techref_cableconstants[1].pdf

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D I g S I L E N T T e c h n i c a lD o c u m e n t a t i o n

Cable Systems


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C a b l e S y s t e m s

Rev. Nr. Author Date Reviewed by Date PF Version

01 F. Fernndez 15.04.2010 14.0.516

02 F.Fernndez 02.03.2011 14.1.0

DIgSILENT GmbH

Heinrich-Hertz-Strasse 9

D-72810 Gomaringen

Tel.: +49 7072 9168 - 0

Fax: +49 7072 9168- 88

http://www.digsilent.de

e-mail: [email protected]

Cable Systems

Published by

DIgSILENT GmbH, Germany

Copyright 2005. All rights

reserved. Unauthorised copying

or publishing of this or any part

of this document is prohibited.

07 Mrz 2011


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T a b l e o f C o n t e n t s


Table of Contents

1. Introduction ................................................................................................................................... 4

2. Definition of the cable system....................................................................................................... 5

1.1 The single core cable type (TypCab) ........................................................................................................ 5

1.1.1 Filling factor of conducting layers ........................................................................................................ 5

1.1.2 Temperature coefficient ..................................................................................................................... 6

1.2 The cable system type (TypCabsys) ......................................................................................................... 6

3. Calculation of electrical parameters ............................................................................................. 7

1.3 Internal Impedance ................................................................................................................................ 8

1.4 Internal Admittance ................................................................................................................................ 9

1.5 Semiconducting layers .......................................................................................................................... 10

1.6 Parallel Single-Core Cables .................................................................................................................... 10

1.6.1 Impedance ..................................................................................................................................... 10

1.6.2 Admittance ..................................................................................................................................... 11

1.7 Pipe Type Cable ................................................................................................................................... 12

1.7.1 Impedance ..................................................................................................................................... 12

1.7.2 Admittance ..................................................................................................................................... 13

5. Input Parameters ........................................................................................................................ 16

6. Calculation Results ...................................................................................................................... 18

7. References ................................................................................................................................... 21


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1.Introduction

This document describes the definition of a cable system in terms of its geometry, the properties of the

conducting, semi-conducting and insulating layers, installation characteristics (buried directly underground, in a

pipe). Besides it details calculation of its frequency-dependent electrical parameters.

The definition of a frequency-dependent cable system success in PowerFactorywith help of two type objects: a

single core cable type TypCabwhich describes the constructive characteristics of the cable and a cable system

type TypCabsys, which defines the coupling between phases, i.e. the coupling between the single core cables in a

multiphase/multi-circuit cable system.

A built-in cable constants function in the cable system type calculates then the frequency-dependent electrical

parameters (impedance and admittance matrices). The function can handle coaxial cables consisting of a core,

sheath and armour directly undergrounded or installed in pipes (pipe-type cables). This function can be started in

a stand-alone case from the Calculate button on the edit dialog of the cable system, in which case the results

are printed to the output windows, or be automatically called by any simulation function in PowerFactory, eg.

when running a frequency scan or when adjusting the model for an electromagnetic transient simulation.

Finally, the reader should notice that this cable system type supports the definition of the cable in terms of

geometrical data; is the cable to be defined in terms of electrical data, the reader is referred to[1] where the

general line/cable element (ElmLne) is used instead.


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2.Definition of the cable system

1.1

The single core cable type (TypCab)

The single core cable type TypCabsupports up to three tubular conducting layers in coaxial arrangement, i.e.

core, sheath and armour, separated by three insulating layers.Figure 1 shows the typical layout of a HV AC single

core cable. The model also supports the definition of a core-outer and insulation-outer semiconducting layer.

Figure 1: Cross section of a single core cable including the core, sheath and armour.

Error! Reference source not found.in section5 shows the complete list of input parameters including units,

ange and the symbol used in this document. Hover the mouse pointer over the input parameters in the edit

dialog of TypCabto display the name of the input parameter. This is the name listed in the first column of the

table.

The input data in the edit dialog of TypCabis organized according to lyers, i.e. the conducting, insulation and

semiconducting layers, if available. Use TypCabto enter all the geometrical data defining the cross section of the

single core cable and the properties of all constitutive materials.

