Phase Arrangement of Parallel Medium-Voltage Cables

[OSR]

TL;DR Summary

Phase Arrangement of Parallel Medium-Voltage Cables

Hi

If the length of parallel medium-voltage cable runs is approximately 20 meters, and cable sheath is grounded only at one end, does it matter how the parallel phases are installed on the cable rack? If the straightforward installation method doesn't follow the rule for arranging the phases on the rack correctly, is there any significance to it in terms of cable load capacity or any other aspect?"

 

[berkeman]

Can you link to those manufacturer recommendations?

How high is your "medium voltage"? Are you using a Delta 3-phase distribution? What are the cable specs? (insulation voltage, current spec, wire gague and thicknesses, etc.)

EDIT/ADD -- In the US, this might be dictated by the National Electric Code (NEC) -- I'll have to check my copy when I get your details above. I don't know if you have similar regulations to the US NEC in your country.

 

[DaveE]

I think the idea here is to achieve equal current sharing in parallel conductors considering the complete circuit (i.e. return currents). Sharing is sensitive to small impedance variations (inductance) since the conductors are in parallel (I think). So the preferred distribution you showed has the three phases grouped together into two symmetric groups to achieve balance. The other grouping you showed has a significant difference between an L1-L2 current vs. an L1-L3 current path. How much this actually matters would depend on your specific installation, of course. 20m doesn't seem that long to me, but I guess it could matter for very high currents.

Maybe ask google? This was one (the first appropriate) link I found, although not exactly your configuration:
https://www.researchgate.net/public...n_in_single-core_cables_connected_in_parallel

In any case, the cable manufacturer likely didn't invent that solution. You should be able to research it and find why they said what they said.

It's also not great for EMC for similar reasons (a bigger antenna loop).

Anyway, symmetry is good, minimum loop area is good.

 

[alan123hk]

In any case, the cable manufacturer likely didn't invent that solution. You should be able to research it and find why they said what they said.
It's also not great for EMC for similar reasons (a bigger antenna loop).

I agree, it has something to do with EMC, an electrician once told me that three phase transmission lines are triangular because the conductors are more closely spaced and the magnetic field strength is lower than when they are lined up. This also means that the transmission line has minimal inductance and produces minimal magnetic interference.
https://iopscience.iop.org/article/10.1088/1757-899X/791/1/012033/pdf

 

[OSR]

I work on a 20 kV substation project in which the existing parallel single core cables with a cross-sectional area of 800 mm² per phase should be doubled, meaning the rated current would increase from 2000 A to 4000 A. The existing cables are currently installed in a non-electromagnetically optimal manner. Externally, it seems that the cables have held up quite well. For this reason, I have been contemplating whether the optimal phase sequence really matters in short distances and what the underlying idea is.

Have I understood even aproximately correctly that when examining cables installed on the same level, where conductors of the same phase form a common bundle, it results in a stronger magnetic field intensity that penetrates the parallel conductors of the adjacent phase, forming a loop and thus inducing current into the loop? And ideally positioned cables, the magnetic fields would nearly cancel each other out, resulting in minimal induced loop current, is that correct? I attempted to illustrate this with the image below.

 

[alan123hk]

I majored in electronic and information engineering, and my understanding of large-scale power systems is very superficial, but some basic theories and concepts should be applicable to both small electronic systems and large-scale power systems.

I don't fully understand your diagram, but it reminds me of the proximity effect. I believe many people have heard that the skin effect causes current to flow concentratedly through the surface of a conductor, resulting in increased resistance and loss.

However, when current flows through multiple layers of wire in the same direction, a proximity effect occurs, further pushing the current to flow only on one side of the winding wire. This phenomenon will make losses much more severe than when single-wire skin effect is considered. The principle of proximity effect is not difficult to understand, but the calculation and evaluation methods are more complicated.

