Skin Effect and High Currents

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Hey freaks....

Some discussion about Skin Effect..
Skin effect is inversely proportional to frequency and conductivity of material. And it means that passing this depth the current amplitude decay around 37%.
On AC mains 60 Hz the skin depth is around 9 mm, and on wikipedia says: "In Engineering Electromagnetics, Hayt points out that in a power station a bus bar for alternating current at 60 Hz with a radius larger than one-third of an inch (8 mm) is a waste of copper, and in practice bus bars for heavy AC current are rarely more than half an inch (12 mm) thick except for mechanical reasons."

But what we saw (at least I see all the time) are wire bigger than 8 mm, for currents higher than 50 A. BUT the cable are with little wires (around 0.2 mm, not isolate between them), are this little wires that make the difference for the skin effect? I mean, the skin depth isn't anymore the 8 mm?

Discussion about skin effect on real world!! :lol:

Regards,

Bruno Muswieck

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Computers don't make errors - What they do they do on purpose.

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For long distance power transmission lines, the "wires" (at least in the US) are hollow cylinders made from interlocking spiral strips of copper. If this were not done, the cables would be far heavier, requiring stronger insulators and towers and more wire material would be needed which increases cost.

But, in sub stations, the bus bars appear to be solid rectangular cross-section bars. One can surmise that these are used at lower voltages because there appears to be little effort to round corners for corona reduction.

Early in the design of radio receivers and transmitters, a kind of wire called Litz Wire (see Wikipedia) was used. This wire uses fine strands that are individually insulated. Using this wire, you could make inductors with much lower loss. This was particularly important at the frequencies we now call LF and VLF, where high inductances required really long lengths of wire; in those days, there were no ferrite cores. As far as I know, Litz Wire was used for RF rather than power.

Stranded wire is mostly used to achieve flexibility (as in appliance cords). I don't believe that loss is a consideration in most places where stranded wire is used.

Jim

 

Until Black Lives Matter, we do not have "All Lives Matter"!

 

 

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Mains frequencies and high currents require low resistance wiring. Thus bigger cross section and even current distribution is desirable, so for flex cables stranded wire is used. Welding for instance. Fixed connections usually are made from thick flat copper or alu buses.

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The stranding does not change skin depth much; it is the self inductance of the total current that drives the electrons to the periphery. However stranding allows the central core to be steel or alloy for strength or cheapness, and a larger diameter also reduces corona. http://www.southwire.com/products/ACSR.htm, amusingly they give bird names to each overhead wire size.

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Quote:
Mains frequencies and high currents require low resistance wiring. Thus bigger cross section and even current distribution is desirable, so for flex cables stranded wire is used.

But this isn't what sking effect say. I came with this discussion, mainly when you are using a VFD that can work from 1.25, 2,5 .... kHz, so the sking depth is less than 9 mm..
Quote:
and a larger diameter also reduces corona.

Corona??

Or you guys, think that with Stranded Wire the skin depth will not be 9 mm on 60 Hz

Regards,

Bruno Muswieck

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Bruno,

Skin effect becomes unimportant at the frequencies in question.

As already noted, mechanical attributes dictate construction of the conductors.

In long line transmission ( at mains frequency) in a polyphase system it is the phase to phase capacitance imbalance that is most deleterious.
A careful observation of these lines will reveal that phases are transposed on the pylons at regular intervals to mitigate this imbalance.

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Quote:
Skin effect becomes unimportant at the frequencies in question.

But on the Engineering Electromagnetics, they say oposite or it's because the case is in long lenght wires?

But Ignoramus, 60 Hz and 2.5kHz the skin depth has some big differences, 9 mm to 1.5 mm.

Regards,

Bruno Muswieck

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Just as a silly question. An 18mm diameter conductor is going to be fairly difficult to handle.

I have never seen a 500kV underground cable. I presume that they are multi-stranded copper with armour and hefty insulation.

Regular overhead lines are steel cores with multi-stranded aluminium on the outside. The 500kV lines have both aluminium and steel strands that are only about 3mm diameter.

I presume that it is low voltage distribution where you get the massive currents in underground cables.

I very much doubt that skin-effect would make any difference. Nor would you insulate individual strands of the same cable.

David.

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David my concern is about three-phase 380V, where you get connections for motors from 50 to 300 cv and 18 mm is nothing in this cases..