1.1.1Filling factor of conducting layers

To account for the compacting ratio of the cross section of the conducting layers (stranded conductors, shaped

compact, etc.) the users can enter a filling factor Cf.. This filling factor is related with the dc resistance of the

cable by the following equation:

2 21

[ / ] 10DCf

R km cmr q C

where rand q are the outer and inner radius of the conducting layer respectively.

The user chooses the input parameter between the filling factor in % or the DC resistance in ohm/km by clicking

the selection arrow ; note that one of them is always greyed out indicating its dependency on the other one.


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1.1.2Temperature coefficient

If the temperature dependency of line/cables option is enabled in the load flow calculation, the resistivity of theconducting layers is adjusted by the following equation

20 1 20T C T

where is the temperature coefficient of resistance. The resistivities and temperature coefficient of common

metals are given inTable 1 for reference.

Table 1: Resistivities and temperature coefficient of resistance

MaterialResistivity at 20 C

[.cm]

Temperature coefficient at 20C

[1/C]

Aluminum 2.83 0.0039

Copper, hard drawn 1.77 0.00382

Copper, annealed 1.72 0.00393

Brass 6.4-8.4 0.0020

Iron 10 0.0050

Silver 1.59 0.0038

Steel 12-88 0.001-0.005

1.2

The cable system type (TypCabsys)

The cable system type TypCabsysis used to complete the definition of a cable system. It defines the coupling

between phases, i.e. the coupling between the single core cables in a multiphase/multi-circuit cable system. As in

general the cables are laid close together this coupling has to be taken into account.

Among other factors, this coupling depends on how the cables are laid. The PowerFactory model supports

following two options:

Parallel single-core cables: the cables are grounded direct into ground. This is normally the case of

underground HV AC cables.

Pipe-Type cables: the cables are drawn into a pipe, usually made of steel, and the pipe laid into

ground. This is in widespread use in submarine cables.

The input parameter Buried: Direct in ground/in Pipe lets the user choose between both models. In case of

pipe-type cables additionally data is required for the pipe. The complete list of input parameters is shown inTable

3 in section5.

The cable system type also defines the bonding conditions of the sheath and armours when available.


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3.Calculation of electrical parameters

The calculation of the impedance and admittance of the cable is based on the cable constants equations

formulated by A. Ametani[3] and underlies the following assumptions:

Coaxial arrangement of the conducting and insulating layers inside the single core cable

Single core cables inside the pipe are concentric with respect to the pipe

Each conducting layer of the cable has constant permeability. Furthermore, conducting layers are non-

magnetic so that the cable model does not account for current-dependent saturation effects

Displacement currents and dielectric losses of the insulating layers are negligible.

A general formulation of the series impedance and shunt admittance of the cable is given by:

x U Z I (1)

x I Y U (2)

where [ ]U and [ ]I are the voltage and currents vectors at a distance x along the cable.

The dimension of [ ]Z and [ ]Y depends on the total number of cables in the system and the total number of

layers per single core cable. For instance in a three phase cable system with three conducting layers per single

core cable (core, sheath and armour) the dimension of the [ ]Z (i.e. [ ]Y ) results 9 (=3 phases x 1 single core

cable/phase x 3 conducting layers/cable).

[ ]Z and [ ]Y are symmetric square matrices that can be expressed in the following terms:

0I P CZ Z Z Z Z (3)

1

0I P C

Y s P

P P P P P

(4)

where [ ]P is a potential coefficient matrix and s the Laplaces operator (complex frequency).

The matrices with subscript I account for the internal impedance and admittance respectively and matrices withsubscript O for the earth or air return path. In case if a pipe enclosure cable the matrices with subscript CandPdefine the impedance and admittance of the pipe; these matrices becoming zero if the cable is laid directlyunderground. In the next sub-chapters we will discuss the physical meaning of these sub-matrices and the

formulas used to calculate them.

Following naming convention is used in this document:

Subscript I accounts for the internal impedance, subscript O for the earth or air return path and

subscripts Cand Pfor the pipe enclosure if available.

Subscripts ,c s and a (lower case) are used for core, sheath and armour in cable layer equations


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Subscripts ,i j and krefer to the cables in the system (typically three cables in a three phase cable

system).

