Obscure Cable Geometry Question: ABB T&D Book, Geometric Factor

[brainsalad]

Hello,

My problem is to determine the shunt capacitive reactance of a 3/C, 500MCM, non-shielded, 5kV cable...

This question is mostly for those familiar with the ABB/Westinghouse T&D Book, Chapter 4, Electrical characteristics of cables, or those familiar with cable geometry.

The cable geometric factor "G" I have seen cited as G = 2.303*log_10(2*r_i/d) where r_i = inner sheath radius and d = conductor diameter.

Does anyone know how this is derived? This appears in the T&D book with little derivation.

Can anyone say if this is also the same formula used for 3/C cables as well (see Figure 10 of this chapter)?

Thanks for your help.

 

[magoo2]

This equation was derived from Gauss's law in which you integrate the electric field over a closed surface. The geometry applicable for this equation is a coaxial conductor. For this reason, the equation applies for a shielded conductor and not for an unshielded one.

I'm looking at my copy of the Westinghouse T&D book and the curves for 3-conductor cables are based on shielded cable also.

 

[Marmite]

The attached may be of use. Section 2.7.
Regards
Marmite

 

[melec]

I am also having a similar problem to brainsalad.

It seems that the values given on figure 10 (Westinghouse, page 36) are valid for 60Hz frequency.

Would anyone have an equivalent table which can be used for the calculation of GMR in applications where the frequecy is 50Hz?

Many thanks.

 

[brainsalad]

Thanks all. I learned that the formula for the geometric factor curves (for zero sequence capacitance) in Chapter 4, Figure 9 of T&D are from Simons, Cable Geometry and the Calculation of Current Carrying Capacity, IEEE, 1923.

My cable is unshielded but using the cable model of Figure 9 should be conservative for calculating shunt capacitance.