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# reactive power generation of underground cables

## reactive power generation of underground cables

(OP)
I need to estimate the reactive power generation of medium voltage (e.g. 20kV) underground cables at nominal-load and no-load.
Can anyone help by pointing to reliable technical info sources?

### RE: reactive power generation of underground cables

You need the cable capacitive reactance.  The cable manufacturer may be able to provide values.  In general, unless you are working with a very large amount of cable you won't need to worry much at that voltage.

### RE: reactive power generation of underground cables

(OP)
davidbeach

If nothing mentioned, cable capacitive reactances X_C (mho) are usually being given per phase or 3phase?

Assuming that they are quoted per phase I get:

Q_per_phase = (V_line_line/sqrt(3))^2/X_C VAr per phase

and total cable Q = 3*Q_per_phase.

Does it seem correct?

### RE: reactive power generation of underground cables

A power cable presents an inductive reactance in series and a shunt capacitive reactance as davidbeach mentioned.
The reactive power produced by inductive reactance power depends indeed on current intensity meaning the load.
This reactive power will be drawn from the source.
At no-load only the capacitive current -if the cable will be energized-will produce -flowing through the conductor-a small amount of inductive reactive power.
The capacitive reactive power depends on voltage between cable conductor and shield.
This kind of reactive power is returned to the source as "generated" by the cable.
The capacitive reactive power depends- slightly- also on load as the voltage drop reduces the cable voltage.
The total reactive power generated by a cable is the difference between capacitive reactive power and inductive reactive power.
In order to calculate more accurately the reactive power generated in a cable you may follow the procedure detailed in the following article [for instance]:
http://www.bme.hu/ptee2000/papers/fetea.pdf
The cable capacitance and inductance could be provided by Manufacturer-it would be recommended-but you could appreciate it knowing the cable dimensions as conductor cross-section area, conductor diameter, inner shield diameter and distance between phases- cables or cores.
Let's take an example: 3 single core cable lying in flat position 8" apart. [N2XS2Y 12/20 kV 1X240 rm/16]. Condia=20.6 mm; Shield dia.= 33 mm; overall dia.=39 mm.; length=1000 ft[304.8 m] distance between center line 8"= 203mm.The average distance between center lines S=203*2^(1/3)= 256 mm.
VS=20/SQRT(3)= 11.547 kV.
Using Kerite indicated formula Xind=2*frq*pi*(0.1404*LOG10(2*S/condia)+0.0153)/10^3=0.079 ohm/1000 ft .
Proceeding as per above article we have to split the cable into 2 parts one for "source" and one for "receiver" .Then the capacitance cap=eps.r/18/LN(shdia/condia)/10^6*0.3048*length/2000 [original formula is for metric dimensions] cap= 4.565E-08 F [or 4.565/100 micro F].
Xcap=1/2/frq/pi/cap= 58106 ohm.
At first let say IR=400A  PF=0.8 at "receiver" end.
You can follow the way indicated in the above article but with enough accuracy you may appreciate:
Qind=3*I^2*Xind =3*400^2*0.079/1000= 38.2 kVAR
Qcap=3*VS^2/Xcap= 3*11.547^2/4.564E-08*1000= 13.76 KVAR
So to the reactive power required by "Receiver" from the "Source" you have to add another 38.2-13.76=24.4 kVAR.
If IR=0 [no-load] then only capacitive reactive power will be transmitted to the source[13.76 kVAR].

### RE: reactive power generation of underground cables

(OP)
Thanks 7anoter4

kokotiko

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