The only way to know if skin effects does affect on this frequencies with the right size of wire are: is the cable getting hot? If yes and it's hot because the amount of current on the surface of the cable.
What you think?

The other question still is open for Ignoramus. ;)

Regards,

Bruno Muswieck

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Bruno,

Please post the link to the reference You are citing.

In long distance power transmission there will be losses. In some countries ( notably former USSR ) high voltage DC links are used to achieve highly efficient distribution.

This is not because skin effect at DC is non existent this is because of other effects. Capacitance between phases will become significant and resultant current will be set up.
Additionally on very long lines the transmission lines start to act as radiators ( antenna) contributing to the inefficiencies of the transmission of energy.

David,

Yes they ( underground cables) are semi rigid multi strand affairs with either single conductor ( single circuit more correctly) or poly-phase cables.

Generally they have a non conducting core bundle around which the rest of the cable is structured.
On the outside steel wire armoring and waterproof sheath.

As a rule the conductor cross sectional area in underground cabling is significantly larger than equivalent aerial installation due to reduced cooling beneath the soil.

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I will do an inspired guess. I am sure that there are qualified people out there.

Once you start having > 500kW motors you turn to higher supply voltages. You definitely start having high voltage distribution around your site.

1000A is relatively hefty current at 440V. The copper size is not that unmanageable. But I bet you use stranded cables.

Where you start getting serious currents s with low voltages.

Anyway, surely you look up in the cable tables for the power rating of your motors. Then do a swift sum on the length of cabling. You will have massive inrush currents but the run currents will not heat the cables too much. You design for the inrush current.

David.

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Quote:
Please post the link to the reference You are citing.

Ignoramus it's on the final part of example part.
http://en.wikipedia.org/wiki/Skin_effect
Quote:
Additionally on very long lines the transmission lines start to act as radiators ( antenna) contributing to the inefficiencies of the transmission of energy.

On long lines where wave lenght (lambda) is less than the wire lenght you will have problem with impedance macthing, so reflections will happen.

David, Stranded cables are used. As I had seen.

Guys I'm not talking about transmission lines (long lenght, the case is less than 100 m) I'm talking about 60 Hz, and for the VFD 2.5 kHz and high current. The discussion is, if you have a thicker wire is the same of have multiples wires (less thicker)? Skin effect doesn't affect?

I will check about the cable temperatures, tomorrow I will go to a place where I can check it... ;)

Regards,

Bruno Muswieck

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Quote:
motors from 50 to 300 cv

I do not know what this means. You normally rate motors in kW (or horsepower for US citizens). A horsepower is about 0.75kW. So if your 'cv' is horsepower, this means motors from 38kW to 225kW.

If you are installing these motors, there are tables for the recommended wire cross-section-area. The motors and switchgear come with the overload and starter gear.

I very much doubt that skin effect will make any difference at 60Hz. Even at 2.5kHz it will be trivial.

It sounds very much to me like the gold knobs and 'solid silver wire' for ultimate hi-fi quality.

I am sure you can do a lengthy mathematical analysis. Otherwise, you look in the tables, do some rough calculations on the back of the cigarette packet. Add a good safety margin and drive down to your electrical wholesaler.

David.

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Stranding doesn't decrease resistance, it increases it. (For the same wire size.) It's done to provide flexibility, as was previously stated. The increase in resistance is small.

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Brunoi,

in that section You popinted to the telephone cable is specified in terms of resistance per 1000 feet of length as a function of frequency.

Please note:

Frequency resistance per 1000 feet

1Hz------------52.50
1KHz-----------52.51
10KHz----------52.64

for a change in frequency in the order of FOUR ORDERS OF MAGNITUDE you have a change in resistance of 1%

In summary insignificant change in resistance with frequency at the lower end of frequencies ( audio frequencies)

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Stranding of the wires does not help against the skin effect. It can help against eddy currents in a transformer or coil.

The 8 mm are not a brickwall, but the depth where current density drops to 1/2.7 - probably in 1 D geometrie, not a circular cross section.

The comparison with the telephone line does not help much here, as the wires are much thinner. The skin depth depends on the square root of the frequency - so 60 Hz with a 6 mm wire is equivalent to 6 kHz with the 0.6 mm phone wire.

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It helps to illustrate CHANGE in resistance with frequency.

As for eddy current losses they are more the domain of laminated magnetic path rather than copper conductors.

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Quote:
I will check about the cable temperatures, tomorrow I will go to a place where I can check it...

