Zero sequence mutual impedance for underground cables 6

[eltekeng]

Hi to everyone. I have been searching for the zero sequence mutual impedance equation for underground cables for a while. I am aware that this equation exists for overhead cables but does it so also for the underground cables? If not, how can I reach a rational result from existing formulas?

For instances;

There is a system consists of 2 circuits which have 3-phase cables separately.

- Can I use the self impedance formula for each cable separately and then mutual impedance formula for 1 circuit and in the end mutual impedance formula for 2 circuits?

- Should I consider the images of the cables above the ground?

- I actually need three values;
. B/w cable - cable
. B/w cable - earth
. B/w conductor - sheath

Thanks in advance for you helps.

 

[redfurry]

Are you sure you mean 'zero sequence mutual impedance'?

By definition, sequence impedances do not have mutuals (unless you're talking about ugly cases where there are different impedance paths for different phases).

If you are referring to 'phase-ground mutual impedances', then for underground lines I believe you would normally consider the cable neutral (either concentric neutral or tape-shielded) to prevent any interaction between the phase conductors in one cable with any of the currents in the second cable. So these mutuals would be zero.

 

[davidbeach]

By definition two parallel lines have a full compliment of sequence mutual impedances. In general the only one of these sequence mutuals that is used for anything is the zero sequence mutual between the lines, but there are all possible combinations including between different sequences of the same line. If the line is fully transposed the mutuals between sequences of the same line are zero, and are generally very small if the line isn't fully transposed. Between lines the mutuals that involve either a positive or a negative sequence will be small and are also generally ignored. The mutual impedance between zero sequences is very important and should not be ignored.

For cables, the mutual impedances that involve either positive or negative sequence will be even smaller than for open lines as the three phases of a given line are much closer together.

The actual calculations for cable impedances seems to involve a bit of black magic and proprietary information. I'd refer the question to the cable manufacturer and see what kind of response you get from them.

 

[davidbeach]

One of the papers on the schedule at WPRC is Utility Experience with Zero-Sequence Mutual Coupling (Z_om) for parallel 230 kV Underground Lines. Might be worth attending if zero sequence mutuals of cables are of interest.

 

[eltekeng]

Hi again.. I know it has been very long time to write but I wanted to post my solution in order to help the next questions..

Firstly, I used Carson's equations to build the matrix system. My system was double circuit actually but there were 7 meters between the circuits so I neglected the second one. Otherwise the matrix would be 6x6. Now the matrix is 3x3.

After managing to build the matrix, It was easy to calculate the rest. There is a conversion from Zprimitive matrix into sequence impedance matrix using the A and A^(-1) matrices. After all the resulting matrix diagonal terms consists of zero, positive and negative sequence impedances..

I have listed most of the documents I used for my research.

Thanks for everyone who helped me..


1) S. Herraiz, J. Meléndez, V.A. Barrera, J. Sánchez, M. Castro, Estimation of Zero-Sequence Impedance of Undergrounds Cables for Single-Phase Fault Location in Distribution Systems with Electric Arc
2) Prof. Dr. Jim McCalley, Notes (

http://www.ee.iastate.edu/~jdm/ee455/ee455schedule.htm)

3) Westinghouse Electric Corporation, Electrical Transmission and Distribution Reference Book
4) William H. Kersting, Distribution System Modeling and Analysis
5) R. E. Fehr, Sequence Impedances of Transmission Lines
6) ELECTRA 283, Special Bonding Of High Voltage Power Cables
7) Fernando Calero, Mutual Impedance in Parallel Lines – Protective Relaying and Fault Location Considerations
8) Williarn A. Thue (editor), Electrical Power Cable Engineering

 

[Jennett]

This may be slightly off topic but is there a reason why OHL manufactures supply zero sequence data for their lines and cable manufacturers do not? Is it related to how underground cables are installed?

Does anyone know where I can access electrical data for OHL and underground cable at 11kV? Ideally positive, negative and zero sequence resistance, inductance and capacitance? The data I have is supplied by a utility and is incomplete.

Any help would be appreciated.

 

[Jennett]

EDIT: As per the suggestion of another post I've had a look at the Kerite cable manufacturers website. This is the data I'm looking for but unfortunately at the wrong voltage levels (US rather than UK). Does anyone know of an equivalent UK site?

 

[davidbeach]

I've never seen any manufacturer provided sequence impedance data for any cable used in OHL construction. They provide the information necessary to calculate the impedances, but that calculation depends on the line geometry. And, you'll likely never find negative sequence data.

 

[Jennett]

My original post was misleading. The utility provided zero sequence data for the OHL but not for underground cables. From David's post I guess this is because the OHL configuration is defined in the data sheet whereas the underground cable layout is not?

This seems to agree with Kerite engineering catalogue where the zero sequence data is given assuming the cable is laid in a triangular configuration: (pg 8)

http://www.kerite.com/pdf/Kerite Engineering Catalog.pdf

To return to the previous question does anyone know of an equivalent Kerite UK website that gives the zero sequence data based on how the cable is laid? Or can point me to an explanation of how to calculate zero sequence line resistance, inductive reactance and capacitive reactance based on how the cable is laid?

 

[radug]

IEC 60909-2:2008 has typical sequence impedance data for different elements including underground cables. It also gives equations for calculating sequence impedances of cables.
So I think you could use those equations to calculate your needed sequence impedances.

 

[Jennett]

Thanks radug. That's a useful standard. Anyone looking for this document it's available at:

https://bsol.bsigroup.com/en/Bsol-Item-Detail-Page/?pid=000000000030179166

 

[jghrist]

The Westinghouse T&D Reference Book (now ABB) has equations for sequence impedance of single circuit cables. It also has detailed methods of calculating sequence impedances, including mutuals, of other configurations. It can get quite complex and involves solving sets of voltage drop equations.