Mutual Inductive Interference of 400 kV Cable Systems

R. MURATOVIC1, E. SCHMAUTZER, L. FICKERT, R. WOSCHITZ

Graz University of Technology

H. LUGSCHITZ, A. MACHL, K. REICH

Austrian Power Grid

M. KLEIN, G. SVEJDA

Wiener Netze GmbH

Austria

SUMMARY

The paper proposes a suitable model for the calculation of the mutual inductive and ohmic interference

of 400 kV cable systems particularly of the induced currents and voltages in cable shields, cross

bonding joints and earthing systems. Based on practical relevant examples, typical scenarios were

defined and the effects of parallel laid 400kV cable systems are shown and discussed. For the

calculation of voltages and currents due to mutual inductive and ohmic coupling of parallel laid

underground cable systems, the following parameters have to be considered: electrical symmetry of

the cable systems, cable laying arrangement, distances between systems and phases, system and cross-

bonding section length, influencing current, cross-section arrangement with detailed sub-section

design, earthing configuration of the cable shields and joint cases, parallel earth continuity conductors,

specific soil resistivity and laying depth. Considering the isolation materials of cables, the distances

between phases and related cable shields, between phases themselves and between three-phase

systems are much lower than the distances on overhead lines. Therefore, the mutual coupling, the

symmetry of the entire system and the earthing arrangement play an essential role regarding induced

voltages and currents. Not only the number of sections, but also the section length varies in many

cases. For each of these sections, the impedance matrix is computed by using the self-impedances of

all conductors and the coupling-impedances between all conductors using Dubanton’s approximation.

These coupled cable sections are combined with the earthing resistances of the joints to form a chain

model. The voltage and current distribution across 400 kV cable systems through the inductive

interference can be finally calculated in all accessible places. Measurements at 400 kV cable systems

of a DSO in Austria were carried out to validate the simulation model and the calculation results

respectively. The presented results show a good correlation with the measurement results.

KEYWORDS

HV cable systems, mutual inductive and ohmic interference, cross-bonding, metallic cable shield,

workers’ safety, maintenance, repair

1 redzo.muratovic@tugraz.at

21, rue d’Artois, F-75008 PARIS B1-105 CIGRE 2016

http : //www.cigre.org

2

Introduction To provide the same electric energy transmission capacity and reliability with high-voltage power

cables as with high-capacity overhead power lines two or more cable systems per each overhead

power line systems are necessary.

AC high-voltage overhead power lines usually consist of two to four systems each with up to

quadruple-conductors per phase, suspended by towers, isolated by air and have one or more earth

wires. In contrast, high-voltage cable systems are usually laid underground (e.g. buried directly in

earth or laid in pipes, in ducts or in tunnels) and exhibit a much more complex structure. Every phase

has its own isolating system, its own metallic cable shield(s) and sometimes, additional earth

continuity conductors (ECC) are laid parallel in the vicinity of the cable systems.

Thus, dealing with cable systems, completely different environmental and laying conditions occur and

different risk options arising from mutual inductive interference have to be taken into account

compared to overhead lines. With cables much more active and passive/earthed conductors have to be

considered and due to the different isolation materials, the different distances between phase-

conductors, cable shields and between three-phase systems the mutual coupling of conductors are

quite different. This leads to completely different system characteristics e.g. positive and zero

sequence components, operating and fault behaviour and ohmic, inductive, capacitive and

electromagnetic interference.

This paper proposes a suitable model for the calculation of the mutual inductive and ohmic

interference of 400 kV cable systems particularly of the induced currents and voltages in metallic

cable shields, cross bonding joints and earthing systems. Based on examples from practice, typical

scenarios were defined and the effects of parallel laid 400kV cable systems are shown and discussed

[1-13].

Design of extra high voltage cable systems In practice, there are various ways to lay 400 kV cables. Due to system symmetry considerations, the

cable shields of 400 kV cables are generally cross-bonded regularly along the cable route. At each

major cross-bonding section (usually every third joint location), the cable shields are earthed directly.

