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1Panel Session on Data for Modeling System TransientsInsulated
Cables
Bjrn GustavsenSINTEF Energy Research
N-7465 Trondheim, [email protected]
Abstract: The available EMTP-type programs have dedicatedsupport
routines (Cable Constants) for calculating an
electricrepresentation of cable systems in terms of a
seriesimpedance matrix Z and a shunt admittance matrix Y, basedon
cable data defined by geometry and material properties. Zand Y are
then used as the basic input for the various cablemodels applied in
time domain transient simulations. Thispaper describes necessary
procedures for converting theavailable cable data into a new set of
data which can be usedas input for Cable Constants. In particular,
the paper showshow to handle the semiconducting screens of single
corecoaxial type cables. In situations where the cable plays
animportant role in the transient simulation, the user shouldalso
consider obtaining a specimen of the cable in order toverify the
geometrical data provided by the manufacturer. Therecommendations
in this paper are supported by field testresults.
Keywords: Electromagnetic Transients, Insulated Cables,Modeling,
EMTP.
I. INTRODUCTION
The modeling of insulated cables for the simulation of
electromagnetictransients requires1) Calculation of cable
parameters from geometrical data and material
properties [1],[2].2) Conversion of the cable parameters into a
new set of parameters
for usage by the transmission line/cable model.
This paper deals with the first step in the procedure, namely
thecalculation of cable parameters. All the commonly used programs
forsimulation of electromagnetic transients (EMTP/ATP/EMTDC)
havededicated support routines for this task. The routine(s) have
verysimilar features and will in this presentation be given the
commongeneric name Cable Constants (CC).
Data conversion is often needed by the user in order to bring
theavailable cable data into a form which can be used as input by
CC. Thisconversion is needed because1) The data can have
alternative representations with CC only
supporting one of the representations.2) The CC routine does not
consider certain cable features, such as
semiconducting screens and wire screens.
The situation is made further complicated by the fact that
thenominal thickness of the various layers (insulation,
semiconductingscreens) as stated by manufacturers can be smaller
than the actual(design) thickness of the layers. Therefore, the
information ongeometrical data from the manufacturer can be
inaccurate from theviewpoint of cable parameter calculations.
This paper demonstrates the needed conversions for one real
caseof a single core coaxial cable system, and proposes how to best
use theavailable data to produce a reliable cable model. The effect
of inaccuratedata on a time domain simulation is also shown. The
paper furtherdiscusses the shortcoming of CC in taking into account
possibleattenuation effects caused by the semiconducting
screens.
II. CABLE PARAMETERS
The basic parameters used by transmission line/cable models are
thefollowing:
)()()( wwww LjRZ += (1)
)()()( wwww CjGY += (2)
where R,L,G,C are the series resistance, series inductance,
shuntconductance and shunt capacitance per unit length of the cable
system.These quantities are n by n matrices where n is the number
of(parallel) conductors of the cable system. The variable w
reflects thatthese quantities are calculated as function of
frequency. Z and Y arecalculated using CC based on the geometry and
material properties ofthe system [1],[2].
III. ACTUAL CABLE VS. CABLE CONSTANTSREPRESENTATION
A. Geometry
In the following we consider CC applied to systems of parallel
singlecore coaxial type cables (SC cables). The user must specify
thefollowing input data: The location of each cable (x-y
coordinates). The geometry of each SC cable.
In general, CC represents each SC cable by a set of
concentricallylocated homogenous pipes, separated by insulating
layers. Figure 1shows the representation which would be used for a
SC cable withoutarmour.
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2 Fig. 1 CC representation of system of 3 SC cables
Figure 2 shows an actual XLPE single core coaxial cable.
Clearly,this cable design is different from the simple
configuration assumed inFigure 1. In particular, the user needs to
decide how to represent The core stranding The inner semiconducting
screen The outer semiconducting screen The wire screen (sheath)
Fig. 2 SC XLPE cable
B. Material properties
The user must specify the following material constants: The soil
resistivity and relative permeability rg , mg The core resistivity
and relative permeability rc , mc The sheath resistivity and
relative permeability rs , ms The insulation relative permittivity
er(In non-magnetic materials the relative permeability equals
1.0.)
