movement of overhead conductors due to short circuit forces

[magoo2]

I'm interested in knowing from this group what tools or techniques are available to model the movement of 2 parallel conductors carrying short circuit currents of approximately 3000 to 6000 amperes. The application is for an electric utility line in which a short circuit occurs between 2 of the 3 phase conductors.

Under these conditions, the faulted wires move apart and, following the interruption of current by a protective device, the wires often swing back together and make contact causing a new short circuit 1000 ft or so ahead of the original short circuit location.

My own efforts to model this situation follows Coulomb's law. In representing the span of wire, I modeled each of the wires as a pendulum at a length equal to the average sag of the wire. In an iterative calculation, I start with initial spacing when short circuit occurs. Then I increment the calculation, the new spacing reduces the repelling force. I calculate the displacement, velocity and acceleration of the 2 wires and repeat the calculation.

My objective is to start with the normal spacing and see if there's a likelihood of the wires coming together. If it is likely then I try changing the spacing or height of one to see if that avoids the collision. A collison means that another protective device operates and makes it a larger area of customers that are affected.

In a more rigorous sense, how could one model this situation? Since the wire follows a catenary path, can this be represented rather than the simpified way that I did it?

 

[MintJulep]

Interesting problem, which I am sure has been solved as you can't be the first one to ever attempt this.

You might want to repost on one of the electrical forums.

It would seem that you can't model the entire length of wire between supports as a single element. The electromagnetic force acting on each finite length of wire is a function of that wire's distance from the other wire, and the other way around. So the EMF is clearly not a constant along the length.

A free-body diagram for any finite element of length would include tension, gravity and EMF. You're iterative approach of calculating the EMF seems valid for a finite element.

 

[magoo2]

Sorry, I meant to post this on the Magnetic Engineering forum.

 

[GregLocock]

Modelling catenaries is fun. Since my particular hammer is ADAMS, and your question looks like a nail, I'd model the cable as a series of weighted bars joined by hookes joints joints. The excitation force would be represented as a non linear force depending on the distance between the two catenaries (ie going to highly repulsive as the distance drops to zero).

I would expect to model the behaviour quite quickly, but I imagine that getting good real world correlation will need a fair bit of fine tuning.

Aero damping might well be important.





Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[cbrn]

Hi,
yes, Greg's suggestion is very good if you have access to a program like ADAMS. About the same thing, but perhaps a little less efficiently, could be done with a FEA's implicit solver.
For what I know, this kind of work has been done by ENEL (Italy) in the early '70, with a custom-programmed FE system which ran on the first supercomputer they had. Nowadays the same calculation can be done in full-transient e.g. in ANSYS on a common PC platform (line-elems are so fast and efficient that the calculation power wouldn't even need to be very high...).
If you don't have access to anything like that, from a mechanical point of view I think that your approach is foundamentally correct. In order to "absorb" the simplification in the schema, I'd apply a multiplying factor to the swing amplitudes (or apply a factor of safety over the minimum distance that the conductors must stay apart).

Regards

 

[hacksaw]

the cheap solution is to calculate the total sag for the peak current case and check this against your conductor spacing. a bit rough, but at least conservative estimate

 

[GregLocock]

Does that catch the problem that a short at one location sets up a lateral wave that travels along the catenary and sets off another short?



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[magoo2]

Just to clarify what GregLocock asked, each span of wire is tied to insulators on the crossarms at each pole. A span may be anywhere between 250 to 300 feet long.

When a short circuit between 2 phase wires occurs, all the spans back to the source are subject to movement from the forces (because they all see the same currents). The most susceptible ones are the longer spans which normally have a greater amount of sag than the shorter spans do.

Think of 2 jump ropes side by side. The critical point, as hacksaw recognized, is the center of each span where the sag is the greatest. When this swings, the maximum sag point of each wire and the forces involved will determine whether the wires get together or not.

So there is a repulsion force or lateral wave from the electromagnetics involved that causes each conductor to swing away from each other. The motion is constrained in that both ends of the wire are fixed. This is why the pendulum modelling made sense even though you're dealing with an arc of wire rather than a lumped mass on a string. When the short circuit in interrupted, the return swing of the 2 wires in many situations can cause them to strike each other.

I'm not familiar with ADAMS and haven't used ANSYS either. I appreciate all the good suggestions from this group. Although I posted here by mistake, I received valuable inputs so far and haven't heard anything from the magnetic engineering community yet. Go figure!

 

[jistre]

http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/61/27676/01234715.pdf?arnumber=1234715

Seems that the IEEE has already done a study on this.

 

[magoo2]

jistre
Yes, but that study contains all the simplifications that I discussed in this thread.

It's not that I don't have a workable solution. I just want to improve upon it.