This means that every major section is earthed at both ends. At the intermediate joints, the cable

shields are transposed and earthed over surge arresters to keep the sheath losses, caused by induced

cable shield currents as small as reasonable. A major cross-bonding section consists of three

consecutive minor sections.

In the case of short circuit currents, the usage of surge arresters limits the induced shield voltages, thus

protecting the outer cable shield isolation. Figure 1 shows a selected, very symmetric laying profile

and longitudinal cable laying arrangement whereby, many others are also conceivable.

Figure 1: Laying profile and longitudinal laying arrangement (profile 1, see Table 1)

Due to mutual inductive interference of neighbouring parallel high voltage cables, the induced

voltages can cause remarkable currents, especially in earthed conductors, such as metallic cable

shields generally are.

3

Depending on the height of the load or fault currents, the length of the parallel running, the self-

impedances of the conductors and the coupling-impedances (dependent on the geometrical distances

of the conductors to each other, the transposition and phase configuration), the induced currents can

reach high values. To calculate the currents and voltages resulting from inductive coupling, the

complete description of the configuration by the impedance matrix is required, and therefore also

knowledge of certain parameters is essential, especially for the calculation of self- and coupling-

impedances. Calculation parameters can change alongside an underground cable system several times.

Therefore, the system has to be subdivided into multiple sections for the calculation, in which all the

relevant parameters are the same. If only one of the relevant parameters changes (see chapter on

Principles), a new calculation segment must be defined.

Principles The classical arrangement for the inductive coupling is shown in Figure 2. The electric circuit of the

power line 1 closed over earth conducts the current I1 (influencing source U1) and causing the induced

voltage U2 in the open conductor loop of the influenced line 2. The coupling impedance Z12 is decisive

for the inductive coupling of the two conductor loops.

U2U1

a

l

1 2

I1Influencing Line

Influenced Line

Z12

Figure 2: Classical arrangement for inductive coupling

The coupling impedance depends on geometrical data (position of the two conductors to each other),

on the frequency and specific soil resistance. In the simple case shown here, the induced longitudinal

voltage U2 results as a product of the coupling impedance and the inducing current.

The complete impedance matrix (see Equation 1) is based on the cross section laying arrangement and

the theoretical relations (see next equations). In the following, these matrices serve as a basis for the

calculations.

𝑼𝟏

⋮

𝑼𝒏

=

𝒁𝟏𝟏 … 𝒁𝟏𝒏

⋮ ⋱ ⋮𝒁𝒏𝟏 … 𝒁𝒏𝒏

𝑰𝟏⋮

𝑰𝒏

Equation 1: Central equation

The impedance matrix of Equation 1 consists of self-impedances Zii and coupling-impedances Zik of

the influenced conductors.

The self-impedances of the matrix describes the impedance of the respective conductor-earth loop and

can be calculated using the following Equation 2 [10]:

Zii' = (re + R) + j(xii + x i i)

Equation 2: Self-impedance of conductor i per meter

4

xii = ωμ0

2π∙ ln

De

Ri

x i i = ωμ0

2π∙μr

4

re =

ωμ0

8 Ground resistance per length in Ω/m

R Ohmic resistance of the conductor per length in Ω/m

xii Self-reactance of the conductor-earth loop per length in Ω/m

x(i)i Inner reactance of the conductor i per length in Ω/m

De= 2e

γδE Equivalent distance to the earth return = earth current depth in m

Ri Effective radius of the conductor in m

The coupling-impedance describes the interference of the indexed conductors (i and k) to each other

and can be calculated using the approximation of Dubanton, as shown in the following Equation 3

[12]:

Zik' = jω

μ0

2πln

hi + hk + 2p 2

+ xik2

dik

Equation 3: Coupling-impedance between conductor i and k per meter

p = 1

jωμ0ρ

= e-jπ4

1

ωμ0ρ

= 1 - j δE 2

1,85137

p Complex equivalent earth current depth in m

dik = xik

2+ hi - hk 2 Distance between the coupled conductors in m

xik Horizontal distance between the coupled conductors in m

hi Height of influencing conductor in m

hk Height of the influenced conductor in m

δE =

1,8514

α Earth current depth of infinite long conductors in m

ρ Specific soil resistance in Ωm

Simulation Model

General requirements

For the calculation of the mutual inductive interference of conductors and shields of parallel laid

