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Abstract —This paper investigates the operation of single core

underground medium voltage cables connected in parallel. The

examination is based on an existing power cable arrangement

connecting a 38 MW wind farm with the transmission grid. The

cable arrangement consists of nine single core cables connected in

parallel to form a triple 3-phase system. Several connection

scenarios such as the earthing of the cable sheaths at one or both

ends and the application of sheath cross-bondings are examined.Various simulation parameters are also investigated such as the

grounding resistance of the cable sheaths and the number of the

cable sheath transpositions. The respective voltages and currents

induced on the cable sheaths are calculated under steady-state

and short circuit conditions.

Index Terms —ATP/EMTP, cross-bonding, sheath currents,

underground power cables.

I. I NTRODUCTION

HE research interest on single core power cables is

increasing over the last years, due to their continuous use

in many Medium Voltage (MV) and High Voltage (HV)

installations. Typical cases where the utilization of underground single core cables has met significant growth are

the wind farms. In a wind farm underground MV power cables

are used both in the internal electric grid and for the

connection to the transmission grid. The deployment of

single-core cables over long distances has renewed the interest

on research fields, such as the induced voltages and currents

on the cable sheaths for various operational conditions.

The simulation of MV cables including different cable

sheath configurations has been examined in the literature

[1] - [5]. Several configurations have been proposed, resulting

in varying sheath voltage profiles. In the most common

configuration, usually applied in cables with small lengths, thecable sheaths are grounded at one or at both cable ends in

order to reduce the sheath voltages. In cases of cables with

longer lengths, the proposed configuration is the cross-

bonding of cable sheaths. Using cross-bonding, sheaths are

properly transposed, thus the sheath induced voltages are

minimized. The number of the sheath cross-bondings is

K.V. Gouramanis, Ch. G. Kaloudas, T. A. Papadopoulos, G. K.Papagiannis are with Power Systems Laboratory, Department of Electrical and

Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki

GR-54124, Greece (corresponding author G.K. Papagiannis:[email protected], telephone: +30 2310 996388, fax: +30 2310 996302,

P.O. Box 486).

K. Stasinos is with the Rokas Renewables – C. Rokas Group, Halandri,Athens, Greece (e-mail: [email protected]).

difficult to be predefined and must be calculated for each

specific cable arrangement.

In its initial form, IEEE Std. 575 suggested the application

of approximate equations in order to calculate the induced

voltages and currents at cable sheaths. In the new revised form

IEEE Std. 575-1988 [6] suggests that the induced voltages

must be calculated for each case using proper simulations.

According to [6] sheath voltages must not exceed 65-90 Vthroughout the whole length of the cables under normal

operating conditions. On the other hand, according to the

IEEE Std. 80-2000 [7] the maximum sheath voltage at the

cable ends should not exceed 50 V.

Therefore, it is clear that, although there are general

guidelines concerning the sheath configuration depending on

the cable length, each installation must be individually

examined, especially in cases with long cable lengths. In this

paper the induced voltages and currents at the cable sheaths

are investigated under various cable arrangements and

operating characteristics. The cable arrangement under

configuration is a real one used for the interconnection of a

38 MW wind park to the MV/HV substation of the Greek mainland transmission grid.

Several cable arrangements have been investigated, such as

grounding of the cable sheaths through various

groundingresistances and the application of sheath cross-

bonding at various positions, in order to reduce the sheath

induced voltages. These arrangements have been examined for

steady-state operation of the cable system and during

short-circuits. The Alternative Transients Program -

Electromagnetic Transients Program (ATP/EMTP) [8] has

been used for the calculation, while cable arrangements are

simulated using cable models with lumped parameters in the

time domain.

