Author Topic: Does 50Hz have a small skin effect?  (Read 6207 times)

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Offline Michael George

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Does 50Hz have a small skin effect?
« on: February 24, 2016, 01:50:14 pm »
A technician said: Its better to use a solid cables for homes (not stranded cables).

I did not use any calculations but I think that stranded cables are better due to skin effect. We use 220V / 50Hz.

Is 50Hz too low frequency so that we can consider it as DC and "skin effect" has a very small effect at that frequency?

Is there any factors other than "skin effect" so that he recommends solid cables?

I'm speaking about cable that have 10 mm sq at most. And length is less than 20 m.

Thank you,
 

Offline rs20

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Re: Does 50Hz have a small skin effect?
« Reply #1 on: February 24, 2016, 01:59:59 pm »
Firstly, plain old stranded wire doesn't help with skin effect -- the inner strands are prevented from carrying the current, and the copper there is wasted -- just like the middle of a solid core wire. The only way to exploit stranding to circumvent skin effect is to use Litz wire, which is many strands which are a) individually insulated [unlike normal stranded wire] to prevent the electricity just jumping strands to stay on the outside of the overall cable and b) wound in a special way to make sure each strand spends equal time in the centre of the cable [unlike normal stranded wire].

All of that aside, 50 Hz skin depth is trivially found with a google search to be 8mm. So not relevant to normal mains wiring. When you need to carry lots of current, flat bars of copper are used (and I believe the flatness of the bars is due to concern for skin depth).

In short -- you are wrong about skin effect being relevant. Solid core is preferred for permanent, non-moving wiring in the walls because it's less likely to corrode and probably cheaper or something. Even ethernet cable has this stranded-for-cables-you-see, solid-for-the-cable-in-the-walls dichotomy.
 

Offline Richard Crowley

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Re: Does 50Hz have a small skin effect?
« Reply #2 on: February 24, 2016, 02:01:15 pm »
The skin effect of 50Hz in copper is ~9mm.  Is your wire larger than that?



https://en.wikipedia.org/wiki/Skin_effect
« Last Edit: February 24, 2016, 02:02:56 pm by Richard Crowley »
 

Offline Milmat1

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Re: Does 50Hz have a small skin effect?
« Reply #3 on: February 24, 2016, 02:36:43 pm »
I'm more curious to know what type of issue you are seeing at 50Hz? If Any ?

The thing I always tell people to remember is "Surface Area"...

At 50Hz. (60Hz here) I have never seen any real problems.  I have had to mitigate noise issues within a 60Hz system but it has always been from higher frequency signals trying to ride on the mains etc....
Never tell the customer: "It Can't do that" !
 

Offline Michael George

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Re: Does 50Hz have a small skin effect?
« Reply #4 on: February 24, 2016, 03:10:02 pm »
I was asking especially about the main cable of a home (department). The cable that is connected to the main automatic circuit breaker.

I was also asking about normal home applications that uses much current such as: air-conditioner and so on ...

My cables does not exceed area of 10 mm sq and the length is less than 20 meter.

Thank you very much for all replies and answers,
 

Offline G7PSK

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Re: Does 50Hz have a small skin effect?
« Reply #5 on: February 24, 2016, 03:10:31 pm »
The only skin effect you will see with 240 volt 50 HZ house wiring is when you touch a live wire. :-DD

 

Offline edavid

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Re: Does 50Hz have a small skin effect?
« Reply #6 on: February 24, 2016, 07:46:07 pm »
Even ethernet cable has this stranded-for-cables-you-see, solid-for-the-cable-in-the-walls dichotomy.

That's different... stranded wire is preferred for patch cords because it's more flexible, otherwise solid wire is preferred because it's easier to terminate.
 

Offline T3sl4co1l

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Re: Does 50Hz have a small skin effect?
« Reply #7 on: February 24, 2016, 07:55:24 pm »
Small, no, it's large! ;)

Stranded wire does have some advantage over solid, but it's in the 10% range, not the >50% advantage from using proper Litz.  (As measured at frequencies where skin effect is significant: for example, the Q factor of resonant inductors in the 500kHz range.)

For any wire used in a household, there will be no noticeable difference.

For modest sized transformers (some kVA?) there will be some advantage, because proximity effect multiplies the skin effect.

Tim
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Offline uncle_bob

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Re: Does 50Hz have a small skin effect?
« Reply #8 on: February 26, 2016, 12:34:35 am »
I was asking especially about the main cable of a home (department). The cable that is connected to the main automatic circuit breaker.

I was also asking about normal home applications that uses much current such as: air-conditioner and so on ...

My cables does not exceed area of 10 mm sq and the length is less than 20 meter.

Thank you very much for all replies and answers,

Hi

If you dig a bit deeper into skin effect you will find that the often quoted number is "from each surface". A wire of 16 mm diameter has zero area that is outside one "skin" deep. The current does not go to zero at that point, it simply drops off a bit. As you go into a wire, the main part of the cross section is towards the edge rather than the center (go in 1 mm from the outer edge of a 10 mm wire, that's a lot more area than the center 1 mm radius section). The cross section effect means that the practical impact on a cable is quite small even in the 16 to 20 mm range.