The CC-routine assumes the relative permittivity er of each
insulatinglayer to be real )0( =e and frequency independent,
therebyneglecting any relaxation phenomena in the insulation. This
implies :
)()()( wwww LjRZ += (3)
CjY ww =)( (4)
C. Eddy current effects
The CC-routine takes into account the frequency dependent skin
effectin the conductors, but neglects the proximity effect between
parallel
cables. This means that CC assumes a cylindrically
symmetricalcurrent distribution in all conductors. The assumed
cylindricaldistribution also means that the helical winding effect
of the wirescreen is not taken into account.
IV. MODELING REQUIREMENTS VS. PHENOMENON
For situations with straight sheaths (i.e. no crossbondings),
highfrequency transients propagate mainly as uncoupled coaxial
waveswithin each SC cable. The earth characteristics have in this
situationonly a mild effect on the resulting phase voltages and
phase currents.In the following we shall therefore focus on the
representation of thecable within the protective jacket
(oversheath).
V. CONVERSION PROCEDURES
A. Core
The CC-routine requires the core data to be given by the
resistivity rcand the radius r1. However, the core conductor is
often of the strandeddesign (Figure 2), whereas CC assumes a
homogenous (solid)conductor. This makes it necessary to increase
the resistivity cr ofthe core material to take into account the
space between strands:
ccc A
r 21prr = (5)
where Ac is the efficient (nominal) cross sectional area of the
core. Theresistivity cr for to be used for annealed copper and hard
drawnaluminum at 20C is according to IEC 28 and IEC 889: Copper:
1.7241E-8 Wm
Aluminum 2.8264E-8 Wm
If the manufacturer provides the DC resistance for the core,
thesought resistivity can alternatively be calculated as
l
rRDCc
21pr = (6)
B. Insulation and semiconducting screens
ProcedureThe semiconducting screens can have a substantial
effect on thepropagation characteristics of a cable in terms of
velocity, surgeimpedance and possibly the attenuation [3],[4].
Unfortunately, CCdoes not allow explicit representation of the
semiconducting screens,so an approximate data conversion procedure
must be applied :
1) Calculate r2 as r1 plus the sum of the thickness of
thesemiconducting screens and the main insulation.
2) Calculate the relative permittivity er1 as
0
121 2
)/ln(
pee
rrCr = (7)
where C is the cable capacitance stated by the manufacturer
ande0 = 8.854E-12. If C is unknown, er1 can instead be calculated
based onthe relative permittivity erins of the main insulation:
)/ln(
)/ln( 12ins1 ab
rrrr ee = (8)
where a and b are the insulation inner and outer radius,
respectively.For XLPE erins equals 2.3.
Inner semiconductorOuter semiconductor
Wire screen
CoreInsulation
rg , m g
corer1
r2
r3
r4
sheath
e1e2
rc, mc
rs, ms
Insulation
x
y
air
soil
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3JustificationThe inner and outer semiconducting screens have a
relative permittivityof the order of 1000, due to the high carbon
content used in thesemiconducting screens. This implies that the
capacitance of thescreens is much higher than that of the
insulation and will tend to act asa short circuit when calculating
the shunt admittance between core andsheath. A similar effect is
caused by the ohmic conductivity of thesemiconducting screens,
which is required by norm to be higher than1E-3 S/m.
At the same time the conductivity of the semiconducting screens
ismuch lower than that of the core and the sheath conductors,
implyingthat the semiconducting screens do not contribute to the
longitudinalcurrent conduction.
This implies that when entering the geometrical data in CC,
theuser should let the XPLE insulation extend to the surface of the
coreconductor and the sheath conductor, and increase the
relativepermittivity to leave the capacitance unaltered. Note that
this modelingneglects the possible attenuation caused by the
semiconductingscreens. The attenuation could have a strong impact
on very highfrequency transients. This is discussed in Section
X.