II. MODELING OF MV CABLES

The cable installation examined has a total length of

18360 m, connecting the wind park of Arachneo in Greece

with the local 20kV/150kV substation of the Public Power

Corporation (PPC), as shown in Fig. 1. The wind park has 19

double fed induction generators, 2 MW each, with the

corresponding step-up transformers and connection cables. A

group of nine medium voltage (MV) single core cables type

A2XSY/12/20KV, 630mm2 is installed in an underground

arrangement of triple 3-phase circuits S1, S2 and S3 with the

cables in trefoil formation in each circuit, as shown in Fig. 2.

The cable ditch has a total depth of 1.4 m. Each cable consists

Sheath Voltage Calculations in Long Medium

Voltage Power CablesK. V. Gouramanis, Member, IEEE, Ch. G. Kaloudas, Student Member, IEEE, T. A. Papadopoulos,

Member, IEEE, G. K. Papagiannis, Senior Member, IEEE, K. Stasinos, Non-Member, IEEE

T

Paper accepted for presentation at the 2011 IEEE Trondheim PowerTech

978-1-4244-8417-1/11/$26.00 ©2011



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of an aluminum core with XLPE insulation and copper sheath

with PVC outer insulation, as shown in Fig.3. The cable

geometrical and electric data are shown in Table I.

Fig. 1. System under study.

Fig. 2. Configuration of 9 underground single core cables in three trefoil

formations.

Fig. 3. MV single core cable used for the interconnection of the wind park

with the substation.

The cable parameters have been calculated using the

CABLE CONSTANTS/PARAMETERS supporting routine of

the ATP/EMTP [8] taking into account the topology of the

configuration, the skin effect and the influence of earth. In

order to simulate the 18360 m long cable arrangement,

Pi-equivalents with lumped parameters were implemented.

Each Pi-equivalent represents 306 m of cable length and

therefore the whole cable is simulated using 60 cascaded

Pi-equivalents.

TABLE I

DATA OF EACH SINGLE CORE CABLE

Core radius, r 1 0.015 m

Main insulation radius, r 2 0.0223 m

Sheath radius, r 3 0.02255 m

Outer insulation radius, r 4 0.02505 mCore resistivity 3.7566 x 10-8 ȍ.m

Sheath resistivity 2.19 x 10-8 ȍ.m

Inner insulator, İr 2.3

Outer insulator, İr 6

All relative permeability, ȝr 1.0

Cable length Ɛ is measured starting from a zero value at the

cable connection point to the PPC substation side and retains a

18360 m value at the corresponding point at the wind park

side.

The use of cable equivalents with lumped parameters

(Pi-equivalents) for simulation of the cable arrangement has

been chosen for the cases under consideration instead of the

JMarti frequency domain or the time domain Bergeron model.

There are certain drawbacks on the use of the JMarti

frequency domain (FD) model for cable arrangements [9] ] -

[10]. Due to this fact, combined with the complexity of the

application, the JMarti model for the case of the mutually

coupled nine cable cores and nine cable sheaths was not

chosen for the simulation.

Furthermore, all calculations of the cable arrangements are

conducted solely for steady-state conditions at power

frequency, since the transient behavior is not examined. Thus,

the use of the lumped parameter equivalents is adequate and

this model is preferred in respect to the Bergeron time domainmodel. The validation of the model used in the simulations is

accomplished also with the comparison of the results to the

corresponding by relative references [2], [11], which showed a

very good agreement.

III. STEADY-STATE CALCULATIONS

For the steady-state calculation the worst case scenario

corresponding to the maximum power flow from the wind

park to the electric grid is assumed. Two 3-phase symmetrical

voltage sources connected at the terminals of the cascaded

Pi-equivalent cable model represent 20 kV busbars of the wind

farms and of the PPC substation, as shown in Fig. 4. The

voltage source data are calculated according to the results of a

load flow study, using the NEPLAN software [12] for the

maximum power flow conditions. Simulations have been

conducted and the voltage distribution along the cable sheaths

has been calculated using the ATP/EMTP [8] software.