I personally think that the layout on the right side of the picture below will be better than the layout on the left side of the picture below in terms of EMC or Proximity effects.

https://en.wikipedia.org/wiki/Proximity_effect_(electromagnetism)
http://www.e-magnetica.pl/doku.php/proximity_effect
Quote from the link above : -
Proximity effect can be several orders of magnitude greater than skin effect.
The effect is also important at power frequency (50 or 60 Hz) in thick conductors such as three-phase busbars. Skin effect alone limits thickness of busbars to below 10 mm, and parallel connection of closely positioned conductors leads to significant increase in power loss. In the worst case the power loss can increase faster than the effective cross-sectional area, which is a particular problem for busbars operating at very high currents (>1kA).9)

 

[OSR]

What I meant with my image in the previous message is that, in my opinion, a bundle of conductors of the same phase generates a larger magnetic field around the conductor bundle than an individual subconductor. This magnetic flux then passes through, for example, the loop formed by the L2 phase conductors. If the L1 phase is distributed on both sides of the L2 phase, then, in my opinion, the magnetic fields passing through the loop L2 phase conductor bundle would be in different directions, and one could think that no current would be induced in the L2 loop by its parallel conductors. The current flowing in the loop can cause heat, which would lead to a greater imbalance in impedances. It is possible that my theory is incorrect.

The proximity effect you mentioned could be at least a contributing factor to what causes the imbalance in parallel conductors. On the other hand, one could consider that this proximity effect affects each conductor pair in the same way, so the current imbalances between phases would be zero, even though there might be more losses in the conductors as a result of this. I could perhaps try to make a simple simulation and study how these aforementioned theories are reflected in it."

 

[Babadag]

First, I am not sure, I understood well your problem. You have 2 single core cables per phase, of 800 mm^2 copper conductor XLPE insulated [20 kV] each, for 4000 A.
If the cables run in a rack at a distance of minimum one cable overall diameter, maximum current per one cable, up to 90oC, will be only 1700 A. [my calculation, of course].
The problem of current imbalance is that one cable may be overloaded and so the conductor temperature may be over 90oC.
Since the load is close to the top, any current imbalance can get worse.

 

[OSR]

First, I am not sure, I understood well your problem. You have 2 single core cables per phase, of 800 mm^2 copper conductor XLPE insulated [20 kV] each, for 4000 A.
If the cables run in a rack at a distance of minimum one cable overall diameter, maximum current per one cable, up to 90oC, will be only 1700 A. [my calculation, of course].
The problem of current imbalance is that one cable may be overloaded and so the conductor temperature may be over 90oC.
Since the load is close to the top, any current imbalance can get worse.

Currently, at the substation, the cabling is done with two single-core cables per phase. The distance between the cables is approximately 50 mm. The cable type is AHXCMK 1 x 800, i think it's XLPE insulated. The cables are mounted on a rack in an outdoor area with good ventilation, and the ambient temperature typically stays just above 20°C. The phases are arranged as follows.

With the current setup, the current capacity is defined as 2000 A per phase, according to the main diagram.
Now, the plan is to increase the capacity from 2000 A to 4000 A by doubling the number of cables, meaning 4x1x800mm^2 per phase. The current consideration is whether the phase sequence is essential for short cable runs and what the reasons are for a particular phase sequence and which phenomena influence it. Such AHXCMK 1 x 800 cable is relatively rigid, and for ease of installation, it might be easier to install the cable in a way that is not electromagnetically optimal. This way, the previous cabling wouldn't need to be dismantled and rearranged. What kind of calculations did you make about the load capacity of the cable?

 

[alan123hk]

Proximity Effect Simulation

https://quickfield.com/

 

[Babadag]

So, this cable conductor is waterproof, round aluminium rope and it is not copper.
Calculated, according IEC 60287-2 [and -1], at 30oC air -no wind, no sun-current capacity is 1279A per cable, and you have 4 cables in parallel per one phase. If distance is 128 mm centre-line to centre-line for 20 m length the unbalance is negligible. If the cables are in touch-no clearance between cables- the arrangement is very important in order to decrease the unbalance.
If you will follow the cable arrangement as per fig.10, the unbalance will be the minimum, also.
See-for instance:
A CABLE CONFIGURATION TECHNIQUE FOR THE BALANCE OF CURRENT IN PARALLEL CABLES DISTRIBUTION by San-Yi Lee
https://files.engineering.com/downl...9b3b03d12&file=Balance_in_parallel_cables.pdf

 

[Babadag]

That's the part that looks like your case

 

[OSR]

Proximity Effect Simulation

https://quickfield.com/

This program looks interesting, perhaps a bit similar in style to Ansoft Maxwell, which I've used a bit. I'll have to try how cable resistance changes in my case due to the proximity effect.