C. Wire screen
When the sheath conductor consists of a wire screen, the
mostpractical procedure is to replace the screen with a tubular
conductorhaving a cross sectional area equal to the total wire area
As. With aninner sheath radius of r2, the outer radius r3
becomes
223 r
Ar s +=
p(9)
VI. APPLICATION TO 66 kV CABLE
A. Manufacturers data
The procedures outlined in the previous sections will be
demonstratedfor a 66 kV cable similar to the one shown in Figure 3.
For this cable(manufactured in the 1980s), the following data were
provided by themanufacturer:
2mm1000=cAnF/m24.0=C
/m59.2DC -= ERmm5.191 =r
Thickness of inner insulation screen: mm8.0Thickness of
insulation: mm14Thickness of outer insulation screen: mm4.0Wire
screen: 2mm50=sA
B. Data consistency
In Section VB it was justified that the insulation screens can
berepresented by short circuit when calculating the shunt
admittance.This is equivalent to a capacitance between two
cylindrical shells withradius :
mm3.20mm)8.05.19( =+=amm3.34mm14 =+= ab
)/ln(
2 0ab
C repe
= (10)
With a relative permittivity of 2.3 for XLPE, this defines
acapacitance of 0.244 nF/m which is in agreement with the
capacitanceof 0.24 nF/m stated by the manufacturer.
C. Data conversion
Core
From the manufacturer:
mm5.191 =rThe resistivity is calculated by (6) :
/m104643.3 8-=cr
Insulation and insulation screens
mm7.34)4.0148.0(12 =+++= rr486.21 =re (by (7))
Wire screen
The outer radius is calculated using (9):
mm93.343 =r
/m8718.1 -= Esr (copper)
VII. INACCURACY IN DATA FROM MANUFACTURER
The relevant cable norms (e.g. IEC 840, IEC 60502) puts
limitations onthe minimum thickness of each cable layer (in
relation to the nominalthickness), but not on the maximum
thickness. Therefore, themanufacturer is free to use thicker layers
than the nominal ones, e.g. toaccount for dispersity in production
and ageig effects. This situation isprevalent for both the main
insulation, the oversheath, and thesemiconducting screens.
By measurement on a specimen of the 66 kV cable it was foundthat
the insulation and in particular the semiconducting screens
werethicker than stated in the data sheets :
Thickness of inner insulation screen: 1.5 mm
Thickness of insulation: 14.7 mm
Thickness of outer insulation screen: 1.1 mmSeparation between
outer insulation screen and centre ofeach conductor in wire screen:
1 mm
This gives a modified model :
mm5.191 =rmm8.372 =r
856.22 =re (by (7))
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4VIII. SENSITIVITY
At high frequencies, the asymptotic (lossless) propagation
velocityand surge impedance are given as
CLv 0/1= (11)
CLZ c /0= (12)
where
)/ln(2 12
00 rrL p
m= (13)
with 740 -= EpmWe will now compare the asymptotic propagation
characteristics
as calculated by the following procedures:
Case #1:Neglecting the semiconducting screens. Capacitance and
inductancecalculated using (10) and (13) with a=r1=19.5 mm,
b=r2=33.5 mm, ander1=2.3.
Case #2:Taking the semiconducting screens into account.
Capacitance andgeometrical data from the manufacturer: r1=19.5 mm,
r2=34.7 mm, ander1=2.486.
Case #3:Taking the semiconducting screens into account.
Capacitance from themanufacturer, geometrical data from cable
specimen: r1=19.5 mm,r2=37.8 mm, and er1=2.856.
Using the inductance calculated from (12), the velocity
andcharacteristic impedance are calculated as:
Table 1. Sensitivity of cable propagation characteristics
case #1 case #2 case #3
v [m/s] 197.7 190.1 (-3.8%) 177.4 (-10.3%))
Zc [W] 21.39 21.91 (+2.4%) 23.49 (+9.8%)
Thus, the cable propagation characteristics are highly sensitive
tothe representation of the core-sheath layers.
