Zero sequence mutual impedance for underground cables
Zero sequence mutual impedance for underground cables
(OP)
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.
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.






RE: Zero sequence mutual impedance for underground cables
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.
RE: Zero sequence mutual impedance for underground cables
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.
RE: Zero sequence mutual impedance for underground cables
RE: Zero sequence mutual impedance for underground cables
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
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
RE: Zero sequence mutual impedance for underground cables
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.
RE: Zero sequence mutual impedance for underground cables
RE: Zero sequence mutual impedance for underground cables
RE: Zero sequence mutual impedance for underground cables
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
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?
RE: Zero sequence mutual impedance for underground cables
So I think you could use those equations to calculate your needed sequence impedances.
RE: Zero sequence mutual impedance for underground cables
RE: Zero sequence mutual impedance for underground cables