So, this cable conductor is waterproof, round aluminium rope and it is not copper.
Calculated, according IEC 60287-2 [and -1], at 30oC air -no wind, no sun-current capacity is 1279A per cable, and you have 4 cables in parallel per one phase. If distance is 128 mm centre-line to centre-line for 20 m length the unbalance is negligible. If the cables are in touch-no clearance between cables- the arrangement is very important in order to decrease the unbalance.
If you will follow the cable arrangement as per fig.10, the unbalance will be the minimum, also.
See-for instance:
A CABLE CONFIGURATION TECHNIQUE FOR THE BALANCE OF CURRENT IN PARALLEL CABLES DISTRIBUTION by San-Yi Lee
https://files.engineering.com/downl...9b3b03d12&file=Balance_in_parallel_cables.pdf

Ok, I will have a look of that document, seems to contain relevant information for this case.

 

[Babadag]

Skin effect and proximity effect it can be calculated according to IEC 60287-1-1 2.1.2 Skin effect factor ys and 2.1.4 Proximity effect factor yp for three-core cables and for three single-core cables

 

[OSR]

I made a simple current density simulation with Ansoft Maxwell, as there was an issue with the element limit in QuickField student version. In the image below, on the left, is the arrangement as per the 'balance of parallel cables' document, and on the right is a more unbalanced situation in terms of current distribution by default. Both have three different scenarios with a 120-degree phase shift. By comparing the results, it is clear that the left-side cable layout is balanced in terms of sub conductor current density, compared to the situation on the right. However, it remains somewhat unclear to me that the 'balance of parallel cables' document mentions that equations (1) and (2) do not include skin and proximity effects., yet the equations contain variables that define factors such as the distance between conductors. Thus, it remains unclear which phenomenon affects current distribution if it’s not proximity effect. In any case, the installation method according to fig.10 of the 'balance of parallel cables' document is beneficial for this substation project. In this way, the old installation can be preserved, and a mirrored second set of cables can be added alongside.

 

[alan123hk]

Thus, it remains unclear which phenomenon affects current distribution if it’s not proximity effect

I haven't fully understood the details of San-Yi Lee's article, but I believe the reason for the uneven current flow in different wires of the same phase is the mutual impedance mentioned in the article. For example, it can be seen from Figure 1 in the article that the position distribution of all conductors belonging to the same phase or out of phase is completely asymmetric in space, so the mutual inductance between them is completely irregular, and the mutual impedance is actually caused by the mutual inductance.

In my opinion, if the current within the same wire accumulates on the left or right side, it should be classified as proximity effect. If you add the effects of skin effect and proximity effect, the overall situation may be more serious than mutual impedance alone. Fortunately, a good simulation software should comprehensively display the results including all factors.

I'm not sure about the exact arrangement in your simulation, can you tell me?
is that so?
Left
AABBCC CCBBAA
AABBCC CCBBAA

Right
AABBCC AABBCC
AABBCC AABBCC

Reference https://www.faculty.ece.vt.edu/kekatos/pdsa/Lecture4.pdf

 

[OSR]

I haven't fully understood the details of San-Yi Lee's article, but I believe the reason for the uneven current flow in different wires of the same phase is the mutual impedance mentioned in the article. For example, it can be seen from Figure 1 in the article that the position distribution of all conductors belonging to the same phase or out of phase is completely asymmetric in space, so the mutual inductance between them is completely irregular, and the mutual impedance is actually caused by the mutual inductance.

In my opinion, if the current within the same wire accumulates on the left or right side, it should be classified as proximity effect. If you add the effects of skin effect and proximity effect, the overall situation may be more serious than mutual impedance alone. Fortunately, a good simulation software should comprehensively display the results including all factors.

I'm not sure about the exact arrangement in your simulation, can you tell me?
is that so?
Left
AABBCC CCBBAA
AABBCC CCBBAA

Right
AABBCC AABBCC
AABBCC AABBCC

Reference https://www.faculty.ece.vt.edu/kekatos/pdsa/Lecture4.pdf

If you look that image closely there is letters for cable arrangement. There is four single core cables per phase. Current was 4000 A total per phase.

Left side:
ABCCBA
ABCCBA

Right side:
AABBCC
AABBCC

I think that my simulation model probably doesn't involve mutual impedance at all; instead, the currents are likely distributed based on their current phase angles and possibly due to proximity effects and, possibly, skin effect. There is some impedance matrix option in Maxwell, but i don't know how to use it correctly. Based on visual inspection, the results on the left side do appear significantly more symmetric. Indeed, the mutual inductance influenced by the magnetic fields of adjacent conductors is likely the reason for current distribution,as mentioned in the document, without taking into account proximity and skin effects. My English skills are somewhat limited, so I may miss some points.