1.3Internal Impedance

The internal impedance is associated to the longitudinal voltage drop due to the magnetic field inside the single

core cable and it is given by the following equation:

c cc cs ca c c

s sc ss sa s I s

a ac as aa a a

U Z Z Z I I

x U Z Z Z I Z I

U Z Z Z I I

(5)

where the layer internal impedances in (5) are defined in terms of coaxial loop impedances as follow:

11 12 22 23 33

12 22 23 33

23 33

22 23 33

33

2 2

2

2

cc

cs sc

ca ac sa as

ss

aa

Z Z Z Z Z Z

Z Z Z Z Z Z

Z Z Z Z Z Z

Z Z Z Z

Z Z

(6)

The impedances with subscript 1,2 and 3 are referred as loop impedances. For instance11

Z is the impedance of

the inner most loop of concentric tubular conductors and therefore that of the loop core-sheath.

11 , / , ,

22 , / , ,

33 , ,

12 21 ,

23 32 ,

c OUT c s INS s IN

s OUT s a INS a IN

a OUT a INS

s MUTUAL

a MUTUAL

Z Z Z Z

Z Z Z Z

Z Z Z

Z Z Z

Z Z Z

(7)

The impedance of the tubular conductors are found with the modified Bessel functions with tube= c, sand a

respectively:

, 0 1 0 1

, 0 1 0 1

,

( ) ( ) ( ) ( )2

( ) ( ) ( ) ( )2

2

tube IN

tube OUT

tube MUTUAL

mZ I mq K mr K mq I mrqD

mZ I mr K mq K mr I mq

qD

ZqrD

(8)

where


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1 1 1 1( ) ( ) ( ) ( )D I mr K mq I mq K mr (9)

1jmp

(10)

The parameter m is the reciprocal of the depth of penetration p and are both frequency-dependent complex

values.

INSZ accounts for the longitudinal voltage drop due to the magnetic filed in the insulating layers. For the general

case of non-concentric tubular conductors it results:

2

0 ln 12

kINS

i k

q diZ j

r q

(11)

and in the case of concentric tubular conductors 0id and (11) reduces to

0 ln2

kINS

i

qZ j

r

1.4

Internal Admittance

The internal admittance matrix is associated to the capacitive coupling and dielectric losses due to the insulating

layers within the single core cable. The capacitance and dielectric losses of each insulating layers is given by:

02 1

ln

ri

i

i i

CPr

q

G C tg

(12)

withi

Pthe potential coefficient of the insulating layer.

Assuming that the single core cable consist of three layers, hence the insulation between core and sheath, sheath

and armour and outermost insulating layer of the single core cable, it follows:

c s a s a a

I s a s a a

a a a

P P P P P P

P P P P P P

P P P

(13)

1I

I

CP

(14)

I I IY G j C (15)


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1.5

Semiconducting layers

The model supports the definition of a semiconducting layer on the conductors outer surface and the insulationsouter surface. These semiconducting layers mainly influence the admittance of the insulation. Their effect on the

impedance of the conductor is rather minor and therefore not considered by the moment in the model.

The capacitance and conductance of the tubular semiconducting layer is given by the following equations:

01

2ln /

SC rSC

SC SC

Cr q

2 1

ln /SC

SC SC SC

Gr q

where rSCand qSC are the outer and inner radius of the tubular semiconducting layer respectively, rSC the

relative permittivity and SC the resistivity.

Hence the equivalent admittance of the insulation under consideration of the semiconducting layers is calculated

in the following form:

1 1 1

iIns IL SC G G G

1 1 1

iIns IL SC C C C

1.6

Parallel Single-Core Cables

1.6.1Impedance

Lets assume being , ,i j kthree parallel single core cables each of them consisting of core, sheath and armour.

Eq. (1) can be expanded as:

,

,

,

0, 0, 0,

0, 0,

0,

0 0

0

:. ...

: . ...

i I ii

j I jj

k I kk

ii ij ik i

jj jk j

kk

U Z

x U Z

U Z

Z Z Z I

Z Z I

Z

k

I

(16)


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where0,sZ and 0,mZ are the self and mutual earth-return impedance matrices of the cable system given

as:

, , ,

0, , , ,

, , ,

, ,

e s e s e s

s e s e s e s

e s e s e s

Z Z Z

Z Z Z Z s jj kk ll

Z Z Z

(17)

, , ,

0, , , .