IX. FIELD TEST AND TIME DOMAIN SIMULATION
A field test was carried out on a 6.05 km length of the cable.
One coreconductor was charged up to a 5 kV DC voltage and then
shorted toground. Thus, a negative step voltage was in effect
applied to the cableend (see Figure 3).
Fig. 3 Cable test setup
Figure 4 shows the measured initial inrush current flowing into
the coreconductor in p.u. of the DC-voltage. The initial current
corresponds to
the surge admittance of the cable core-sheath loop, which is the
inverseof the surge impedance.
The inrush current was also simulated using EMTDC v3 with aphase
domain cable model [5],[6]. The CC routine was applied for thethree
different cases defined in Section VIII. It is seen that using
thecable representation in case #3 gives a calculated response
which is infairly close agreement with the measured response. The
two otherrepresentations have a much larger discrepancy. (The spike
occurringat about 50 s resulted because of long leads connecting
the two cablesections).
Fig. 4 Measured and simulated inrush current
X. IMPROVED MODELING OF SEMICONDUCTINGSCREENS
Reference [3] suggests to model the admittance between the core
andthe sheath using the circuit in Figure 5, in which each
semiconductingscreen is modeled by a conductance in parallel with a
capacitor. Withcomponent values obtained from measurements, they
obtained a goodagreement between measured attenuation and
calculated attenuation inthe range 1 MHz125 MHz. The attenuation
effect of thesemiconducting screens was strong.
Reference [4] gives a systematic investigation of the effects
ofsemiconducting screens on propagation characteristics.
Fig. 5 Improved model of insulation screens [3]
The conductivity and permittivity of the semiconducting
screensdepends very much on the amount of carbon added, the
structure of
core
Inner semiconducting screen
Outer semiconducting screen
Main insulation
G1
G2
C1
C2
C
sheath
Y
3.85 km 2.2 km15 m
core
sheath
Negativestep voltage
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5the carbon, and the type of base polymer. Very high
carbonconcentrations are used (e.g. 35%). IEC 840 requires the
resistivity tobe lower than 1000 Wm for the inner screen, and below
500 Wm forthe outer screen. One manufacturer stated that they use a
much lowerresistivity, typically 0.1 Wm10 Wm. The relative
permittivity isvery high, typically of the order of 1000. The
permittivity andconductivity can be strongly frequency
dependent.
In order to investigate the possible attenuation effects of
theinsulation screens of the cable considered in this paper,
arepresentation as in Figure 5 was employed assuming
frequencyindependent conductances and capacitances. The component
valueswere calculated as follows:
m/nF24.0=C (from manufacturer))/ln(/2 201 brC repe=)/ln(/2 102
raC repe=
)/ln(/2 21 brG ps=)/ln(/2 12 raG ps=
wherea: Outer radius of inner semiconducting screenb: Inner
radius of outer semiconducting screener : Relative permittivity of
semiconducting screenss : Conductivity of semiconducting
screens
Figure 6 shows the attenuation per km, for a few combinations
ofs and er. The curves define to which peak value a sinusoidal
voltage of1 p.u. peak value decays to over a distance of 1 km. (The
signal decaysexponentially as function of length). The model
predicts a significantcontribution from the semiconducting screens
for a low value of boththe relative permittivity (10, 100) and the
conductivity (0.001). Withthe high permittivity (1000), the
capacitance tends to short out theconductance, and no appreciable
increase of the attenuation is seen.The lowest value for the
permittivity (10) is probably unrealistic.
Fig. 6 Effect of semiconducting screens on attenuation
XI. DISCUSSION
This paper has focused on the importance of correctly modeling
thesemiconducting screens of single core coaxial type cables. It is
shownthat a careless modeling tends to produce a model with a too
low surgeimpedance and a too high propagation velocity. The
importance ofaccurate modeling is strongly dependent on the type of
transientstudy. If the cable is part of a resonant overvoltage
phenomenon, theaccurate representation of the cable the surge
impedance andpropagation velocity is crucial.
