IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005 2045

Parameter Determination for Modeling SystemTransients—Part II: Insulated Cables

IEEE PES Task Force on Data for Modeling System Transients of IEEE PES Working Group on Modeling and Analysisof System Transients Using Digital Simulation (General Systems Subcommittee)

B. Gustavsen, J. A. Martinez, and D. Durbak

Abstract—EMTP-type programs include dedicated supportroutines (cable constants) for calculating an electric representa-tion of cable systems in terms of a series impedance matrixand a shunt admittance matrix , based on cable data defined bygeometry and material properties. and are the basic input ofthe various cable models that are used in time-domain transientsimulations. This paper discusses the modeling of high-voltagecables: single-core, three-phase, and pipe-type cables. Materialproperties are given for commonly used conductive and insulatingmaterials, and how to represent semiconductive screens, lossy in-sulation materials, and magnetic armors is shown. The significanceof the grounding condition of sheaths and armors is discussed.In transient calculations, it is always important to accuratelyrepresent the core conductor, insulation, semiconductive layers,and the metallic sheath. Frequency-dependent losses of paper-oilinsulation need to be taken into account for very-high-frequencytransients. The significance of conductors external to the cabledepends on the shielding effect of the cable sheath, which dependson the sheath design and the frequency content of the transient.The conclusions are supported by numerical simulation results.

Index Terms—Insulated cables, modeling, power system tran-sients, simulation.

I. INTRODUCTION

SEVERAL line models have been implemented in com-monly available EMTP-type programs which can accu-

rately represent the frequency dependence of cable systems[1]–[3]. All of these models require the same type of input pa-rameters, namely the series impedance matrix and the shuntadmittance matrix . Sufficiently accurate input parametersare, in general, more difficult to obtain for cable systems thanfor overhead lines as the small geometrical distances makethe cable parameters highly sensitive to errors in the specifiedgeometry. In addition, it is not straightforward to representcertain features, such as wire screens, semiconductive screens,armors, and lossy insulation materials. The situation is madefurther complicated by uncertainties in the geometrical dataas provided by the manufacturer as they define guaranteedmeasures, but not necessarily the actual measures.

Most EMTP-type programs have dedicated support routinesfor calculating cable parameters. These routines have very sim-ilar features, so hereinafter they will be given the generic name

Manuscript received March 1, 2004; revised August 9, 2004. Paper no.TPWRD-00106-2004.

Task Force Members: J. A. Martinez (Chairman), D. Durbak, B. Gustavsen,B. Johnson, J. Mahseredjian, B. Mork, R. Walling.

Digital Object Identifier 10.1109/TPWRD.2005.848774

“cable constants” (CC). These programs have some shortcom-ings in representing certain cable features. The paper providesguidelines on how to apply CC routines to the most commontypes of high-voltage cable systems. The discussion considersboth cables with extruded solid insulation (XLPE, PE) and ca-bles with oil-impregnated paper.

II. INPUT DATA

The basic equations used to represent overhead lines and in-sulated cables have the following form:

(1)

(2)

where and are, respectively, the series resistance, se-ries inductance, shunt conductance, and shunt capacitance per-unit length of the cable system. These quantities are ma-trices, being the number of (parallel) conductors of the cablesystem. The variable reflects that these quantities are calcu-lated as function of frequency.

and are calculated by means of CC routines, using cablegeometry and material properties as input parameters. In gen-eral, users must specify:

1) Geometry• location of each conductor ( - coordinates);• inner and outer radii of each conductor;• burial depth of the cable system.

2) Material properties• resistivity and relative permeability of all conduc-

tors ( is unity for all nonmagnetic materials);• resistivity and relative permeability of the surrounding

medium ;• relative permittivity of each insulating material .

The calculation of and from the geometry and mate-rial properties follows similar steps for all CC routines. Thereader is referred to [4]–[6] for details. The main challenge isthe impedance calculation which is based on computing sur-face impedances and transfer impedances of cylindrical metallicshields, as well as self and mutual ground impedances. CC rou-tines differ in the actual expressions that are used in the calcula-tion of these quantities. It is worth noting that these routines takethe skin effect into account but neglect any proximity effects. Aprocedure for including proximity effects is given in [7].