400 kV underground cable systems, it is necessary to use a method, with which relevant factors listed

below can be considered:

Number of sections (typically restricted to the cable length per drum)

Number of cable systems and number of cable phases per electrical system

Operating conditions (normal operation, maintenance, critical load (thermal limit), fault)

Longitudinally symmetry of the cable systems

5

Earthing configuration (fault- and touch-voltages)

Earthing resistances (effect of aging and/or corrosion)

Specific soil resistance (local and effective electric resistivity of soil)

System and cross-bonding section length

Transposition type (cross-bonding of cable shield with/without transposition of cable phases)

Laying arrangement (trefoil, flat, laying depth, distances system/system and phase/ phase

Parallel earth continuity conductors

Electrical cable data

Calculation of the mutual inductive interference of high voltage cable systems with unilaterally or

bilaterally earthed cable shields

To start calculating the mutual inductive interference of e.g. a single three-phase cable system (see

Figure 3) the matrix equation (see Equation 4) for all sections (left subscripted index 1 … n) has to be

formed. The currents in the phases IL1, IL2 and IL3 induce voltages (e.g. IL1 induces: 1EL2L1, 1EL3L1,

1ES1L1, 1ES2L1, 1ES3L1) in all other conductors of the section 1 (cable conductors L and shields S).

Figure 3: Three-phase cable system with cable shield transposition (above), equivalent circuit diagram

(below)

The following matrix Equation 4 is the result of the mesh equations of the equivalent circuit diagram,

represented in the lower part of Figure 3 with which the longitudinal voltage drops (U) for all

conductors can be calculated with ZLi (self-impedance of the conductor i) and ZLiSk (coupling-

impedance between phase conductor i and cable shield k).

∆𝑼𝑳𝟏

∆𝑼𝑺𝟏

∆𝑼𝑳𝟐

∆𝑼𝑺𝟐

∆𝑼𝑳𝟑

∆𝑼𝑺𝟑

=

𝒁𝑳𝟏 𝒁𝑳𝟏𝑺𝟏 𝒁𝑳𝟏𝑳𝟐 𝒁𝑳𝟏𝑺𝟐 𝒁𝑳𝟏𝑳𝟑 𝒁𝑳𝟏𝑺𝟑

𝒁𝑺𝟏𝑳𝟏 𝒁𝑺𝟏 𝒁𝑺𝟏𝑳𝟐 𝒁𝑺𝟏𝑺𝟐 𝒁𝑺𝟏𝑳𝟑 𝒁𝑺𝟏𝑺𝟑

𝒁𝑳𝟐𝑳𝟏 𝒁𝑳𝟐𝑺𝟏 𝒁𝑳𝟐 𝒁𝑳𝟐𝑺𝟐 𝒁𝑳𝟐𝑳𝟑 𝒁𝑳𝟐𝑺𝟑

𝒁𝑺𝟐𝑳𝟏 𝒁𝑺𝟐𝑺𝟏 𝒁𝑺𝟐𝑳𝟐 𝒁𝑺𝟐 𝒁𝑺𝟐𝑳𝟑 𝒁𝑺𝟐𝑺𝟑

𝒁𝑳𝟑𝑳𝟏 𝒁𝑳𝟑𝑺𝟏 𝒁𝑳𝟑𝑳𝟐 𝒁𝑳𝟑𝑺𝟐 𝒁𝑳𝟑 𝒁𝑳𝟑𝑺𝟑

𝒁𝑺𝟑𝑳𝟏 𝒁𝑺𝟑𝑺𝟏 𝒁𝑺𝟑𝑳𝟐 𝒁𝑺𝟑𝑺𝟐 𝒁𝑺𝟑𝑳𝟑 𝒁𝑺𝟑

𝑰𝑳𝟏𝑰𝑺𝟏𝑰𝑳𝟐𝑰𝑺𝟐𝑰𝑳𝟑𝑰𝑺𝟑

Equation 4: Longitudinal voltage drops for one section per meter

As the cable shield currents IS1 to IS3 are still unknown, the matrix in Equation 4 has to be rearranged

in a way that the voltages of the phase conductors as well as the cable shields and other earthed

conductors (ECC, pipelines, PEN,…) are grouped; this leads to the following Equation 5:

