How to calculate cable inductance and capacitance parameters

[tiftif]

Based on this file from ABB, We can get the capacitance and inductance parameters of a cable

https://library.e.abb.com/public/321b7c021cb73fefc1257a40004c237c/2012 XLPE Users Guide_USA.pdf

I'm confused.
- Per page 21
C = Er/59/ln(r0/ri) = 2.5/59/ln(r0/ri); ro seems straight forward from Table 19 column 6 i.e. 2.14, 2.32, ..etc. How to compute ri to get 0.069, 0.079, etc? What is ri value?

- Same for inductance
L = 0.0152+ 0.061*ln(K.S/rc) mH/1000feet;
What is the arrangement in Table 19 to get the inductance? look to columns 11 & 12, What is S spacing factor used here and how the values in 0.224 & 0.122 determined in column 12 [mH/1000feet] without S value?

 

[7anoter4]

I verified only 1000 MCM 69 kV cable from page 19[Table 19]
conductor diameter 1.059” insulation thick.0.354” insulated core diameter 1.88”
C= 2.5/59/ln(ro/ri) where :
ro = external radius of the insulation (inches)=1.88/2=0.94 inches
ri= radius of conductor, including shield (inches)
for conductor shield see page 17.
Since the conductor shield thickness it is not shown in Table we have to calculate it.
The insulated core diameter is 1.88 the insulation is 0.354 then
ri=(1.88-2*0.354)/2=0.586 inches
C= 2.5/59/ln(0.94/0.586)=0.897 microF/1000 ft.
For inductance calculation- as I calculated it- the arrangement it is as shown[triangle or flat]without any space between.
L=0.0152+0.061*LN(K*s/rc) for triangle K=1 s=2.5 inches[overall cable diameter] rc=1.059/2=0.5295
L=0.0152+0.061*LN(1*2.5/0.5295)=0.1099 mH/1000 ft.

 

[tiftif]

Thank you &anoter4 very much.
For flat using 1.26, I get 0.124 this is far from 0.202. What I am missing
L=0.0152+0.061*LN(1.26*2.5/0.5295)=0.124 mH/1000 ft.

 

[7anoter4]

You are right, tiftif: for the flat formation inductance the distance center-line to center-line between cables it is 9 inch.[s=9 inch for all conductor cross section area].I don’t know why. By the way, NEC 2014 Figure 310.60 the distance between duct center-lines it is only 7.5 inches.

 

[jghrist]

Page 21 says that ro is radius of the conductor, or 0.736/2 inches (736/2 mils)for 500 kcmil cable. It should be the radius over the conductor shield, or the radius over the insulation minus the insulation thickness, 1.54/2 - 0.354 = 0.416 in. ri is radius over the insulation, or 1.54/2 inches. If you use ro = 0.416, you calculate C = 0.069 µF/1000ft.