# Why do underground cables “require a higher degree of reactive power compensation” than overhead lines?

I was reading a brag sheet for a certain company's giant transformers, and I came across this sentence:

Furthermore, in some regions, the existing over head lines are being replaced by underground cables, which require a higher degree of reactive power compensation.

Why is this?

• I'm not a EE, so I'm not going to try to answer, but remember that the lines in the power grid are transmission lines. They have distributed inductance along the length of the conductors, and they have distributed capacitance between the conductors. The geometry of an underground line is very different from the geometry of an overhead line, so you should expect it to have a different characteristic impedance and, I don't know what else. – Solomon Slow Dec 8 '17 at 16:29
• Correct @jameslarge , that Characteristic impedance is the key difference and of course the length of the line. Do you know what it is for U/G and O/H power cables? – Tony Stewart Sunnyskyguy EE75 Dec 8 '17 at 19:23
• I also came across this lecture, which explains how transmission lines work: egr.unlv.edu/~eebag/TRANSMISSION%20LINES.pdf I really appreciate the answers, I understand this way better than before. Lots of math involved though, I guess I should sit down and figure it out sometime :) – user60561 Dec 8 '17 at 21:37
• The capacitance between the power leads in an underground duct is much higher than for overhead wires because the wires are very much closer together. The cable size is chosen for its current carrying capacity - so, if you demand that the power wires carry reactive current, you need to buy heavier gauge power wires. So, greenies cost society more. – Brian Dec 13 '17 at 2:13
• @Brian "because the wires are very much closer together" -- this is not correct. Each wire is sheided, so that is why the capacitance is much higher, the proximity of the other wires is much less signficant. See Tony Stewart's answer (which I've confirmed by looking at high-voltage underground cables in catalogs) – user60561 Dec 13 '17 at 22:41

Short answer: Underground (U/G) cable uses coaxial with earth gnd shield.

So it is the white PE ( polyethylene ) material that increases underground capacitance since it separates the centre core and the copper braid ground sheath and not the proximity of phase to phase lines (although this has some effect.)

Below is just a single phase example.

The design of power distribution cables has improved over the decades and they now have historical experience on what works best.

They use non-coaxial conductor clad steel core with/without insulation cladding. This makes the power line capacitance negligible compared to the coaxial cable used for U/G since the insulation line to ground is orders of magnitude higher in coaxial cable.

The ABB unit in question has superior dynamic range for handling the wide range of reactive impedance power factor correction of cables that may include O/H and XLPE coaxial U/G cable.

• Shunt reactors are used to compensate the line shunt capacitance under light load or no load to regulate voltage.
• Series capacitors are often used to compensate the line inductive reactance in order to transfer more power and increase network stability

• each 3 wire bundle carries same voltage to reduce arc and wind effects.

Underground (and sometimes overhead) sheathed cable (shielded XLPE cable)

Cross Link shielded high voltage cable always used for underground power lines.

## Technical background

The capacitance of a single-phase transmission line is given by the ratio of separation and effective radius.

$C=\dfrac{2πε}{ln(\frac{D}{r})}$ Where r is the effective radius of the phase conductor.

O/H lines benefit from spacing 2,3 or 4 conductor far apart for added strength against wind and raised breakdown effects from reduced E field divergence radius. This lowers L and raises C slightly but is still very low C values/km compare the high C/km of coaxial U/G cable due to the small gap r of the centre conductor to coaxial sheath.

Below is Telegrapher's model of all transmission lines including ethernet, cable TV, phone lines and AC or DC power lines. (except shunt leakage R is neglected here)

The resistance at DC is not the same as the distributed impedance that affects reflections and surge voltages due to disturbances.

O/H lines are often triaxial as above.

O/H cable is often rated SIL characteristic wave impedance of 400 ohms and U/G cables are 50 ohms =+/-25% depending on ampacity and BIL rating.

This makes black start surge currents higher for U/G cables so shunt reactance needs to be adjusted.

Photos to follow.

## Other

Overhead, O/H cables are much cheaper per km to buy and install but frequency of repairs is higher due to lightning, hurricane, and tree exposure. But then they are also faster and cheaper to repair. But looking at the devastation in Puerto Rico and other locations with poor infrastructure the life cycle cost advantages of underground U/G power cables in spite of higher easement costs, cable cost and repair costs results but at a higher MTBF ( if done properly) results in lower life cycle costs. Environmental stress always affects these decision.

• Quick note; XLPE is cross-linked polyethylene, not cross-linked polyurethane. – Li-aung Yip Dec 9 '17 at 3:41
• Brain fart. TY Yip – Tony Stewart Sunnyskyguy EE75 Oct 10 '18 at 11:31

As the conductors of underground lines are packed closer together than for overhead lines, the capacitance is higher. This capacitance can take quite a substantial charging current.

Incidentally, the inductance, as they include a smaller loop area, is lower.

• Underground (U/G) cables for distribution are always ground sheathed and only sometimes for O/H cables therefore the sheathed cables have much higher uF/km. It has no comparison with wire gap. It can vary from 0.1 to 2uF/km – Tony Stewart Sunnyskyguy EE75 Dec 8 '17 at 18:14
• It is not the phase-phase wire gap in U/G cables , rather it is the phase to shield (gnd sheath) gap that makes the difference in C and the length/diam d vs length for L – Tony Stewart Sunnyskyguy EE75 Dec 8 '17 at 19:26
• Overhead lines tend to have more inductance, which just requires a cheap capacitor in parallel to correct. However underground lines are dominated by capacitance which requires expensive inductors to correct the power factor – teambob Dec 8 '17 at 22:41
• But the magnetic whatever-it-is of earth is greater than that of air, so the inductance (and inductive losses) of the buried cable will be greater than the same cable suspended in air. – Hot Licks Dec 8 '17 at 23:03
• @Neil_UK If you examine the typical construction of O/H vs U/G cables you will find the U/G are coaxial shield per phase. It is NOT that phase bundling closer that increases capacitance but that fact that all U/G needs to be coaxial for moisture, mechanical, and thermal reasons and thus use a high grade purity of XLPE insulation in the coaxial cable. So closer yes but wrong, that is not why C is higher. Sorry -1 – Tony Stewart Sunnyskyguy EE75 Dec 8 '17 at 23:43

Question: Why do underground cables “require a higher degree of reactive power compensation” than overhead lines?

Because underground line capacitance for power cables is far higher than overhead line capacitance.

Main reasons for this:

• Wires are closer to each other.

• Wires are closer to the earth (within a few inches).

The inductance is lower as well.

Also, because (as a result of above characteristics) underground lines have 20-75 times the line charging current that an overhead line has (depending on line voltage).

Source:

https://www.puc.nh.gov/2008IceStorm/ST&E%20Presentations/NEI%20Underground%20Presentation%2006-09-09.pdf

Also, if you want to take a closer look at the general characteristics of transmission lines via math, you can checkout this document also (others have posted this one as well):

http://www.egr.unlv.edu/~eebag/TRANSMISSION%20LINES.pdf

• Since U/G cables are shielded, closer does not matter in this case nor closer to ground, nor lower Inductance which is based on wire length/gauge ratio which in this case must carry a similar rated current if we compare apples and distance. So none of your assumptions are correct, but the math links are correct. Next time compare open wires to coax. Sorry but -1 – Tony Stewart Sunnyskyguy EE75 Oct 11 '18 at 17:33