, , ,

, ,

e m e m e m

m e m e m e m

e m e m e m

Z Z Z

Z Z Z Z m jk kl lj

Z Z Z

(18)

,e mZ is the mutual earth-return impedance between two parallel cables ,i j given by:

0, 0 0e jk ik ik ik ik Z j K m d K m D P jQ

(19)

and ik ik P jQ the terms of the Carsons serie (see[6] for further reference).

,e sZ is the self earth-return impedance of the single core cable. Its value is obtained from (19) by replacing d

with R, D with 2h and h+y with 2h.

1.6.2

AdmittanceAs the cable is directly laid underground and the earth surrounding the cable being assumed an equipotential

surface, there is no capacitive coupling effect among the single core cables. It follows then that 0P in (4)and therefore the admittance matrix of the cable results:

,

,

,

1

0 0

0 0

0 0

I i

I I j

I k

P

P P P

P

Y P

(20)

i i

j j

k k

I U

x I Y U

I U

(21)

and the submatrices in the main diagonal according to (13).


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1.7

Pipe Type Cable

1.7.1

Impedance

Assuming again a system of three single core cables , ,i j keach of them consisting of core, sheath and armour,

equation (3) can be expanded as follows for the case of a pipe type cable:

,

,

,

, , ,

, ,

,

0 0 0

0 0

:. ... 0

0 0 0 0

0

0

: . ... 0

0 0 0 0

i I ii

j I jj

k I kk

p

P ii P ij P ik

P jj P jk

P kk

U Z

U Zx

U Z

U

Z Z Z

Z Z

Z

1 1 1 2

1 1 2

1 2

2 2 2 3

0 0 0 0

0 0 0

0 0

0 0 0 0

: . ...

: . ...

C C C C

C C C

C C

C C C C

i

j

k

Z Z Z Z

Z Z Z

Z Z

Z Z Z Z

IZ Z Z Z

IZ Z Z

IZ Z

Z Z Z Z

pI

(22)

PZ defines the self and mutual impedances of the pipe-return path of the single core cables. A submatrix is

given by:

, , ,

, , , ,

, , ,

P ij P ij P ij

P ij P ij P ij P ij

P ij P ij P ij

Z Z Z

Z Z Z Z

Z Z Z

(23)

Self impedance of the with pipe-return path for the i-th cable ( )i j :


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2

00, '

11

2

2

n

r r niP ii

n r n n

K mq K mqdZ j

mqK mq q n K mq mqK mq

(24)

Mutal impedance between the i-thand thej-thcables with common pipe-return path ( )i j :

00,

2 21

2 '1

ln2 2 cos

2 1cos

P ij r

i j i j ij

n

i j r n

ij

n r n n

K mqqZ j

mqK mqd d d d

d d K mqn

q n K mq mqK mq n

(25)

CZ s the connection impedance matrix between the pipe inner and outer surfaces. The submatrix1CZ ,

2CZ and

3CZ are given by:

1 1 1

1 1 1 1

1 1 1

C C C

C C C C

C C C

Z Z Z

Z Z Z Z

Z Z Z

(26)

where1C

Z ,2CZ and 3CZ are calculated using equations (8) to (11) for the impedance of tubular conductors

and tubebeing the pipe as follows:

1 , , ,

2 , , ,

3 , ,

2C pipe OUT pipe INS pipe MUTUAL

C pipe OUT pipe INS pipe MUTUAL

C pipe OUT pipe INS

Z Z Z Z

Z Z Z Z

Z Z Z

(27)

Finally,0Z represent the impedance of the earth return-path of the pipe. The diagonal submatrix 0Z is

given by:

0 0 0

0 0 0 0

0 0 0

Z Z Z

Z Z Z Z

Z Z Z

(28)

where0

Z is the self earth return impedance of the pipe according to eq (19).

1.7.2Admittance

The admittance follows the general definition in terms of the potential coefficient matrix as follows:


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,

,

,

, , ,

, ,

,

0 0 0

0 0: . ... 0

0 0 0 0

0

0

: . ... 0

0 0 0 0

: . ...

I ii

I jj

I kk

P ii P ij P ik

P jj P jk

P kk

C C C C

C C C

C C

C C C

P

PPP

P P P

P P

P

P P P P

P P P

P P

P P P P

C

(29)

where

,

1,

,

0 0 0

0 0 0

0 0 0

0 0 0 0

I i

I j

I k

G

GY j P

G

(30)

i i

j j

k k

p p

I U

I Ux Y

I U

I U

(31)

Note in (30) that dielectric losses of the pipe are not being considered.

