Surface conduction at 60 Hz

"Roy L. Fuchs" wrote:


>>>http://www.audioholics.com/techtips/audioprinciples/interconnects/SkinEffect_C
All correct, except that the reason for the multiple phase conductors has to do with the system voltage, not skin effect. At high voltages, the E field strength in the vicinity of a small radius conductor will exceed the ionization potential of the surrounding air. This ionization will result in power loss (it can be modeled by an equivalent resistance from conductor to ground per mile). A conductor bundle simulates a single conductor with a diameter equivalent to the bundle spacing. The field strength around this larger radius 'surface' is reduced below the ionization potential.
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Paul Hovnanian mailto: snipped-for-privacy@Hovnanian.com
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wrote:

In addition, the use of bundled conductors appreciably reduces the series inductance of the line even though it does produce a small increase in capacitance to ground and ground level fields. This is not a negligable factor.
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Don Kelly @shawcross.ca
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On 2/26/06 4:26 PM, in article BGrMf.75842$H%4.60848@pd7tw2no, "Don Kelly"

It may be so, but it is not immediately obvious to me that parallel bundles of spaced wires will lower the electric field at the cylindrical surfaces. Locally, the cylindrical surface of the individual conductor is going to have the same radius as the conductor. To convince me, I would have to go through a Schwarz transformation to solve the two dimensional potential problem. I am not moved to do that.
Except for the skin effect, the velocity of propagation in the TEM mode along the line will be the speed of light. This means that the product of inductance and capacitance of the line stays relatively constant.
Bill
-- Ferme le Bush
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wrote:

I have done it the easy way -through computer modelling. The model used is valid, external to the conductors, for multiple conductors above a ground plane. The assumption in the program is that the charge of a conductor is at its center, which is excellent for the typical distances involved -the distance between the line charge location within the conductor to make it an equipotential surface, and the true center of the conductor is negligable. Corrections can be made but except for special cases such as cables where distances are short, there is no point in doing so. Input information is dimensional data (radii, height above ground plane, spacing, etc) and voltage (instantaneous or rms) of each conductor with respect to ground. There will be a reduction in surface E field and in a short distance from the conductor bundle,-say 2 or 3 bundle radii- the field will be near that of a single conductor of much large radius . Here is a simple case. Single conductor radius 2 cm at height 10m and voltage of 100kv surface field under conductor is 724.+ kV/m and at side it is 723+ kV Two conductors, same size and voltage, spaced 30cm apart field below E3kV/m, inside A8 kV/m and outside 478 kV/m I also see that the charge on each conductor is appreciably lower than that on the single conductor at the same voltage although the total charge is greater. The effective radius of the bundle is about 7.75cm in this case. The ground level field is increased slightly in the bundled case as the field is a bit more uniform. The line capacitance is increased by bundling and the inductance is decreased. The decrease in line inductance is of more importance, in most cases, than the increase in C. Note that in general capacitance is based on the conductor radius while, for inductance, the concept of GMR is considered and this takes into account internal flux linkages. For ACSR, the GMR is measured but it can be calculated different geometries in the absence of magnetic materials.
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Don Kelly @shawcross.ca
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On 2/26/06 10:40 PM, in article M9xMf.76311$H%4.16564@pd7tw2no, "Don Kelly"

I was thinking a bit more about this and have resolved the paradox in my mind.
For a given power capacity of a line, the voltage required is going to be proportional to V^2/Zo. By putting multiple conductors in parallel, (per unit length) the inductance is decreased while the capacitance is increased. This lowers the characteristic impedance of the line. Thus, the voltage required to transmit the original power is dropped, and the likelihood of corona is diminished.
Bill -- Ferme le Bush
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wrote:

Actually, that's not bad; good going!
Pop
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On 2/27/06 8:22 PM, in article weQMf.78742$H%4.46124@pd7tw2no, "Don Kelly"
<sni>

Although power lines ordinarily do not run with impedance matched loads, you still have forward and backward traveling wave on the lines. Each of these two waves individually does have voltage/current = the characteristic impedance.
Bill
-- Ferme le Bush
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wrote:

True but not really of use in analysis of a power line's performance. One goes from distributed parameters ("telegrapher's equations") to a lumped model for a given line. Consideration of a standing wave can be used for estimation of mid-line voltages where needed but even this can be avoided by simply using multiple pi sections. For switching and lightning surges, the travelling wave model is used where necessary. Dr. Hermann Dommel did a lot of work on this and the models have become quite sophisticated.
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Don Kelly @shawcross.ca
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On 2/25/06 1:09 PM, in article SH3Mf.3535$UN1.2478@trndny08, "ehsjr"

The purpose of the steel core is to provide the tensile strength that allows longer spans (fewer towers) and less thermal expansion. Because of skin effect, copper in the center of a large conductor is wasted. Skin depth is about 6 mm. How much steel core and haw much copper or aluminum is placed on top of the core is an economic decision. Remember that the radii of conductors could be in the neighborhood of 20mm.
If copper were very cheap and spans small, wasting a bit of conducting metal would not be a big deal.
Bill -- Ferme le Bush
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Salmon Egg wrote:

Exactly. The steel is required for strength, *not* to increase the amount of copper at the surface. The copper at the surface is required to reduce the electrical resistance of the cable, as copper or aluminium is a much better conductor than steel.

