Causes:- Issues with
Skin effect
 

A phrase you have no doubt heard about, especially if you've had any dealings with RF nutters, but does it exist at 50Hz? Read on!

There are two types of skin effect and they are easily confused until the "mechanics" of each are clearly understood. The first is thermal (although not truly a 'skin' effect, it has adopted the name), the second electromagnetic.



THERMAL

This skin effect is when, during high current draw, the outside of the conductor remains cool while the inner heats up. This is as a result of the outer managing to radiate some of the heat generated by the current flow while the inner has to pass any heat to the outer to then be radiated. The electrical result is the innermost portion of the core has a higher resistance than the outer, and as the resistance is higher there is a greater voltage drop meaning more heat is generated,....... and the vicious circle scenario lives on.

Although larger conductors will allow more current to be carried, the problem is also made worse as thicker conductors have a greater distance between the inner and outer (more material for the heat to be passed through) but they also have a greater surface area that can cool the conductor down.

There is a point, however, where this cooling can no longer keep up with the heat generated and the conductor size vs current carrying capacity ratio becomes uneconomical. Usually the cure is multiple conductors or a change in shape such that the surface area is made larger to effectively radiate any heat generated. Triangular shapes are now more common place as they offer a greater surface area, a greater cross-sectional area, require less insulating material, and yet keep a realistic cable diameter.



INDUCTIVE

The mechanics of this type of skin effect is rather interesting. As electrons flow they create magnetic fields within the conductor. These magnetic fields induce voltages within the conductor such that they "operate in parallel".

Think of the outer and inner of a conductor as the primary and secondary of a 1:1 transformer. Any voltage generated on the outer surface will be met with an equal voltage on the inside. Because the inner already has this voltage no current will flow in the inner. As there is no magnetic material (hopefully) within the wire the amount of coupling is dependent on frequency. The higher the frequency the better the coupling and the only area not affected is that which has no material next to it i.e. the surface.

Because the current flow is concentrated near the surface, the amount of conductor doing any work is reduced. As there is less cross-sectional area at play, the apparent resistance of the conductor increases by the ratio of used vs. overall conductor area. And note: This effect is over and above the inductance of the conductor.

The extent of this effect can be measured and formulae are now available to calculate the depth to which this effect takes place. The formula for the depth of skin effect in copper is:

depth (mm) = 66.04 F

where F is frequency in Hz. The graph below shows the skin-depth of copper from 50 to 5000Hz (100th harmonic). For aluminium, multiply the result by 1.24

skin effect depth in copper

As can be seen from this the depth at 50Hz is 9.3mm, therefore a conductor of up to ±20mm diameter will effectively have no skin effect issue. However, harmonics can be a problem. If we simply take the 3rd (150Hz, a strong component with hi-tech equipment) we'll see the depth reduces to 5.4mm. This makes any conductor larger than 11mm diameter susceptible to this harmonic. The 5th harmonic (usually the one associated most with SMPS units) starts affecting conductors of a mere 8.5mm diameter and more.

However, the depth of skin effect is not a sharply defined distance but rather a "grey line" at or about the distance indicated above. It is generally accepted that skin effect is not considered on conductors with diameter from less than and up to 3 times the skin effect depth at the frequency concerned.

One of the things that will probably have been noticed is I never made any reference to whether the conductor was solid or multi-strand. Contrary to popular belief (and I have met those who, like myself, have proved this), it makes no difference to the skin effect of the conductor as a whole if the individual strands can touch each other, as they do in a stranded conductor.

If, and only if each individual strand is insulated from the surrounding strands (which actually means each strand is insulated), will the skin effect then be relevant to each individual strand. But, there is another stipulation! The insulation has to be thicker than the skin effect depth.



400Hz FUNDAMENTAL

Through all of this we have been referencing to a 50Hz fundamental. What this page should also highlight is the issues surrounding higher fundamental frequencies such as 400Hz. This fundamental is equivalent to the 8th harmonic of 50Hz and thus starts at a skin depth of 3.3mm only as opposed to 9.3mm for 50Hz.

This is one of the primary reasons high-current switches designed for 50Hz should not be used in 400Hz applications. It's exactly the same as 50Hz gear being burned up through harmonics, except it is no longer a harmonic doing the damage, but the fundamental.

Contact area Is the primary issue as large contacts used on 50Hz switches are no longer suitable for the higher frequency fundamental. A contact of e.g. 10mmx10mm will only have the outer 3.3mm being used for conducting the current, the centre of the contact not doing any work at all.

A few switch operations and the outer area of the contact will be neatly burned, if not the whole switch having melted itself to destruction through heat build-up on the contacts and other elements that hold the contacts in place.

Wiring too is trickier as the maximum diameter for a cable on 400Hz is about 9mm i.e. 63mm² - and then one is stretching it a little! Cables upwards of 70mm² therefore need to be derated for 400Hz work.

With relays and other devices operating at higher frequencies, increasing the contact area, so as to increase the available workable surface area, increases the cost without a significant improvement in workable surface area. A more economical approach is to fit each active 'part' with multiple contacts (older post-office relays were a prime example of this as you would almost invariably find two, if not four contacts per relay contact).

However, I wish to not digress too far as this book is not about special power systems such as aircraft and the like, but more about the stuff each one of us uses on a daily basis. But, it has neatly led us in to the next issue we face in everyday power usage.

Issues with Noise  >>


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