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
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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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