Techref_cableconstants[1].pdf

DIgSILENT Technical Documentation

Cable Systems

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 März 2011

Rev. Nr.

Author

Date

01

F. Fernández

15.04.2010

14.0.516

02

F.Fernández

02.03.2011

14.1.0

Cable Systems

Reviewed by

Date

PF Version

Table of Contents

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

Cable Systems

Table of Contents

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 PowerFactory with help of two type objects: a single core cable type TypCab which 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.

Cable Systems

Table of Contents

2. Definition of the cable system 1.1 The single core cable type (TypCab) The single core cable type TypCab supports 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 section 5 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 TypCab to 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 TypCab is organized according to lyers, i.e. the conducting, insulation and semiconducting layers, if available. Use TypCab to enter all the geometrical data defining the cross section of the single core cable and the properties of all constitutive materials.

1.1.1 Filling 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:

RDC [ / km]      cm  where

1 10    r  q2   C f 2

r and 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.

Cable Systems

Table of Contents

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

T  20C  1   20  T  where

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

metals are given in Table 1 for reference.

Table 1: Resistivities and temperature coefficient of resistance Resistivity at 20 °C [μΩ.cm] 2.83

Temperature coefficient at 20°C [1/°C] 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

Material Aluminum

1.2 The cable system type (TypCabsys) The cable system type TypCabsys is 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 in Table 3 in section 5. The cable system type also defines the bonding conditions of the sheath and armours when available.

Cable Systems

Table of Contents

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 nonmagnetic 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:

where

[U ]

 x U     Z    I 

(1)

 x  I    Y   U 

(2)

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:

 Z    Z I    Z P    ZC    Z 0 

(3)

Y   s   P   P    PI    PP    PC    P0 

(4)

1

where

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

The matrices with subscript subscript

I

account for the internal impedance and admittance respectively and matrices with

O for the earth or air return path. In case if a pipe enclosure cable the matrices with subscript C

and

P define the impedance and admittance of the pipe; these matrices becoming zero if the cable is laid directly underground. 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

subscripts

C

Subscripts

c, s and a

Cable Systems

accounts for the internal impedance, subscript and

P

O for the earth or air return path and

for the pipe enclosure if available. (lower case) are used for core, sheath and armour in cable layer equations

Table of Contents



Subscripts

i, j and k

refer to the cables in the system (typically three cables in a three phase cable

system).

1.3 Internal 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:

U c   Z cc     x U s     Z sc U a   Z ac

Z cs Z ss Z as

 Ic  Z ca   I c       Z sa    I s     Z I    I s   I a  Z aa   I a 

(5)

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

Z cc  Z11  2  Z12  Z 22  2  Z 23  Z 33 Z cs  Z sc  Z12  Z 22  2  Z 23  Z 33 Z ca  Z ac  Z sa  Z as  Z 23  Z 33

(6)

Z ss  Z 22  2  Z 23  Z 33 Z aa  Z 33 The impedances with subscript 1,2 and 3 are referred as loop impedances. For instance

Z11 is the impedance of

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

Z11  Z c ,OUT  Z c / s , INS  Z s , IN Z 22  Z s ,OUT  Z s / a , INS  Z a , IN Z 33  Z a ,OUT  Z a , INS

(7)

Z12  Z 21   Z s , MUTUAL Z 23  Z 32   Z a , MUTUAL The impedance of the tubular conductors are found with the modified Bessel functions with tube = c, s and a respectively:

m I 0 (mq)  K1 (mr )  K 0 (mq)  I1 (mr ) 2 qD m Z tube,OUT  I 0 (mr )  K1 (mq)  K 0 (mr )  I1 (mq) 2 qD  Z tube, MUTUAL  2 qrD Z tube, IN 

where

Cable Systems

(8)

Table of Contents

D  I1 (mr )  K1 (mq)  I1 (mq)  K1 (mr )

j

m The parameter



 1

(9)

(10)

p

m is the reciprocal of the depth of penetration p

and are both frequency-dependent complex

values.

Z INS 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:

Z INS

2  0  qk   di      j  ln  1      2  ri   qk   





and in the case of concentric tubular conductors

Z INS  j

(11)



di  0 and (11) reduces to

q  0  ln  k  2  ri 

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:

Ci 

2 0 r

 q

ln r



1 Pi

(12)

Gi  Ci  tg   with

Pi the 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:

 Pc  Ps  Pa  PI    Ps  Pa  Pa

 CI  

Ps  Pa Ps  Pa Pa

1  PI 

YI   GI   j CI 

Cable Systems

Pa  Pa  Pa 

(13)

(14)

(15)

Table of Contents

1.5 Semiconducting layers The model supports the definition of a semiconducting layer on the conductor’s outer surface and the insulation’s outer 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:

CSC  2 0   rSC GSC 

2

 SC



1 ln  rSC / qSC 

1 ln  rSC / qSC 

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

 rSC the

 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   GiIns GIL GSC 1 1 1   CiIns CIL CSC

1.6 Parallel Single-Core Cables 1.6.1 Impedance Let’s assume being

i, j , k

three parallel single core cables each of them consisting of core, sheath and armour.