The examined cable arrangements are:

• Arrangement a, with cable sheaths grounded at one

end,

• Arrangement b, with cable sheaths grounded at both

ends,

• Arrangement c, with sheath cross-bonding at two or

five points combined with sheath grounding at both

cable ends



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• Arrangement d , where cable sheaths are grounded at

intermediate points along the cable length.

In all cases the use of different grounding resistances has

been also examined. All the above cable arrangements are

shown in Fig. 5, for one of the three 3-phase cable systems.

For each configuration and examined case the inducedvoltages and currents at the cable sheaths are calculated.

Fig. 4. Steady-state simulation model.

Fig. 5. Examined cable arrangements.

Figs. 6 – 9 illustrate the voltage distribution at the cable

sheaths for each of the examined arrangements. It is shown,

that in the cases of cable sheath grounding either at one or at

both ends, without cross-bonding, the induced voltages at the

cable sheaths can be significant, especially at the cable

terminals, depending on the value of the grounding

resistances. Typical values for grounding resistances at 1 Ohm

or 2 Ohm have been examined, since such low grounding

resistances are common in substations. For higher values of

grounding resistances the voltage at the cable ends can reach

very high values. Furthermore, when cable sheaths are

grounded at both ends the induced currents become relatively

high, reaching up to 90 A for grounding resistance equal to 1

Ohm, thus causing increased cable losses.

The application of cross-bonding significantly reduces the

induced sheath voltage to a maximum of 120 V for 2

cross-bondings and 60 V for 5 cross-bondings, respectively, asshown in Figs 8 and 9. Voltages at the cable terminals are also

small, below 50 V in accordance to [7]. The respective

induced sheath currents are minimized and are in all cases

below 10 A, thus reducing the respective cable losses.

Fig. 6. Induced voltage at the cable sheaths. Sheaths are grounded only at one

end (PPC side) using different grounding resistances.

Fig. 7. Induced voltage at cable sheaths. Sheaths are grounded at both ends

using different grounding resistances.

Fig. 8. Induced voltage at sheaths. Cable sheaths are grounded at both ends

using different grounding resistances and sheaths are cross-bonded at two

points (every 6120 m).

In cases where cross-bonding is used, the value of the

grounding resistance has minor effects on the induced sheath

voltages, compared to the non cross-bonded case, especially at

the cable terminals. These are the points with the higher risk

for human safety, since they are accessible by the technical

personnel.



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using different grounding resistances and sheaths are cross-bonded at five

points (every 3060 m).

Fig. 10 illustrates the voltage profiles at the cable sheaths,

when sheaths are grounded at both ends with a 2 Ohm

grounding resistance and also at 12 equidistant points along

the cable length (every 1530 m), using different grounding

resistances. It is shown that unless a very low grounding

resistance, for example 2 Ohm or less, is achieved at allintermediate grounding points the sheath voltage is high.

However, to attain such values for the grounding resistances

along the cable routing is not at all easy. Furthermore, this

arrangement also causes higher sheath currents in respect to

the cross-bonding case, due to the high number of internal

loops formed by the numerous grounding points. The sheath

current has been calculated equal to 35 A for the case of

2 Ohm grounding resistances.


using grounding resistances equal to 2 Ohm and at 12 points along the cable

with varying grounding resistances.

Finally, the influence of the number of cables in thearrangement is investigated. The system under study

comprises a group of nine single core cables. Modeling of the

cable system with only 3 or 6 cables results in significant

differences in the calculated voltages, compared to those of

the full cable system model. Fig. 11 shows the different

voltage profiles along the cable sheaths for sheaths grounded

at both ends with 2 Ohm grounding resistance. Cable systems

consisting of 3, 6 and 9 cables are examined. The voltages

induced by the adjacent cables, due to the system asymmetries

result in higher sheath voltages with increasing cable system

complexity.

Fig. 11. Induced voltage at the sheaths when the cable sheaths are grounded

at both ends with 2 Ohm grounding resistances, for cable systems consisting

of 3, 6 and 9 cables.