6

∆𝑼𝑳𝟏

∆𝑼𝑳𝟐

∆𝑼𝑳𝟑

∆𝑼𝑺𝟏

∆𝑼𝑺𝟐

∆𝑼𝑺𝟑

=

𝒁𝑳𝟏 𝒁𝑳𝟏𝑳𝟐𝒁𝑳𝟏𝑳𝟑

𝒁𝑳𝟐𝑳𝟏 𝒁𝑳𝟐 𝒁𝑳𝟐𝑳𝟑

𝒁𝑳𝟑𝑳𝟏𝒁𝑳𝟑𝑳𝟐 𝒁𝑳𝟑

𝒁𝑳𝟏𝑺𝟏𝒁𝑳𝟏𝑺𝟐𝒁𝑳𝟏𝑺𝟑

𝒁𝑳𝟐𝑺𝟏𝒁𝑳𝟐𝑺𝟐𝒁𝑳𝟐𝑺𝟑

𝒁𝑳𝟑𝑺𝟏𝒁𝑳𝟑𝑺𝟐𝒁𝑳𝟑𝑺𝟑

𝒁𝑺𝟏𝑳𝟏𝒁𝑺𝟏𝑳𝟐𝒁𝑺𝟏𝑳𝟑

𝒁𝑺𝟐𝑳𝟏𝒁𝑺𝟐𝑳𝟐𝒁𝑺𝟐𝑳𝟑

𝒁𝑺𝟑𝑳𝟏𝒁𝑺𝟑𝑳𝟐𝒁𝑺𝟑𝑳𝟑

𝒁𝑺𝟏 𝒁𝑺𝟏𝑺𝟐𝒁𝑺𝟏𝑺𝟑

𝒁𝑺𝟐𝑺𝟏 𝒁𝑺𝟐 𝒁𝑺𝟐𝑺𝟑

𝒁𝑺𝟑𝑺𝟏𝒁𝑺𝟑𝑺𝟐 𝒁𝑺𝟑

𝑰𝑳𝟏𝑰𝑳𝟐𝑰𝑳𝟑

𝑰𝑺𝟏𝑰𝑺𝟐𝑰𝑺𝟑

Equation 5: Longitudinal voltage drops for one section, partitioned impedance matrix

After partitioning, it is apparent that the left upper submatrix only contains impedances of the cable

conductor (indices L), the right lower submatrix only contains impedances of the metallic cable

shields (indices S) and the two other submatrices contain the coupling impedances between the cable

conductors and the metallic cable shields.

In a shortened notation, the matrix can be written as:

∆𝑼𝑳

∆𝑼𝑺 =

𝒁𝑳𝑳 𝒁𝑳𝑺

𝒁𝑺𝑳 𝒁𝑺𝑺

𝑰𝑳𝑰𝑺

Assuming that the metallic cable shields are earthed on both sides, the equation system can be

simplified as follows:

∆𝑼𝑳

𝟎 =

𝒁𝑳𝑳 𝒁𝑳𝑺

𝒁𝑺𝑳 𝒁𝑺𝑺

𝑰𝑳𝑰𝑺

Equation 6: Simplified equation system, partitioned impedance matrix

With the second row of the matrix Equation 6, cable shield currents, caused by the inductive coupling

between conductors depending on the operating currents, can be calculated. Besides other factors, the

laying arrangement is considered during the calculation of the elements of the submatrices.

𝑰𝑺 = − 𝒁𝑺𝑺 −𝟏

𝒁𝑺𝑳 𝑰𝑳

Equation 7: Calculation of the shield-currents By inserting these cable shield currents in the first row of the Equation 6 they are eliminated and the 6-

wire system is virtually reduced to a 3-wire system. In the literature, this step is termed as

modification of line parameters [13]. In that way, the longitudinal voltage drops of the phases ∆UL can

be calculated with the reduced line parameter matrix Z*.

