In Engineering Electromagnetics, Hayt points out that in a power station a
bus bar for alternating current at 60 Hz much more than 1/3rd of an inch (8
mm) thick is wasteful of copper, and in practice bus bars for heavy AC
current are rarely more than 1/2 inch (12 mm) thick except for mechanical
This seems to imply that the bulk of the current is in the outermost 4mm.
This does not mean that conductors, at 60 Hz, which are less than 8mm in
diameter do not show skin effect. 60 Hz AC resistance/DC resistance for
commonly used conductors (say 12 to 6 gauge) may be 1.1 to 1.25 in practice-
this includes skin and proximity effects . However, anyone wanting to do
the math from scratch better be familiar with Bessel functions. Are you?
Skin effect, per se, is not a concern with ACSR power cables as there are a
number of other factors which are more important.
Possibly the approximations for high frequencies are not valid at 60Hz but
this does not mean that skin effect is negligable- except for conductors 000
or higher - provided they are straight. .
The point is that there is no hard and fast "rule" covering all situations
I have been watching this thread for days. I like your answer. It's
allways give and take, no hard and fast rules that fit every situation.
And even better yet, You made your point without slamming anybody..
Well Done, Hats off....
For one thing, they are primarily designed for high tensile strength
as they have to stay mounted through all weather and environmental
After that, their resistance is an issue as the primary material has
to be steel for the tensile forces involved. They usually get clad in
Aluminum as copper is too costly for such long runs, and the losses in
using aluminum are little in comparison. This is also the reason that
high voltages are used in long haul transmission lines. The loss
over 2000 feet of line with 120 volts on it is significantly different
than the loss over 2000 feet of line with 20,000 volts on it.
Corona will become a problem as that line voltage is raised. At
that time line spacing becomes an issue.
Tower spacing is a function of the terrain being traversed. Line
spacing ON a given tower design is a function only of the voltage that
is proposed to be carried, and the total number of conductors.
Skin effect, in these high tension line realms is only an issue if
the idiots that made the wire didn't know how deep to make the
cladding. If the wire is clad to thinly, there will be more loss as
the steel is more resistive, and the wire will heat more as well.
If it is clad too thickly, an unnecessary cost is introduced.
This is specifically because the skin depth is so deep at this
frequency, NOT due to it being a thin depth! So in power line cases,
the effect is an issue of how deep the cladding is, not how thin.
In RF transmission lines, which are typically nickel or silver
plated, it becomes a cost issue, and claddings are made as thin as
possible for a given application frequency. These cases are where one
will see hollow conductors, or plated tube or solids. This is where a
Litz configuration or plated conductor will assist one in design of a
At 60Hz, a high voltage step up transformer will have some transfer
efficiency number. At switching frequencies, the same transformer
design (wire turn count wise) will operate better if the primary, and
or secondary have litz wire used in them as the effective resistance
of the winding will be reduced at the higher frequencies.
Gee - I thought I^2R loss depended on the current, not the voltage. For a
given power you are right but you didn't state this.
Right -and I have seen ACSR cable with an aluminum depth that exceeds 2cm.
This is unusual and now smaller conductors in bundles (spaced 30-45cm
between conductors ) because of lower inductive reactance and surface fields
that result-notghing to do with skin effect.
Not a big deal. The usual skin depth rules go out the window because of the
magnetic core material and the fact that you have strands of aluminum in
Note that the equivalent of Litz wire has been used and is used in 60 Hz
generator windings. Wonder why? The individual strands are too small to have
an appreciable skin effect but there is also the proximity effect which can
be more of a problem.
Current begins to fall off monotonically from the very surface for any
wire size at any AC frequency. There's no hard "skin boundary", and
the 1/e density is just a handy if arbitrary measurement point.
I don't see why this needs arguing over. In a given situation, you
just calculate the effects and decide how they affect things.
Sometimes a 200% increase in resistance doesn't matter, and sometimes
a 1% increase does. But skin effect does often matter in real
situations at 60 Hz, and shouldn't be always/automatically discounted.
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