Skin Effect 1

[Clyde38]

I’m looking for some help with respect to skin effect. On a PM synchronous motor, the windings are subjected to the rotational frequency from the PM rotor and to PWM frequency that is driving the motor. I feel that the fundamental frequency of the rotor is the main contributing factor to skin effect however, I have colleagues that feel that the main contributing factor is the PWM frequency. Any help would be appreciated.

Clyde Hancock
Design & analysis of electric motors and generators

http://www.motorconsultants.com

 

[Gr8blu]

Skin effect occurs when trying to pass a high-frequency waveform along a conductor that has an inductive component (i.e. multiple turns or a "twisted/braided" conductor construction, such as a cable). So to answer your question: is the PWM switching frequency associated with the current waveform you're trying to pass through the winding higher than some other frequency which might distort the current waveform in the stator winding?

For a PM synchronous machine:
Slip frequency = (sync rpm - actual rpm) = 0
Pole pass frequency = (# poles) x (slip frequency) = 0
Winding slot pass frequency = (# stator slots) x (rpm) = ??
Rotor "bar" pass frequency = (# "bars") x (rpm)

Typical switching frequencies of PWM drives are in the 2-10 kHz range, with most industrial usage at 3-5 kHz. Also recall that magnetic field strength (and hence the amount of distortion introduced) is inversely proportional to the air gap length - which can be fairly large for a PM design.



Converting energy to motion for more than half a century

 

[waross]

Skin effect is related to frequency and current.
Higher current and or higher frequency will cause greater skin effect.
Skin effect will increase the effective resistance of the windings.
This will be considered in the design of the motor.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

 

[onatirec]

Skin effect occurs when trying to pass a high-frequency waveform along a conductor that has an inductive component (i.e. multiple turns or a "twisted/braided" conductor construction, such as a cable)

I have to disagree about the skin effect being due to multiple turns or braids, but it is fundamentally due to magnetic induction in single wire strands and creation of Eddy currents therein.

Op I think this is a very interesting question. I can say that we ignore pwm frequencies when thinking about skin effect in copper. Pwm frequencies are often times an order of magnitude or more higher than electrical commutation frequencies, e.g. many of our motors might commutate at 3-400Hz, and we don't consider significant impacts from skin effects in the copper (there are also skin effects even in the steel once you start approaching these frequencies). We generally switch our inverters at 8kHz. This would drive significant skin effect increases in resistance. If we were to consider the pwm as being dominant, we would have to treat the machine resistance as much higher than that measured offline, even at low commutation frequencies. Frankly I just don't see this result in real world testing.

I will think more about why this might be the case and run some tests at different switching frequencies next week. I'm guessing the harmonic content from the pwm (which if you measure it, is not constant at the switching frequency, but fans out depending on commutation speed and rotor poles) has much lower amplitude than the fundamental commutation frequency, and therefore by superposition adds very little to the skin effect in the wire.

There are of course increased losses in the inverter when increasing pwm frequency.

 

[bacon4life]

Skin effect is related to current, so the applied voltage waveform is only relevant in so far as it affects the the current, (and the creation of any current harmonics). The inductive component of the motor smooths out the high frequency PWM voltage into a lower frequency current.

As a crazy example of skin effect on single conductors, an 8 inch diameter aluminum pipe bus has nearly the same AC resistance as a solid 8 inch diameter rod.

 

[dpc]

Skin effect is directly related to frequency, so a PWM output is going to present a variety of frequencies and effective impedances. The higher frequency components will see a higher impedance. There's skin effect in a single straight conductor due to the internal magnetic field creating higher reactance closer to the center of the conductor. It also slightly increases the effective ac resistance since the current is not equally distributed.

In practice, I don't know the specific impact in the motor winding, but there are a lot of motors running on AFDs, so I would imagine there is information available in IEEE papers, if you can conjure up the correct search terms.

 

[waross]

As a crazy example of skin effect on single conductors, an 8 inch diameter aluminum pipe bus has nearly the same AC resistance as a solid 8 inch diameter rod.

