MotorCAD: Skin and Proximity Effect Losses in Stator Windings

In AC machines, such as electric motors and transformers, copper losses are divided into DC copper loss and AC copper loss. AC copper losses are dependent on the frequency and the magnetic flux density at the conductor's location squared, and they are divided into proximity effect and skin effect.

Proximity effect is typically higher among these two. Now, let's see how to approach them in MotorCAD. We will start with the skin effect and proximity effect calculation using an IPM machine, which is a parallel tooth motor with a hairpin winding.

Let's go to the calculation tab, define the operating point (6000 rpm, 250 rms), phase advance of 51 degrees, and a skewed rotor divided into three slices. We will only activate the torque calculation. Next, let's go to input data losses AC winding and define a full FEA analysis for all slots.

The Torque calculation will be more accurate, even though it will take a long amount of time. The idea is to calculate this to then calibrate the hybrid model, which is much faster.

Once the calculation is completed, we go to the output data tab and see that the AC loss is 846 watts, which is considerable in front of the DC copper loss. The total conductor loss will be the sum of these two. If we go to e-magnetics, we can see the loss distribution.

It's clear in watts per kg how the conductors that are closer to the rotor have higher losses. Now, let's calculate the DC loss. We will calibrate the hybrid FEA model, which is much faster.

We will select a hybrid FEA model, initially use an adjustment factor of 1, and leave the cuboid size as automatic. We will run the same analysis again, this time it will solve much faster. Now, we can see that the losses are divided into proximity and skin effect.

The total is a bit less than what we got with the full FEA. So, we must make a calculation dividing the losses we obtained from the full FEA to the losses we have just obtained, and the ratio of that is the adjustment factor.

Next, let's take a look at a similar motor but with stranded windings and a bit different tooth shape. This motor has two parallel pads and a single layer. We can see that the motor is fast. However, compared to the original, this motor has a thinner pad and a tail.

So, this motor is rather slow because of its limits than the previous one, which is very low. Now, if we go to DC guiding, we can see the DC is fast. The filament strength is high, and this is true.

So, if we change the value a little bit because this motor is not very high, the Democrats, of course, because of its inside best performance should be a J equation, which generates a satisfying confidence of a very high accuracy value that is very nice.

While running FEA AC conductor losses, the aspect ratio of 1 makes this conductor's arrangement to be sort of squared. Now, we put a bundle aspect ratio of 2. We can see that the conductors are arranged more leaning in a horizontal distribution.

This will have a lot of impact in the AC conductor losses. If we exaggerate this value and put a bundle aspect ratio of 5, we will see that now the conductors are almost completely horizontal.

So, now the approximate effect losses will be much higher than what you would get with a lower aspect ratio. Therefore, we need to make the aspect ratio realistic but also conservative.

A realistic value would be between 1 to 1. 5. A bit more conservative, meaning it would give probably higher losses than what you would obtain, is 2. Regarding the calculation, make sure you disable everything you don't need and only enable torque calculation at the specific operating point.

We will likely get an error if we calculate the FEA analysis for all slots because there are too many conductors. So, we will probably need to shift that to plot the loss distribution. We can see that the losses are mostly concentrated in the conductors near the rotor.

Now, let's solve the hybrid FEA model using the same bundle aspect ratio, the automatic default number of cuboids. The idea is to perform this calculation to calibrate it and then be able to calculate AC copper losses much faster.

In this case, we are getting 1209, which is much lower than what we got with the full FEA. So, the hybrid losses are adjusted with a 2.9 factor. Now, we will be able to perform FEA hybrid AC copper losses at different operating points much faster and very accurately.