Skin effect and proximity effect calculations for three-phase motor power cables 724A 600Hz

A

aledam

Member
Location
Denmark
Occupation
Electrical Engineer
Hello everyone,

I have been struggling a lot in calculating the consequences of skin and proximity effects of power cables for our motor. As mentioned in the title, the motor runs up to 600HZ and 724A. It can reach 700Hz by applying field weakening, but the amperage is lower at that frequency.

We are planning to use four multi-core cables in parallel, each of them with three phases + earth. I would expect to use either 95mmSQ or 120mmSQ of cables. This means that each cable should carry 181A. I am aware of the deratings due to the ambient temperature, but I am really struggling to find tables for the derating factors caused by the high frequency.

Each of these multi-core cables is approximately 3 meters long. In this length:
- 0.7meters are stripped to allow the connection to the sine-wave filter. The ambient temperature can reach 45-50 degrees Celsius, ventilated.
- 2.3meters are NOT stripped, in an environment that can reach 55 degrees Celsius, ventilated.

By stripped, I mean that the four cores (three phases + ground) are spread to attach them to the terminal of the filter. Each core still has its own isolation, but we are missing the external isolation that would group the cores together.

How can I calculate the derating due to skin and proximity effect?
Would the short length have a positive impact on the ampacity of the cable? Almost 25% of the cable is stripped, with a better heat dissipation. Would this stripped portion act as a "heat sink"?

Thank you all for the replies!
 
tom baker said:
I’ll approve this but it’s a unique question and may not generate many answers on a NEC forum
Click to expand...
Thank you for the approval. I am really running out of options. None of the cable suppliers that I have contacted want to run this analysis. All I can have is just an approximation. I have applied the formulas for IEC 60287-1-1, but I do not have all the data. I have managed to calculate the variation of the AC resistance. Thus now I am comparing the AC resistance between 50Hz and 600Hz and calculate a possible derating based on that. I already know the ampacity at 50Hz. From the AC resistance at 50Hz, I can calculate the Joule losses. Then I calculate the AC resistance at 600Hz and the current that would match the same Joule losses that I have obtained at 50Hz. However, this approach seems to me very "amatorial".

I would really like to know if the very short length of the cable, and the stripped portion, can have a positive impact on that.
 
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aledam said:
Thus now I am comparing the AC resistance between 50Hz and 600Hz and calculate a possible derating based on that. I already know the ampacity at 50Hz. From the AC resistance at 50Hz, I can calculate the Joule losses. Then I calculate the AC resistance at 600Hz and the current that would match the same Joule losses that I have obtained at 50Hz. However, this approach seems to me very "amatorial".

I would really like to know if the very short length of the cable, and the stripped portion, can have a positive impact on that.
Click to expand...

The approach you are taking (matching Joule losses in the application to the Joule losses in the normal rating case) is the approximation that I would use.

Rough hand waving I expect your resistance to roughly double at 600 Hz in 120mm^2 conductors; does that match your calculations?

There will be some thermal conductivity from the center of the cables to the ends, but this is generally ignored in US ampacity calculations. IMHO it is conservative to ignore this. Basically because heat is carried away by the terminations the cable should run cooler than you'd expect, but you shouldn't waste time trying to figure this out because you don't save very much by making the cables a bit smaller.

Your goal here should not be trying to calculate the exact minimum cable size you can get away with; the over-all system sounds very expensive and these cables are very short, so the savings using 95mm2 rather than 120mm2 is next to nothing. (For the US folk: say you are _certain_ that 4/0 conductors work, but maybe if you spend a day doing calculations you think you can demonstrate that 2/0 conductors are fine. The cable run is 10 feet long and the terminations fit 4/0. Do you spend the time doing the calculation to use the smaller wire?)

My biggest concern in this application is making sure that the current divides evenly between the parallel cables, rather than assuming this will be the case.

-Jonathan
 
Is this a prototype for different installations?

If so, I would calculate as best as you can and pick a cable size. Then measure the voltage drop and cable temp and see what you get. Then adjust the cable size as necessary.

For initial calcs, there are online proximity calculators. And skin effect is just basic AC circuit theory. You just need to know the Z and R of the cable.
 
For the best answer for skin and proximity effect -- it is best to model the system with Ansys, Quickfield, Maxwell, or similar finite element analysis (FEA) electric and magnetic field software .
I do a lot of 360 to 800 Hz power distrubution analysis and also need to build custom transformers into the hundreds of kHz ranges.

Once you build a physical model, the FEA programs will spit out the impedances, etc.
Here is an example of skin and proximity effects of a thin foil transformer winding at a few hundred kHz showing that current crowding even goes to teh edges of foil windings.

1752541896812.png
Have fun!
 
In order to calculate the current carrying capacity [ampacity] of the assembly some details are required:
1-the cable conductor is circular or sectorial and the grounding conductor is the same as live conductors.
2-are conduits enclosing the cables and are they exposed to sun
A sketch of the assemble would be useful.
 
It could be a temperature decrease at the 2.3 m cable run ends but on the middle point the temperature has to be elevated. In my opinion 3 parallel cables of 4*185 mm^2 copper XLPE insulated, and PVC jacketed will do the job [ calculated as per IEC 60287-2-1 and 1-1 of course]
 
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