:
Question. Does the reactance for B phase (middle phase) relative to that of A and C differ in an un-transposed 70 mile line and why/why not? Would the reactance change if the line was transposed evenly such that every phase ended up with even shunt capacitance relative to each other? Would transposition increase the surge impedance loading or have no effect on it?

Two configurations of where "A" "B" and "C" phase are present have been included for reference and discussion purposes. Assume 138kV for all circuits.





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Click to expand...
Ask that book why transmission lines are transposed in the first place.
That may help answer the question.
 
MyCleveland said:
You are trying to take site to places few on here will ever go.
Not saying topics are not worth discussing, just limited number of guys to hold interest.

I believe the eng tips site addresses these questions quicker for you.

Youtube has many videos that discuss this and goes through the calc technics.
Click to expand...

I trust folks here many times over than Youtube.

In the end the physics is still the same.

Reactance and its increase in relation to increased distance, as well as capacitors off setting reactive VARs holds true for LV as well as HV.

I'm well aware that any discussion here will be over simplified, however IMO oversimplification is a good starting point to climbing up the more advanced ladder.
 
Hv&Lv said:
Ask that book why transmission lines are transposed in the first place.
That may help answer the question.
Click to expand...

I don't have the book, just this pic, which I am using as a reference to initiate a clear starting point. :)

For example, what is all 3 conductors increased to 5.4m away from the tower?
 
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Hv&Lv said:
Ask that book why transmission lines are transposed in the first place.
That may help answer the question.
Click to expand...
To keep everything balanced since one phase is in the middle and the other two are on the outsides (for the first diagram anyway).
 
steve66 said:
To keep everything balanced since one phase is in the middle and the other two are on the outsides (for the first diagram anyway).
Click to expand...


Is this because the middle phase has a lower capacitance, a greater distance from the tower, or interacting with two opposing fields instead of one? Or is it all 3?

Also, as a side question- how would this effect protective relay settings as a fault on B phase would technically be different than a fault on A or C phase?

The theory behind it is what makes me ask.
 
Taking with my transmission-line EE.

Yes, juxtaposition does affect line impedance, but he can't be specific.

Transpositioning is what's done to equalize it.
 
LarryFine said:
Taking with my transmission-line EE.

Yes, juxtaposition does affect line impedance, but he can't be specific.

Transpositioning is what's done to equalize it.
Click to expand...


I am beginning to realize they truly are among the most brilliant minds humanity has to offer.
 
The reactance in the middle phase is higher than the other two based on position.
Different structures present different line reactances simply because of asymmetrical spacing. This leads to unbalanced voltage drop on the line with the different reactances.
The goal behind transposing transmission lines is to try to equal out the total line end to end reactance by dividing the line into thirds.
The math involved is made simpler by calculating a single phase circuit reactance. Three phase reactance calculations can get extremely tedious. Breaking the lines into thirds with the same (or real close) structure types allows the single phase equivalent circuit calculations to be used.

length? Roughly every 15 miles for horizontal structures (depending on wire size) and about every 30 miles for triangular structures.(again, depending on wire size)
 
Hv&Lv said:
The reactance in the middle phase is higher than the other two based on position.
Different structures present different line reactances simply because of asymmetrical spacing. This leads to unbalanced voltage drop on the line with the different reactances.
The goal behind transposing transmission lines is to try to equal out the total line end to end reactance by dividing the line into thirds.
The math involved is made simpler by calculating a single phase circuit reactance. Three phase reactance calculations can get extremely tedious. Breaking the lines into thirds with the same (or real close) structure types allows the single phase equivalent circuit calculations to be used.

length? Roughly every 15 miles for horizontal structures (depending on wire size) and about every 30 miles for triangular structures.(again, depending on wire size)
Click to expand...


Thanks :)

Now bare with me. If the middle phase had identical spacing from the tower, would B phase then have the same the same X as A and C phase?
 
