`What are eddy and circulating currents, and why they matter`

If you have any experience in electromagnetism, you have certainly heard the term skin effect. If you work on power supplies or inductors, you may have heard of proximity effect. And if you are me, or high-speed machines happen to be your business, you probably know about circulating currents.

But what are they, really?

EDIT: For a more thorough (and arguably better) explanation, read Pavel’s awesome article here.

### Skin effect

Both the skin and proximity effect fall under an umbrella term called eddy currents. In other words, currents induced inside a conductor. But tet’s start with the easier one: skin effect.

You probably know the prototypical example of a long circular conductor in empty space. When fed with high-frequency sinusoidal voltage, the current density inside the conductor gets crowded towards its surface.

Like illustrated below.

We have the old fella Lenz to thank for this phenomenon. The alternating current in the conductor of course creates an alternating magnetic field. And as the power of Lenz compels, this alternating field creates an induced electric field. This electric field then of course influences the current density in the conductor. After all, the total electric field is what’s driving the current in the first place.

Simple as that. Well, the principle is. In practice, the change in the current density also changes the magnetic field, and so on and so on. So, for an exact solution, everything has to be solved together at once. But the basic principle still stands.

So, that’s skin effect. But what about the proximity effect then?

### Proximity effect

Also the proximity effect is related to a time-varying magnetic field, excited by a time-varying current. Only the location of this current differs.

With skin effect, the field responsible for the current crowding is excited by the current in the conductor itself. By contrast, with proximity effect some nearby conductors are to blame. They are generating the time-varying magnetic field, that then influences the current density via the induced electric field. Indeed, the name of the phenomenon suggests exactly that – something in the proximity causing the current to be focused in some parts of the conductor.

A simple example is illustrated in the figure below.

The four conductors in the bundle are all carrying the same net AC current to the same direction. For a single conductor, the current density would follow the skin effect pattern shown earlier. But, now that we have four conductors instead, most of the current is packed into the red segments, as far from the bundle axis as possible.

### Skin and proximity effect in electrical machines

Both phenomena can often look somewhat different in electrical machines and other magnetic components. After all, they rarely consist of conductors floating alone in the vacuum. Or even conductor bundles in a vacuum, for that matter.

Instead, they often place their conductors inside slots in iron. This will of course change the pattern of the flux, and correspondingly the current density. Also in this case, a figure is worth a thousand words, and most electrical engineers are certainly familiar with the figure below.

The shaded rectangle is the conductor, and the roughly U-shaped black line denotes the slot. The dotted line is then of course the flux, driving the red current density towards the slot opening.

The same slot-example can also illustrate the proximity effect. Just split the one huge conductor into several small ones, and connect them all in series. The figure below illustrates this.

The pattern of the flux is still quite similar, although not exactly the same. All the small conductors carry the same total current alright. But inside each of them, the current density is crowded towards their middle line, rather than the slot opening.

#### What’s the difference?

So you might be asking “What makes this latter case different?” And you’d be right to do so – skin and proximity effects are very much similar.

Indeed, it’s often difficult to find a pure example of either. The single-conductor example is purely skin-effect, yes, and you might find such a situation inside the rotor bar of an induction machine. But pure proximity effect is much rarer.

For instance, if you closely consider the multi-conductor example above, you realize it’s actually a mix of skin- and proximity-effects. Think of any conductor, and the current crowding happening inside it. This is crowding is caused by the alternating magnetic field, and this field is partly caused by the conductor itself. So that’s skin effect. But of course, most of the field is due to the other tens of conductors nearby – so proximity effect there.

So simply put: the more conductors there are close by, the more proximity-dominant the eddy currents tend to be.

But now, something completely different.

### Circulating currents

Circulating currents are the first cousin of eddy currents. Remember, the latter basically referred to an un-even current density inside a conductor. By contrast, with circulating currents everything happens between conductors.

Let’s say we have two conductors in parallel, both with different impedances. If we connect both conductors to a voltage source, one of them will of course draw a higher current. So we have two different currents.

On the other hand: we could just as well say we have an average current going through both conductors, and then a circulating current looping between them. Like below.

Unsurprisingly, this is indeed why the phenomenon has the name it has. Any time we have two or more parallel conductors, we can decompose their currents into the average one, plus a number of circulating terms. These are purely mathematical concepts, mind you. In reality, we have the conductor currents and that’s it.

### Why they matter

Both eddy and circulating currents increase power losses. It’s simple. Resistive losses are proportional to the square of the current (density), so of course having a uniform current everywhere is optimum. Move some current from this point to that, and the losses will increase.

And that obviously decreases the efficiency.

Boooring. That’s what efficiency is, in my honest personal opinion. At least when considered in isolation. Electrical machines are already quite darn efficient. Pushing the number from 90 to 95 per cent won’t have that much of an effect on the total energy consumption. So you won’t really see it on your electricity bill, or the range of your Tesla. I’ve already briefly written about this.

However, eddy- and circulating current losses are losses. Losses mean heat, and that heat you’ll have to dissipate somewhere that’s not in the motor. Power electronics people get that, and folks designing high-performance motors have to get it. Cut the resistive losses by 33 %, and you’ve instantly relaxed the cooling demands by one third (at least for the winding part; other losses matter too of course). Or the other way round, increased the permissible overload time (like accelerating a vehicle hard) by a corresponding amount.

### Conclusion

So, today’s lesson briefly:

• Skin effect: uneven current density inside a conductor, caused by the conductor itself.
• Proximity effect: uneven current density inside a conductor, caused by other nearby conductors.
• Circulating currents: uneven distribution of total current between conductors in parallel.

And they all matter because

• You can make your machines more awesome when you don’t ignore them.

Have anything to add? Hit the comment box below!

-Antti

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What are Skin and Proximity Effect, or Circulating Currents

### 4 thoughts on “What are Skin and Proximity Effect, or Circulating Currents”

• Pavel says:

Hi,
I kind of feel that the second figure in “Skin and proximity effect in electrical machines” is not representative for proximity effect. From the figure it is clearly seen that skin effect within a slot dominates each separate conductor, whereas proximity effect (where current density tends to be further from the neighbouring conductors) is not possible to notice in this figure. I tried to think about it from the standards point of view some time ago here https://doi.org/10.13140/RG.2.1.2081.9368 . My conclusion at that time was that “proximity effect” (according to standards and to your definition) in electrical machines with iron cores is negligible.
BR, Pavel

1. Hi Pavel, and thanks for the great comment!

You are indeed right; I’ve changed the current density now to correspond roughly to the transformer problem of Dowell. It’s probably fully representative of electrical machines, but it might be the least bad choice nevertheless.

And thanks for the paper link too! I definitely agree about the division between skin and proximity effects being somewhat arbitrary, and people using the terms in a confused manner. My idea was to bring some clarity to the situation with this post, but it seems that I only ended up doing this:
https://xkcd.com/927/
Well, it’s been a learning experience 😀

• Pavel says:

And also what to do with PM induced fields – those fields can cause current distributions close to what is depicted in the the second figure in “Skin and proximity effect in electrical machines”. But it is hardly related to the standard definition of the proximity effect.

1. Yeah I know the phenomenon – it seems that nobody bothered to come up with a unique name for it.