`Winding losses in random-wound machines`

One of my journal articles has been steadily gaining reads on ResearchGate. Maybe it’s because of the new Tesla model coming out – this paper is somewhat relevant – maybe it’s for some other reason.

In this article, titled “Monte Carlo Analysis of Circulating Currents in Random-Wound Electrical Machines”, we analysed a specific type of power losses, highly relevant in many medium-size electrical motors. You can find the full post-print for free here, and the final (as soon as IEEE finishes their formatting) print here.

But maybe you’d prefer a shorter, more down-to-earth explanation. In that case, you have come to the right place.

### What are random-wound machines?

So let’s begin with random-wound machines. The term pretty much refers to machines that have coils wound from a large number of thin copper wires called strands. These strands are connected in parallel near the terminals of the machine. This way, the number of series-turns can be low enough, as can be the total coil resistances due to the large effective cross-section.

Below, you can see a small random-wound induction machine, autopsied open in my group. The red circle highlights a part of the winding, with lots of wires visible if you look closely.

And after looking closely, you can possibly guess the reasoning behind the name random. Indeed, it refers to the fact that with so many strands that thin, it’s pretty much impossible to exactly control where each of them ends up inside the machine. In other words, the locations of the strands are uncertain until you actually cut open the machine and see. Hence – random.

### What are circulating currents, then?

So, with the name of the machine properly explained, what are circulating currents? Remember how the strands – wires – ended up nobody exactly knows where? Well, this has more effects besides the academic lack of knowledge about them.

Namely, the position of each strand will influence its inductance – how large a voltage will be induced on it by a current of a certain magnitude. Likewise, the relative positions of any two strands will determine the mutual inductance between them. And the same of course goes for all the strands in the machine. And believe me, there are many.

Now, these inductances (along with the strand resistances) will, in turn, determine the currents flowing through them when the machine is switched on. And since the positions – and by extension the inductances – of all bazillion strands are uncertain, it is very unlikely that all of them would have the same inductance. Simply ain’t gonna happen.

Instead, the inductances will vary quite a bit from one parallel-connected strand to another. So, the ones with the lowest inductances will, of course, draw a disproportionally large part of the total current flowing in the coil.

This is precisely what we mean by circulating currents. Of course, in reality nothing circulates – it’s just the same current divided unequally between several parallel conductors. But, it kind of does look like we had an evenly-distributed current biased by some loop currents.

(By the way – you can read more here.)

So I guess that explains the name. I didn’t invent it.

### Why they matter

Anyway, since resistive losses are proportional to the square of the current, the total losses of the coil can be greatly increased. And this is precisely what happens regularly. For example, in many high-speed induction machines, the winding losses have as much as doubled. As you can probably guess, this is not a good thing.

And because of the uncertainty in the strand positions, analysing these circulating currents and the associated losses is far from simple. But that’s exactly what I have done.

How?

Read the next post to find out!

### P.S.

Wonder why I mentioned Tesla Motors in the opening paragraph? Well, it turn’s out that at least some of their models have what else but random-wound induction motors under the bonnet.