Positive Sequence Resistance of Concentric Neutral Cable

[SSLA]

Folks:

I've got metering at the wrong end of some direct buried concentric neutral XPLE cable, three single phase cables, 1000MCM Cu with 1/3 neutral, XLPE, grounded both ends.

I need to correct for losses. The load is well balanced so I am focusing on positive sequence current.

When I look in the Pirelli tables I see the positive sequence resistance is 47 micro-Ohm/ft or 0.2482 ohm/mile. The manufacturer says R1 is 0.1286 ohm/km or 0.207 ohm/mile under standard spacing etc. When I carry out the calculations in Anders book "Rating of Electric Power Cables", page 125, I get 0.0793 ohm/mile.

Why would there be such a disparity between Anders "AC resistance" (which based on IEC 287) and the R1 value published by the cable manufacturers? Do the manufacurers assume there will be current in the neutral?

 

[SSLA]

Folks:

A little reflection has revealed that concentric neutral is different from overhead line. Positive sequence current in the cable will induce current in the neutral an increase in the kW loss even on balanced load. Intuition syas this should be 20 to 30% increase not the 300% difference noted above between the resistance of the phase conductor alone adjusted for temperature, skin and proximity effects.

I hope to estimate the kW loss a 3 X Iphase**2 x R1. Any advice on how to proceed?

Adjustment for the reactive power generated by the cable is not required.

 

[dpc]

Your .0793 ohms/mile value is pretty close to what I get.

Are you sure the Pirelli data was for R1 and not Z1?

 

[SSLA]

pdc:

Thanks for the reminder! I checked the data from Pirelli. The 47 micro-ohm/foot figure is for aluminum (!) and my cables are copper.

But...the Pirelli data lists "+/- Sequence Impedance Resistance" as 38 micro-ohms/ft. The positive and negative sequence reactance is listed as 39 midro-ohm/ft. The resistance would be 0.2006+j0.2059 ohm/mile.

Nexans indicates their 1000MCM cable is 0.1286+j0.1331ohm/km or 0.2070+2.1420johm/mile.

My ancient McGraw Edison Distribution Systems Protection Manual lists R1 as 0.04 ohm/1000ft for 1000MCM or 0.2112 ohm/mile.

So it looks as if we have concensus from the cable manufacturers that R1 is about 0.2 ohm/mile for 1000MCM copper, 1/3 neutral, direct buried at 90 deg C.

Is it really possible that the circulating current in the neutral could increase the positive sequence resistance from 0.0793 to 0.2 ohm/mile (250%)?

 

[dpc]

If you have a Westinghouse T&D book, there is a discussion in there regarding compensation for "sheath" currents. But the increase in conductor resistance in their example is very small - nothing close to what you are indicating. In any event, the actual conductor resistance does not change - this is just a way to cover the extra losses.

BTW, 1000 kcmil copper is an absolute pig of a cable to work with. And sizes above 750 kcmil (copper) or so are generally not cost effective because the increased ampacity is not offset by the increased cost. Ampacity does not increase proportionally with cross section. But I'm sure you have your reasons. I'll just give thanks that I'm not installing it.

 

[dpc]

OK, I did find a reference book (A Guide to Short-circuit calculations - C. St. Pierre) that give a chart of proximity effect for ac cables.

It doesn't have concentric neutral cable, but for metallic shield, the multiplier at 1000 kcmil is about 1.3.

ac/dc ratio is about 1.07 at 1000 kcmil.

Hope that helps.

Dave

 

[SSLA]

Dave:

Thanks for the help. I do the the T&D book and will read up. The good news is that the cable is already installed. We are just moving the metering from one end to the other. That's when I started to read up on losses and found that concentric neutral cables behave differently than the overhead lines I am long used to.

Thanks, SSLA

 

[SSLA]

Ok Folks...I did my homework. I obtained basic data from a cable manufacturer on the resistance and GMR of the conductor, dimensions of the cable and number and size of conductors in the concentric neutral. I adjusted the resistance of the conductor for skin and proximity effects at 7.5 inch flat spacing and 90 degree C temperature using the method on pg 125 of Anders "Rating of Electric Power Cable". I adjusted the neutral resistance to 70 degress C. Next I applied the matrix method described in Chapter 4 of "Analysis of Faulted Power Systems" by PM Anderson. Anderson uses the Carson model of the line to build a primitive branch impedance matrix followed by Kron reduction to get to the abc frame of reference followed by the conversion to the sequence frame of reference using the alpha operator. All this is easy in Mathcad. The sequence impedances I got match very closely to the sequence impedances listed in the tables posted by Pirelli so I am confident the calculation is producing a reasonable result. And the result is:

Conductor resistance: 0.0471 ohm/km
Positive Sequence resistance: 0.1277 ohm/km

What's going on? It turns out there is high inductive coupling between the phase conductor and the concentric neutral even when only positive sequence current flows. The circulating current in the neutral and surrounding earth increases I2R loss by a whopping 270% (!)

This was big surprise for me since I have made hundreds of calculations over the years for overhead lines which when carrying only positive sequence current induce a negigible earth/neutral currents.

Positive sequence resistance increases with conductor spacing. Reducing the spacing to trefoil (the cables are clamped together in a triangle so they are separated by one cable diameter) yields R1 = 0.0633 ohm/km. That makes sense: less coupling smaller loss.

At a spacing of 5 feet R1 becomes 0.1562 ohm/km to the rate of increase tapers off at larger spacings.

Man all this education in a single week!