Each of the,I iiP submatrices of IP is the internal potential coefficient matrix of the single core cable

according to (20).

PP is the pipe internal potential coefficient matrix and defines the capacitive coupling between the outermostlayer of the single core cables and the pipe and hence the dielectric medium between the cables and the pipe.

Each of the submatrices,P ij

P of PP is a matrix with equal elements given in the following form:


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, , ,

, , , ,

, , ,

P ij P ij P ij

P ij P ij P ij P ij

P ij P ij P ij

P P P

P P P P

P P P

(32)

with

2

0

1ln 1

2

iii

r i

dqP

R q

(33)

22 210

1 1ln cos

2 2 cos

n

i j

ij ij

nr i j i j ij

d dqP

n qd d d d

(34)

CP is the potential coefficient matrix between the pipe inner and outer surfaces and hence the capacitance dueto the dielectric layer surrounding the pipe. A submatrix and the last column and row elements are given by:

C C C

C C C C

C C C

P P P

P P P P

P P P

(35)

0

1ln

2C

r

rP

q

(36)

It is assumed in the model that the pipe is underground. Therefore the outer surface of the insulating layer

surrounding the pipe is in direct contact with the earth (equipotential surface with U=0). Hence no additional

capacitive effect exists between the insulating layer of the pipe and ground.


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5.Input Parameters

Table 2: Input parameter of the single core cable type (TypCab)

Name Description Unit Range Default Symbol

loc_name Nameuline Rated voltage kV x>=0 0 UtypCon Shape of the core CompactdiaCon Outer diameter of the core mm x>=0 5 r

diaTube Inner diameter of the core mm x>=0 0 q

cHasEl Exists: use this flag to enable/disable the conducting layers 1rho Resistivity (20C) of the conducting layers cm x>0 1.7241

my Relative Permeability of the conducting layers 1r

cThEl Thickness of the conducting layers mm 2.5

Cf Filling factor of the conducting layers % x>0 andx=0 0.00393

cHasIns Exists: use this flag to enable/disable the correspondinginsulation layers

1

tand Dielectric Loss Factor of the insulating layer, i.e. tg of the

insulation. Set this value to zero to neglect insulation losses.

0.02

epsr Relative Permittivity of the insulating layer 3r

thIns Thickness of the insulating layer mm x>=0 1cHasSc Exists: use this flag to enable/disable the semiconducting

layers0

rhoSc Resistivity of the semiconducting layer cm x>0 1000000

mySc Relative permeability of the semiconducting layer 1 ,r SC epsrSc Relative permittivity of the semiconducting layer 3

,r SC

thSc Thickness of the semiconducting layer mm x>=0 1tmax Max. Operational Temperature C x>=0 80rtemp Max. End Temperature C x>0 80

Ithr Rated Short-Time (1s) Current kA x>=0 0diaCab Overall Cable Diameter mm 15


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Table 3: Input parameter of the cable system (TypCabsys)

Name Description Unit Range Default Symbolloc_name Name

frnom Nom. Frequency Hz 50

rhoEarth Resistivity of the earth return path .m x>0 100

cGearth Conductivity of the earth return path = inverse of the earth

resistivity.

S/cm 100

iopt_bur To specify is the cable is laid direct in ground (parallel single core

cables) or in a pipe (pipe-type cable)

gnd

nlcir Number of circuits defining the cable system x>=1 1

pcab_c Single core cable type: select from the library the single core

cable type (TypCab) of each circuit

TypCab

nphas Number of phases 3

dInom Rated current kA 1red Reduced: assert this option to automatically bond the sheaths

and armours of the cable. This operation will reduced the Z/Y

matrices of the cable to nphas x nphas.