0885-8977/$20.00 © 2005 IEEE

2046 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

TABLE IRESISTIVITY OF CONDUCTIVE MATERIALS

Fig. 1. Circumferential permeability. Steel wire diameter = 5 mm [8].

III. MATERIAL PROPERTIES

A. Conductive Materials

Table I shows appropriate values for the resistivity of somecommon conductor materials.

Stranded conductors need to be modeled as massive conduc-tors. The resistivity should be increased with the inverse of thefill factor of the conductor surface so as to give the correct re-sistance of the conductor.

The resistivity of the surrounding ground depends strongly onthe soil characteristics, ranging from about 1 m (wet soil) toabout 10 k m (rock). The resistivity of sea water lies between0.1 and 1 m.

Submarine cables are normally designed with (magnetic)steel armor. The armor consists of a number of steel (round orsquare/flat) wires, or of steel tapes. In the case of a wired armor,the permeability depends on the wire diameter, the laying angle,and the intensity of the circumferential magnetic field.

Bianchi and Luoni [8] obtained curves for the permeabilityof round wire steel armors due to a magnetic field in the cir-cumferential direction. Their calculations were based on mea-sured permeability in the longitudinal direction of steel wires,and an assumption of the permeability in the perpendicular di-rection lying between 1 and 10. Fig. 1 shows the permeabilityin the circumferential direction (magnitude) as function of thecircumferential magnetic field strength, for different lay anglesand depending on the assumed permeability in the perpendic-ular direction.

B. Insulating Materials

The relative permittivity of the cable main insulation can beobtained from the manufacturer. Table II shows typical valuesfor common insulating materials at power frequency. XLPE isan extruded insulation while mass-impregnated and fluid-filleddenote paper–oil-based insulations.

TABLE IIRELATIVE PERMITTIVITY OF INSULATION MATERIALS

Fig. 2. Complex permittivity of paper–oil insulation, according to (4).

Most extruded insulations, including XLPE and PE, arepractically lossless up to 1 MHz whereas paper–oil-type in-sulations exhibit significant losses also at lower frequencies.The losses are associated with a complex, frequency-dependentpermittivity

(3)

where is the insulation loss factor. Presently, none of theavailable CC routines allows to enter a frequency-dependentloss factor, so a constant value has to be entered. However, thisleads to nonphysical frequency responses which cannot be accu-rately fitted by frequency-dependent transmission-line models.Therefore, the loss-angle should instead be specified as zero.

Breien and Johansen [9] fitted a Debye model to the mea-sured frequency response of insulation samples of a low-pres-sure fluid-filled cable, in the frequency range 10 kHz–100 MHz.The permittivity is given as

(4)

The permittivity at zero frequency is real valued and equal to3.45. It is stated in [9] that the frequency-dependent permittivitycauses additional attenuation of pulses shorter than 5 s. Thefrequency variation in (4) is shown in Fig. 2.

Equation (4) is a rational function in frequency , soits inclusion in a CC routine would yield rational frequencyresponses which can be accurately fitted. Therefore, CC rou-tines should be modified to allow the permittivity to be speci-fied in a Debye model, see (4), with user-specified parameters.

GUSTAVSEN et al.: PARAMETER DETERMINATION FOR MODELING SYSTEM TRANSIENTS—PART II 2047

TABLE IIIPARAMETERS OF SEMICONDUCTIVE LAYERS (INDICATIVE VALUES)

Fig. 3. SC XLPE cable, with and without armor.

Section IX-A shows the effect of insulation losses on a transientresponse.