IV. SHORT CIRCUIT CALCULATIONS

The cable model is also used in order to calculate the cable

sheath voltages during 3-phase and single phase short-circuits(SC). As the worst case scenario, a 3-phase or single phase to

ground fault in the PPC or the wind park busbars has been

considered. The SC currents in the cable cores have been

simulated using proper current sources equal to the expected

SC current, as calculated according to the IEC 60909 [13]. A

3-phase SC at the grid side is simulated using a current source

representing the total fault current at the wind farm busbar,

connected at the wind farm side of the cable and all phases

short circuited at the grid side cable end. For the simulation of

a single-phase short circuit, a current source is connected at

the faulted cable phase. In this case, the other two phases are

assumed to be open-circuited at both ends. The simulation

model used is illustrated in Fig. 12.

Fig. 12. Simulation model used for a short-circuit at the grid side.

A. Three-phase Short Circuits

All results calculated for the 3-phase symmetrical SC are

quite similar in form to the corresponding derived from the

steady-state analysis. The grounding of cable sheaths at one or

at both ends does not sufficiently reduce the induced sheath

voltage when dealing with long cable lengths. Furthermore,

the grounding at both cable ends leads to significant currents

at the cable sheaths. The application of two or five

cross-bondings for the examined 18360 m long cable



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arrangement reduces the sheath voltage to a maximum of 500

V and 300 V respectively, as shown in Figs. 13 and 14. In Fig.

14, the maximum sheath voltage for the case of cross-bonding

at 5 points seems to depend significantly on the value of the

grounding resistance, due mainly to the high currents that flow

in the sheaths during the short-circuit.

Fig. 13. Induced voltage at cable sheaths. Cable sheaths grounded at both

ends and cross-bonded at two points (every 6120 m). 3-Phase Short Circuit atthe Wind Park side.

Fig. 14. Induced voltage at sheaths. Cable sheaths grounded at both ends andcross-bonded at five points (every 3060 m). 3-Phase Short Circuit at the Wind

Park side.

In order to further reduce the induced voltage additional

measures such as Sheath Voltage Limiters (SVLs) must be

used [14]. The SVLs are non linear devices connected

between the sheaths and earth, usually installed at the points of

the sheath cross-bonding. Under normal operating conditions,

the SVLs behave as an open circuit. When the sheath voltage

increases over the rated SVL voltage, the SVL grounds the

sheath at the installation point to reduce the overvoltage. Since

in this analysis the transient behavior of the short circuit and

the SVLs is not examined, the SVLs when energized aretreated as grounding points with specified grounding

resistances.

Fig. 15 shows the sheath voltage for the case of five SVLs

connected at the five sheath cross-bonding points. The

respective sheath voltage profile of the arrangement without

the SVLs is shown in Fig. 14. In Fig. 15, the voltage profiles

represent different combinations of grounding resistances,

where Rearth,ext corresponds to the grounding resistance at the

cable ends and Rearth,int to the grounding resistance at the

SVLs. As shown, the voltage is reduced to a maximum of

300V depending on the value of the grounding resistances.

Fig. 15. Induced voltage at sheaths for a 3-phase short circuit when sheath

cross-bonding and SVLs are used.

B. Single-phase Short Circuits

Similar calculations have been conducted for single-phase

short circuits, as determined by [13]. Simulation results show

that when single-phase SCs occur, the cross-bonding of the

cable sheaths does not affect the induced voltage. This is

expected since during a single-phase SC the 3-phase cables donot carry symmetrical fault currents. Therefore, the

transposition applied to the sheaths does not eliminate the

induced voltage as it is not equally induced from the three

phases.

Fig. 16 illustrates the sheath voltage profile corresponding

to phase a and b of a 3-phase cable system. The single phase

short circuit occurs in phase a. In the examined cable

arrangement sheaths are grounded at both ends with a 2 Ohm

grounding resistance, while five cross-bondings are applied.