0

bond Assert this option to cross bond the sheaths 0

xy_c Coordinate of Line Circuits: enter the coordinates of the single

core cables in the cable systems. Cables buried direct

underground have positive Y-distances with respect to the

ground surface. For pipe type cables, X- and Y-coordinates are

referred to the center of the pipe.

m 0

dep_pipe Depth of the center of the pipe (parameter only required for

pipe-type cables).

m x>=0 0

rad_pipe Outer Radius of the pipe m x>0 0.1

th_pipe Thickness of the pipe mm x>=0 0

th_ins Thickness of the pipe outer insulation mm x>0 1

rho_pipe Resistivity of the pipe .cm x>0 20

my_pipe Relative permeability of the pipe x>0 1

epsr_fil Relative permittivity of the filling material (insulating material

between the single core cables and the pipe)

x>0 1

epsr_ins Relative permittivity of the pipe outer cover. Se x>0 1


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6.Calculation Results

The cable constants function in stand-alone mode can be started from the Calculate button on the edit dialog of

the cable system type TypCabsys. Then PowerFactoryprints the resulting impedance and admittance matrices to

the output windows.

It follows an extract of the output window for a 132 kV, 3-phase cable system, 630 mm2, directly underground.

The first two matrices correspond to the unreduced layer impedances and admittances in phase components;

cores first, followed by sheaths. Cables are in the same order as the input. Rows follow real and imaginary part.

DIgSI/info - Layer Impedance Matrix (R+jX) in Ohm/km

1:R(1) 2:R(2) 3:R(3) 4:R(1) 5:R(2) 6:R(3)

1:R(1) 7.66524e-002 4.90955e-002 4.90948e-002 4.90991e-002 4.90955e-002 4.90948e-002

1:X(1) 6.57078e-001 4.22839e-001 3.79288e-001 5.88752e-001 4.22839e-001 3.79288e-001

2:R(2) 4.90955e-002 7.66524e-002 4.90955e-002 4.90955e-002 4.90991e-002 4.90955e-002

2:X(2) 4.22839e-001 6.57078e-001 4.22839e-001 4.22839e-001 5.88752e-001 4.22839e-001

3:R(3) 4.90948e-002 4.90955e-002 7.66524e-002 4.90948e-002 4.90955e-002 4.90991e-002

3:X(3) 3.79288e-001 4.22839e-001 6.57078e-001 3.79288e-001 4.22839e-001 5.88752e-001

4:R(1) 4.90991e-002 4.90955e-002 4.90948e-002 3.78537e-001 4.90955e-002 4.90948e-002

4:X(1) 5.88752e-001 4.22839e-001 3.79288e-001 5.87900e-001 4.22839e-001 3.79288e-001

5:R(2) 4.90955e-002 4.90991e-002 4.90955e-002 4.90955e-002 3.78537e-001 4.90955e-002

5:X(2) 4.22839e-001 5.88752e-001 4.22839e-001 4.22839e-001 5.87900e-001 4.22839e-001

6:R(3) 4.90948e-002 4.90955e-002 4.90991e-002 4.90948e-002 4.90955e-002 3.78537e-001

6:X(3) 3.79288e-001 4.22839e-001 5.88752e-001 3.79288e-001 4.22839e-001 5.87900e-001

Self and mutual impedances of the cores

Self and mutual impedances of the sheathsMutual impedances

between cores and sheaths


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DIgSI/info - Layer Admittance Matrix (G+jB) in uS/km

1:G(1) 2:G(2) 3:G(3) 4:G(1) 5:G(2) 6:G(3)

1:G(1) 0.00000e+000 0.00000e+000 0.00000e+000 -0.00000e+000 0.00000e+000 0.00000e+000

1:B(1) 5.17257e+001 0.00000e+000 0.00000e+000 -5.17257e+001 0.00000e+000 0.00000e+000

2:G(2) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 -0.00000e+000 0.00000e+000

2:B(2) 0.00000e+000 5.17257e+001 0.00000e+000 0.00000e+000 -5.17257e+001 0.00000e+000

3:G(3) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 -0.00000e+000

3:B(3) 0.00000e+000 0.00000e+000 5.17257e+001 0.00000e+000 0.00000e+000 -5.17257e+001

4:G(1) -0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

4:B(1) -5.17257e+001 0.00000e+000 0.00000e+000 5.85832e+002 0.00000e+000 0.00000e+000

5:G(2) 0.00000e+000 -0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

5:B(2) 0.00000e+000 -5.17257e+001 0.00000e+000 0.00000e+000 5.85832e+002 0.00000e+000

6:G(3) 0.00000e+000 0.00000e+000 -0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

6:B(3) 0.00000e+000 0.00000e+000 -5.17257e+001 0.00000e+000 0.00000e+000 5.85832e+002

The next two matrices are the impedances and admittances in symmetrical components in 0-1-2 sequence. Idem

before, cores come first followed by the sheaths. Cables are in the same order as the input. Rows follow real and

imaginary part.

