Individually Screened Cable zero sequence impedance 2

Possibly some help here in Appendix B:

Thanks for your reply MKFPE,

The document you linked is a good resource but does not explain how to calculate the zero sequence mutual impedance of the screen for a cable with screens around each core, which is where I am getting stuck.

Refer equation 9 and 10 from the linked document. I don't understand what to use for the GMR of the sheath (ri and ro).

Surely this is a simple problem for experienced earthing engineers who must calculate the fault current splits of cable screens / ground regularly?


Andy

Andy,

Sorry I read your post quickly, not thoroughly.

Kersting's book "Distribution System Modeling and Analysis" covers calculation of impedances of concentric neutral cable. Cooper's "Distribution-System Protection Manual" does as well.

A Cooper sales engineer gave me a free copy of their book years ago, I don't know if they still do that. Kersting's book is one of the best investments any power engineer can make. The circuit matrix representations can be set up directly in Matlab or Freemat or Octave, or similar, essentially as outlined in the book, and by changing parameters for your specific problem, "job done".

I can't provide copies of the applicable pages due to copyright, but I hope this provides some direction: Calculate impedances by procedures given in these references, do sanity check by comparison with published tabular values such as in the Kerite Engineering Catalog (on-line), follow method in the NZCCPTS document to complete the calculation.

BTW, this is not a calculation that I recall having had to make, I am primarily a substation engineer, my power cable shields are open-circuited at the remote end and a separate neutral conductor is used. But the above is how I would proceed.

The following text originates from the BICC Electric Cables Handbook, Third Edition, pages 175-177. Refer to the calculations for SL type cable.

Zero sequence resistance
The zero sequence resistance of the conductors per phase is the a.c. resistance of one conductor at ambient temperature (normally 20°C) without the increase for proximity effect described in chapter 2. The increase for skin effect is included. To this value is
added the following as appropriate:
for 3-core cables:three times the resistance of the metallic covering;
for single-core cables:the resistance of the metallic covering;
for SL cables:
the resistance of one metallic sheath in parallel with three times the resistance of the armour.

The metallic covering for 3-core and single-core cables may be a metal sheath,armour or a copper wire and/or tape screen, whichever is the metallic layer which will carry earth fault current. If the cable has a metallic sheath and armour, the resistance of the metallic covering is the resistance at ambient temperature of the two components in parallel.
Some 3-core cables may contain interstitial conductors or copper wire screens on each core to carry earth fault currents. In general, where there is such a component for each core, it is the resistance of one of them which is considered. When the earthing component is a collective one, i.e. a common covering for all three cores, its resistance is multiplied by three. Where both types of earth current carrying components are present, the example given for the SL cable (three sheaths but only one armour) is followed. In effect the calculation is equivalent to determining the resistance of all the earth paths in parallel and multiplying by three for the resistance per phase.
The resistances are calculated from the cross-sectional areas and resistivities of the metallic layers. For a sheath the cross-sectional area can be calculated from the iameter and thickness. For wires, the resistance of a single wire may be divided by
the number of wires and a correction made for their lay length as applied. When wires re applied helically or in wave form, their individual lengths exceed the length of the cable by an amount depending upon the ratio of their lay length to their pitch diameter.
For example, armour wires applied with a lay of eight times their pitch diameter have a length approximately 7.4% greater than the length of the cable. Technical Data Applicable to Cable Planning and Usage 177
Zero sequence reactance
For single-core cables, the zero sequence reactance of the cable per phase can be calculated from the equation
X0 = 2 pi f × 10 -3 [0.21oge(D/d) + K] (Q/km) (10.6)
where X0 = zero sequence reactance
f = frequency (Hz)
D = mean diameter of metallic covering (mm)
d = conductor diameter (mm)
K = a constant depending on the conductor construction as in chapter 2,
equation (2.2)
The similarity between this and the combination of the equations for inductance and reactance in chapter 2 is evident. The value D, which amounts to twice the spacing from the conductor axis to the metallic covering, replaces the 2S where S is the axial spacing
between conductors in normal operation.
For a frequency of 50 Hz the equation simplifies to
X0 -- 0.31410.46 lOglo(D/d) + K] (Ohm/km) (10.7)
For a 3-core cable the equation is
Xo = 0.4341oglo(D/GMD) (Ohm/km) (10.8)
where GMD is the geometric mean diameter of the conductors in the laid-up cable. Conventionally, the value of GMD is taken as 0.75 of the diameter of the circle which circumscribes the conductors in the laid-up cores, assuming the conductors to be circular.
The equation for the 3-core cable is analogous with that for single-core cable, the value K now not being relevant and the 0.434 including multiplication by 3 for reactance per phase.


Regards
Marmite