∆𝑼𝑳 = 𝒁𝑳𝑳 𝑰𝑳 − 𝒁𝑳𝑺 𝒁𝑺𝑺 −𝟏

𝒁𝑺𝑳 𝑰𝑳

∆𝑼𝑳 = 𝒁 ∗ 𝑰𝑳

In order to calculate the voltages of one side earthed conductors or the currents of both side earthed

conductors along the complete system length, the impedance matrices of the individual sections have

to be summed up to a total impedance matrix Zt and transformed in a way that the resultant vector of

the resulting equation system contains the required phasors.

𝒁𝑡 = 𝒁1 + 𝒁2 + ⋯+ 𝒁𝑛

7

Calculation of the mutual inductive interference of high-voltage cable systems with multiple-

earthed cable shields

The calculation method presented above is only applicable as long as the metallic cable shields are

earthed at the beginning and end of the cable system. If the cable shields are earthed additionally at

several joint locations, the calculation method presented above has to be extended.

For every minor section, an impedance matrix Z is generated in accordance with the method described

above. For the example presented in Figure 4, three impedance matrices, which were calculated with

the software package Matlab, are summarized into one major section matrix and transferred to a

Simulink simulation model, which is also shown in Figure 4. In total, 12 minor and 4 major sections

are shown. The lower half of Figure 4 shows only one three-phase system (including cable shields –

dotted lines) while the upper half shows 4 three-phase systems (12 phases and 12 cable shields).

The model is realised with Matlab Simulink Toolbox SimPowerSystems. Each of the four visible

mutual inductance blocks contain three impedance matrices of the minor sections, accordingly

representing the major cross-bonding sections. The vertical subsystems on the left and right hand side

of the model contain other necessary blocks as current sources, sinks, breakers and measurement

blocks, etc. The three horizontal subsystems of the model represent the three joint locations, where the

cable shields are earthed and contain the necessary blocks as earthing resistances, grounds, breakers

and measurement blocks, etc. All twelve coupled minor-sections are combined with the earthing

resistances of the earthed joint locations to form a chain model. Finally, the voltage and current

distribution along the 400 kV cable system can be calculated in all places of interest. The calculation

results of the proposed method are presented in the following.

Figure 4: Simulation model for multiple-earthed cable shields (profile 1, see Figure 1)

Calculation Results

Shield currents and joint voltages, touch- and fault-voltages, earthing currents and vagabond voltages

in the direct area and vicinity of the cable system that are of interest to the line operator have to be

calculated in advance to meet the necessary protection measures. The following list gives an idea of

which operational conditions and variations of a cable system need to be analysed: initial state, fault

case, conductor reinstalling process, variation of transposition type, different cross-section

profiles, variation of the influencing current, variation of the specific soil resistance,

variation of the section length, variation of the laying depth, variation of the earth resistances

(value and position).

Initial State

For the initial state it is assumed that all cable systems are in normal operating mode. That means, all

cable conductors carry the currents given in Table 1 and all cable shields are earthed at the beginning

and the end of the cable system and in every third joint (grounding sections, see Figure 4).

8

This generally corresponds to the normal operating mode of 400kV cable systems. The currents

induced in the earthed cable shields are presented in Figure 5. Figure 6 presents the voltage drops, that

occur on the earthing resistances caused by the currents flowing through the earthed cable shields (i.e.

earthing voltages). The voltages shown in Figure 6 are the maximum possible potential differences

between the cable shields and the reference earth resulting from a variety of calculations.