I think I answered the question. B phase reactance is higher based on position. Higher reactance, more VD. Hence, the reason for transposing longer lines.

magnetic flux produced by a three phase line can be ”seen” by drawing the three phases, then drawing concentric circles around each conductor. Yes, it gets messy and lines intersect all over each other. It is what it is…

I’m not going into a bunch of math and formulas here to give exact numbers…plus it’s aggravating putting the formulas in here on an iPad.

the magnetic flux at a point (P) from say A phase is determined by adding the flux produced by currents on each phase wire, A,B, and C. So you would have flux produced by I on conductor A at point P, plus flux produced by I on B phase at conductor A point P, plus flux produced by I on C phase at conductor A point P.

Simply put B (middle) has the most intersecting lines, so you can see why it would be higher.

Transposing:
B phase is in the middle, A on left, C on right for 1/3 distance.
1/3 distance line positions are swapped so then B on right, A in middle, C on left.
at last 1/3 distance, C goes to middle, A on right, B on left.
 
Hv&Lv said:
I think I answered the question. B phase reactance is higher based on position. Higher reactance, more VD. Hence, the reason for transposing longer lines.

magnetic flux produced by a three phase line can be ”seen” by drawing the three phases, then drawing concentric circles around each conductor. Yes, it gets messy and lines intersect all over each other. It is what it is…

I’m not going into a bunch of math and formulas here to give exact numbers…plus it’s aggravating putting the formulas in here on an iPad.

the magnetic flux at a point (P) from say A phase is determined by adding the flux produced by currents on each phase wire, A,B, and C. So you would have flux produced by I on conductor A at point P, plus flux produced by I on B phase at conductor A point P, plus flux produced by I on C phase at conductor A point P.

Simply put B (middle) has the most intersecting lines, so you can see why it would be higher.

Transposing:
B phase is in the middle, A on left, C on right for 1/3 distance.
1/3 distance line positions are swapped so then B on right, A in middle, C on left.
at last 1/3 distance, C goes to middle, A on right, B on left.
Click to expand...

Alright, this is a starting point! :)

Reading what your posting it sounds like the reactance is higher due to B phase interacting with two magnetic fields vs one.

But, any idea why this would cause X to up instead of going down? My understanding at it stands (I know its off) is that B phase field has two fields to cancel into vs only field as with A and C phase- my line of thought being that reactance goes down when conductors are inside conduit vs going up when a conductor is run separately because the opposing field is closer vs further away. In my mind having more/stronger opposing fields would lower X, but of course it does not, and as we know 3 phase power comes in angles...
 
Hv&Lv said:
I’m not going into a bunch of math and formulas here to give exact numbers…plus it’s aggravating putting the formulas in here on an iPad.
Click to expand...


Do you have (4 x 3.14 x f / 10 to the 4th power x the inches diameter radius) in mind to obtain the reactance per phase?
 
I would suggest getting copy of old textbook like "Elements of power system analysis" by W. Stevenson. These books are pretty inexpensive and you can sometimes find solution manuals to problems. It quite specifically covers inductance/capacitance for equalateral spacing and unequal spacing. I have a 4th edition from 1982.
 
mbrooke said:
Is this because the middle phase has a lower capacitance, a greater distance from the tower, or interacting with two opposing fields instead of one? Or is it all 3?

Also, as a side question- how would this effect protective relay settings as a fault on B phase would technically be different than a fault on A or C phase?

The theory behind it is what makes me ask.
Click to expand...

You have 3 capacitances between lines as well as 3 from line to ground. The latter are symmetrical for all 3 so we can ignore. But the capacitance from A to B and B to C is much larger than A to C due to the geometry involved. Hence you get an imbalance over distance on B phase compared to A and C from the higher shunt capacitance. Standard transmission line theory.

By transposing the 3 lines…rearrange so that all 3 spend roughly equal distance as the center phase, you can keep this difference in check,

Because it is pure reactance and most load is resistive it only becomes significant under fault conditions. The counter argument is that it hardly matters in the grand scheme of things except at extreme distances.
 
dkarst said:
I would suggest getting copy of old textbook like "Elements of power system analysis" by W. Stevenson. These books are pretty inexpensive and you can sometimes find solution manuals to problems. It quite specifically covers inductance/capacitance for equalateral spacing and unequal spacing. I have a 4th edition from 1982.
Click to expand...

Got this in PDF by chance? 😇
 
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