Reactive Power Production of AC XLPE Submarine Cable

[whitbuzben]

Dear Sirs,

I have an XLPE submarine cable with the following characteristics:

Cable Vn (kV) In(A) Rac(Ω/Km) L (mH/Km) C (μF/Km)
150 1088 0.0205 0.352 0.233

Using the parameters above can someone demonstrate how to calculate the reactive current in the cable in A/km and the reactive power generated by the cable in MVAR/km.

Is it then possible to work out the amount of active power that the cable is able to transmit at a length of 100 km. Finally is it possible to work out the critical length of the cable. Any help with these calculations would be appreciated. The cable is uncompensated at this stage.

Many Thanks

 

[FPelec]

dear whitbuzben,
a closed-form expression for evaluating the maximum active power and, consequently, the critical length of a cable is reported in:
F.M. Gatta, A. Geri, S. Lauria, M. Maccioni, “Steady-state operating conditions of very long EHVAC cable lines”,EPSR Volume 83, Issue 1, February 2012

http://www.sciencedirect.com/science/article/pii/S0378779611002689

Si duri puer ingeni videtur,
preconem facias vel architectum.

 

[7anoter4]

The line surge impedance Zo=sqrt((R+jwL)/(G+jwC))
Simplifying the problem then
we may neglect R and G then Zo=sqrt(L/C)
Zo=sqrt(0.352/1000/(0.233/10^6))=39 ohm
The surge impedance loading [SIL]:
SIL=VLL^2/Zo
SIL=150^2/39=577 MVA
The line power:
S=SQRT(3)*150*1.088=282.7 MVA
Since SIL>S then the line power factor is leading[capacitive]
If we'll neglect the Ferranti effect at no-load the cable capacitive reactance:
Xcap=1/2/pi()/f/Cap/length=1/2/pi()/50/0.233/100*10^6=136.6 ohm
Neglecting voltage drop [about 4-5%]:
Qcap=150^2/136.6=164.7 MVAr
Inductive reactive power losses in a three_phase cable could be 3*XL*In^2
XL=2*PI()*50*0.352/1000*100=11.058 ohm [50 Hz,100 km]
QL=3*11.058*1.088^2=39.27 MVAr
The line produces 164.7-39.27=125.43 MVAr capacitive.

 

[krisys]

7anoter4,

Nicely explained. However, for a long time, I was trying to find out the importance of surge impedance and its applications for the system design.

Would you please elaborate this concept little more?