Using NEC Ch.9 Table 9 at other temperatures

[svenoaks]

For a project I am working on I need to adjust the values presented in Ch.9 Table 9 (AC resistance and reactance) at different temperatures (the table is only good for 75C operating temperature).

Using a K value for copper and aluminum I can arrive at the values for AC resistance in PVC conduit as presented in the table (which I assume is the same as NO conduit) but I don't know how to correctly adjust for aluminum and steel conduits.

Any suggestions or other resources I should consider?

 

[G._S._Ohm]

http://www.electrician2.com/articles/ampacity.htm
but you'll need to find thermal conductivities and convert them into the proper units.

 

[G._S._Ohm]

Misread your post, sorry.

By using the temperature coefficient of resistance for copper and assuming the cable reactance is independent of temperature you can calculate the new impedance at a new temperature by calculating the new wire resistance.

Impedance Z is R + jXL and XL = (Z^2) - (R^2) so you figure the R at 75C and calculate the XL, then use the same XL and figure a new impedance Z at a new temperature.

The variation in XL due to a ferrous metal conduit is a whole 'nother animal because the permeability of air is way different from the permeability of steel. If you can find links stating the inductive reactance of conductors in steel tubing we can probably work backwards into the answer you need.

 

[svenoaks]

Would it be terribly wrong to adjust the AC resistance given in Table 9 by the formula at the bottom of Table 8:

R2 = R1[1 + a (T2 - 75)]

??

 

[G._S._Ohm]

Would it be terribly wrong to adjust the AC resistance given in Table 9 by the formula at the bottom of Table 8:

R2 = R1[1 + a (T2 - 75)]

??

I guess not.

There's another formula based on absolute zero and both results are shown below with an >.
Neither takes skin effect into account.
BTW, I thought the temperature coefficient of resistance for copper was 0.00393 but I'm sure the NEC has a good reason for choosing their value.

75 R@this temp = 1
100 =new temperature
334.5 = A = 234.5 + new temp
309.5 = B = 234.5 +
75
>1.080775444 =resistance ratio

R2 = R1, [1 + α (T2 − 75)] where αcu = 0.00323, αAL = 0.00330 at 75?C.
if R1 = 1 then
100 T2
25 T2 - 75
0.08075 alpha x T2-75
>1.08075 =resistance ratio

 

[mivey]

BTW, I thought the temperature coefficient of resistance for copper was 0.00393 but I'm sure the NEC has a good reason for choosing their value.

It is 0.00393 at 20?C. They are using the 75?C coefficient.

 

[G._S._Ohm]

It is 0.00393 at 20?C. They are using the 75?C coefficient.

Thanks.
I guess with Excel you could make your own table with varying coefficients as the temperature changes and get high (but perhaps unnecessary) precision and accuracy.

 

[mivey]

Thanks.
I guess with Excel you could make your own table with varying coefficients as the temperature changes and get high (but perhaps unnecessary) precision and accuracy.

You would also need to get the correct conductivity. The 20?C 0.00393 is at 100% conductivity but you also have 0.00401 at 102%, 0.00397 at 101%, 0.00389 at 99%, 0.00385 at 98%, 0.00383 at 97.5%, etc.

Just not worth it for what we are doing.

 

[Julius Right]

1. Reactance
Okonite [see: http://www.okonite.com/engineering/ac_dc_ratios.htm ]
Engineering Technical Center , Conductor Reactance uses the following formulae:
X=2*pi()*frq*(0.1404*log10(S/R)+0.0153)*10^(-3) ohm/1000 ft
For single core cable in conduit -nonmagnetic-[PVC or Aluminum] a 1.2 factor is employed for "random lay" and for magnetic pipe or conduit [steel, iron] 1.5.
As NEC Table 9 [footnote] consider single core cable in cradle formation S=1.1*overall dia. [considering conduit diameter as sqrt(3*2.5)*o/dia -the cables occupied area=40% from inner conduit area].Calculating following this way one could get the Table 9 values.
As already was written in the above posts no dependence of temperature is involved here.
2. Resistance
The resistance calculation is more complicated as skin effect and proximity effect depend on temperature.
Up to 250 kcmil [MCM] this effect is negligible and the resistance may be calculated using Rt2=Rt1*(1+at2*(t2-t1)) taking into consideration at2=1/(1/a20+(t2-20)).
See: http://www.aluminum.org/AM/CM/ContentDisplay.cfm?ContentFileID=57305&FusePreview=Yes
For conduit resistance one may follow:
"The Calculation of the Temperature Rise and Load Capability of Cable Systems" by J.H.NEHER and M.H.McGRATH
using formulae: Rac/Rdc=1+Yc+Ys+Yp where Yc=Ycs+Ycp skin effect and proximity effect factors ; Ys=shield losses factor[here Ys=0] and Yp=conduit factor.
Yp=396/(Rp*Rdc)*(2*s/Dsm)^2 for Aluminum conduit.[ Rp =conduit resistance per foot,Dsm=average conduit diameter]
Yp=(0.34*S+0.175*Dp)/Rdc for steel pipe.

 

[G._S._Ohm]

The OP asked, and Yea, Verily, he got answers.