Your are comparing steel clad copper versus copper clad steel, by implication. Do you seriously believe that, for a given core diameter and a given cladding thickness, a copper core, steel clad cable would be as strong as a steel core, copper clad cable for the transmission lines we're talking about?
Whether copper in the center would be wasted or not is irrelevant. The need for a large steel core for strength puts the copper or aluminum on the surface in the first place, so there is no need to consider skin effect.
Ed
Skin depth is

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On 2/26/06 7:51 PM, in article fHuMf.1060$FY1.982@trndny06, "ehsjr"

I hope this statement is not attributed to me because I never considered steel clad copper.

Central copper in large conductors is wasted! Skin effect can be significant. Thin copper cladding on steel is often used for antennas where the skin effect would make thick cladding very wasteful indeed.
Skin effect also shows up in large ac electrical machines. To use the copper effectively, it is broken up into smaller separate conductors that are smaller than the skin depth. These conductors are insulated from each other and transposed. It is, in a sense, the machine analog of litz wire.
Bill

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Salmon Egg wrote:

It says, if you read it, *by implication*. If you did not consider steel clad copper, then you realize that the larger diameter is created for the strength that the steel core offers. Therefore, since the diameter is already increased for strength, the reason for increasing the diameter *cannot* be skin effect. In other words, skin effect is negligible. The resistance of the steel core, however, cannot be neglected. That is why it is copper clad. Nothing to do with skin effect.

Of for goodness sake. We are talking about *60 Hz*. We are *not* talking about antennas and hardline.
Enough, already. Post something real that demonstrates that skin effect often cannot be neglected at 60 Hz.

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On 2/28/06 8:26 PM, in article 8o9Nf.82843$H%4.69488@pd7tw2no, "Don Kelly"

I should add, that the subdivision of conductors also reduces the proximity effect. Sometimes that can be of greater import than the skin effect. In any event, skin effect and proximity effect are both manifestations of eddy currents.
Bill
-- Ferme le Bush
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us:

NOT TRUE! First off, there are no steel clad copper cables. There is no reason to place the poorer conductor on the outside of a cable, and the CORE of a cable MUST have a higher tensile strength than the jacket or the cable will fail to work as designed.
The thin steel CENTRAL "carrier strand" is just that... A CARRIER. It bears the weight of the cable, NOT the current. It is the mechanism for providing a strong tensile link between towers. It is clad with copper not to make the cable bigger, but to make it conduct better.
A steel cable WILL work fine at the voltages carried on those towers. The benefit from having the copper cladding is that nearly ALL of the current will be IN the copper, and SKIN EFFECT IS the reason the current will be there, and IS the reason the industry clads steel cables in copper for HV power transmission lines.
So, yes, the cable has a lower resistance, but much of that lower resistance is due to skin effect, as it relates to the characteristic impedance of a given segment of high tension cabling.
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Roy L. Fuchs wrote:

Exactly right. You seem to be the only one who understands what is going on. Salmon egg seemed to imply that there might be such a thing as steel clad copper cable.

Exactly right.

Here we may disagree, not in the facts, but in the rationale. I think the disagreement is probably a nit, based on your last paragraph, below. I'll address the apparent disagreement: The steel cable already must be some specific diameter, for strength. While steel would work, it doesn't work well enough for the power utility economics. The steel is too lossy. So they use copper clad to lower the resistance. The reason it lowers the resistance is that copper is a better conductor than steel.

That's the key. You understand the issue. What would be nice is some real world numbers. I assume that in designing the cable, skin effect is taken into consideration as one of the factors to determine how thick to make the cladding. I suppose they could use a standard - make a steel core big enough that could be clad with 9+ mm of copper - but I doubt that's real world.
Ed
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us:

They used to be ALL steel. We used to cherish our copper a lot more in the days of full metal jackets, and we went through 3 wars conserving it monetarily and industrially as well. The losses are very low when one considers the voltage. At 100,000 Volts a couple hundred volts lost is a very low number. It DOES add up though, so yes, using copper clad cables reduce those losses considerably.
The losses I can't stand is where in Ohio, I could walk past a high tension line and NOT hear leakage, and that is a high humidity part of the world. Here in California, I can walk past nearly ANY high tension insulator and line, and hear it leaking badly. I'd say that california loses 20% more juice to leakage than any other state I have ever been in. They just don't service their lines.
WE PAY FOR THAT... so they don't care! That is the OTHER reason why privately held utilities suck big time. The bastards are worse than the worst NYC landlord that ever lived. Rent keeps going up... while quality of service keeps going down. Major LAME.
The criminals of Enron and Sempra energy ought to be lined up at a wall and stoned to death with very small stones... thrown very hard, like from a paintball gun(s). Either way, I want have my payments over the last seven years back. The bastards!
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Gave

Skin effect is also a problem in the short runs of bus-work used in substations. These do not have a steel core (no need for excessive tensile strength), but the bus-work is *not* solid aluminum or copper rods. It is aluminum tubing with a large ID. The tubing wall isn't more than about 1/2 inch thick (close to 9mm). For larger ampacities, larger diameter tubing is used, not tubing with different wall thickness.
daestrom
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us:

It CAN be and IS negligible in low power applications or where the conductor diameter is smaller than the skin depth times two.
When the cable size is great enough that the skin depth can be a factor, it WILL be a factor, and IS a factor on large diameter high voltage high tension power lines.
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