C. Semiconductive Materials

The main insulation of high-voltage cables is always sand-wiched between two semiconductive layers. This is the case forboth extruded insulation and paper–oil insulation. The electricparameters of semiconductive screens can vary between widelimits; Table III gives indicative values for extruded insulation.For cables with extruded insulation, the resistivity is required bynorm (IEC 60840) to be smaller than 1000 m and 500 m forthe inner and the outer semiconductive layers, respectively. For-tunately, semiconductive layers can, in most cases, be taken intoaccount by using a simplistic approach, as shown in Section IV.

IV. SINGLE-CORE SELF-CONTAINED CABLES

Single-core (SC) cable systems are comprised of three sep-arate cables which are coaxial in nature (Fig. 3). The insula-tion system can be based on extruded insulation (e.g., XLPE) oroil-impregnated paper (fluid filled or mass impregnated). Thecore conductor can be hollow in the case of fluid-filled cables.

SC cables for high-voltage applications are always designedwith a metallic sheath conductor (Fig. 3). The sheath conductorcan be made of lead, corrugated aluminum, or copper wire. Suchcables are also designed with an inner and an outer semiconduc-tive screen, which are in contact with the core conductor andthe sheath conductor, respectively. Submarine cables are nor-mally designed with steel armor to provide additional mechan-ical strength.

None of the available CC routines permit the user to directlyspecify the semiconductive layers. These must therefore be in-troduced by a modification of the input data. As explained in[10], semiconductive layers which are in contact with a metallicconductor can be taken into account by replacing the semicon-ductors with the insulating material of the main insulation, andincreasing the permittivity of the total insulation so that the elec-tric capacitance between the core and the sheath remains un-changed. The validity of this approach has been verified by mea-surements up to at least 1 MHz [11].

The actual conversion of the permittivity is done as follows:

(5)

Fig. 4. Three-phase cable designs.

where and are the core radius and the sheath inner ra-dius, respectively; and are the inner and outer insulationradii, respectively; and is the permittivity of the insulatingmaterial.

The effect of semiconductive layers on the series impedanceis subject to a rigorous treatment in [12].

V. THREE-PHASE SELF-CONTAINED CABLES

Three-phase cables essentially consist of three SC cableswhich are contained in a common shell. The insulation systemof each SC cable can be based on extruded insulation or onpaper–oil. Regarding the modeling in CC routines, most cabledesigns can be differentiated into the two designs shown inFig. 4.

Design #1: one metallic sheath for each SC cable, SC cablesenclosed within metallic pipe (sheath/armor). This design canbe directly modeled using the “pipe-type” representation avail-able in some CC routines, where “pipe” denotes the commonmetallic enclosure. See Section VI.

Design #2: one metallic sheath for each SC cable, SC cablesenclosed within insulating pipe. None of the present CC routinescan directly deal with this type of design due to the commoninsulating enclosure. This limitation can be overcome in one ofthe following ways.

i) Place a very thin conductive conductor on the inside ofthe insulating pipe. The cable can then be represented asa pipe-type cable in a CC routine.

ii) Place the three SC cables directly in earth (ignore the in-sulating pipe).

Both options should give reasonably accurate results whenthe sheath conductors are grounded at both ends. However, theseapproaches are not valid when calculating induced sheath over-voltages.

The space between the SC cables and the enclosing pipe isfor both designs filled by a composition of insulating mate-rials; however, CC routines only permit to specify a homoge-nous material between sheaths and the metallic pipe. Fortu-nately, the representation of this medium is not very important,as explained in Section VIII.

VI. PIPE-TYPE CABLES

Pipe-type cables consist of three SC paper cables that are laidasymmetrically within a steel pipe, which is filled with pressur-ized low-viscosity oil or gas (Fig. 5). Each SC cable is fitted with

2048 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

Fig. 5. Pipe-type cable.

a metallic sheath. The sheaths may touch each other. Most CCroutines have an input template available which is specificallydedicated to this cable design.