Eq. (1) can be expanded as:

 U i      Z I ,ii   0   0         Z I , jj   0     x  U j           U k     :.  Z I ,kk   ...    Z 0,ii   Z 0,ij   Z 0,ik      I i             Z 0, jj   Z 0, jk       I j         :.       ... Z I  0,kk      k   

Cable Systems

(16)

Table of Contents

where

 Z 0,s  and  Z 0,m  are the self and mutual earth-return impedance matrices of the cable system given

as:

 Z e,s   Z 0, s    Z e, s  Z e, s

 Z e,m   Z 0,m    Z e,m  Z e,m Z e,m

Z e,s Z e,s Z e,s

Z e,m Z e,m Z e,m

Ze,s   Z e,s  Z e , s 

Z e,m   Z e. m  Z e,m 

s  jj , kk , ll

m  jk , kl , lj

is the mutual earth-return impedance between two parallel cables

Z e, jk  j

(17)

(18)

i, j

given by:

0  K  m  dik   K0  m  Dik     Pik  jQik    0

(19)

and

Pik  jQik

Z e,s

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

the terms of the Carson’s serie (see [6] for further reference).

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

1.6.2 Admittance As 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

 P0    in (4)

and therefore the admittance matrix of the cable results:

  PI ,i  0 0        P  P  0 P 0    I  I, j     PI ,k   0  0 

(20)

Y    P 

1

  I i    U i        x   I j     Y    U j         I k    U k   and the submatrices in the main diagonal according to (13).

Cable Systems

(21)

Table of Contents

1.7 Pipe Type Cable 1.7.1 Impedance Assuming again a system of three single core cables

i, j , k

each of them consisting of core, sheath and armour,

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

 U i        U j     x    U k        U p  

  Z I ,ii   0   0     Z I , jj   0    :.  Z I ,kk  ...  0 0  0

  Z P ,ii       :.   0   Z C1       :.   Z C 2   Z 0       :.   Z 0

0  0  0  0 

 Z P ,ij   Z P ,ik  0    Z P , jj   Z P , jk  0    Z P ,kk  0  ...  0 0 0   Z C1   Z C1  Z C 2    Z C1   Z C1  Z C 2    Z C1  Z C 2  ...  ZC 2 Z C 2 Z C 3   Z 0   Z 0  ... Z0

 Z 0  Z 0    Z 0  Z 0    Z 0  Z 0   Z0 Z 0 

   I i         I j         I k        I p 

(22)

 Z P  defines the self and mutual impedances of the pipe-return path of the single core cables. A submatrix is given by:

 Z P ,ij   Z P ,ij    Z P ,ij  Z P ,ij 

Z P ,ij Z P ,ij Z P ,ij

Z P ,ij   Z P ,ij  Z P ,ij 

Self impedance of the with pipe-return path for the i-th cable

Cable Systems

(23)

(i  j ) :

Table of Contents

Z P ,ii

  j 0 2

 r K 0  mq    d 2 n  2r K n  mq    i    '  mqK1  mq  n 1  q  nr K n  mq   mqK n  mq  

Mutal impedance between the i-th and the j-th cables with common pipe-return path

Z P ,ij  j

0 2

  q   ln 2 2   di  d j  2di d j cos ij

(24)

(i  j ) :

 K 0  mq    r   mqK1  mq  

 2r K n  mq  dd  1      i 2 j  cos  nij     ' n 1  q   nr K n  mq   mqK n  mq  n 

(25)

n



 Z C  ìs the connection impedance matrix between the pipe inner and outer surfaces. The submatrix  ZC1  , Z C 2 and Z C 3 are given by:  Z C1   Z C1    Z C1  Z C1 where

Z C1 , Z C 2

and

Z C1 Z C1 Z C1

Z C1   Z C1  Z C1 

(26)

Z C 3 are calculated using equations (8) to (11) for the impedance of tubular conductors

and tube being the pipe as follows:

ZC1  Z pipe,OUT  Z pipe, INS  2  Z pipe, MUTUAL ZC 2  Z pipe,OUT  Z pipe, INS  Z pipe, MUTUAL

(27)

ZC 3  Z pipe,OUT  Z pipe, INS Finally,

 Z 0  represent the impedance of the earth return-path of the pipe. The diagonal submatrix  Z 0  is

given by:

 Z0   Z 0    Z 0  Z 0 where

Z0 Z0 Z0

Z0   Z0  Z 0 

Z 0 is the self earth return impedance of the pipe according to eq (19).