When carrying rated current.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

 

[onatirec]

I don't think the inductance of the machine truncates the high frequency current ripples from the pwm switching. If you stick an accelerometer on a motor, you will see vibrations centered around the pwm frequency, fanning out at odd harmonics of the electrical commutation frequency. These are fundamentally e/m excitations which must come from high frequency ripples in the convolution of rotor and armature fluxes, i.e. driven by high frequency ripples in the armature current.

There is a paper here that discusses skin effect and proximity losses due to pwm switching frequencies:

https://eprints.whiterose.ac.uk/9077/1/Zhu_Influence.pdf

I suppose my position is still that the relatively lower magnitude of the higher frequency (pwm) content "mitigates" the impact on losses as compared to having the fundamental electrical commutation as high as the pwm frequency. But they both have an effect.

 

[bacon4life]

Waross- What do you mean by mentioning rated current? My understanding is the ratio of AC versus DC resistance for an all aluminum conductor is not impacted by the current actually flowing.

(I will note that the opposite is true for single layer ACSR cables since the aluminum wires are wrapped around a steel core. This creates an iron core inductor, which changes impedance as the iron core wire saturates at higher currents. The saturation effect is largely mitigated in multilayer ACSR since the aluminum layers are wrapped in opposite directions.)

onatirec-It would have been interesting if the paper had also shown estimate of losses just based frequency spectrum of the current waveform.

 

[Clyde38]

I will think more about why this might be the case and run some tests at different switching frequencies next week. I'm guessing the harmonic content from the pwm (which if you measure it, is not constant at the switching frequency, but fans out depending on commutation speed and rotor poles) has much lower amplitude than the fundamental commutation frequency, and therefore by superposition adds very little to the skin effect in the wire.

Have you run any testing?

Clyde Hancock
Design & analysis of electric motors and generators

http://www.motorconsultants.com

 

[onatirec]

I did run a quick, crude test on a motor we had mounted on the dyno. Frankly, I could not make sense of the results at the time and shelved it. Maybe I can revisit it with a better approach.

What I did is spin the (smallish ~11kW) motor up to 3000rpm with a load of about 7Nm, held it there and changed the switching frequency across our max range from 16k to 8k, 4k, 2k, and 1kHz, writing data at each point. All done in about 30s. I was hoping to see motor voltage decreasing with switching frequency, which, at the same speed and current, might suggest that resistance is falling since there is a resistive drop in available voltage. In fact I saw motor voltage increase with decreasing switching frequency, and for some reason the current angle drifted towards the d-axis - which shouldve itself pushed the motor voltage downward. I should probably talk to our inverter/controls guys about what factors I'm overlooking.

 

[waross]

Skin effect is related to current, both the magnitude of the current and the rate of change of the current.
The rate of change of the current is affected by the induction of the circuit.
Even a straight conductor has some self induction and hence some skin effect.
However, in a motor, the induction of the motor winding will limit the rate of change of the current and thus limit the skin effect.
So, the skin effect may be much less than you may expect.
That said, I was once responsible for a 480 Volt, 600 KVA diesel generator that was wound with parallel flat copper strips rather than round conductors to limit eddy currents in the conductors.
When the winding was inadvertently destroyed, the machine was re-wound with conventional round conductors with no noticeable change in performance.
The unit was not instrumented, but was often run at near 80% of full capacity.
The unit was in a generating plant and when the load exceeded about 80% to 85% another set would be added to the lineup.

Anecdote Alert;
How was the winding destroyed?
It started with hurricane Mitch.
Mitch hit our station five times in five days.
Mitch tore the roof off of the station and dumped sea water on our sets.
All of our sets were saturated with sea water.
After reclaiming one set, we decided to send the other four sets up to Miami to be flushed, dipped and baked.
The 600 KVA generator end was being returned to us by sea in an old freighter.
The unit was packed in a wooden crate.
The crew put the lifting slings around the ends of the wooded crate.
The generator end did not extend to the ends of the crate and broke through and dropped back into the hold of the old freighter.
The flat copped windings broke through the insulation and shorted to ground.
The unit was shipped back to Miami where it was stripped and rewound with conventional round conductors.


--------------------
Ohm's law
Not just a good idea;
It's the LAW!