Skin-effect losses in rectangular and round conductors

I freaking love my job.

This week, our professor emeritus came to me, asking me to do a simple verification simulation. A reader had spotted an error in his book, related to skin effect losses in slot-bound conductors.

Together, they had traced the error to the works of Richter in the early twentieth century. If you don’t know who Richter is, I won’t speak to you ever again. Anyways, Mr. R. had apparently referenced his own earlier work incorrectly.

Specifically, he’d claimed that the skin-effect losses in a circular slot-bound conductor are 50-something percent of the losses in a rectangular conductor of the same height. By contrast, his earlier work (and the supporting analytical calculations) had predicted 43 %.

An obviously huge difference (hope you understand sarcasm), but still an annoying little discrepancy.


Long story short, I was (t)asked to do a verification simulation. Just the kind of a single-slot-only case you see in the textbooks. Below is an actual output of the simulation script for rectangular conductors. You’ll find the corresponding one for round wires at the end of the post.

A textbook example with six rectangular conductors.

Now, of course something with a GUI would be the natural choice for such a simple problem, like the FEMM software for instance. However, I thought this would make a nice example, and opted for the colossal-overkill option, using my SMEKlib library for Matlab.

You can find the parametric simulation script here. It uses Matlab’s pdetool for mesh generation, so a relatively new version is required. If you are using an older version, you can skip the lines featuring the model object slot_model, and do the meshing with [p, e, t] = initmesh(slot_dl); instead.

But enough of the details. Let’s move on to the results.


The professor was right. 43 % seems to be the correct loss ratio. The simulations predicted something a little higher, in the order of 44-45 %. But, that difference can be attributed the non-ideality of the simulation compared to the assumptions of the analytical model.

The same problem with round conductors. Notice the singularities at the cusp nodes between conductors. Naah just a plotting error – the script on Pastebin has now been updated.

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