VII. GROUNDING OF SHEATHS AND ARMORS

CC routines require users to specify the grounding condi-tions of metallic sheaths and armors. Grounding a conductor ina CC routine means that this conductor will be assumed to be onground potential at any point along the cable, which results inthe conductor being eliminated from and and, thus, fromthe resulting cable model. The main advantage of this optionover manual grounding (i.e., grounding is achieved by placinga very small resistor between the conductor and ground) is ashorter simulation time. A disadvantage is that one loses the pos-sibility of monitoring the current flowing through the eliminatedconductor.

The armor can, in nearly all situations, be assumed to be atground potential. In submarine cables, the armor is usually quitethick; thus preventing any high-frequency flux to penetrate thearmor, so no voltage drop will develop along it. Also, manysubmarine cables have a wet construction where the conductivesea water is allowed to penetrate the armor.

Sheath conductors are usually grounded at both cable ends.In this situation, the ideal grounding option usually applies be-cause induced (transient) sheath voltages along the cables are,in general, very small compared to voltages on core conductors.Sheaths must, however, be included when high voltages can de-velop along them. This includes situations with a high groundpotential rise at the cable grounding point (ground fault current,injection of lightning current), and cross-bonded cable systems.Their inclusion may also be needed in situations with the sheathgrounded at one end through arresters. The cable sheaths must,of course, be included in any study of sheath overvoltages.

VIII. SENSITIVITY OF TRANSIENTS TO CABLE PARAMETERS

AND CABLE DESIGN

All cable designs described in this paper (single core, three-phase, pipe type) are based on three single-core cables havinga core conductor and a sheath conductor. High-frequency cabletransients essentially propagate as decoupled coaxial waves be-tween cores and sheaths [13], [14], so the transient behavior ofthe cable is sensitive to the modeling of the core, main insula-tion, semiconductors, and the metallic sheath. The sensitivity ofthe coaxial wave can be summarized as follows.

1) Increasing the core resistivity increases the attenuationand slightly decreases propagation velocity.

2) Increasing the sheath resistivity (or decreasing the sheaththickness) increases the attenuation.

3) Increasing the insulation permittivity increases thecable capacitance. This decreases velocity and surgeimpedance.

4) With a fixed insulation thickness, adding semiconductivescreens increases the inductance of the core-sheath loopwithout changing the capacitance. This decreases velocityand increases surge impedance.

Since the sheath conductors are normally grounded at bothends, the potential along this conductor is low as compared tothat of the core conductor, even in transient conditions. As a re-sult, the simulated transients on phase conductors are insensitiveto the specified properties of insulating materials external to thesheath.

The magnetic flux external to the sheath is small at frequen-cies above which the penetration depth is smaller than thesheath thickness

(6)

It follows that high-frequency transients are not very sensitiveto the conductors/ground external to the sheaths. The shieldingeffect increases with decreasing resistance of the sheath.

Some care is needed when modeling armored SC cables atlow and intermediate frequencies as the return path of eachcoaxial mode divides between the sheath and the armor. Thismakes the propagation characteristics sensitive to the modelingof the armor (and to the separation distance between the sheathand armor). The armor permeability now becomes an importantparameter.

In studies of ground fault situations, a significant zero-se-quence current at power frequency will flow in conductors ex-ternal to the sheaths (armor, pipe) as the sheath will not shieldthe magnetic flux. In such situations, it is necessary to modelthe armor/pipe with care as they can strongly affect the zero-sequence impedance of the cable and, thus, the magnitude ofthe fault current.

IX. CALCULATED RESULTS

A. Single-Core Cable

1) Test System: In this example, a system of three 145-kVSC cables is considered (Fig. 6). The cable design uses a coppercore and XLPE insulation, being the core radius and insulationthicknesses as those shown in Table IV. Semiconductor layersare taken into account by using (5).

Using the so-called universal line model (ULM) [3], thevoltage caused by a step voltage excitation is calculated at thereceiving end of a 5-km cable (Fig. 7). All sheaths are treatedas continuously grounded.

2) Sensitivity to Sheath Resistance: The resulting stepvoltage is calculated for the following cable sheaths: 1, 2, and3 mm Pb; 0.215 mm Cu (which represents a 50-mm wirescreen).