Now, if you are talking about high voltage primary distribution cables with conductors that are often well over 25 mm diameter, yes, they start going hollow or putting steel filler in the center of the cable.

The other disclaimer is that this assumes you are not using pure nickel wire in your house ...

Bob
 

Offline Richard Crowley

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Re: Does 50Hz have a small skin effect?
« Reply #9 on: February 26, 2016, 12:39:35 am »
Now, if you are talking about high voltage primary distribution cables with conductors that are often well over 25 mm diameter, yes, they start going hollow or putting steel filler in the center of the cable.
So maybe that copper-clad steel cable we see coming from China isn't as bad as we thought?   :P
 

Offline uncle_bob

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Re: Does 50Hz have a small skin effect?
« Reply #10 on: February 26, 2016, 12:48:20 am »
Now, if you are talking about high voltage primary distribution cables with conductors that are often well over 25 mm diameter, yes, they start going hollow or putting steel filler in the center of the cable.
So maybe that copper-clad steel cable we see coming from China isn't as bad as we thought?   :P

Hi

If the conductor is > 25 mm diameter and it's got > 10 mm of copper over it, that will work ok. That only gives you a 5mm diameter steel core. Most copper clad is the opposite, lots of steel and not much copper at all.

Bob
 

Offline T3sl4co1l

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Re: Does 50Hz have a small skin effect?
« Reply #11 on: February 26, 2016, 12:52:55 am »
If you dig a bit deeper into skin effect you will find that the often quoted number is "from each surface". A wire of 16 mm diameter has zero area that is outside one "skin" deep. The current does not go to zero at that point, it simply drops off a bit. As you go into a wire, the main part of the cross section is towards the edge rather than the center (go in 1 mm from the outer edge of a 10 mm wire, that's a lot more area than the center 1 mm radius section). The cross section effect means that the practical impact on a cable is quite small even in the 16 to 20 mm range.

Close, but not quite! :)

The actual condition is for a half-infinite conductor.  Thus, the surface is an infinite plane, and there is unlimited depth behind it (current drops off exponentially with depth from the surface, never quite reaching zero, but getting close enough for engineering purposes by about 3 depths).  The surface is perfectly uniform, no curvature and no interference from other currents.

An infinite plane is also the surface of a cylinder or sphere with infinite radius.  If you shrink the radius, the surface becomes curved, but this still isn't very important until the radius is on the same length scale as the skin depth.

When the radius is less than 3 skin depths or so, you want to use a different analysis.  The cylindrical case (for a lengthwise current down a solid cylindrical wire) ends up with a Bessel function instead of an exponential.  Thus, there are in fact zeroes within the depth of the wire!  This can be imagined by considering that the conductor necessarily exhibits attenuation and phase shift: as the current diffuses into the depth of the conductor, it is phase shifted, and therefore interferes with the waves diffusing in from other sides.  Thus, there can be one or more shells where current goes to zero, and in fact reverses inbetween each!

As an approximation, the infinite-plane case is still a good estimate.  For cylinders of radius under 1 skin depth, the current density is still pretty uniform (i.e., the radius is less than the first zero of whatever Bessel function shows up here).

When you have nearby currents, things get tremendously more complicated, with only a few simple cases having analytical solutions I think.  You tend to get elliptical integrals from mirror-symmetrical and rectangular geometries, like twin-lead or PCB traces, which quickly get easier to compute by brute force (general EM field solver) than trying to work the equations.

You can still hand-wave your way through things, so for example, a thin strip will have most of the current flow along the edges of the strip, and little in the center.  The skin depth is working in from the edges, even though the thickness of the strip is much less than it.  So it's "edge depth" rather than "skin depth", but the physics is identical.  (This can be treated as a 2D diffusion problem, where the strip is thin enough to consider as a plane conductor with resistance/sq instead of bulk resistivity.  A thinner strip has deeper edge effect, because its area resistivity is higher.)

Which pretty quickly gives rise to being able to foresee and describe (if not compute) the edge effect, current crowding and proximity effect of windings in a transformer or inductor.  The effects are all scaled by the same frequency dependence, but the multipliers can be quite large, 10 or 20 times worse for wires deep in a winding or Litz bundle!

Tim
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
Bringing a project to life?  Send me a message!
 

Offline Richard Crowley

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Re: Does 50Hz have a small skin effect?
« Reply #12 on: February 26, 2016, 12:55:56 am »
If the conductor is > 25 mm diameter and it's got > 10 mm of copper over it, that will work ok. That only gives you a 5mm diameter steel core. Most copper clad is the opposite, lots of steel and not much copper at all.
But if you are using it for GB-speed Ethernet or something, then we don't care about LF conductivity, do we?
 

Offline uncle_bob

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Re: Does 50Hz have a small skin effect?
« Reply #13 on: February 26, 2016, 02:01:26 am »
If the conductor is > 25 mm diameter and it's got > 10 mm of copper over it, that will work ok. That only gives you a 5mm diameter steel core. Most copper clad is the opposite, lots of steel and not much copper at all.
But if you are using it for GB-speed Ethernet or something, then we don't care about LF conductivity, do we?

Hi

Signaling is a different thing. You then likely care as much about dielectric losses as your copper losses. Now, indeed skin depth does matter more as frequency goes up. You quickly get out of the "millimeters of copper" range.

Bob
 


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