The voltage profile shows that the voltage at both sheaths is

equally significant, since the cross-bonding does not help in

the mitigation of the sheath induced voltages.


with 2 Ohm grounding resistances and cross-bonded at five points.

Single-phase a SC at the Wind Park side .

On the contrary, the installation of SVLs at certain points of

the cable routing, practically at the points of the sheath

cross-bondings, has shown that the induced voltage at the

cable sheaths is reduced. Fig. 17 shows the induced voltage in

the case of a single-phase short-circuit at the wind farm side.

The induced voltage is reduced due to the five SVLs that are

connected at the cable sheaths. Additionally, sheaths are

grounded with different grounding resistances at both ends.

The voltage, depending on the grounding resistances, is lower

than 280 V in all cases. The respective voltage induced when

only cross-bondings are applied has been calculated equal to600 V at the cable ends.



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Fig. 17. Induced voltage at the cable sheaths in the case of a single-phase SC

when cross-bondings and SVLs are used.

V. CONCLUSIONS

The problems that may occur in parallel MV single core

cables with long lengths have been examined in this paper. It

is shown that significant voltages can be induced at the cable

sheaths if specific measures are not taken. The calculation of

the cable sheath voltages has been conducted using the

ATP/EMTP software. A real cable arrangement has been

investigated in order to determine the effects of various

parameters on the induced sheath voltages under steady-state

and short-circuit conditions.

It is shown that the sheath induced voltage at cables with

significant length can be reduced only by applying both sheath

cross-bonding and grounding at the cable ends combined with

small grounding resistances. Grounding resistances greatly

affect the induced voltages and therefore small grounding

resistances at least at the cable terminations at the substations

is crucial in order to reduce the sheath voltage at the cableends. The number and the location of the sheath cross-bonding

points depend on the cable length and configuration and must

be calculated for each case individually.

The application of sheath grounding only at the cable ends,

besides of the induced sheath voltages results also in high

sheath currents that increase the cable losses.

The application of sheath cross-bonding is not adequate in

cases of three-phase and singe-phase short circuits. In order to

reduce the sheath voltages the use of SVLs at the points of

cross-bonding is necessary. In both cases of three-phase and

single-phase short-circuits, it is shown that SLVs can reduce

the induced voltages considerably. In the case of single-phase

short-circuits the cross-bonding of the sheaths does not affectthe induced voltage due to the asymmetrical fault currents in

the 3-phase cable system.

VI. R EFERENCES

[1] Nasser D. Tleis, Power Systems Modeling and Fault Analysis, Published by Elsevier Ltd, 2008, pp 140-186.

[2] C. Adamson, H. Taha, L. M. Wedepohl, "Comparative Steady – State

Performance of Crossbonded Cable Systems", Proc. IEE, vol. 115, no.

8, pp. 1147-1155, Aug. 1968.

[3] E. H. Ball, E. Occhini, G. Luoni, "Sheath Overvoltages in High–Voltage

Cables Resulting from Special Sheath-Bonding Connections," IEEE Trans. on Power Apparatus and Systems, vol. PAS-84, no. 10, pp. 974-

988, Oct. 1965.

[4] J.R. Riba Ruiz, Antoni Garcia, X. Alabern Morera, "Circulating sheath

currents in flat formation underground power lines," in Proc.

"International Conference on Renewable Energies and Power Quality

(ICREPQ'07)" , Sevilla 28,29 and 30 Mach 2007[5] N. Drossos G. Kyritsis D. Tsanakas S. Papathanassiou, "Examination Of

Alternative Formations For 150 KV Cables - Possibilities And

Advantages From The Use Of Trefoil Formation," in Proc. MedPower 2004, Nov. 2004, Lemessos.

[6] IEEE Guide for the Application of Sheath-Bonding Methods for

Single-Conductor Cables and the Calculation of Induced Voltages and Currents in Cable Sheaths, ANSI/IEEE Std 575-1 988.