 

[unclesyd]

Knowing this thread is about overhead wire and shorts between phases he is an example eluding to the lateral motion mentioned by GregLocock and magoo2. I was almost a participant in a situation where a 12000 V line was first shorted between phases and then one phase went to ground. The electrical cables about 1 mile long and were in a cable try about 25 feet above ground. When the first part of the short occurred 2 of the cables broke all the straps in tray and a caterpillar like hump went back toward the main substation and as the second phase of the short occurred one of the cables had the hump returning to the short only this time it was 3 time higher. From what I could see it was about twenty feet above the cable tray. This cable broke loose from the substation right next to where I and salesman where exiting a control room. this cable feel on my plant truck and the hood of the salesman's car. Fortunately it was de-engergized as the mag breakers on this system and one on the plant feed had actually blown up.
This participated a shutdown of the whole site with a resultant cost in excess of $8,000,000. The loss of site power was due to powerhouse operator switching a feeder into a open circuit. As I understand it the operators in the power plant that feeds us where having kittens. I also heard that the feed lines to the plant were putting on quite a show. There are two separate feeds and both were in play.

 

[prex]

magoo2,
I would solve your problem by finite differences.
To better explain what I mean, let me show how the common catenary (cosh) shape would be calculated.
We take:
-H as the (constant) longitudinal component of the tension in the wire,
-mg as the weight per unit length of the wire,
-L as half the developed length
-d as half the distance of the suspension points
-the x axis from the mid point of the wire parallel to the conjunction of the suspension points
-the y axis vertical upwards
-[α] as the slope of the wire at any point
By dividing the length L of the wire in a number of equal segments [Δ]L, the equation in finite differences is simply
tan([α]_i)-tan([α]_i+1)=(mg/H)[Δ]L.
Starting with a trial value of H from the mid point (x=0), the x of the end point is calculated and compared with d: then H is iteratively adjusted till a value of x at end point sufficiently close to d is found.
This setup requires a few minutes in Excel (if you are accustomed to iterations) and of course the result for y(x) closely follows the cosh analytical solution.
Coming back to your problem, it is a simple extension of the above. We now define z as the third axis to be horizontal; [α] is now the projected angle in the xy plane and [γ] the projected angle in the xz plane. Calling F(z) the horizontal force due to the magnetic repulsion (presumably proportional to the inverse of z+c), the equations are now
tan([α]_i)-tan([α]_i+1)=(mg/H)[Δ]L
tan([γ]_i)-tan([γ]_i+1)=(F(z)/H)[Δ]L.
The form of F(z) adds no difficulty here: the numerical method is very tolerant on that.
The above system of equations is solved in just the same way as the preceding one and will give the position of the wire under the action of the repulsive force and I suppose this is the starting position of the movement when the repulsion disappears. I assume in all this that the starting position is a stable one and that the repulsion disappears suddenly: if you have more complex assumptions the method can be adapted.
Now the system of two equations is modified by putting F=0 and adding the two inertial terms -m[Δ]Ld²y/dt² and -m[Δ]Ld²z/dt² (where t is time): the solution is calculated at incremental time steps to get the movement of the wire (once again the inertial terms add no special difficulties).
As you see, it's not an elementary task, but it's doable.
Personally I don't think that the effort is worth the result. With respect to the elementary treatment as a pendulum, the only sensible difference is to account for the longitudinal distribution of the repulsive force, that will give a different initial shape (but just slightly different and probably the pendulum assumption is on the safe side).
Anyway, if you want to go on on the path outlined above, come back or contact me in one of the sites below.


prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[magoo2]

I finally got one reply from the magnetic group. Wasn't too helpful or detailed. By contrast, this group has been most helpful.

My thanks to all who offered their suggestions. And, jistre, that was my paper that you referenced.

As I mentioned, I have a working model and I was able to do some field work to show how a change in spacing could solve the problems in special cases. Even raised one conductor (center) with respect to the other 2. Causes the separation distance to be greater, but more importantly, the return swings of the 2 conductors are more likely to miss each other.

And prex, thanks for the modeling suggestions. Not sure at this point "if the juice is worth the squeeze", but I may be contacting you in the future.

 

[jistre]

HA!

That is pretty funny. Well, it's good you wrote the paper because now you don't have to read it.

I'm kinda curious, though. Is this interest for personal curiosity, or is the issue that important to your employer that your previous work isn't sufficient.

Also, I don't even want to think about calculating the reaction forces between two catenaries that are secured at different elevations. Angular nastiness.

Good luck!

 

[unclesyd]

Magoo2 might be one of them fellows that swing on these lines while doing maintenance work.

Good luck on your project.

 

[magoo2]

Hey jistre,
I just thought that lumping the mass together as a pendulum was possibly too much of a shortcut. In actuality, you have 2 chains that are swinging in a symmetrical fashion but in opposite directions. Does the chain behave like a pendulum or if it were modeled more like a chain (conductor), would the results change enough?

I guess it's more than just intellectual curiousity on my part. As an experiment based on my simulations, I changed from standard 4 foot spacing between conductors to 5 foot spacing and I've seen the improvement in subsequent swings, but this represents a fairly significant change. In other words, the conductors slapped together before and now we don't have that happening.

The different elevation situation is exactly the same model as the 2 conductors at the same elevation. It just took me a while to understand that the results made sense. Intuitively I didn't expect the result because when I used the conductors at different elevation, I also decreased the spacing. So the repulsion force became greater but the paths didn't intersect.

It's been a learning experience.