HV underground cable - double circuits configuration 2

[eejacky]

For 132kV double circuits, the configuration of the two circuits as laid in the same trench would likely be mirror image. That is YRB:BRY either in trefoil or flat formation. Why the configuration should be like this? Is it related to the reduction of energy loss due to inductance?

 

[RajT]

Could it be that the arrangement ensures no cross overs when the cables emerge to be terminated on to switch yard bus bars,

 

[cuky2000]

Inductance and reactance are dependent of the physical configuration of the circuit in the trench. The inductance and inductive reactance could be calculated as follow:
L = k₁. Ln(GMD/GMR) and X = k₂. Ln(GMD/GMR)
_{Where:
GMD =Geometric Mean Distance. GMR = Geometric Mean Radius.
.k1 = 2x10-7 H/m. k2= 0.0754 Ohm/km @ 60 Hz}

To support this statement, consider simplified cases of double circuit in a trench neglecting the effect of the earth. The physical arrangements of the conductor are in flat configuration each phase locate a distance d from any contiguous conductor. The estimated inductance and impedance are as follow:

CASE I: Y1R1B1(top) & Y2R2B2 (bottom)

X = k/2[Ln(Ds/4d)-Ln(5^1/2]

CASE II: Y1R1B1(top) & B2R2Y2 (bottom)

X = k/2[Ln(Ds/4d) +Ln(5^1/3]

CASE III: Y1R2B1(top) & B2R1Y2 (bottom) .. Trefoil Configuration

X = k/2[Ln(Ds/4d) +Ln(5^1/3]

 

[eejacky]

Hi cuky2000,

Thank you for your reply. Could you elaborate more about how to devise these equations. Also, how about the case of Y1R1B1(Left) and B1R1Y1(Right)?

Jacky

 

[cuky2000]

Hello eejacky:

Considering the editing limitations I will try to answer the best I could.

1-. Could you elaborate more about how to devise these equations.?

Equivalent Geometric Mean Distance (GMDeq)
The total equivalent GMD is: GMDeq = (Dsy.Dsr.Dsb)^1/3
Where Dsy, Dsr and Dsb are the equivalent GMD per phase.

For 2 parallel YRB YRB
Conductors YRB BRY
Dsy = (Ds.Dsy)^1/2 (Ds.d)^1/2 (Ds.5^1/2d)^1/2
Dsr = (Ds.Dsr)^1/2 (Ds.d)^1/2 (Ds.d)^1/2
Dsb = (Ds.Dsb)^1/2 (Ds.d)^1/2 (Ds.5^1/2d)^1/2

(Dsy.Dsr.Dsb)^1/3 (Ds.d)^1/2 5^1/3.(Ds.d)^1/2

Equivalent Geometric Mean Radiuos(GMReq)
The total equivalent GMR is: GMReq=(GMRyr.GMRrb.GMRyb)^1/3
For 2 parallel conductors:
GMRyr = (Dy1r1.Dy1r2.Dy2r1.Dy2r2)^1/4
GMRrb = (Dr1b1.Dr1b2.Dr2b1.Dr2b2)^1/4
GMRyb = (Dy1b1.Dy1b2.Dy2b1.Dy2b2)^1/4

Where Dsy, Dsr and Dsb are the equivalent GMD per phase.

For 2 parallel YRB YRB
Conductors YRB BRY
GMRyr 2^1/4. d 2^1/4. d
GMRrb 2^1/4. d 2^1/4. d
GMRyb 20^1/4. d 4^1/4. d

GMReq 80^1/12.d 16^1/12.d


The equation X = k.Ln(GMD/GMR)could be approximated as follow:
For YRB/YRB: X₁ = k[(Ln(Ds/d))/2+0.37]

For YRB/BRY: X₂ = k[(Ln(Ds/d))/2+0.31]

Therefore X₁ > X₂


2.- How about the case of Y1R1B1(Left) and B1R1Y1(Right)?
Since the distance remain the same, the equivalent reactance of top/bottom or left/right configurations will be also equals. However, the allowable conductor ampacity may have small different because the heat dissipation model are affected by the depth of burial and laying configuration.

 

[ItAintMe]

Depending on the environment in which the cables are being laid, it could also be to reduce emf levels which create interference with some electrical equipment in the vicinity, or make local residents angry and worried about health effects.

The preferred configuration to reduce emf is trefoil, although this will also increase mutual heating, reducing rating.

 

[jbartos]

Suggestion: Reference:
K.A. Petty "Calculation of Current Division in Parallel Single-Conductor Power Cables for Generating Station Applications," IEEE Transactions on Power Delivery, Vol. 6, No. 2, pp 479-485, April 1991
The self-reactances and mutual-reactances of conductors need to be considered.
Software is convenient to use. Reference refers to MathCAD for matrix manipulations.

 

[jbartos]

Suggestion: Check:
OTI, Inc. (ETAP)

http://www.etap.com

for ETAP 5.0 U/G Raceway