Cross section

all currents per 1 phase distances

Profile Cable / Shield Laying

arrangement Inormal operation Ithermal limit

Number of

Systems

system to

system

Phase to

phase

laying

depth

1 2500/155 mm² flat,

horizontal 1035 A 1725 A 4 1,8 m 0,45 m 1,75 m

2 2500/155 mm² in tunnel,

vertical 1035 A 1725 A 4

1,18 m

(7,52 m) 0,54 m 2,10 m

3 2500/155 mm² in tunnel,

vertical 1035 A 1725 A 4

1,9 m

(8,9 m) 0,54 m 2,45 m

4 2500/155 mm² flat, trefoil

horizontal 1500 A 2000 A 4 varies varies varies

5 not cooled

(cooled) 1200/410 mm² trefoil 750 A (1125 A) 1000A (1500 A) 2 5 m 0,27 m 2,40 m

6 not cooled

(cooled) 1200(Cu)/1120(Al)mm² flat 750 A (1125 A) 1000A (1500 A) 2 5 m 0,3 m 1,74 m

Table 1: Overview of analysed scenarios

Figure 5: Profile 1, initial condition, induced cable shield currents

9

Figure 6: Profile 1, initial condition, voltage drops

Fault Case

The results presented in this chapter are based on the following scenario. A single-pole earth fault

occurs at the end of a unilaterally supplied cable system. It is assumed that a fault current of 20 kA

occurs. The affected phase is varied and the currents flowing in the earthed cable shields are

calculated. These currents cause voltage drops on the earthing system of the cable shields. It is

important to note that the following presented voltage drops represent a worst-case scenario, which

means that these are the maximum possible voltage drops, referred to earth potential. The maximum

induced cable-shield currents for the profiles listed in Table 1 range between 5675 A and 6259 A. The

calculations are performed with earth resistances of the cable shields in the substation/riser pole A and

B of 0.1 Ω and in the grounding sections of 1 Ω. Hence, the voltage drops, referred to the reference

earth, occur in a range between 567.5 V and 625.9 V during a single-pole earth fault.

Conductor reinstallation while neighbouring systems stay in operation

In order to investigate inductive interference during a reinstallation servicing process, profile 1 (see

Table 1) was used. As shown in Figure 1 and Figure 4, the profile consists of twelve sections

measuring 0.92 km, which means a total length of approximately 11 km. The systems are laid directly

in earth, horizontal, flat (see Figure 1) at a depth of 1.75 m. The phase distance is 0.45 m and the

system distance (middle phase – middle phase) is 1.8 m. A reinstallation process of a cable can

become necessary i.e. due to external mechanical damage of a conductor. Therefore, in this scenario

the affected system is turned off (out of operation) while the three remaining systems are in operation.

The maximum voltage for profile 1 (see Figure 1) during the installation process occurs at the

installation of the phase L3 of the system 1, reaching 132.2 V at the inner conductor (phase) and

85.1 V at the outer conductor (cable shield). Hence, further detailed calculations are necessary to make

credible statements concerning workers’ safety during a reinstallation process.

Variation of the transposition type

Different laying profiles and longitudinal laying arrangements for the profiles 1 to 6 (see Table 1)

were investigated in detail. All results include an impact of the applied transposition type, whereas the

impact of the transposition type cannot be fixed exactly, as further boundary conditions (number of

systems, cable types, materials, geometry, cross section, specific soil resistance, laying depth, different

influencing currents, …) vary from profile to profile as well and have a strong influence on the results.

Profile 1 was always applied under the same assumptions in order to evaluate four different

transposition types presented in Figure 7. The calculations have shown that only transposition type 3

(cable shields transposed, phases not transposed) and transposition type 4 (cable shields and phases

10

transposed in opposite directions) concerning the inductive interference are practically relevant.

Transposition type 2 (cable shield and phases transposed in the same direction) does not lead to any

reduction of the induced voltages and currents in comparison to the variant without transposition

(transposition type 1).

1 2

3 4 Figure 7: Transposition types

Specific soil resistance and laying depth

The specific soil resistance and laying depth of the cables have a negligible influence on the inductive

interference based on the assumptions in this paper (variation of the parameters only within a certain

bandwidth). The standard value of the specific soil resistance for profile 4 was assumed to be 100 Ωm

and for all other profiles to be 200 Ωm. The variation of a factor 20 downward and of a factor 5

upward respectively shows no significant influence. The standard laying depth for each of the

researched profiles is given in Table 1. Laying the systems 2 m deeper, and in a next step, 5 m deeper

than the standard depth, has no significant influence on the induced values either.