Checked... A VFD for a 224 kW motor, the current was around 320 A, switching frequency of 2.5 kHz. The cable lenght from VFD - Motor has two types of cable: one solid cooper of 400 mm2 and other part was 2 cable per phase of 120 mm2 (stranding), which one get hotter?
The 400 mm2 cable, why? I think it's because of skin effect.

The temperature difference was to high, but I din't measure it, I just felt it touching them..

Regards,

Bruno Muswieck

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Why do you have different cables?

Surely you have 3 identical cables for each phase. You can measure the individual phase currents with a clamp meter. Each phase should be about the same. If not then you have a serious problem.

I presume that you mean that you have 50m run of 3-phase 400mm2 from your supply to the VFD and a 10m run of 2x120mm2 from the VFD to the motor.

The VFD run will be at 2.5kHz and the supply run will be at 50Hz.

If the 400m2 cable has the 2.5kHz, then I am very surprised by the difference in temperature. I would expect 50Hz to have trivial skin-effect. Even 2.5kHz should be no problem.

Replace the 400 mm2 by 120 mm2 cables. The scrap value should go towards paying for the smaller cables.

David.

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The 2.5kHz should be insignificant as it should be small amplitude ripple on the 50Hz.

Letting the smoke out since 1978

 

 

 

 

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david.prentice wrote:
Why do you have different cables?

Surely you have 3 identical cables for each phase.

Sounds like the run from VFD to motor uses solid wire for a portion of the run, and stranded for another portion.

The fact that two significantly different sizes of cable are used indicates that there could be confounding factors to the correlation between cable temperature and power loss within that cable. For instance, the first segment of the run might be larger because it runs through a higher ambient temperature area (and therefore was derated). If that's the case, then it could also explain why that part of the run is getting hotter.

Plus it's hard to trust a touch-test comparison--perception of temperature is not very consistent or accurate.

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I can imagine rigid cable up to a motor, then flex for the last meter or so, where it is subject to vibration and start/stop "jerks". Purely mechanical.

Jim

 

Until Black Lives Matter, we do not have "All Lives Matter"!

 

 

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Quote:
Why do you have different cables?

I thought that could results this doubts...
The both cables sizes are from VFD to motor. Image that the distance from VFD to motor is 40m, so 20m with the 400mm2 and 20m with 2x120mm2.
Why do you have different cables? Because they have the 400 mm2 that will not use in other place, economical problem.

Regards,

Bruno Muswieck

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After a talking that I have with my teacher, he gave other thought, area calculus...

The skin effect says: the current amplitude decay 39% (around) at 1 depth. So the right thing is to calculate the area of 1 depth (60Hz ~ 9mm) of both cables 120 mm2 and 400 mm2 and compare the areas.

Does you know the current handling of 1 mm2 of cooper and aluminum?

Well my ideia is that skin effect does happen on 60Hz.

Regards,

Bruno Muswieck

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Bruno,

when You do the calculation for rectangular conductor make sure You do take into consideration corner effects.

Conformaly map the rectangle into upper half plane ( using Greens theorem) solve for current distribution and map back into real space.

It would be interesting to see just how significant the effect is at 60Hz

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Ignoramus, the calculus I will do for circular geometry.. ;)

Quote:

Conformaly map the rectangle into upper half plane ( using Greens theorem) solve for current distribution and map back into real space.

First I will make some aproximations only...

Backing that question:
Does you know the current handling of 1 mm2 of cooper and aluminum?

Regards,

Bruno Muswieck

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Bruno,

On the question of calculus,, just joking.

On the question of current density:

a) will the conductor be in free air
b) inside a conduit ion free air
)c underground? some other installation mode?

The problem is not so much current carying capability of a copper conductor as much as how it is installed and whether the I2R losses ( in the conductor ) can be dissipated safely

Now for some practical numbers from my old copy of AS3000 -1976 ( yes it was new when I bought it)

!kv non armoured cables in metalic or non metalic conduit installed in free air

area-----two single insulated conductors----voltage drop mV/A.m

1........14.................................46
10.......53.................................4.6
35.......115................................1.4

The two conductors are a single phase and neutral

So these are practical engineering numbers whic take into consideration the effect of heating and voltage loss along the feed.

Above current ratings should be multiplied by 0.8 if considering round cables where cooling may be reduced due to cable construction.

Thank goodness for cable tables... otherwise we would really have to go to first principles and God forbid indulge in calculus :-|