DIgSI/info - 012 Impedance Matrix (R+jX) in Ohm/km

1:R(0) 2:R(1) 3:R(2) 4:R(0) 5:R(1) 6:R(2)

1:R(0) 1.74843e-001 1.25721e-002 -1.25724e-002 1.47290e-001 1.25721e-002 -1.25724e-002

1:X(0) 1.47372e+000 -7.25883e-003 -7.25838e-003 1.40540e+000 -7.25883e-003 -7.25838e-003

2:R(1) -1.25724e-002 2.75571e-002 -2.51443e-002 -1.25724e-002 3.81014e-006 -2.51443e-002

2:X(1) -7.25838e-003 2.48756e-001 1.45177e-002 -7.25838e-003 1.80430e-001 1.45177e-002

3:R(2) 1.25721e-002 2.51448e-002 2.75571e-002 1.25721e-002 2.51448e-002 3.81014e-006

3:X(2) -7.25883e-003 1.45168e-002 2.48756e-001 -7.25883e-003 1.45168e-002 1.80430e-001

4:R(0) 1.47290e-001 1.25721e-002 -1.25724e-002 4.76728e-001 1.25721e-002 -1.25724e-002

4:X(0) 1.40540e+000 -7.25883e-003 -7.25838e-003 1.40454e+000 -7.25883e-003 -7.25838e-003

5:R(1) -1.25724e-002 3.81014e-006 -2.51443e-002 -1.25724e-002 3.29442e-001 -2.51443e-002

5:X(1) -7.25838e-003 1.80430e-001 1.45177e-002 -7.25838e-003 1.79578e-001 1.45177e-002

6:R(2) 1.25721e-002 2.51448e-002 3.81014e-006 1.25721e-002 2.51448e-002 3.29442e-001

6:X(2) -7.25883e-003 1.45168e-002 1.80430e-001 -7.25883e-003 1.45168e-002 1.79578e-001


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DIgSI/info - 012 Admittance Matrix (G+jB) in uS/km

1:G(0) 2:G(1) 3:G(2) 4:G(0) 5:G(1) 6:G(2)

1:G(0) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

1:B(0) 5.17257e+001 0.00000e+000 0.00000e+000 -5.17257e+001 0.00000e+000 0.00000e+000

2:G(1) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

2:B(1) 0.00000e+000 5.17257e+001 3.55271e-015 0.00000e+000 -5.17257e+001 -3.55271e-015

3:G(2) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

3:B(2) 0.00000e+000 3.55271e-015 5.17257e+001 0.00000e+000 -3.55271e-015 -5.17257e+001

4:G(0) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

4:B(0) -5.17257e+001 0.00000e+000 0.00000e+000 5.85832e+002 0.00000e+000 0.00000e+000

5:G(1) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

5:B(1) 0.00000e+000 -5.17257e+001 -3.55271e-015 0.00000e+000 5.85832e+002 5.68434e-014

6:G(2) 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000 0.00000e+000

6:B(2) 0.00000e+000 -3.55271e-015 -5.17257e+001 0.00000e+000 5.68434e-014 5.85832e+002


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7.References

[1] Schaums Outline Series, Electric Power Systems, McGraw-Hill, 1990

[2]

DIgSILENT PowerFactoryTechnical Reference Overhead Lines and CablesModels, 2009

[3] A.Ametani, A general formulation of impedance and admittance of cables, IEEE Transaction on Power

Apparatus and Systems, Vol. PAS-99, No. 3 May/June 1980.

[4]

IEC 60071: International Standard Insulation Coordination, 8th Edition, 2006.

[5]

IEEE Working Group on Estimating the Lightning Performance of Transmission Lines. IEEE WG Report.

Estimating the Lightning Performance of Transmission Lines II-Updates of Analytical Models, IEEE Trans.

PWRD, Vol 8,1993, pp 1254-1267.

[6] DIgSILENT PowerFactoryTechnical Reference Overhead Lines Constants, 2009

techref_cableconstants[1].pdf

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