System and section length

The influence of the system and the section length on the induced voltages and currents can be

reduced by a symmetric structure. If the complete cable system shows a high electrical symmetry,

which means that the number of sections is divisible by three, the conductor of a system is transposed

at every joint (phases and shields not in the same direction) and in every third joint location the cable

shields are earthed, the length of the sections has a negligible influence on the induced values in

normal operating mode. Further all earthing resistances alongside the cable route should have the same

height. This does not apply to asymmetrical, short systems with a small number of sections.

Distances between systems and phases

An increase in the distances between cable systems has a positive effect on induced values. The

induced voltages and currents decrease between influenced conductors or systems with increasing

distance. Due to the characteristics of the coupling impedance, the induced values only decrease to a

small extent at a further increase in the distances after reaching a limit distance.

Variation of the earth resistances

In the presented paper, the term earth resistance RE includes the total occurring earthing system, all

contacts, lines and the earth electrode resistance. This earth resistance may rise, for example, with the

age of the facilities, due to loosened connections of the conductors or corrosion effects. This increase

in earth resistances has an influence on the induced currents in earthed cable shields and thus also on

the voltage drops. The increase in earth resistances in the grounding sections was investigated (see

Figure 4) while the earth resistances in the substations/riser poles at the start and the end of the cable

systems stayed constant.

In the earthing sections (see Figure 1, joint locations 3, 6 and 9), the occurring voltages of the cable

shields (referred to the reference earth), increase with increasing RE. The influence of the increasing

11

earthing resistances on the voltages is not linear because of the lattice network effect. The currents,

which flow into the earth, decrease expectedly with increasing resistances. By adapting the resistances

of the grounding sections (joints) from 1 Ω to 0.1 Ω in the simulation, the voltages occurring in the

grounding sections can be strongly reduced (see Figure 8).

Figure 8: Variation of earth resistances in grounding sections for profile 4 (see Table 1)

In terms of workers’ safety, it can be concluded that joint earthing systems should have a low

impedance. On the other hand, earthing systems with low impedance lead to higher cable shield

currents and thus to higher shield losses.

When varying the position of the concerned joint locations and the values of the earth resistances in

the simulation, the following effects are apparent: the increase of the earth resistance RE of one joint

location affects the voltages in the mentioned joint location and in the neighbouring joint locations

noticeably, although these are, for example, for profile 1 up to 2.76 km away. However, if the

neighbouring earthing system has a low impedance, then the occurring voltages there stay unaffected.

Conclusion In order to verify the simulation model and thus the calculation results presented in this paper,

measurements were performed during regular maintenance and service tasks on multiple existing

400kV cable systems. Participation at these measurements has led to a better understanding of the

complex problems of inductive and ohmic interference and the questions of workers’ safety. The

calculation results show that a variety of influencing factors affect the induced voltages and currents to

a broad extent. Unbalanced design of the cable systems, i.e. different geometrical distances of

conductors to each other in cross-bonding minor-sections, which may also have different lengths,

results in asymmetry. This asymmetry has a strong negative impact on the values of the induced

voltages and currents. Conductible, earth-touching or multiple earthed installations in the vicinity of

an energy cable route have a reducing effect on the voltage, induced in isolated conductors. All

analysed configurations show unanimously that the influence of the specific soil resistance and the

laying depth, concerning the mutual inductive interference of parallel running, underground 400 kV

cable systems exists, but can be declared negligible with the taken assumptions. The factors listed

below are the ones with substantial influence on the induced values:

the electrical symmetry of the cable systems

the earthing configuration

the interfering current (operation, fault)

the number of systems

the transposition configuration and

the distances between the conductors and the systems.

12

The specific soil resistance, the laying depth and the cable shield cross-sectional area of symmetrical

systems have a negligible effect on induced voltages and currents with the taken assumptions.

In low load operation, the simulation model was verified and proven. Due to the very good correlation

of the calculation results with the measurement results, the findings published in this paper are of great

relevance for all those engaged in the planning, construction, operation and service of high-voltage

cable systems. These results can contribute to the timely recognition and prediction of possible

dangerous situations and can help to provide countermeasures. Safety aspects need to be considered

already in the planning phase of cable lines, however may lead to slightly reduced transmission

capacity.

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