GUSTAVSEN et al.: PARAMETER DETERMINATION FOR MODELING SYSTEM TRANSIENTS—PART II 2049

Fig. 6. Cable configuration.

TABLE IVTEST CABLE PARAMETERS

Fig. 7. Step voltage excitation.

The receiving end voltages are shown in Fig. 8, assuming1-mm semiconductive layers. It can be seen that reducing thethickness of the lead sheath from 2 to 1 mm leads to a strongincrease of the attenuation, whereas a reduction from 3 to 2 mmhas little effect. This can be understood by considering thatthe dominant frequency component of the transient is about10 kHz. At this frequency, the penetration depth in lead is2.4 mm, according to (6). Thus, increasing the thickness of thelead sheath beyond 2.4 mm will not lead to a significant changein the response.

3) Sensitivity to Semiconductor Thickness: Assuming a0.215-mm Cu sheath, the step response is calculated for dif-ferent thicknesses of the semiconductor layers: 0, 1, 2, 3 mm.

The responses in Fig. 9 show that the semiconductors lead toa decrease of the propagation speed, as previously explained inSection VIII.

4) Sensitivity to Insulation Losses: In this example, theXLPE main insulation is replaced by paper-oil insulation. Itis further assumed that the cable has a 2-mm lead sheath andno semiconductive screens. The open-end voltage is calculatedby applying a 2 and a 10- s width square-voltage pulse. The

Fig. 8. Effect of sheath design on overvoltage.

Fig. 9. Effect of semiconductor thickness on overvoltage.

simulation is performed with the following representations ofthe main insulation:

a) Lossless insulation [i.e., dc value in (4)].b) Lossy insulation by (4).Fig. 10 shows an expanded view of the initial transient (re-

ceiving) end. It can be seen that the lossy insulation gives a muchstronger reduction of the peak value for the narrow pulse (2 s)than that for the lossless insulation. This reduction is an effect ofboth attenuation and frequency-dependent velocity. It is furtherseen that the travel time of the lossy insulation is smaller thanthat of the lossless insulation, which is caused by the reductionin permittivity at high frequencies, according to (4).

B. Armored Cable

In this example, an armor of 5-mm steel wires and a 5-mmouter insulation are incorporated into the cable design. It is fur-ther assumed XLPE main insulation, a 2-mm lead sheath, and1-mm semiconductive screens. Only one cable is considered.

2050 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 3, JULY 2005

Fig. 10. Effect of insulation losses on overvoltage.

Fig. 11. Effect of armor permeability on overvoltage.

The resulting voltage of the open-circuit step response is cal-culated for different values of the armor permeability:

, being the cable length of 50 km, see Fig. 11. It isseen that increasing the permeability strongly increases the ef-fective attenuation of the voltage. The reason is that a perme-ability increase reduces the penetration depth in the armor, thusincreasing the resistance of the inner armor surface impedance.For a 5-km cable length, the significance of the armor was foundto be small as the magnetic field would not appreciably pene-trate the sheath conductor, due to the increased frequency of thetransient.

X. CONCLUSION

This paper has considered cable data for simulating transientson phase conductors of single core cables, three-phase cables,and pipe-type cables. The main conclusions can be summarizedas follows.

1) It is always necessary to accurately specify the geom-etry and material properties of the core conductor, themain insulation, and the sheath conductor. It is also im-portant to take the semiconductive layers into account. Asimple procedure for achieving the latter is proposed inSection IV.

2) Lossy effects of paper-oil insulation lead to a strong atten-uation and dispersion of narrow pulses. Presently, none ofthe existing CC routines can take this into account.

3) The representation of insulating layers external to thesheath conductors is not very important when the sheathsare grounded at both ends.

4) The representation of metallic conductors external to thesheath conductors is important at low frequencies wherethe penetration depth exceeds the sheath thickness.

5) Transient voltages can be strongly sensitive to the perme-ability of any steel armoring when the magnetic field pen-etrates the sheaths.

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