XII. CONCLUSIONS
This paper describes necessary conversion procedures for the
availablecable data for usage by Cable Constantstype routines (CC),
withfocus on single core (SC) coaxial type cables. The main
conclusions arethe following:
CC does not directly apply to SC cables with
semiconductingscreens, so a conversion procedure is needed before
entering thecable data into CC. This paper describes the needed
conversionsand also describes the conversions needed for handling
the corestranding and wire screens.
The nominal thickness of the various insulation
andsemiconducting cable screens as stated by manufacturers can
besmaller than those found in actual cables. This can result in
asignificant error for the propagation characteristics of the
cablemodel.
CC has no means for taking into account any additional
attenuationat very high frequencies resulting from the
semiconducting screens.
XIII. REFERENCES
[1] L.M. Wedepohl and D.J. Wilcox, Transient Analysis
ofUnderground Power Transmission System ; System-Model andWave
Propagation Characteristics, Proc. IEE, vol. 120, No. 2,February
1973, pp. 252-259.
[2] A. Ametani, A General Formulation of Impedance andAdmittance
of Cables, IEEE Trans. PAS, Vol. 99, No. 3,May/June 1980, pp.
902-909.
[3] G.C. Stone and S.A. Boggs, "Propagation of Partial
DischargePulses in Shielded Power Cable, Proceedings of Conference
onElectrical Insulation and Dielectric Phenomena, IEEE 82CH1773-1,
October 1982, pp. 275-280.
[4] W.L. Weeks and Yi Min Diao, Wave Propagation inUnderground
Power Cable, IEEE Trans. PAS, Vol. 103, No. 10,October 1984, pp.
2816-2826.
[5] A. Morched, B. Gustavsen, and M. Tartibi, A Universal
LineModel for Accurate Calculation of Electromagnetic Transients
onOverhead Lines and Cables, IEEE trans. PWRD, vol. 14, no. 3,July
1999, pp. 1032-1038.
[6] B.Gustavsen, G. Irwin, R. Mangelrd, D. Brandt, and K.
Kent,"Transmission Line Models for the Simulation of
InteractionPhenomena between Parallel AC and DC Overhead
Lines",IPST'99 International Conference on Power System
Transients,Budapest, 1999, pp. 61-67.
XIV. BIOGRAPHY Bjrn Gustavsen was born in Norway in 1965. He
received theM.Sc. degree in 1989 and the Dr.-Ing. degree in 1993,
both from the
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6Norwegian Institute of Technology in Trondheim. Since 1994
hehas been working at SINTEF Energy Research (former EFI).
Hisinterests include simulation of electromagnetic transients
andmodeling of frequency dependent effects. He spent 1996 as
aVisiting Researcher at the University of Toronto, and the summerof
1998 at the Manitoba HVDC Research Centre, Winnipeg,Canada.
APPENDIX DATA CONVERSION
The following Matlab code does the recommended data
conversionfor the case described in Section VI. All geometrical
quantities are inmeters.
INPUT:
C =0.24e-9; %capacitance stated by manufacturer [F/m]Acore
=1000e-6; %core nominal cross sectional areaAsheath=50e-6; %sheath
nominal cros sectional areatins =14e-3; %thickness: main
insulationtins1 =0.8e-3; %thickness: inner insulation screentins2
=0.4e-3; %thickness: outer insulation screenr1 =19.5e-3; %core
radiusRDC =2.9e-5; %core DC resistance [ohm/m]eps0 =8.854e-12;
%vacuum permittivity
OUTPUT:
rhoc=RDC*pi*r1^2 %core resistivityr2=r1+tins1+tins+tins2;
%sheath inner radiusr3=sqrt(Asheath/pi+r2^2); %sheath outer
radiusepsr1=C*log(r2/r1)/(2*pi*eps0); %effective rel. permittivity
%of core sheath layer