[7] IEEE Guide for Safety in AC Substation Grounding , ǿǼǼǼ 80-2000, 01-

May-2000.[8] H. W. Dommel, ‘EMTP Theory Book’, Bonnevile Power Administratio

n, Portland, OR, 1982.

[9] L. Marti, "Simulation of Transients in Underground Cables withFrequency – Dependent Modal Transformation Matrices," IEEE Trans.

on Power Delivery, vol. 3, no. 3, pp.1099-1110, Jul. 1988.

[10] L. Marti, "Simulation of Electromagnetic Transients in Underground

Cables using the EMTP," in Proc. 2nd IEE International Conf. on

Advances in Power System Control, Operating and Management , Hong

Kong, Dec. 1993.[11] R. Benato, A. Paolucci, EHV AC Undergrounding Electrical Power:

Performance and Planning , Springer-Verlang, London, 2010.

[12] NEPLAN© User’s Guide V5 Tutorial.

[13] IEC 60909-0, Short-circuit currents in 3-phase a.c. systems – Part 0:

Calculation of currents, IEC First edition 2001-07.

[14] B. Parmigiani, D. Quaggia, E. Elli, S. Franchina, "Zinc Oxide SheathVoltage Limiter For HV and EHV Power Cable: Field Experience and

Laboratory Tests," IEEE Transactions on Power Delivery, Vol. PWRD-1, No. 1, January 1986.

VII. BIOGRAPHIES

Kostas Gouramanis was born in Athens, Greece, on September 22, 1979. Hereceived his diploma in Electrical and Computer Engineering from the

Department of Electrical and Computer Engineering at the Aristotle

University of Thessaloniki, Greece in 2003, and his Ph.D. degree from thesame university in 2007. He is currently working as a consultant in the areas

of industrial electrical installations, electrical energy saving, and renewable

energy sources. His research interests are in the fields of power electronics, power quality and renewable energy sources.

Christos G. Kaloudas was born in Xanthi, Greece, on May 4, 1983. He

received his Dipl. Eng. Degree from the Department of Electrical andComputer Engineering at the Aristotle University of Thessaloniki, in 2006.

Since 2006 he is a postgraduate student at the Department of Electrical and

Computer Engineering at the Aristotle University of Thessaloniki. His specialinterests are power system modeling and computation of electromagnetic

transients.

Theofilos A. Papadopoulos was born in Thessaloniki, Greece, on March 10,

1980. He received his Dipl. Eng. Degree and Ph.D. from the Department of

Electrical and Computer Engineering at the Aristotle University of Thessaloniki, in 2003 and 2008, respectively. He is currently a researcher at

the Power Systems Laboratory of the Department of Electrical and Computer Engineering of the Aristotle University of Thessaloniki, Greece. His special

interests are power system modeling, powerline communications and

computation of electromagnetic transients. Mr. Papadopoulos has received theBasil Papadias Award for the best student paper, presented at the IEEE

PowerTech 07 Conference in Lausanne, Switzerland.

Grigoris K. Papagiannis was born in Thessaloniki, Greece, on September 23,1956. He received his Dipl. Eng. Degree and his Ph.D. degree from the

Department of Electrical and Computer Engineering at the Aristotle

University of Thessaloniki, in 1979 and 1998 respectively. He is currentlyAssociate Professor at the Power Systems Laboratory of the Department of

Electrical and Computer Engineering of the Aristotle University of

Thessaloniki, Greece. His special interests are power system modeling,

computation of electromagnetic transients, distributed generation, powerline

communications and smart grids.

Kostantinos Stasinos received his Dipl. Eng. Degree from the Department of Electrical and Computer Engineering at the Aristotle University of

Thessaloniki, in 2003. Since 2005 he is Electrical Works Coordinator in the



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RES Engineering & Construction Dept of the ROKAS-IBERDROLA

Renewables S.A.

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