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

Cable Systems

(28)

Table of Contents

   PI ,ii       P       :.    0   PP ,ii       :.   0



 PC     :.   PC

0  0   PI , jj   0  ... 0

0  0   PI ,kk  0   0 0

 PP ,ij   PP ,ik  0    PP , jj   PP , jk  0    PP ,kk  0  ...  0 0 0  PC   PC  PC     PC   PC  PC    ...  PC  PC    PC PC PC  

(29)

where

 GI ,i  0 0   0 GI , j  0 Y    GI ,k  0  0  0 0  0

0  0   j  P  0  0





1

  I i    U i         I j    U j    x     Y       I k    U k        I p   U p 

(30)

(31)

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

 PI ,ii  submatrices of  PI 

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 outermost layer of the single core cables and the pipe and hence the dielectric medium between the cables and the pipe. Each of the submatrices

Cable Systems

 PP ,ij 

of

 PP  is a matrix with equal elements given in the following form:

Table of Contents

 PP ,ij   PP ,ij    PP ,ij  PP ,ij 

PP ,ij PP ,ij PP ,ij

PP ,ij   PP ,ij  PP ,ij 

(32)

with

 q Pii  ln  2 0 r  Ri  1

  d 2    1   i      q    

  q   Pij  ln 2 0 r   di2  d 2j  2di d j cos ij   1

(33)

   1  d d n      i j   cos ij    n 1 n  q 2    

(34)

 PC  is the potential coefficient matrix between the pipe inner and outer surfaces and hence the capacitance due to the dielectric layer surrounding the pipe. A submatrix and the last column and row elements are given by:

 PC  PC    PC  PC

PC 

PC PC PC

PC  PC  PC 

r  ln   2 0 r q 1

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.

Cable Systems

(35)

(36)

Table of Contents

5. Input Parameters Table 2: Input parameter of the single core cable type (TypCab) Name

Description

Unit

loc_name uline typCon diaCon diaTube cHasEl rho

Name Rated voltage Shape of the core Outer diameter of the core Inner diameter of the core Exists: use this flag to enable/disable the conducting layers Resistivity (20°C) of the conducting layers

my

Relative Permeability of the conducting layers

cThEl Cf

Thickness of the conducting layers Filling factor of the conducting layers

mm %

rpha

DC-Resistance (20°C) of the conducting layers

 / km

alpha cHasIns tand

Temperature coefficient of the conducting layers 1/K Exists: use this flag to enable/disable the corresponding insulation layers Dielectric Loss Factor of the insulating layer, i.e. tg of the

epsr

insulation. Set this value to zero to neglect insulation losses. Relative Permittivity of the insulating layer

thIns cHasSc

Range

kV

x>=0

mm mm

x>=0 x>=0

 cm

x>0

x>0 and x<=100 x>=0

Default

Symbol

0 Compact 5 0 1 1.7241

r q

1

r

2.5 100

Cf

0.8780769

Rdc

0.00393 1

U





0.02 3

rhoSc

Thickness of the insulating layer Exists: use this flag to enable/disable the semiconducting layers Resistivity of the semiconducting layer

mySc

Relative permeability of the semiconducting layer

1

r ,SC

epsrSc

Relative permittivity of the semiconducting layer

3

 r ,SC

thSc tmax rtemp Ithr diaCab

Thickness of the semiconducting layer Max. Operational Temperature Max. End Temperature Rated Short-Time (1s) Current Overall Cable Diameter

Cable Systems

mm

x>=0

1 0

 cm

x>0

1000000

r

mm °C °C kA mm

x>=0 x>=0 x>0 x>=0

1 80 80 0 15

Table of Contents

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

Description

loc_name

Name

frnom

Nom. Frequency

rhoEarth

Resistivity of the earth return path

cGearth

Conductivity of the earth return path = inverse of the earth resistivity.

iopt_bur

To specify is the cable is laid direct in ground (parallel single core cables) or in a pipe (pipe-type cable)

nlcir

Number of circuits defining the cable system

pcab_c

Single core cable type: select from the library the single core cable type (TypCab) of each circuit

nphas

Number of phases

dInom

Rated current

red

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.

bond

Assert this option to cross bond the sheaths

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

dep_pipe

Depth of the center of the pipe (parameter only required for pipe-type cables).

m

rad_pipe

Outer Radius of the pipe

th_pipe

Thickness of the pipe

th_ins

Thickness of the pipe outer insulation

mm

x>0

1

rho_pipe

Resistivity of the pipe

μΩ.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

Cable Systems

Unit

Range Default Symbol

Hz Ω.m

50 x>0

μS/cm

100 100 gnd

x>=1

1

TypCab 3 kA

1 0

0 0

x>=0

0

m

x>0

0.1

mm

x>=0

0

Table of Contents

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 PowerFactory prints 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.

Self and mutual impedances of the cores

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

Mutual impedances between cores and sheaths

Cable Systems

Self and mutual impedances of the sheaths

Table of Contents

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

Cable Systems

Table of Contents

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

Cable Systems

Table of Contents

7. References [1]

Schaum’s Outline Series, “Electric Power Systems”, McGraw-Hill, 1990

[2]

DIgSILENT PowerFactory Technical Reference “Overhead Lines and Cables Models”, 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 PowerFactory Technical Reference “Overhead Lines Constants”, 2009

Cable Systems